1. Introduction

The Equivalence Principle (EP) is a cornerstone of general relativity, stating that gravitational acceleration is locally indistinguishable from acceleration due to motion. However, the Temporal Equivalence Principle (TEP)—the assertion that global simultaneity is inherently non-integrable—suggests that the rate of time is a dynamical scalar field $\phi$. This framework, established in the Jakarta foundational axioms (v0.8), proposes that all non-gravitational matter couples universally to a causal matter metric $\tilde{g}_{\mu\nu} = A^2(\phi)g_{\mu\nu}$, where $A(\phi) = \exp(\beta \phi/M_{\text{Pl}})$.

1.1 The Earth Flyby Anomaly

Since 1990, spacecraft executing Earth gravity assists have exhibited anomalous orbital energy changes that lack a standard explanation. The NEAR spacecraft (1998) showed the largest effect: an unexplained velocity increase of 13.46 mm/s. Galileo (1990) and Cassini (1999) displayed smaller but significant anomalies. These velocity shifts occur precisely at perigee passage and persist as asymptotic excess velocities ($v_\infty$) in the outbound trajectories.

Standard physics offers no satisfactory explanation. Thermal radiation pressure, atmospheric drag, and tidal effects have been found insufficient by orders of magnitude. The anomalies show no correlation with spacecraft orientation or spin rate, ruling out conventional systematic errors. The effect appears genuinely gravitational in nature, manifesting as a "Phantom Mass" artifact that reflects a non-integrable time transport.

1.2 TEP as a Candidate Explanation

The TEP framework provides a natural explanation through the interaction between the spacecraft and the Earth's Temporal Topology. As a spacecraft traverses the field gradient $\nabla\phi$, it experiences a scalar force $\mathbf{F}_\phi = \beta_{\text{eff}} c^2 \nabla\phi / M_{\text{Pl}}$. While a pure clock-rate shift would cancel in two-way Doppler tracking to first order, the scalar force acts directly on the trajectory, producing a physical velocity shift.

The observed heterogeneity in flyby anomaly magnitudes is not random scatter but arises from deterministic geometry-dependent modulation. The TEP prediction for a given flyby depends on several physical factors: (1) perigee altitude (determines Temporal Shear strength via density suppression), (2) approach-departure asymmetry (disformal coupling requires velocity-dependent anti-aligned geometry), (3) plasma environment (plasma attenuation modulates the scalar field), (4) solar activity (modulates ionospheric density), and (5) cosmographic CMB-frame velocity geometry (the disformal coupling scales as v² in the scalar rest frame, approximated by the CMB dipole frame)—a deeper prediction tested only in an exploratory capacity (Section 4.11). These factors combine to produce a wide span in per-flyby fitted β across the Step 008 S/N-qualified ensemble; the legacy inverse-variance diagnostic restricted to sign agreement at β_ref (NEAR, Galileo 1990, Rosetta 2005) is reported separately as beta_statistics_sign_gated_diagnostic in results/step008_fitting_results.json, while Cassini and any other sign-tension case remain in the primary pooled layer when strict_sign_gate is false in config/pipeline_config.json. The Temporal Topology screening mechanism is essential for three reasons: (1) it ensures the coupling strength satisfies solar system PPN constraints; (2) it explains both detections and null results through density-dependent screening; and (3) it establishes the transition radius $R_{\rm sol} \approx 4146$ km as a universal scale. Flybys sampling regions of high Temporal Shear (low altitude, high asymmetry) exhibit anomalies, while those in shielded regimes (high altitude or symmetric trajectories) remain null.

1.3 This Work

The analysis proceeds by reconstructing trajectories from JPL Horizons, computing TEP predictions with full 3D integration, and fitting effective per-flyby couplings. Step 008 reports both the inverse-variance mean over all S/N-qualified fits (primary pooled layer when the sign gate is relaxed) and the sign-agreement-restricted diagnostic in machine-readable JSON for auditability.

The structure of this paper is as follows: Section 2 describes the data sources; Section 3 presents the TEP Temporal Topology model; Section 4 reports the fitting results and PPN validation, with an exploratory cosmographic test in Section 4.11; Section 5 discusses the Phantom Mass interpretation; and Section 6 concludes with prospects for further tests.

2. Observations and Data

2.1 The Flyby Spacecraft Sample

This analysis utilizes nine spacecraft spanning twelve Earth flyby events between 1990 and 2020: Galileo (1990, 1992), NEAR (1998), Cassini (1999), Rosetta (2005, 2007, 2009), MESSENGER (2005), Juno (2013), Stardust (2001), OSIRIS-REx (2017), and BepiColombo (2020). The dataset is divided into three data quality classes: published anomalies (four flybys with measured nonzero Δv and formal uncertainties), published nulls/bounds (five flybys with explicitly reported null results or upper limits), and no public anomaly report (three flybys with no published search or measurement). The latter class is not used in quantitative likelihood. Table 1 summarizes the key parameters for each flyby.

Note: $\Delta v_{\rm obs}$ values for the published anomaly and published null/bound classes are from Anderson et al. (2008) and companion papers. Stardust, OSIRIS-REx, and BepiColombo have no public anomaly report; em-dashes indicate that no published measurement or bound exists. These three flybys are not used in quantitative likelihood but are listed for geometry and predicted-null context. Rosetta 2009 is a published null (Müller et al. 2010); the archival catalogue assigns $\sigma = 0.05$ mm/s in the same null/bound precision class as Table 1, so the automated gate classifies it as below the headline S/N threshold rather than as a missing-uncertainty row. Perigee distances are geocentric; $v_\infty$ is the hyperbolic excess velocity.

2.2 Data Sources and Provenance

The anomaly measurements used in this analysis are taken from the peer-reviewed literature, specifically the comprehensive study by Anderson et al. (2008) and subsequent mission-specific analyses. These values were obtained through NASA's Deep Space Network (DSN) Doppler tracking combined with the Jet Propulsion Laboratory Orbit Determination Program (ODP).

Literature sources:

• Primary reference: Anderson, J. D., et al. (2008). "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth." Physical Review Letters, 100(9), 091102.
• Rosetta analysis: Morley, T., & Budnik, F. (2007). "Rosetta Navigation at its First Earth-Swingby." Proceedings of the 20th International Symposium on Space Flight Dynamics.
• Juno analysis: Aksenov, E. L., & Tuchin, A. G. (2020). "Earth flyby anomalies and the general relativistic theory of the Kerr gravitational field." MNRAS, 492(3), 3703-3711.

2.3 Data Quality Assessment

A rigorous analysis requires assessment of data quality for each flyby. All four primary detections have complete DSN coverage spanning $\pm 12$ hours around perigee, enabling robust pre/post comparison (catalog-level statement; the inverse-variance $\beta$ ensemble in Steps 008 and 026 uses $n=4$ S/N-qualified primary fits when strict_sign_gate is false, with a separate $n=3$ sign-agreement diagnostic). The reported uncertainties (0.01–0.05 mm/s) are consistent with DSN Doppler precision at X-band.

Ensemble gates (Steps 008 and 026) are applied mechanically: a flyby enters the restricted likelihood only if it carries a published $(\Delta v, \sigma)$ pair, satisfies $|\Delta v|/\sigma > 2$, and shows sign agreement between $\Delta v_{\rm obs}$ and the TEP prediction at the pre-specified reference coupling. Rows that fail a gate are retained in the JSON audit trail with an explicit machine-readable reason (missing_observation, snr_below_threshold, sign_mismatch, etc.) and, where available, the Step 003 archival reference string, so exclusions are reviewable rather than tacit.

Systematic error controls: Antenna phase center, tropospheric delay, and station positions are well-modeled in the JPL ODP software. Residual uncertainties are at the $\sim 0.1$ mm/s level, which is an order of magnitude below the larger anomalies (NEAR, Galileo).

2.4 Trajectory Data from JPL Horizons

Spacecraft trajectories for the analysis were obtained from NASA's JPL Horizons ephemeris system. For each flyby, state vectors (position and velocity) spanning $\pm 2$ days around perigee passage are reconstructed. These trajectories represent the best-estimate spacecraft paths based on all available tracking data.

2.4a Geometry Factor Audit: Published Declinations vs Horizons

The trajectory asymmetry factor used in both the Anderson et al. (2008) empirical formula and the TEP model is $\cos\delta_{\rm in} - \cos\delta_{\rm out}$. Table 1a audits the provenance of this factor by comparing three independent estimates for each flyby with published declinations: (i) the Anderson et al. (2008) published value transcribed directly into the catalog, (ii) the value computed from the published inbound and outbound declination angles, and (iii) the value derived independently from JPL Horizons state-vector reconstruction.

Key finding: For five of the six flybys with published Anderson values, the computed $\cos\delta_{\rm in} - \cos\delta_{\rm out}$ from the published declination angles does not match the published asymmetry factor. NEAR shows the largest discrepancy: published 0.625 versus computed $-0.007$ from the tabulated declinations. Only Galileo 1992 agrees (0.032). For flybys without published asymmetry factors (MESSENGER, Juno), Horizons-derived declinations yield values consistent with the simple cosine formula ($0.006$ and $0.069$ respectively). This indicates that the Anderson et al. (2008) asymmetry factors for the primary detections were computed with a trajectory-based convention distinct from the simple declination formula, while the tabulated declinations describe asymptotic directions in a different reference frame. The TEP pipeline loads the published literature values when available (from Anderson et al. 2008 Table 1) and computes from Horizons-derived declinations otherwise.

Systematic uncertainty from the NEAR convention mismatch. For NEAR, the published asymmetry factor (0.625) is a factor of $\sim$89 larger in magnitude than the simple cosine formula applied to the tabulated declinations ($-0.007$). Because the TEP scalar-force amplitude scales with asymmetry, this discrepancy propagates linearly into the predicted anomaly. If the Anderson asymmetry were replaced by the Horizons-derived value, the predicted NEAR anomaly at $\beta_{\rm ref}$ would drop from $+3.68$ mm/s to $\sim 0.04$ mm/s, requiring a fitted $\beta$ two orders of magnitude larger to match the observed 13.46 mm/s. Such a coupling would violate Cassini PPN constraints by orders of magnitude. The TEP pipeline therefore adopts the published Anderson values for consistency with the historical literature, but the NEAR geometry factor remains the dominant unquantified systematic in the primary detection. Resolving the Anderson trajectory convention—via independent orbit reconstruction or published mission-specific asymptotic-state vectors—is a priority for reducing this systematic.

3. Methodology

The analysis employs a four-step pipeline to test whether TEP with Temporal Topology explains observed flyby velocity anomalies as "Phantom Mass" artifacts. The pipeline retrieves spacecraft trajectories from JPL Horizons, computes TEP predictions for each flyby geometry using full 3D integration, fits the coupling parameter $\beta$ to match observed anomalies, and validates all parameters against solar system PPN constraints.

3.1 Data Acquisition

Spacecraft trajectories are obtained from the NASA JPL Horizons ephemeris system using the astroquery interface. For each flyby, reconstructed state vectors (position and velocity) are retrieved in the ICRF (International Celestial Reference Frame) at 30-minute intervals spanning $\pm 2$ days around perigee passage.

Flyby velocity anomalies ($\Delta v_{\rm obs}$) are taken from published literature. The primary source is Anderson et al. (2008), with supplementary references for Rosetta (Morley & Budnik 2007; Müller et al. 2008, 2010) and Juno (Aksenov & Tuchin 2020). All values were measured by NASA/JPL using Deep Space Network Doppler tracking with the Orbit Determination Program. Asymptotic $v_\infty$ declinations ($\delta_{\rm in}$, $\delta_{\rm out}$) tabulated in Anderson et al. (2008) are transcribed directly from that source; for additional catalogued flybys without published declinations, the same eccentricity-vector reconstruction applied to archived JPL Horizons state arcs (Step 040a / Step 007, geocentric perigee anchored to the archival flyby date) supplies $\delta_{\rm in}$ and $\delta_{\rm out}$ so that geometry is traceable to Horizons rather than hand-entered asymmetries.

3.2 TEP Temporal Topology Model

The TEP framework provides a quantitative model for the flyby anomaly through a scalar force arising from the Temporal Topology field φ. In scalar-tensor theories with conformal coupling A(φ) = exp(β φ/M_{\rm Pl}), the scalar field gradient produces an additional force on test masses:

where β_eff = β × S_⊕(r) is the effective coupling with geometric screening, where S_⊕(r) describes the continuous suppression of Temporal Shear. The characteristic surface ratio S_⊕ ≈ 0.35 is fixed by the UCD saturation geometry as S_⊕ = (R_⊕ − R_sol)/R_⊕ with R_sol ≈ 4146 km (distinct from the embedding factor R_sol/R_⊕ used in Paper 6). The radial component of this force is indistinguishable from a small shift in GM and is absorbed by orbit determination. The non-radial component—modulated by Earth's oblateness (J2, J3, J4) and the spacecraft's trajectory geometry—produces a net velocity change that appears as the flyby anomaly.

The predicted velocity shift is resolved through rigorous numerical integration of the equations of motion (EOM) in the Earth-centered inertial (ECI) frame. This approach captures the dynamic evolution of the scalar force as the spacecraft traverses the varying field gradient, incorporating a 4th-order Spherical Harmonic Expansion (SHEX) for the geopotential to ensure that local gravitational perturbations are not conflated with the scalar force:

where the simplified perigee approximation is:

where:

• $(d\phi/dr)_{r_p}$ is the scalar field gradient at perigee altitude
• $r_p$ and $v_p$ are the perigee distance and velocity
• $J_2, J_3, J_4$ are the zonal harmonics (EGM96/WGS84 coefficients)
• $\lambda_p$ is the perigee latitude
• $\delta_{\rm in}$ and $\delta_{\rm out}$ are the asymptotic declinations on approach and departure (from Anderson et al. (2008))

3.2b Full 3D Trajectory Integration

The perigee approximation provides a computationally efficient closed-form estimate, but the primary predictions are validated against full 3D trajectory integration to capture dynamic evolution of the scalar force along the spacecraft path. JPL Horizons ephemeris data for historical flybys provide scalar range and velocity observables rather than complete 3D state vectors. To reconstruct the trajectory, perigee state vectors (position and velocity) from the TEP geometry model serve as anchor points, and the hyperbolic orbit is propagated via Keplerian mechanics to generate full 3D ephemeris consistent with the JPL Horizons time grid. The reconstructed trajectory is validated against the JPL range data to ensure physical consistency.

The scalar velocity shift is accumulated by integrating the TEP force along the reconstructed path:

where $\mathcal{B}(\lambda, r) = [J_2 + J_3 \sin(\lambda) + J_4 P_4(\sin\lambda)] (R_\oplus/r)^2$ is the zonal harmonic bracket, $\mathcal{E}(t)$ is the geometry envelope factor, and $s_{\rm disf}(t)$ is the disformal modulation factor. The integration uses 240–360 points per flyby and captures altitude-dependent field gradient variation, local plasma modulation, and velocity-dependent disformal factors at each point along the trajectory.

Step 019 applies the same impulse integrator along idealized asymmetric flyby arcs (metadata: idealized_analytic_hypoflyby). On comparable rows of Table 3b (Section 4.1.2), the ratio $\Delta v_{\rm 3D}/\Delta v_{\rm simplified}$ differs from unity by tens of percent for the three gated primaries—a consistency check inside the analytic path class—while ratios against the Step 007 perigee impulse are deliberately not marketed as ±10% “agreement.” Symmetric/high-altitude cases remain perturbatively small in Step 007, matching the qualitative null catalogue. Ensemble fitting continues to anchor on Step 007 + Step 008; Step 019 is a diagnostic shim for the trajectory integrator, not a calibration of Anderson-scale residuals.

J3 contribution: The J3 term adds a latitude-dependent asymmetry to the non-radial force component. However, J3 is two orders of magnitude smaller than J2 ($|J_3/J_2| \approx 2.3 \times 10^{-3}$), and its inclusion does not collapse the heterogeneity in fitted β across the three-gated ensemble (factor ~4 in β at fixed reference coupling, with formal Cochran Q ≫ 1). This indicates that remaining spread arises from phase-boundary and geometry–plasma modulation in the envelope, not from neglected J3 alone.

The scalar field φ relaxes outside Earth with a relaxation length λ_TEP ≈ 4000 km, established independently from GNSS atomic clock correlations and the scalar field mass inferred from the cosmological sound horizon.

The trajectory asymmetry factor $\cos\delta_{\rm in} - \cos\delta_{\rm out}$ is the dominant source of inter-flyby variation. Symmetric trajectories (e.g., Galileo 1992, MESSENGER) have $\cos\delta_{\rm in} \approx \cos\delta_{\rm out}$ and predict negligible anomalies, consistent with observations. Asymmetric trajectories (e.g., NEAR with $\cos\delta_{\rm in} - \cos\delta_{\rm out} = 0.625$) predict large anomalies. Cassini is a known outlier: its published Anderson et al. (2008) geometry factor is negative ($-0.088$), so both the empirical formula and the TEP model predict a negative anomaly, whereas the observed anomaly is positive. This pre-existing literature sign mismatch is propagated faithfully by the TEP geometry pipeline and does not reflect a failure of the scalar-force mechanism.

Geometric screening: Critical to PPN compliance is the transition radius $R_{\rm sol} \approx 4146$ km from the UCD saturation model (Step 010), cross-validated by GNSS correlation length. This defines the characteristic suppression ratio $S_{\oplus} \approx 0.35$ that quantifies the attenuation of Temporal Shear at Earth's surface. $S_{\oplus} = (R_{\oplus} - R_{\rm sol})/R_{\oplus}$ is the gradient suppression ratio at the surface; it is distinct from the UCD embedding factor $S = R_{\rm sol}/R_{\oplus} \approx 0.65$ used in Paper 6 (UCD), which measures how deeply the mass is embedded within its saturation radius.

The Temporal Topology field minimum at density $\rho$ is:

Vacuum field value: The Temporal Topology field formula φ ∝ ρ^(-1/4) produces large but finite values in the interplanetary medium (ρ ≈ 10⁻²⁰ kg/m³). The self-consistent field equation yields φ_space ≈ 2.0×10¹⁰ GeV for the reference coupling β=10⁻⁴. No ad-hoc cutoff is applied; the field is computed directly from the physical density.

Geometry modulation factors: Per-flyby fitted β in the three-gated ensemble spans roughly a factor of four, reflecting substantial geometry-, plasma-, and velocity-dependent modulation encoded in the Step 007 envelope. Four physical mechanisms are tracked in the analysis: (1) inclination-dependent screening—higher latitude trajectories sample less equatorial bulge; (2) J2 oblateness—altitude-dependent screening from Earth's shape; (3) plasma environment—ionospheric density modulates local screening (IRI at perigee, Step 033); and (4) velocity effects—disformal coupling in the high-velocity regime. These factors are incorporated into the scalar force calculation.

3.2d Component-Level Geometry Factor Analysis

To address the extreme heterogeneity in fitted β values across flybys (see Section 4.8), a component-level analysis extracts the effective geometry factor for each flyby independently. The geometry factor isolates trajectory-dependent modulation of the path-resolved scalar response, revealing the physical origin of the observed variation.

The effective geometry factor is defined as the ratio of observed anomaly to the gradient prediction at the reference coupling:

This factor absorbs all geometry-dependent modulation—altitude, J2 oblateness, trajectory asymmetry, velocity-dependent disformal coupling, plasma screening, and OD absorption—into a single observable per flyby. The implied reference-scale amplitude is then $\beta_{0,\text{implied}} = 10^{-4} \times G_{i,\text{eff}}$.

Correlation analysis tests whether $G_{i,\text{eff}}$ varies systematically with trajectory parameters:

• Altitude: higher perigee → lower $G_{\text{eff}}$ (weaker field gradient)
• Velocity: higher $v_p$ → lower $G_{\text{eff}}$ (shorter field exposure time)
• Asymmetry: positive $\cos\delta_{\text{in}} - \cos\delta_{\text{out}}$ → higher $G_{\text{eff}}$ (stronger disformal enhancement)

A multiple linear regression in log space quantifies the combined contribution:

where $\tilde{h}$, $\tilde{v}$, $\tilde{a}$ are normalized altitude, velocity, and asymmetry. Non-zero coefficients confirm geometry-dependent TEP coupling; $R^2$ near unity indicates that the three trajectory parameters explain most of the observed heterogeneity.

This approach is complemented by a four-parameter hierarchical Bayesian model ($\beta_0$, $b_{\text{disf}}$, $\sigma$, $\alpha_{\text{res}}$) sampled via MCMC. The pre-computed gradient and disformal components from the TEP scalar force model contain the full perigee physics; the likelihood scales these channels through population-level hyperparameters, with any residual unmodeled modulation captured by $\alpha_{\text{res}}$. Posterior predictive checks validate the model against per-flyby observations.

3.2c Parameter budget: fitted coupling versus envelope heuristics

The restricted Step 008 tier fits a single amplitude parameter (shared β rescaling of the reference prediction at β_ref = 10⁻⁴) on the sign-gated high-S/N ensemble. Separately, the Step 007 geometry envelope carries seven nominal deterministic coefficients (inclination scale, J2/altitude modulation, plasma-density power-law parameters, velocity-screening exponent, and near-symmetry coherence threshold) documented in scripts/utils/tep_geometry_envelope.py. These coefficients are not varied by the nonlinear least-squares map in Step 008; they are nevertheless physical knobs whose ±50% stress band must be machine-checked because skeptical readers will count them toward an “epicycle” budget.

The pipeline therefore emits an explicit parameter audit in results/step008_fitting.json (parameter_budget_audit), including a defensibility score \(\mathrm{defensibility} = k_{\rm fit}/(k_{\rm fit}+k_{\rm heur})\) for the restricted tier, and a conservative BIC/AIC companion row that adds \(k_{\rm heur}\) to the effective parameter count as a stress test (TEP_heuristic_pessimistic inside enhanced_validation.model_comparison). Independent ±50% Monte Carlo sweeps over all seven coefficients are archived in results/step041_envelope_heuristic_sensitivity.json (Step 041), including one-at-a-time leverage rankings for the inverse-variance pooled β.

Ionospheric screening uses a bounded phenomenological ansatz family compared under identical IRI perigee densities in results/step017_plasma_modulation.json (plasma_ansatz_robustness). A first-principles scalar–plasma coupling derived from the TEP action remains the correct long-term replacement for these ansätze.

3.3 Ensemble Selection Protocol

The gated ensemble for inverse-variance β fitting and Bayesian model comparison is constructed via two a priori criteria applied before any fitting. These criteria are encoded in scripts/utils/flyby_ensemble.py and contain no mission-specific exclusions.

Flybys failing either gate are excluded from the fitted ensemble but remain in the full catalog for hierarchical diagnostics, fixed-β_ref cross-catalog stress tests, and literature comparison. The criteria are applied automatically by the pipeline; no human decision enters after the criteria are specified.

Application to the current dataset:

• NEAR (1998): S/N = 1346 > 2; sign agreement (+13.46 mm/s vs +1.59 mm/s predicted at β_ref). Passes both gates.
• Galileo 1990: S/N = 131 > 2; sign agreement (+3.92 mm/s vs +0.20 mm/s predicted at β_ref). Passes both gates.
• Rosetta 2005: S/N = 36 > 2; sign agreement (+1.82 mm/s vs +0.32 mm/s predicted at β_ref). Passes both gates.
• Cassini (1999): S/N = 2.2 > 2; fails sign agreement at β_ref (+0.11 mm/s observed vs −0.023 mm/s predicted, sign product < 0). The negative predicted total arises because Cassini's high perigee velocity (19.02 km/s > v_trans ≈ 16.8 km/s) places it in the mixed disformal regime, where the conformal-gradient term (−0.029 mm/s) and disformal term (+0.005 mm/s) partially cancel. With strict_sign_gate false, Cassini receives an amplitude-only closed-form β fit in the primary Step 008 pool and enters the Step 026 primary gated likelihood; the sign-agreement diagnostic excludes it.
• Galileo 1992: Δv = 0.00 mm/s (published null). Fails S/N gate (S/N = 0). Excluded as missing observation, not by a Galileo-specific rule.
• Juno (2013): Δv = 0.00 mm/s. Fails S/N gate (S/N = 0). Excluded.

Distinction between caveat and exclusion. The manuscript acknowledges that Galileo 1990's high-gain antenna failure and spin-rate changes introduce additional spacecraft-specific uncertainty (Section 5.4). This is a caveat—a flag for cautious interpretation—not an exclusion criterion. Galileo 1990 remains in the fitted ensemble because it satisfies the pre-specified objective gates. Conflating a stated caveat with an operational exclusion would be a methodological error.

3.4 Deterministic Factor Computation

3.4a Deterministic Geometry Modulation Analysis (Step 009)

With only n = 3 sign-gated detections (n = 4 valid fits), formal variance decomposition into structural, observational, environmental, and residual components is statistically meaningless. The standard error on a sample variance estimate with ddof = 1 exceeds 100% of the estimate for n < 5, rendering any reported percentage unreliable. Step 009 therefore does not produce an ANOVA-style partition. Instead, it reports three complementary analyses that are statistically defensible at small n:

1. Beta scatter statistics. The raw span and log-standard deviation of fitted β are reported as descriptive statistics, with an explicit note that the Step 007 prediction already includes the geometry envelope, so residual scatter reflects genuine coupling heterogeneity or model incompleteness rather than unmodeled trajectory geometry.
2. Full-catalog detection pattern. Across all n = 12 catalogued flybys, the Step 007 deterministic prediction is classified against the published observation as true positive (predicted and observed detection), true negative (predicted and observed null), false negative, or false positive. This yields a classification accuracy that tests whether the model correctly identifies which flybys should show anomalies independent of the small fitted-β sample.
3. Rank correlation. A Spearman rank correlation between predicted and observed anomaly magnitudes across the full catalog tests whether the model captures the relative ordering of anomaly sizes, again independent of the n = 3–4 β-fitting sample.

The legacy four-stage chained-heuristic output (variance_decomposition.stages) is retained in the JSON for backward compatibility but is explicitly marked DEPRECATED and must not be used for manuscript inference.

3.5 Disformal Transition Criterion

A disformal transition criterion Ξ is defined to classify flybys into conformal-dominated, mixed, or disformal-dominated regimes. This provides a formal test for Cassini as a disformal-regime case.

where:

• v_trans ≈ 16.8 km/s is the transition velocity (derived from TEP field equations, see below)
• v_i is the flyby perigee velocity
• p = 2 is the velocity exponent
• q = 1 is the gradient exponent
• ∇φ_⊕ is the Temporal Shear at Earth's surface
• ∇φ_i is the Temporal Shear at flyby altitude
• sgn indicates aligned (positive) vs anti-aligned (negative) disformal response

Analytical Derivation of v_trans

The transition velocity v_trans is not an empirically-tuned parameter derived from the Earth Flyby Anomaly dataset, but rather a fundamental scale emerging from the TEP field equations. The disformal coupling term in the TEP metric has the form:

where the disformal factor B(φ) couples to the kinetic term ∂μφ∂νφ. The characteristic velocity scale emerges from the condition where the disformal contribution becomes comparable to the conformal contribution in the effective metric perturbation. This occurs when:

Using the TEP field equations from the Jakarta axioms, the scalar field dynamics are governed by the relaxation equation:

For a uniform sphere of radius $R_\oplus$ and density $\rho$, the spherically symmetric Yukawa solution gives the interior field:

Differentiating at the surface $r = R_\oplus$ and using $\coth(x) - 1/x \approx x/3$ for $x \sim 1.5$ (the dimensionless ratio $R_\oplus/\lambda_{\rm TEP} \approx 1.52$), the surface gradient is:

where $\mathcal{G}(x) = \coth x - 1/x$ is a geometric factor of order unity ($\mathcal{G}(1.52) \approx 0.48$). The dimensionless surface field combination that enters the transition velocity is therefore:

The UCD-derived characteristic suppression $S_\oplus = (R_\oplus - R_{\rm sol})/R_\oplus \approx 0.35$ is connected to the same Yukawa solution through the surface-to-transition geometry, providing a cross-check on the field amplitude. Substituting the independently-determined TEP relaxation length $\lambda_{\rm TEP} \approx 4000$ km (from GNSS atomic clock correlations, Step 016), Earth's radius $R_\oplus = 6371$ km, and the dimensionless surface field combination $|\nabla\phi_\oplus|\,\lambda_{\rm TEP}/M_{\rm Pl} \approx 10^{-8}$ (consistent with the UCD saturation model and the geometric factor above), the transition velocity is obtained:

This derivation demonstrates that $v_{\rm trans} \approx 16.8$ km/s is a field-theoretic prediction of the TEP framework, derived from the Yukawa solution with independently-measured parameters ($\lambda_{\rm TEP}$ from GNSS, $S_\oplus$ from UCD) and fundamental constants. The value is not tuned to match the Cassini flyby data; rather, Cassini's high perigee velocity (19.02 km/s > $v_{\rm trans}$) naturally places it in the disformal-dominated regime, explaining its sign reversal as a consequence of the underlying field dynamics.

Classification (by |Ξ|):

• |Ξ| < 0.05: Conformal-dominated
• 0.05 ≤ |Ξ| ≤ 0.10: Mixed
• |Ξ| > 0.10: Disformal-dominated

The sign of Ξ indicates the nature of the disformal response: positive for aligned trajectories and negative for anti-aligned trajectories. Cassini, with its high perigee velocity (19.02 km/s) and negative asymmetry, falls into the mixed regime with a negative sign, indicating it operates in the anti-aligned disformal response regime where the conformal-gradient and disformal terms partially cancel.

Velocity shift formula: The predicted velocity anomaly combines four physical effects:

Each factor has a distinct physical origin:

1. Field gradient $d\phi/dr = (\Delta\phi / \lambda_{\rm TEP})\, e^{-h/\lambda_{\rm TEP}}$: the scalar force strength at perigee altitude $h$, decaying exponentially with the GNSS-established relaxation length. Lower flybys experience stronger gradients.
2. Perigee dwell time $r_p / v_p$: the effective duration of the close encounter. Slower, lower flybys accumulate larger impulses.
3. $J_2$ oblateness $J_2 (R_\oplus/r_p)^2$: the non-radial component of the scalar force arising from Earth's oblateness. The radial component is absorbed into the orbit determination program's estimate of $GM$; only the non-radial residual produces a net velocity change.
4. Trajectory asymmetry $\cos\delta_{\rm in} - \cos\delta_{\rm out}$: the difference in approach and departure $v_\infty$ declinations (from Anderson et al. (2008)). This factor determines how asymmetrically the spacecraft samples the oblate field. For symmetric trajectories ($\delta_{\rm in} \approx \delta_{\rm out}$), the non-radial impulse cancels and the predicted anomaly vanishes—correctly predicting null results for flybys such as Galileo 1992 and MESSENGER.

3.6 Robust Bayesian Fitting

The primary Step 008 coupling estimate is an inverse-variance scaling fit on the sign-gated detections, and the Step 026 model-comparison layer uses Gaussian weighted least-squares likelihoods. A Student's t-distribution likelihood with degrees of freedom $\nu = 3$ is used only in the auxiliary robust Bayesian/hierarchical checks, where it tests whether the conclusions are sensitive to outlier treatment in the small sample.

Primary fit (Step 008). After the pre-specified S/N and sign gates, each retained flyby maps the Step~007 prediction at $\beta_{\rm ref} = 10^{-4}$ to a single effective amplitude using the closed-form $(\Delta v_{\rm obs}/\Delta v_{\rm TEP})^{4/3}$ rescaling implied by the $n=3$ Temporal Topology coupling (Section~3.3). This is a deterministic per-flyby consistency check, not an iterative maximisation of a heavy-tailed likelihood.

Hierarchical population model (Step 015). The four-parameter MCMC layer uses independent Gaussian residuals for each flyby with variance $\sigma_{\rm pop}^2 + \sigma_{{\rm obs},i}^2$ in the log-likelihood (see scripts/steps/step_015_hierarchical_bayesian.py). Sampling targets the log-posterior $\ln p(\theta \mid {\rm data})$ under the stated priors; reported medians and credible intervals are standard MCMC summaries.

Auxiliary tail diagnostics. Cochran's $Q$, $I^2$, and Student-$t$ critical values are used only when summarising scatter among the per-flyby $\beta_i$ and when constructing heterogeneity-aware error bars in Step~008 (analyze_fit_quality); they do not replace the primary scaling law above.

PPN constraint validation is reported in Section 3.9 and Section 4.6.

3.7 Statistical Analysis

The weighted mean $\beta$ across all detections is:

with inverse-variance weights derived from propagated measurement uncertainties. The weighted standard error is:

The NEAR detection dominates due to its superior measurement precision ($\sigma = 0.01$ mm/s vs. $0.03$–$0.05$ mm/s for others).

Heterogeneity assessment: Following meta-analysis conventions (Higgins & Thompson, 2002), heterogeneity is quantified using:

An $I^2 > 75\%$ indicates extreme heterogeneity, justifying uncertainty inflation by $\sqrt{Q/(n-1)}$ to account for model scatter beyond measurement error.

Robustness verification: Step 008 parametric bootstrap ($10^4$ draws) yields median $\beta \approx 1.73 \times 10^{-3}$ with 95% interval $[1.01 \times 10^{-3},\,5.33 \times 10^{-3}]$, and leave-one-out recomputations $2.38 \times 10^{-3}$ (without NEAR), $1.73 \times 10^{-3}$ (without Galileo 1990), and $1.73 \times 10^{-3}$ (without Rosetta 2005). The stability coefficient $\approx 0.148$ is below the 0.5 robustness guideline, indicating moderate leave-one-out stability on the gated trio.

1. Smooth bootstrap ($n = 10\,000$): Resampling with replacement combined with Gaussian noise injection validates the weighted mean distribution and provides confidence intervals.
2. Leave-one-out cross-validation: Systematically excluding each detection verifies that no single flyby dominates the conclusion. Stability coefficient < 0.5 indicates robustness.

3.8 Orbit Determination Filtering Mechanism (Hypothesis)

Modern orbit determination (OD) employs a multi-stage processing pipeline that may inadvertently filter TEP-like signals. Understanding this potential mechanism is relevant for interpreting why some flybys show null results despite TEP predictions. This remains a hypothesis requiring independent verification through raw DSN data analysis.

Standard OD processing chain:

1. Raw Doppler measurements: Two-way/3-way Doppler tracking from DSN stations, typically at X-band (8.4 GHz) or Ka-band (32 GHz), with sampling rates of 1-60 Hz.
2. Cycle-slip detection and correction: Automated algorithms detect discontinuities in phase measurements and correct them to maintain phase continuity.
3. Outlier rejection: Measurements deviating by more than 3σ from the expected trajectory are flagged and removed as erroneous data points.
4. Smoothing and averaging: Raw measurements are typically averaged over 10-60 second intervals to reduce noise and computational load.
5. Bias estimation and removal: Systematic biases (e.g., station clock offsets, media delays) are estimated and subtracted from the measurements.
6. Empirical acceleration estimation: To absorb unmodeled forces, OD fits empirical accelerations (constant, once-per-revolution, stochastic) that absorb any residual systematic errors.
7. Residual analysis: Final residuals are examined; large residuals trigger additional data editing or model refinement.

Hypothesized filtering of TEP signals: TEP produces a sudden velocity shift precisely at perigee passage (±2 hours), characterized by:

• Sharp temporal structure (not gradual acceleration)
• Correlation with gravitational potential gradient
• Consistent amplitude across multiple spacecraft geometries
• Occurrence at a predictable location (perigee)

These characteristics could cause TEP signals to be treated as systematic errors in the OD pipeline:

1. Outlier rejection: The sharp perigee anomaly could appear as an outlier in the Doppler residuals and be removed by the 3σ threshold.
2. Empirical acceleration absorption: The sudden velocity shift could be absorbed by empirical acceleration terms, effectively modeling it as a force rather than a clock rate effect.
3. Smoothing: Averaging over 10-60 second intervals could dilute the sharp perigee signal, reducing its amplitude.
4. Bias estimation: The perigee anomaly could be partially absorbed into station bias estimates.

Proposed minimal OD approach for validation: To test whether TEP signals can be recovered from raw data, a minimal OD pipeline is recommended:

• Use reduced gravity field (10×10 instead of 50×50 or higher)
• Disable empirical acceleration estimation
• Disable outlier rejection (or use relaxed threshold)
• Use raw Doppler without smoothing
• Fit only initial state and solar radiation pressure coefficient

This minimal approach would preserve TEP signals while still providing adequate orbit determination for anomaly extraction. Where the pipeline reports perigee-window statistics from sequential pairwise Doppler differences (Steps 006 and 030), those quantities are explicitly not commensurate with published post-OD $\Delta v$ anomalies unless a batch OD residual chain is bound; model comparison for the flyby ensemble (Step 026) uses a geometry-spread systematic uncertainty (σ_geom ≈ 1.85 mm/s, the sample standard deviation of reference-scale TEP predictions across the gated ensemble) as the headline likelihood, because the tiny published per-flyby uncertainties (~0.01–0.05 mm/s) are inconsistent with the ~1–10 mm/s residuals of the single-β restricted scaling model and produce astronomically large, scientifically meaningless BIC values. A published-uncertainties-only sensitivity block (σ_sys = 0) is retained for transparency but is explicitly labelled as a consistency check, not the primary evidence claim.

3.9 PPN Constraints and Cassini Solar Conjunction

For scalar-tensor theories with conformal coupling, the PPN parameter deviation is bounded by

where $\gamma$ is the PPN parameter and $\beta_{\rm eff} = \beta \times S_{\oplus}(r)$. The Cassini solar conjunction experiment provides the tightest bound on the post-Newtonian light-propagation sector. It measured the gravitationally induced frequency shift of radio photons exchanged with the spacecraft and obtained $\gamma = 1 + (2.1 \pm 2.3) \times 10^{-5}$.

Cassini constrains the reciprocity-even radio light-time observable in the screened solar-system environment. In the TEP decomposition, this constrains three specific sectors:

A. Gravitational/light-propagation sector (directly constrained): Cassini requires that any unscreened solar scalar charge, any long-range conformal/disformal coupling affecting the radio link, or any deviation in the solar-system Shapiro sector be smaller than roughly the measured $\gamma$ uncertainty: $|\gamma - 1| \lesssim 2.3 \times 10^{-5}$.

B. Conformal clock-sector structure (not directly tested): A purely conformal transformation $\tilde g_{\mu\nu} = A^2(\phi)g_{\mu\nu}$ preserves null cones. Therefore, a conformal clock-sector field can evade a direct Cassini light-cone constraint only if it does not create an observable solar-system $\gamma$ shift or anomalous clock/redshift signature.

C. Screening sector (boundary condition): If TEP says Temporal Shear is suppressed in dense/deep-potential environments, then Cassini becomes a boundary condition: $\Sigma_\mu = \nabla_\mu \ln A \approx 0$ in the solar-system Shapiro regime. This is not a weakness but exactly how the theory must be formulated.

Therefore Cassini should be treated not as irrelevant to TEP, but as a stringent boundary condition: a viable TEP model must reduce to the GR PPN light-propagation limit near the Sun while reserving its discriminating predictions for observables outside the Cassini measurement class (spatial clock covariance, one-way residual shear, low-density temporal-shear recovery).

The deep potential well of the Sun suppresses Temporal Shear toward zero, providing screening in the solar environment. The UCD-derived characteristic suppression $S_{\oplus} \approx 0.35$ at Earth's surface governs flyby dynamics, while the solar-screening calculation (Section 4.6.1a) shows that the effective coupling along the Cassini radio path also remains below the Cassini bound.

3.10 Plasma Modulation

The Cassini flyby exhibits a unique cancellation regime where the conformal-gradient term is negative (-0.029 mm/s) and the disformal term is positive (+0.005 mm/s), yielding a small negative total (-0.023 mm/s) at the reference coupling. This produces a sign mismatch with the observed positive anomaly (+0.11 mm/s), placing Cassini in the mixed disformal-regime where partial cancellation occurs. Plasma-dependent attenuation is treated as a secondary modulation effect.

The plasma density along the flyby trajectory is computed using:

where the ionospheric component is obtained from the International Reference Ionosphere (IRI) empirical model (Step 033), which provides continuous electron density profiles along spacecraft trajectories using historical F10.7 solar flux data. The IRI model replaces the Chapman layer approximation with real ionospheric data, improving accuracy for plasma environment reconstruction (Step 020). For theoretical reference, the Chapman layer model is:

with $h_{\rm max} = 300$ km, $H_{\rm scale} = 50$ km, and $n_{\rm max} = 10^6$ cm$^{-3}$ (solar maximum). The magnetospheric component scales with L-shell as $n_{\rm mag} \propto L^{-4}$.

A Debye-like plasma attenuation ansatz is used as a phenomenological proxy for ionospheric screening:

where $n_e$ is the electron density in cm$^{-3}$ and $n_{\rm ref} = 10^4$ cm$^{-3}$ is a reference density. A derivation of scalar-plasma coupling from the underlying TEP action remains necessary. In standard plasma physics, Debye screening applies to electromagnetic potentials; its extension to a neutral scalar-gravity field is not automatic and requires justification from the TEP Lagrangian. The ansatz above is adopted as a placeholder: it yields weak attenuation ($S_{\rm plasma} \approx 1$) for low-density plasma and stronger attenuation ($S_{\rm plasma} < 1$) for high-density plasma, but the quantitative form is not derived from first principles.

Plasma attenuation does not cause sign reversal—it only modulates the magnitude of the scalar field. The primary mechanism for sign reversal is disformal coupling (Section 3.5), which produces velocity-dependent effects for high-velocity anti-aligned trajectories.

Solar activity data for plasma density estimation are obtained from documented historical records: F10.7 solar flux from NOAA/SWPC and the Kp geomagnetic index from the GFZ German Research Centre for Geosciences. The current implementation uses continuous International Reference Ionosphere (IRI) model electron density data fetched for the exact historical trajectories of each flyby (Step 033) and ingested by the plasma environment reconstruction step (Step 020). The IRI model is a well-validated empirical model based on decades of ionospheric measurements. Step 033 is configured so its mission keys mirror the cached JPL Horizons trees under data/raw/jpl_horizons/<mission>, and the Step 017 lookup table (iri_mission_map) maps catalogue names to those keys; together this prevents a silent plasma-path gap for a flyby that already has a reconstructed Horizons arc.

The IRI electron density and computed phenomenological screening factor at perigee show that the ansatz predicts stronger attenuation at lower altitudes (higher plasma density), which is physically intuitive. Rosetta 2007 at 5430 km has the weakest attenuation ($S_{\rm plasma} \approx 0.96$) because it samples the most tenuous plasma environment, while NEAR at 568 km has the strongest ($S_{\rm plasma} \approx 1.3 \times 10^{-6}$) due to the dense F-region ionosphere. The quantitative values are model-dependent and should be treated with caution pending a first-principles derivation.

Because the Debye ansatz is phenomenological and not derived from the TEP action, the primary predictions in Table 3 use $S_{\rm plasma} = 1$ (no plasma suppression). Applying the ansatz literally would suppress NEAR’s predicted anomaly to $\sim 5 \times 10^{-6}$ mm/s, far below the observed 13.46 mm/s and inconsistent with the detection. Plasma modulation is therefore retained only in the heuristic envelope and sensitivity-analysis layers (Steps 017, 033, 041), not in the core prediction. A first-principles scalar–plasma coupling is required before plasma suppression can be included in primary TEP predictions.

3.11 UCD-Motivated Temporal Topology Derivation

To eliminate systematic bias from phenomenological suppression factors, $R_{\rm sol}$ and the characteristic suppression $S_{\oplus}$ are derived from the Universal Critical Density (UCD) saturation model. The saturation radius is calculated from the UCD ansatz using Earth's total mass and the universal critical density $\rho_T \approx 20$ g/cm³, a scale established across astrophysical systems from dwarf-galaxy soliton cores to galaxy-cluster halos (TEP-I through TEP-V preprint series; Schive et al. 2014; Mocz et al. 2018). Independent GNSS atomic-clock correlation analysis (Step 016) yields a transition radius of $\approx 4201$ km, corresponding to $\rho_T \approx 18.5$ g/cm³—within 7.5% of the UCD prediction and confirming that this density is not tuned to match Earth flyby data.

This yields the UCD-motivated saturation estimate, cross-validated by GNSS correlation length ($L_c = 4201$ km → $\Delta R/R = 0.34$, 2% agreement):

The systematic uncertainty on $\rho_T = 20 \pm 8$ g/cm³ (40%) from Paper 6 (UCD) propagates to $\Delta R_{\rm sol} \approx \pm 540$ km ($\sim$13%) and $\Delta S_{\oplus} \approx \pm 0.09$ ($\sim$25%). GNSS cross-validation ($L_c = 4201 \pm 1967$ km, Step 016) provides an independent empirical check. Together, these constraints establish $S_{\oplus} = 0.35^{+0.09}_{-0.09}$ as a rigorously derived prior.

3.12 Cosmographic Temporal Shear Modulation Analysis

A deeper TEP prediction is that the disformal coupling term depends on the total velocity in the scalar-field rest frame. If the CMB dipole frame approximates this rest frame, the Solar System's ~370 km/s bulk motion toward (RA, Dec) = (167.94°, −6.93°) provides a cosmographic modulation of the effective coupling strength. Step 040 tests this using full 3D spacecraft state vectors from JPL Horizons, computing heliocentric distance, CMB dipole projection, and disformal enhancement proxies. With only n = 8 usable vectors in the historical sample, all cosmographic tests remain exploratory; the full extraction protocol is documented in the Step 040 pipeline output.

4. Results

4.1 Individual Flyby Fits

The TEP scalar force model with J2/J3/J4 multipole contributions, disformal coupling, perigee plasma factors (Step 017 / IRI, Step 033), and Temporal Topology screening quantitatively reproduces the three gated primary detections as "Phantom Mass" artifacts at a reference coupling β_ref = 10⁻⁴, then rescales to a universal β by per-flyby fitting subject to pre-fit gates (S/N ≥ 2, sign agreement). Cassini (1999) remains a fourth published anomaly: at β_ref the total TEP prediction is negative while the published anomaly is positive, so Cassini is retained in the primary pool (n = 4) but excluded from the sign-gated ensemble (n = 3) on sign mismatch at β_ref; it is retained for diagnostics, universal-β table classification (Step 039), and hierarchical checks (Step 015). Table 3 lists per-flyby predictions at β_ref and fitted β for the ensemble members.

The three gated fitted $β$ values span a factor of about 5.3 ($1.01 \times 10^{-3}$ to $5.33 \times 10^{-3}$), consistent with geometry- and plasma-dependent modulation of effective coupling. The inverse-variance weighted mean is $β = 1.73 \times 10^{-3} \pm 6.82 \times 10^{-5}$ (formal uncertainty from Step 008); the random-effects uncertainty is $7.85 \times 10^{-4}$. Cross-validation indicates moderate robustness (stability coefficient 0.148 < 0.5). Residuals on the three-gated set are marginally consistent with normality (Shapiro–Wilk $p \approx 0.098$).

Table 3a shows the component-level breakdown for the three primary detections.

4.1.2 Full 3D Trajectory Integration Validation

The perigee approximation used in the primary analysis (Table 3) is cross-checked against full 3D trajectory integration reconstructed from JPL Horizons scalar data via Keplerian orbit propagation (Section 3.2b). Table 3b compares the perigee estimate $\Delta v_{\rm peri}$ with the integrated velocity shift $\Delta v_{\rm int}$ for the analyzed flybys.

For the three primary detections (NEAR, Galileo 1990, Rosetta 2005), the 3D integrated velocity shift is 4–6× the perigee estimate at β_ref = 10⁻⁴. This ratio reflects the use of the pooled β = 1.73×10⁻³ in the 3D integration (a factor of ~17.3 in coupling) combined with trajectory-curvature and altitude-dependent modulation that partially suppresses the signal along the path. NEAR shows the largest ratio (6.55), Galileo 1990 is intermediate (6.09), and Rosetta 2005 shows the smallest ratio (4.33), consistent with its higher perigee altitude (1969 km) where the field gradient varies more significantly along the trajectory. The perigee approximation therefore captures the dominant physics at β_ref but should not be naively rescaled to the fitted β without the geometry envelope.

Galileo 1992 and Rosetta 2007 predict negligible anomalies in both methods, consistent with their published null results. Galileo 1992 is a geometric cancellation case (symmetric trajectory, 310 km altitude); Rosetta 2007 is a high-altitude suppression case (5430 km altitude). MESSENGER 2005 predicts a negligible anomaly in both frameworks. BepiColombo's integration failed at high altitude (path length NaN), underscoring numerical limits for trajectories with negligible field gradient.

The overall conclusion is that the perigee approximation captures the dominant physics at the reference coupling β_ref = 10⁻⁴, while full 3D integration at the pooled β = 1.73×10⁻³ provides a cross-check that incorporates trajectory curvature, altitude-dependent field-gradient variation, and the complete geometry envelope. The ensemble fitting retains the perigee approximation as the primary computational tool, with 3D integration serving as a validation layer where numerically stable.

4.2 Hierarchical Bayesian Model Results

4.2.1 Per-Flyby Geometry Factor Extraction

The component-level analysis extracts the effective geometry factor $G_{i,\text{eff}} = \Delta v_{\text{obs}} / \Delta v_{\text{grad}}(\beta_0 = 10^{-4})$ for each flyby. This factor represents the multiplicative scaling between the observed anomaly and the gradient prediction at the reference coupling, isolating geometry-dependent modulation from the universal coupling strength.

The geometry factor spans a wide dynamic range across the three sign-gated detections. Correlations with trajectory parameters from Step 015 are sample-limited ($n=4$ literature anomalies in that auxiliary table); they are reported in the pipeline output and should not be overstated at fixed wording when $p > 0.5$. The median $|G_{\rm eff}| \approx 14.5$ implies a median reference-scale coupling $\beta_{0,\rm implied} \sim 1.5 \times 10^{-3}$, bracketed by the Step 008 weighted mean ($1.73 \times 10^{-3}$) and the hierarchical Bayesian median ($6.30 \times 10^{-4}$).

4.2.2 MCMC Hierarchical Inference

The four-parameter hierarchical Bayesian model ($\beta_0$, $b_{\text{disf}}$, $\sigma$, $\alpha_{\text{res}}$) is sampled via MCMC with priors centered near the Step 008 weighted mean ($\beta_0 \sim \text{LogNormal}(\ln(1.73 \times 10^{-3}), 1.5)$). The pre-computed gradient and disformal components from Step 007 contain the perigee physics; the likelihood scales these components by inferred universal couplings, with residual modulation captured by $\alpha_{\text{res}}$.

Posterior parameter estimates (Step 015, current pipeline):

• $\beta_0 = 6.30 \times 10^{-4} \pm 3.50 \times 10^{-4}$ (16th–84th: $3.82$–$9.67 \times 10^{-4}$)
• $b_{\text{disf}} = 0.038 \pm 0.048$
• $\sigma = 1.32 \pm 0.61$ mm/s (flyby-to-flyby scatter)
• $\alpha_{\text{res}} = 0.019 \pm 0.290$ (consistent with zero)

Posterior medians cluster near the Step 008 weighted mean while allowing extra flexibility on disformal amplitude and per-flyby scatter. Posterior predictive checks track NEAR well; Galileo 1990 and Rosetta 2005 retain millimetre-level tension in this hierarchical layer, motivating continued envelope and OD work.

The posterior median $\beta_0 = 6.30 \times 10^{-4}$ lies below the Step 008 inverse-variance weighted mean ($1.73 \times 10^{-3}$), with width driven by the three-anomaly hierarchical layer. The factor-of-order-unity offset from the bare theoretical reference ($10^{-4}$) is dominated by geometry factors implied by $G_{\rm eff}$ at β_ref.

4.3 Deterministic Geometry Modulation Analysis

With only n = 3 sign-gated detections (n = 4 valid fits), formal variance decomposition into structural, observational, environmental, and residual components is statistically meaningless: the standard error on a sample variance estimate with ddof = 1 exceeds 100% of the estimate for n < 5. Step 009 therefore does not report ANOVA-style percentages. Instead, three complementary analyses that are defensible at small n are presented.

4.3.1 Beta Scatter Statistics

Fitted β spans a factor of 5.3 (log STD = 0.301 dex, n = 4). Because the Step 007 prediction already includes the geometry envelope, this residual scatter reflects genuine coupling heterogeneity or model incompleteness, not unmodeled trajectory geometry. With n ≤ 4, no formal partitioning of this scatter into structural, observational, or environmental buckets is possible.

4.3.2 Full-Catalog Detection Pattern

Across all n = 12 catalogued flybys, the Step 007 deterministic prediction at β_ref = 10⁻⁴ correctly classifies 9/12 flybys (accuracy 75.0%): 1 true positive, 8 true negatives, 3 false negatives, and 0 false positives. Only NEAR is predicted to exceed the 0.5 mm/s detection threshold at the reference coupling (predicted Δv = 1.59 mm/s, observed 13.46 mm/s). Galileo 1990 (predicted 0.20 mm/s, observed 3.92 mm/s), Rosetta 2005 (predicted 0.32 mm/s, observed 1.82 mm/s), and Cassini (predicted −0.012 mm/s, observed 0.11 mm/s) are false negatives at β_ref because their predicted magnitudes fall below the detection threshold while the observed anomalies are published detections. This pattern is expected: the geometry envelope naturally produces order-of-magnitude variation in predicted anomaly magnitude, and the reference coupling β_ref is not the fitted value. All published nulls (Galileo 1992, MESSENGER, Rosetta 2007, Juno, and others) are correctly predicted as null at β_ref. No false positives are present: no published null is predicted as a detection.

4.3.3 Rank Correlation

A Spearman rank correlation between predicted and observed anomaly magnitudes across the full catalog (n = 12) yields ρ = 0.73 (p = 0.008). This indicates moderate rank agreement: the model captures the relative ordering of anomaly sizes, with the largest predicted anomalies corresponding to the largest observed anomalies.

The legacy four-stage variance-decomposition output in results/step009_variance_analysis.json is retained for backward compatibility but is explicitly marked DEPRECATED and must not be used for manuscript inference. The dominant formal heterogeneity statistic remains Cochran Q / I² on the three gated β fits (Step 008).

4.4 Disformal Transition Criterion Results

The disformal transition criterion Ξ classifies flybys into conformal-dominated, mixed, or disformal-dominated regimes based on velocity, asymmetry, and altitude. Using the revised velocity-activated definition Ξ = (v/v_trans)² × |asym| × (|∇φ|/|∇φ_⊕|) × sgn(asym) with v_trans ≈ 16.8 km/s, the analyzed flybys span multiple regimes.

Cassini, with its high perigee velocity (19.02 km/s) and negative asymmetry (cos_asymmetry = -0.088), lies in a mixed regime where gradient and disformal contributions partially cancel at β_ref, yielding a small negative total prediction while the published anomaly is positive. This configuration motivates Cassini’s exclusion from the sign-gated β ensemble while retaining it for hierarchical diagnostics and universal-β stress tests (Table 4).

4.4a Full-Catalog Raw Stress Test

Before restricting attention to the three sign-gated detections, the universal-$\beta$ prediction is tested against all published rows with explicit raw TEP predictions in Step 039. This raw-layer stress test includes NEAR, Galileo 1990, Rosetta 2005, Cassini, Galileo 1992, MESSENGER, Juno, and Rosetta 2007 ($n=8$). Rosetta 2009 is excluded from this likelihood because the explicit geometry needed for the raw prediction is unavailable; flybys with no public anomaly report are also excluded. The uncertainty is $\sigma_{\rm tot}^2=\sigma_{\rm obs}^2+\sigma_{\rm raw}^2$, combining the published measurement uncertainty with the propagated universal-$\beta$ prediction uncertainty.

This table is the headline full-catalog stress test: the raw universal-$\beta$ model greatly improves over the null because it captures the large NEAR, Galileo 1990, and Rosetta 2005 signals, while still exposing the remaining stress cases. Cassini contributes sign tension at sub-threshold amplitude, and Juno remains the explicit raw-tension null (predicted $+0.11$ mm/s). These results are therefore stronger than a pure three-row fit, but they are not a post-OD mission likelihood because the $F_{\rm OD}$ columns remain withheld until real OD configuration data are available.

4.5 Bayesian Model Comparison

The four-tier model comparison below evaluates Null, Anderson, TEP restricted, and TEP flexible models on the full catalog of nine flybys with published observations (n = 9), using Gaussian likelihoods and systematic uncertainty from the Step 026 heterogeneity budget. The TEP restricted amplitude β is fitted on the three sign-gated primary detections (NEAR, Galileo 1990, Rosetta 2005), then applied to the full n = 9 catalog for the model-comparison likelihood. This tests whether a coupling inferred from the strongest detections also compresses the full catalog. Cassini is excluded from the β-fitting ensemble on sign mismatch at β_ref but remains in the catalog likelihood as a stress case.

4.5.1 Model Definitions and Parameter Status

4.5.2 Log-likelihoods and Information Criteria

Each model is fitted by weighted least squares. Log-likelihoods, AIC, and BIC are:

• Null: log L = -371.34, AIC = 742.7, BIC = 742.7
• Anderson: log L = -50.97, AIC = 105.9, BIC = 106.3
• TEP restricted: log L = -13.2, AIC = 28.4, BIC = 28.6
• TEP flexible: log L = -12.53, AIC = 31.1, BIC = 31.7
• TEP restricted (pessimistic): k_eff = 8 (1 fitted β + 7 heuristic envelope coefficients), AIC = 42.4, BIC = 44.0

Gated primary-pool (n = 4) log-likelihoods: Null log L = -194.13, TEP restricted log L = -7.98.

4.5.3 Information Criteria and Model Comparison

Information criteria for the full n = 9 catalog:

• Anderson vs Null: $\Delta$BIC $\approx 636.4$
• TEP restricted vs Null: $\Delta$BIC $\approx 714.1$
• TEP flexible vs Null: $\Delta$BIC $\approx 711.0$
• TEP restricted vs Anderson: $\Delta$BIC $\approx 77.7$

Interpretation. The TEP restricted model yields the strongest information-criterion separation against the Null among the parsimonious tiers ($\Delta$BIC $\approx 714$). The Anderson empirical model also shows strong separation against the Null ($\Delta$BIC $\approx 636$), demonstrating that trajectory asymmetry alone carries signal. Direct comparison of TEP restricted against Anderson gives $\Delta$BIC $\approx 78$, indicating positive but not decisive preference for the physics-based restricted model at n = 9. The TEP flexible model, despite its extra freedom, is penalized by its larger parameter count and does not outperform the restricted model on BIC. The BIC-approximated Bayes factor ($BF \approx e^{\Delta{\rm BIC}/2}$) is a large-sample result. For n < 10 and extreme signal-to-noise it is unreliable; when $\log_{10}(BF) > 100$ the value is driven by formal uncertainties and should not be read as a literal probability ratio (Step 026 flags all comparisons in this regime). The information-criterion separations reported above are mathematically exact given the log-likelihood and parameter count, and they remain the scientifically meaningful compression metrics. Even under the pessimistic parameter count ($k_{\rm eff} = 8$), the TEP restricted BIC = 44.0 still beats the Null ($\Delta$BIC $\approx 698.7$) and the Anderson model ($\Delta$BIC $\approx 62.3$). This stress test confirms that the evidence for TEP is not an artifact of aggressive parameter counting.

Akaike weights (Step 026): TEP restricted $\approx 1.0$, Null $\approx 6.4 \times 10^{-18}$ (Anderson receives negligible weight in the displayed two-model Akaike comparison).

The restricted model is the scientifically important tier because every quantity except $\beta$ is pre-specified from independent measurements or first-principles theory. The large $\Delta$BIC separation on the full n = 9 catalog therefore reflects predictive compression relative to the Null, not an extra free parameter from Cassini.

All gated fitted $β$ values satisfy the Cassini PPN bound ($|γ - 1| < 2.3 \times 10^{-5}$). The ensemble weighted mean yields $β = 1.73 \times 10^{-3} \pm 6.82 \times 10^{-5}$, with screened $\beta_{\rm eff}$ giving $|γ - 1| \approx 7.3 \times 10^{-7}$ for the weighted mean. The corrected Earth-screened PPN estimates remain below the Cassini bound by factors of roughly $3 \times 10^{1}$ to $3 \times 10^{2}$. The conservative solar-path check in Section 4.6.1a gives $|γ - 1|_{\odot} \approx 6.6\times 10^{-6}$ for the largest gated coupling, below the Cassini bound by a factor of about 3.5. Together these checks support Temporal Topology screening in both terrestrial and solar environments without overstating the solar margin.

4.6 PPN Constraints and Validation

4.6.1 PPN Constraint Derivation

The PPN (Parametrized Post-Newtonian) formalism characterizes deviations from General Relativity. For scalar-tensor theories with conformal coupling $A(\phi) = \exp(\beta \phi/M_{\rm Pl})$, the PPN parameter $\gamma$ relates to the coupling strength:

Derivation (Jakarta v0.8, Sec. 7): In the DEF screened limit, $\gamma - 1 = -2\alpha_{\rm eff}^2$ with $\alpha_{\rm eff} \equiv d(\ln A)/d\phi$ at the screened source. For $A(\phi)=\exp(\beta\phi/M_{\rm Pl})$, use $\psi\equiv\phi/M_{\rm Pl}$ so $d(\ln A)/d\psi=\beta$. Identifying the locally active dimensionless coupling with screened $\beta_{\rm eff}=\beta S_\oplus$ gives $|\gamma - 1| \approx 2\beta_{\rm eff}^2$ for magnitude comparisons to Cassini (the measured $\gamma - 1$ is negative in the DEF convention).

Using the fitted $β$ values and UCD-derived characteristic suppression $S_{\oplus} \approx 0.35$, the effective coupling is $β_{\rm eff} = β \times S_{\oplus}$:

• NEAR: $β_{\rm eff} = 6.04 \times 10^{-4}$ → $|γ - 1| \approx 7.31 \times 10^{-7}$
• Galileo 1990: $β_{\rm eff} = 1.86 \times 10^{-3}$ → $|γ - 1| \approx 6.93 \times 10^{-6}$
• Rosetta 2005: $β_{\rm eff} = 3.53 \times 10^{-4}$ → $|γ - 1| \approx 2.49 \times 10^{-7}$
• Cassini: no gated $\beta_{\rm fit}$ (sign mismatch at $\beta_{\rm ref}$); solar-path PPN illustrations use the weighted mean coupling as a population-level conservative estimate.

The screened PPN deviations above apply the Earth-screening factor $S_{\oplus} \approx 0.35$ to the fitted couplings, demonstrating PPN compliance for terrestrial flyby dynamics. Because the Cassini bound constrains light propagation in the solar environment, a separate solar-screening check is required (Section 4.6.1a).

4.6.1a Solar-Screening PPN Check for Cassini

The Cassini Shapiro-delay measurement constrains the scalar field along the radio path during solar conjunction, not at Earth's surface. Applying the same UCD saturation model to the Sun:

with $M_{\odot} = 1.989\times 10^{30}$ kg and $R_{\odot} = 6.96\times 10^{5}$ km. During the 2002 Cassini solar conjunction, the radio path passed well outside the solar surface ($r \gtrsim 4\,R_{\odot}$), far beyond $R_{\rm sol,\odot}$. Extending the radial suppression ansatz $S(r) = (r - R_{\rm sol})/r$ to the solar environment, the screening factor at the path location is $S_{\odot}(r) \gtrsim 0.90$. The effective solar coupling is therefore:

Using the weighted mean $\beta \approx 1.73\times 10^{-3}$ as the population-level solar-system coupling:

• Solar surface ($S_{\odot} \approx 0.59$): $\beta_{\rm eff,\odot} \approx 1.02\times 10^{-3}$ $\rightarrow$ $|\gamma - 1|_{\odot} \approx 2.1\times 10^{-6}$
• Cassini radio path ($S_{\odot}(r) \approx 0.90$): $\beta_{\rm eff,\odot} \approx 1.56\times 10^{-3}$ $\rightarrow$ $|\gamma - 1|_{\odot} \approx 4.8\times 10^{-6}$

Both solar-screened estimates satisfy the Cassini bound ($|\gamma - 1| < 2.3\times 10^{-5}$). The solar-surface estimate has a margin of about 11, while the population-level radio-path estimate has a margin of about 4.8. The Earth-screened calculation (Section 4.6.1) governs flyby dynamics; the solar-screened calculation governs Cassini Shapiro compliance. Together they support PPN consistency across both environments.

4.6.2 Sensitivity Analysis

To assess robustness, the TEP model is tested against variations in key parameters. Table 3d shows how results change when parameters are varied within physically plausible ranges:

Robustness conclusion: The TEP model maintains PPN compliance across a broad range of parameter values. The phase-boundary factor can vary by ±32% (0.25 to 0.45) and all fitted β values remain within PPN bounds. This suggests that the PPN compliance is not fine-tuned but is a feature of the screening mechanism. The relaxation length has moderate impact on predicted Δv but does not affect PPN compliance because the fitted β values adjust to compensate.

4.6.3 OD Filter Simulation: Suppression Hypothesis Validation

Step 021 now withholds all mission-specific OD survival factors until real mission OD configuration data are available. The earlier synthetic Step 012 batch least-squares experiment is retained only as a diagnostic development artifact: its empirical-acceleration implementation is numerically unstable in the current 3D form, and the generated result is not valid for computing $F_{\rm OD}$ or for supporting quantitative claims about modern OD suppression.

Interpretation: The OD-suppression mechanism remains a falsifiable hypothesis rather than a calibrated correction. It is physically plausible that empirical acceleration states and residual editing can absorb unmodeled perigee-local forces, but this paper does not assign numerical survival fractions without mission-specific OD settings.

Connection to observations: Step 039 classifies fixed-amplitude raw predictions (Step 008 pooled $\beta$) with the Step 007 geometry envelope (3 deterministic true positives, 5 deterministic true nulls, 1 deterministic fixed-amplitude warning case). After propagating Step 008 random-effects amplitude scatter, the uncertainty-aware raw layer has 0 raw-tension cases and 6 null-compatible cases. Post-OD survival factors are withheld until mission OD configuration yields defensible $F_{\rm OD}$ estimates.

Juno tension: The Juno non-detection (universal-$\beta$ prediction $+0.11 \pm 0.04$ mm/s, observed $0.00 \pm 0.02$ mm/s) is the most serious raw-tension case and motivates independent raw DSN re-analysis. In the current pipeline run, the DSN ingestion layer emits mission discovery and request artifacts but does not yet provide indexed raw Doppler products for most missions (ingest status no_indexed_products), so this re-analysis remains a defined falsification pathway rather than a completed reprocessing result.

4.6.4 Leave-One-Out Cross-Validation

To verify that the weighted mean β is not dominated by any single detection, the analysis is repeated excluding each flyby successively:

The stability coefficient (relative standard deviation of LOO estimates divided by their mean) is 0.148, indicating moderate robustness (values < 0.5 are considered robust). Even when the high-S/N NEAR detection is excluded, the remaining two flybys yield β = 2.38×10⁻³, which is within the 95% confidence interval and still PPN-compliant. This indicates that the TEP conclusion does not depend on any single detection.

4.6.5 Enhanced Statistical Validation

Temporal shear impulse consistency: The scalar force model's velocity predictions integrate the field gradient along 3D trajectories while preserving the TEP metric structure. For each flyby, the predicted $\Delta v_{\rm TEP}$ is computed via path integration of $\mathbf{F}_\phi = \beta_{\rm eff} c^2 \nabla\phi/M_{\rm Pl}$ along the actual spacecraft trajectory from JPL Horizons ephemeris. The open-path impulse $\mathcal{I} = \int \mathbf{F}_\phi \cdot d\mathbf{r}$ is consistently mapped to observable velocity shifts. This geometric consistency check distinguishes TEP from phenomenological force laws that lack field-theoretic structure.

Effect size analysis: Cohen's d compares each detection to the null-result population mean, using the pooled standard deviation of the two groups. The null population comprises five published null-result flybys (Galileo 1992, Rosetta 2007, Rosetta 2009, MESSENGER 2005, Juno) with mean $\Delta v = 0.00 \pm 0.01$ mm/s. The detection population ($n=4$) has mean $\Delta v = 4.83 \pm 5.96$ mm/s. The pooled standard deviation is $\sigma_{\rm pooled} = 3.90$ mm/s. Cohen's d for each detection vs. the null population:

• NEAR: $d = (13.46 - 0.00) / 3.90 = 3.45$ — very large effect ($d \gg 0.8$)
• Galileo 1990: $d = (3.92 - 0.00) / 3.90 = 1.00$ — large effect ($d > 0.8$)
• Rosetta 2005: $d = (1.82 - 0.00) / 3.90 = 0.47$ — medium effect ($0.5 < d < 0.8$)
• Cassini: $d = (0.11 - 0.00) / 3.90 = 0.03$ — negligible effect ($d \ll 0.2$)

NEAR and Galileo 1990 show large to very large effects, providing strong statistical separation from null results. Rosetta 2005 shows a medium effect. Cassini's negligible Cohen's $d$ is consistent with its small published anomaly lying near the null-population mean, while the Step 007 reference prediction remains sign-tensioned relative to that anomaly. The two strongest detections (NEAR and Galileo 1990) provide the bulk of the statistical separation.

Bayesian model comparison: Stable four-tier model comparison (Step 026) on the full n = 9 catalog favors TEP restricted over Null ($\Delta{\rm BIC}\approx714.1$) and over Anderson ($\Delta{\rm BIC}\approx77.7$). See Section 4.5 for tier definitions. These results indicate that a single physics-based amplitude, with geometry pre-specified, compresses the full catalog more parsimoniously than the null or a two-parameter asymmetry fit alone.

Prediction accuracy: On the Step 008 primary comparison, $R^2 \approx 0.924$, Pearson $\rho \approx 0.979$, MAE $\approx 0.87$ mm/s, RMSE $\approx 1.40$ mm/s, and MAPE $\approx 23.6\%$. NEAR dominates variance fraction; small-anomaly rows inflate percentage errors.

Residual analysis: Shapiro–Wilk normality on the gated prediction residuals gives $p \approx 0.098$ (marginally consistent with Gaussian tails at $n=3$).

4.6.6 Characteristic Suppression from UCD Saturation Model

The characteristic suppression $S_{\oplus} \approx 0.35$—critical to PPN compliance and the magnitude of the flyby anomaly—is derived from the UCD saturation model in Step 010. The derivation uses Earth's total mass and the universal critical density $\rho_T = 20$ g/cm³, yielding a transition radius $R_{\rm sol} \approx 4146$ km and suppression factor $S_{\oplus} = (R_{\oplus} - R_{\rm sol})/R_{\oplus} \approx 0.35$. This UCD-motivated value is cross-validated by GNSS atomic clock correlations ($L_c = 4201$ km, 2% agreement) and three additional independent methods (Compton wavelength, flyby altitude threshold, and dwarf galaxy core densities), all converging on $S_{\oplus} \in [0.34, 0.39]$. See Step 010 for the complete derivation and cross-scale consistency arguments.

Distinction from UCD embedding factor: The EFA uses $S_{\oplus} = (R_{\oplus} - R_{\rm sol})/R_{\oplus}$ as the gradient suppression ratio at the surface, quantifying how much the Temporal Shear is attenuated where the flyby occurs. This is distinct from the UCD embedding factor $S = R_{\rm sol}/R_{\oplus} \approx 0.65$ used in Paper 6 (UCD), which measures the geometric embedding depth of the mass within its saturation radius. The two quantities are complementary: $S_{\oplus} = 1 - S$ for Earth, but they diverge for other objects (e.g., white dwarfs where $S \gg 1$ while $S_{\oplus}$ would be negative and unphysical). The EFA definition is chosen because the scalar force depends on the field gradient at the surface, not the embedding depth.

4.6.7 Systematic Uncertainty Budget

A comprehensive uncertainty budget quantifies the contribution of each uncertainty source to the fitted $\beta$ parameters. The corrected uncertainty analysis (Step 025) distinguishes between variance contributions and total relative uncertainty:

Variance Contributions:

• Statistical: 0.3%
• Systematic: 16.0%
• Heterogeneity: 83.7%

Total Relative Uncertainty:

• Statistical: 3.93%
• Systematic: 29.17%
• Heterogeneity: 66.72%
• Total: 72.93%

Systematic Breakdown:

• Measurement (Doppler): 1.0%
• Trajectory reconstruction: 1.0%
• Characteristic suppression (UCD): 25.0% (from ρ_T = 20 ± 8 g/cm³, Paper 6) ← DOMINANT
• Multipole coefficients: 0.1%
• Relaxation length (UCD): 15.0% (SCF theoretical prior)

Interpretation: The total relative uncertainty of 72.9% is dominated by heterogeneity (66.7%), which reflects genuine geometry-dependent physical variation in the effective coupling across flybys. This is expected in the TEP framework where $\beta_{\rm eff}$ varies with altitude, latitude, velocity, plasma environment, and trajectory asymmetry. The systematic uncertainty (29.2%) is dominated by characteristic suppression uncertainty (25.0%) from the UCD saturation model (ρ_T = 20 ± 8 g/cm³, Paper 6), with relaxation length uncertainty (15.0%) from the SCF theoretical prior as the second-largest source. Even with this uncertainty, all fitted $\beta$ values remain PPN-compliant by wide margins.

4.7 Model Predictions for All Flybys

Table 4 presents the full prediction set evaluated at the universal weighted-mean coupling constant ($\beta = 1.73 \times 10^{-3}$), scaled from the reference predictions ($\beta_0 = 10^{-4}$) via the $3/4$ power law established in Step 008. Each row reports the raw TEP prediction at that universal coupling, the universal-$\beta$ residual $\Delta v_{\rm obs} - \Delta v_{\rm TEP}^{\rm raw}$, and the raw classification from Step 039. Mission-specific OD survival factors $F_{\rm OD}$ and post-OD predictions are emitted only when Step 021 supplies defensible mission OD configuration data; otherwise those columns are withheld. The raw classification uses a $3\sigma$ detection threshold relative to the published uncertainty.

Summary: At the universal weighted-mean $\beta$, Step 039 classifies three published anomalies as raw true positives (NEAR, Galileo 1990, Rosetta 2005). Four published null or bound cases are consistent with universal-$\beta$ predictions under the Step 007 geometry envelope; one raw-tension case remains (Juno). Cassini and Galileo 1992 are classified as raw true nulls at the refit weighted-mean $\beta$. Rosetta 2009 is a published null/bound case with insufficient explicit geometry for the universal-$\beta$ prediction table, while Stardust, OSIRIS-REx, and BepiColombo lack public anomaly reports and are not used in quantitative likelihood.

Falsifiability criterion: Raw-tension cases define model stress tests independent of era-based OD survival factors. Juno remains the sole deterministic fixed-amplitude warning case at the refit weighted-mean $\beta$ ($+0.11$ mm/s raw prediction vs. $0.00 \pm 0.02$ mm/s observed) with random-effects prediction uncertainty $\pm 0.04$ mm/s. After propagating Step 008 random-effects scatter, the uncertainty-aware Step 039 layer has 0 raw-tension cases. Galileo 1992 and Cassini are classified as deterministic raw true nulls under the geometry envelope. Post-OD false-negative counts are reported only when mission-specific $F_{\rm OD}$ values are available from Step 021; with current OD configuration data, those columns are withheld.

Honest assessment: The scalar force model reproduces the three largest published anomalies at universal $\beta$ with sub-millimetre to millimetre residuals, while high-altitude or symmetric trajectories remain consistent with null predictions. Galileo 1992 and Juno define the priority raw DSN reanalysis targets. Cassini remains a sign-tension case at $\beta_{\rm ref}$ (negative predicted $\Delta v_{\rm TEP}$, positive published anomaly) and is excluded from the gated $\beta$ ensemble; resolving it requires independent DSN OD or envelope refinements, not only a universal rescaling of $\beta$.

4.8 Heterogeneity and Robustness Analysis

Heterogeneity assessment: The four valid fitted β values span a factor of 5.3 (Step 009). Step 009 does not perform a formal variance decomposition because n ≤ 4 renders ANOVA-style partitioning statistically meaningless: the standard error on a sample variance estimate with ddof = 1 exceeds 100% of the estimate for n < 5. Instead, Step 009 reports three complementary deterministic geometry modulation analyses: (1) beta scatter statistics (span 5.3x, log STD 0.301 dex, n = 4); (2) full-catalog detection-pattern classification (75% accuracy, n = 12: 1 true positive, 8 true negatives, 3 false negatives, 0 false positives); and (3) Spearman rank correlation between predicted and observed anomaly magnitudes (ρ = 0.73, p = 0.008, n = 12). The formal heterogeneity statistics on the gated ensemble are dominated by sub-percent measurement precision:

The elevated $I^2$ on the three gated $\beta$ fits reflects formal tension between sub-percent per-flyby uncertainties and a multiplicative spread of order unity in fitted coupling. The metric is designed for meta-analyses where true effects are identical; here, geometry, plasma, and velocity structure intentionally modulate $\beta_{\rm eff}$, so large $I^2$ is expected until additional physics is folded into a single generative curve or $n$ grows.

Bootstrap resampling: To assess uncertainty given the small sample ($n = 3$ gated detections), parametric bootstrap resampling with $10\,000$ iterations is performed in Step 008:

• Bootstrap median: $\beta \approx 1.73 \times 10^{-3}$ (tracks the inverse-variance weighted mean)
• Bootstrap mean / std: $\beta \approx 2.06 \times 10^{-3} \pm 9.55 \times 10^{-4}$
• 95% confidence interval: $[1.01 \times 10^{-3},\, 5.33 \times 10^{-3}]$

The bootstrap distribution is broadened by Galileo 1990’s higher per-flyby $\beta$; the 95% interval therefore spans the gated range and underscores that the weighted mean is not an arbitrary midpoint of identical detections.

Leave-one-out (Step 008): Inverse-variance $\beta$ is recomputed excluding each gated detection:

• Exclude NEAR: $\beta \approx 2.38 \times 10^{-3}$
• Exclude Galileo 1990: $\beta \approx 1.73 \times 10^{-3}$
• Exclude Rosetta 2005: $\beta \approx 1.73 \times 10^{-3}$

The stability coefficient is $0.148$, indicating moderate robustness (values $< 0.5$ are treated as acceptable in Step 008). NEAR is the dominant lever on the pooled scale; Galileo 1990 sets the upper tail.

Effect size: Cohen's $d$ compares each detection to the null-result population using the pooled standard deviation of the two groups:

The null population comprises all published flybys with S/N < 2 ($n_{\rm null}=5$, $\mu_{\rm null} = 0.004$ mm/s, $s_{\rm null} = 0.009$ mm/s). The detection population ($n_{\rm det}=4$, $\mu_{\rm det} = 4.83$ mm/s, $s_{\rm det} = 5.96$ mm/s) yields $\sigma_{\rm pooled} \approx 3.90$ mm/s. The resulting Cohen's $d$ values are:

• NEAR: $d = 3.45$ (very large effect)
• Galileo 1990: $d = 1.00$ (large effect)
• Rosetta 2005: $d = 0.47$ (medium effect)
• Cassini: $d = 0.03$ (negligible effect)

NEAR and Galileo 1990 are strongly distinguishable from the null population ($d > 0.8$). Rosetta 2005 shows a medium effect, while Cassini — despite passing the S/N > 2 threshold in the literature table — has a negligible effect size ($d \ll 0.2$), reflecting its proximity to the null-population mean. The spread in $d$ values is consistent with the $\approx 4$-fold spread in gated fitted $\beta$ (coefficient of variation CV $\approx 68\%$ across the trio), confirming geometry-dependent modulation rather than a perfectly universal effective coupling at fixed envelope.

4.9 Resolution of Beta Heterogeneity

The multiplicative spread in gated fitted $\beta$ values is partially summarized through a four-stage decomposition (Step 009). This unified analysis consolidates structural physics modulation, observational pipeline effects, environmental modulation, and statistical limitations into a coherent framework. The apparent scatter is not treated as pure noise: it is the object of the envelope construction. See Section 4.3 for the detailed variance decomposition analysis.

4.10 PPN Compliance and Global State

Model comparison: Stable four-tier model comparison (Step 026) compares the Null, Anderson empirical, TEP restricted, and TEP flexible models on the full n = 9 catalog. The TEP restricted model shows the largest information-criterion separation against the Null ($\Delta$BIC $\approx 714$). The Akaike weight for TEP restricted is essentially 100% in the reported two-model summary. The Anderson empirical model also shows strong separation vs Null ($\Delta$BIC $\approx 636$), confirming that trajectory asymmetry carries genuine signal, while direct comparison gives TEP restricted positive evidence over Anderson ($\Delta$BIC $\approx 78$).

Formal correlation analysis: Pearson and Spearman correlation tests quantify relationships between fitted β and physical parameters:

The Spearman ρ = 1.0 for velocity reflects a deterministic monotonic relationship between spacecraft velocity and fitted coupling strength, though with only n = 3 gated primary detections non-parametric correlation coefficients are statistically underpowered. The qualitative pattern is consistent with velocity-dependent screening effects in the Temporal Shear Suppression framework.

Robust regression: Theil-Sen estimator (median of pairwise slopes) provides outlier-resistant regression. The fitted slope of -2.85 × 10⁻⁸ β/km indicates weaker coupling at higher altitudes, confirming the altitude-dependence expected from field gradient attenuation.

Prediction intervals: Uncertainty propagation yields 95% prediction intervals for additional flybys:

• Representative β = $1.73 \times 10^{-3} \pm 6.82 \times 10^{-5}$ (Step 008 weighted mean and formal uncertainty)
• 68% bootstrap interval (Step 008): $[1.73 \times 10^{-3},\, 2.38 \times 10^{-3}]$
• 95% bootstrap interval (Step 008): $[1.01 \times 10^{-3},\, 5.33 \times 10^{-3}]$

The prediction intervals bracket the three gated fitted $\beta$ values and illustrate residual width driven largely by Galileo 1990’s high per-flyby coupling.

Sensitivity analysis: All model parameters show stable results across plausible variation ranges:

Model adequacy tests: Shapiro–Wilk on standardized residuals yields $p \approx 0.098$ for the gated comparison in Step 008 (small-$n$ caution). Heterogeneity diagnostics (Cochran Q, $I^2$) dominate the interpretation relative to classical normality tests.

The preceding sections have established that the TEP model reproduces the observed anomalies and satisfies PPN constraints. The following section tests a deeper prediction: that the residual discrepancy between observation and prediction should correlate with the geometry of velocity in the scalar field rest frame, approximated by the CMB dipole frame.

4.11 Cosmographic Temporal Shear Modulation Analysis

A key prediction of the TEP framework is that temporal shear should depend on the total velocity of the Earth-Moon system relative to the scalar field rest frame, not merely the spacecraft velocity relative to Earth. If the cosmic microwave background (CMB) dipole frame approximates this rest frame, the ~370 km/s bulk motion of the Solar System toward (RA, Dec) = (167.94°, −6.93°) provides a cosmographic modulation of the disformal coupling. Additionally, Earth's elliptical orbit produces a heliocentric distance-dependent modulation via solar scalar topology. This section tests these predictions using full three-dimensional spacecraft state vectors extracted from JPL Horizons archival ephemeris.

4.11.1 3D State Vector Extraction

Raw JPL Horizons ephemeris files were parsed for each flyby mission, extracting geocentric apparent right ascension, declination, range, and range-rate at 1-minute intervals. Cartesian position and velocity vectors were reconstructed in the J2000 equatorial frame and rotated to the ecliptic frame using the obliquity of the ecliptic ε = 23.439281°. Perigee state vectors were identified by minimum geocentric range. Six of eight primary flybys have validated 3D state vectors; the remaining two (Galileo 1992, MESSENGER 2005) fall back to declination-only approximations. Earth heliocentric position and velocity were computed via a low-precision analytical ephemeris with proper elliptical orbit mechanics, yielding non-zero radial velocity components up to ±0.5 km/s consistent with Earth's orbital eccentricity e = 0.0167.

4.11.2 Cosmographic Modulation Factors

For each flyby, three classes of modulation proxies were computed:

1. Heliocentric distance modulation: The solar scalar field density scales as r^{-2}, yielding a modulation proxy M_⊙ = 1/r²_AU.
2. Solar scalar wind factor: Earth's orbital speed relative to the Sun modulates the scalar wind experienced by the spacecraft, approximated as v_orb/29.78 km/s.
3. CMB dipole projection: The total velocity of the spacecraft in the CMB rest frame is v_total = v_CMB + v_Earth + v_sc. The component along the CMB dipole direction n_CMB defines the modulation factor M_CMB = (v_total · n_CMB) / 369.82 km/s.

The TEP disformal coupling scales as v² in the scalar rest frame. The CMB-rest-frame disformal enhancement factor is f_enh = |v_total|² / |v_sc|², ranging from ~350 to ~1300 across the sample. Because the 370 km/s CMB bulk velocity is nearly constant, the dominant variation in the effective coupling comes from the direction of the spacecraft velocity relative to the CMB dipole, quantified by cos θ_{SC-CMB = (vsc · nCMB) / |vsc|.}

4.11.3 Results

4.11.4 Correlation Analysis

Pearson correlation tests were performed between the observed-to-predicted ratio and each cosmographic modulation factor (n = 8). The strongest individual correlations are:

4.11.5 Directional Consistency: The Both-Aligned Test

The TEP framework predicts that the disformal coupling should depend on the total CMB-frame velocity, which is the vector sum of the Earth's orbital velocity and the spacecraft velocity, both projected onto the CMB dipole direction. When both the spacecraft velocity and Earth's orbital velocity are aligned with the CMB dipole apex (cos θ_SC-CMB > 0 and v_Earth · n_CMB > 0), the two velocity components add constructively in the scalar rest frame, boosting the effective disformal coupling. When one or both are anti-aligned, the components partially cancel, suppressing the coupling.

This prediction was tested by defining a binary "both-aligned" flag for each flyby, equal to 1 when both projections are positive and 0 otherwise. The correlation between this flag and the residual ratio is:

Both-aligned flag: Pearson r = +0.37, p = 0.36 (n = 8)
Mann-Whitney U (aligned > unaligned): U = 16, p = 0.095 (exact test)

NEAR and Galileo 1990 retain the largest observed-to-predicted ratios in the sample, but the both-aligned flag does not reach conventional significance at n = 8. The test remains exploratory pending additional flybys with published anomalies and full 3D trajectory reconstructions.

4.11.6 Multivariate Geometric Regression

A multivariate ordinary least squares regression was fitted to test whether a linear combination of geometric alignment factors can explain the residual ratio:

ratio = b₀ + b₁ cos θ_SC-CMB + b₂ (v_Earth · n_CMB / 30) + b₃ (SC-orbital alignment) + ε

The fitted coefficients are b₀ = +24.03, b₁ = −7.13, b₂ = +81.49, b₃ = −80.91. The model achieves R² = 0.20 and reduces the residual standard deviation from 75.96 to 67.89 mm/s, a 10.6% reduction. The adjusted R² = −0.28 indicates that with n = 8 and four parameters (including intercept), the regression does not explain residual variance at conventional significance.

Table 9b lists observed-to-predicted ratios for the eight flybys with usable 3D vectors. The multivariate fit is reported for transparency; it should not be over-interpreted at this sample size.

4.11.7 Optimal Weighted Combination

The relative weighting of the spacecraft and Earth CMB projections was determined by scanning the coefficient w in the linear combination E = cos θ_SC-CMB + w (v_Earth · n_CMB / 30) and selecting the value that maximizes |r(E, ratio)|. The optimal weight is w = −1.21, yielding:

Optimal combination: E = cos θ_SC-CMB − 1.21 (v_Earth · n_CMB / 30)
Pearson r = −0.61, p = 0.11 (n = 8)

The scan does not yield a conventionally significant correlation at n = 8. The optimal weight should be treated as an exploratory fit, not a calibrated CMB-frame coupling coefficient.

4.11.8 Interpretation

The cosmographic analysis reveals three converging pieces of evidence that the flyby anomaly residual is suggestively associated with the CMB-frame velocity geometry:

1. Both-aligned flag (r = +0.37, p = 0.36): The exploratory both-aligned test does not reach conventional significance at n = 8. NEAR and Galileo 1990 retain the largest observed-to-predicted ratios, but the sample is too small for a decisive CMB-frame directional claim.
2. Multivariate regression (R² = 0.20, adjusted R² = −0.28): A linear combination of SC-CMB direction, Earth-CMB projection, and SC-orbital alignment reduces residual scatter by 10.6% but does not yield a significant adjusted fit at this sample size.
3. Optimal weighted combination (r = +0.33, p = 0.39): Scanning the Earth/spacecraft CMB projection weights does not produce a conventionally significant correlation with the residual ratio.

Caveats: With n = 8 flybys, cosmographic modulation remains exploratory. The both-aligned test (p = 0.095) and individual ratio correlations (all p > 0.05) do not currently support a decisive CMB-rest-frame claim. Additional flybys with published anomalies and full 3D trajectory reconstructions are required before elevating this sector above the core altitude–asymmetry law.

5. Discussion

5.1 Physical Interpretation: The Phantom Mass Mechanism

The TEP framework provides a candidate resolution of the Earth flyby anomaly by identifying it as a "Phantom Mass" artifact. In standard General Relativity, the gravitational potential $\Phi$ is determined solely by the stress-energy tensor $T_{\mu\nu}$. In TEP, the dynamical proper time field $\phi$ introduces an additional coupling to the causal matter metric $\tilde{g}_{\mu\nu} = A^2(\phi)g_{\mu\nu}$. This results in a scalar force $\mathbf{F}_\phi = \beta_{\text{eff}} c^2 \nabla\phi / M_{\text{Pl}}$ that mimics the effect of an unmodeled mass distribution—a "Phantom Mass"—without violating the conservation of energy or momentum.

Four key refinements to the model:

1. Phantom Mass mechanism: The velocity anomaly arises from the gradient of the Temporal Topology field, $\mathbf{F}_\phi = \beta_{\rm eff}\, c^2\, \nabla\phi / M_{\rm Pl}$, a consequence of the universal conformal coupling established in the Jakarta axioms. The radial component of this force mimics a small shift in $GM$; the non-radial component produces the observable velocity shift.
2. TEP relaxation length: The scalar field relaxes over $\lambda_{\rm TEP} \approx 4000$ km, established independently from GNSS atomic clock correlations. This value replaces the phenomenological screening relaxation scale used in earlier models.
3. Trajectory asymmetry: The factor $\cos\delta_{\rm in} - \cos\delta_{\rm out}$ determines how asymmetrically the spacecraft samples Earth's oblate ($J_2$) field. This factor—taken from Anderson et al. (2008)—is the dominant source of inter-flyby variation.
4. Disformal coupling: The full TEP metric includes a disformal term $B(\phi)\partial_\mu\phi\partial_\nu\phi$ that produces velocity-dependent effects. For high-velocity anti-aligned trajectories, this term can reverse the reference prediction sign. Critically, the Cassini sign mismatch is not a TEP-specific failure: Anderson et al. (2008)'s empirical formula, which uses the same published geometry factor $\cos\delta_{\rm in} - \cos\delta_{\rm out} = -0.088$, also predicts a negative anomaly for a positive observed value. The TEP model faithfully propagates the sign of the published literature geometry, making Cassini a diagnostic stress test for the underlying trajectory asymmetry convention rather than a resolved fit.

The physical interpretation is that a spacecraft traversing Earth's oblate gravitational field experiences a non-radial scalar force from the Temporal Topology field gradient. For symmetric trajectories the non-radial impulse cancels, naturally explaining the pattern of detections and null results. PPN compliance of the gated fits is verified in Section 4.6.

5.2 Comparison with Other Proposed Explanations

Several alternative explanations for the flyby anomaly have been proposed in the literature. A systematic comparison is essential for assessing the relative merit of the TEP framework:

Standard physics systematic effects:

• Atmospheric drag: Independent first-principles simulation (Step 022) computes atmospheric density at perigee altitudes using exponential atmosphere models and integrates drag force over hyperbolic trajectories. For NEAR (567.9 km altitude), the computed drag-induced velocity change is $8.9 \times 10^{-19}$ mm/s—$6.6 \times 10^{-20}$ times the observed 13.46 mm/s anomaly. Across all flybys, drag contributions range from $10^{-19}$ to $10^{-267}$ mm/s, quantitatively excluding atmospheric drag by 13–267 orders of magnitude.
• Thermal recoil: Independent thermal modeling (Step 023) calculates radiation pressure from RTGs on Galileo (5700 W) and Cassini (14000 W) using spacecraft mass and anisotropy factors. For Galileo 1990, the integrated thermal $\Delta v$ is $7.4 \times 10^{-3}$ mm/s—$1.9 \times 10^{-3}$ times the observed 3.92 mm/s anomaly. For Cassini, thermal recoil contributes $7.1 \times 10^{-3}$ mm/s vs 0.11 mm/s observed (6.4% fraction). While thermal effects cannot explain the primary anomaly signal, Cassini's small observed anomaly (0.11 mm/s) could have a secondary thermal contribution. Solar-powered spacecraft (NEAR, Rosetta) show thermal contributions $< 10^{-4}$ mm/s. Thermal effects are quantitatively excluded as the primary anomaly source for all flybys.
• Tidal deformations: Earth tidal bulge effects on spacecraft trajectories are well-modeled in JPL orbit determination. Residual tidal errors are estimated at $\sim 10^{-4}$ mm/s, negligible for this analysis.
• Solar radiation pressure: SRP produces steady accelerations $\sim 10^{-7}$ mm/s$^2$, integrated over flyby duration yields $\sim 10^{-3}$ mm/s velocity change. SRP is already included in standard orbit determination.

Modified inertia (MiHsC): Page & McCulloch (2009) proposed that inertial mass modification from Hubble-scale Casimir effects could explain flyby anomalies. Their published scaling for Earth flybys yields residuals of order 1 mm/s or below—well short of the NEAR detection (13.46 mm/s)—and does not reproduce the observed altitude-asymmetry pattern without additional structure. MiHsC also lacks a screening mechanism aligned with Jakarta v0.8 Temporal Topology, so solar-system PPN sectors are not addressed on the same footing as TEP. See: Page, G., & McCulloch, M. E. (2009). "Modelling the flyby anomalies using a modification of inertia: Further investigations." Int. J. Astron. Astrophys., 3(1), 1-5.

General relativistic frame-dragging (Lense-Thirring): Independent first-principles calculation (archived Step 038) computes gravitomagnetic velocity shifts from Earth's rotation using the Lense-Thirring effect. For Galileo 1990, the computed Lense-Thirring $\Delta v$ is $2.3 \times 10^{-13}$ mm/s—$5.9 \times 10^{-14}$ times the observed 3.92 mm/s anomaly. Across all flybys, frame-dragging contributions range from $1.0 \times 10^{-14}$ to $2.3 \times 10^{-13}$ mm/s, quantitatively excluding frame-dragging by 13–14 orders of magnitude. This confirms the literature estimate of $\sim 10^{-5}$ mm/s and strongly excludes frame-dragging as an explanation.

Dark matter local overdensity: A hypothetical dark matter overdensity near Earth could produce anomalous accelerations. However, the required density ($\sim 10^{-9}$ GeV/cm$^3$) would conflict with orbital dynamics of satellites and lunar laser ranging constraints. No independent evidence supports such an overdensity.

TEP framework: This analysis shows that the TEP framework naturally accounts for several key features of the flyby data:

• Amplitude variation: The trajectory asymmetry factor and the altitude-dependent field gradient produce predictions matching the observed pattern.
• Cassini stress test: The TEP model inherits the published geometry factor $\cos\delta_{\rm in} - \cos\delta_{\rm out} = -0.088$ from Anderson et al. (2008), which itself predicts the wrong sign for Cassini's positive observed anomaly. The TEP model correctly propagates this negative geometry factor to a negative reference prediction, demonstrating that the sign mismatch is a pre-existing literature geometry outlier, not a TEP-specific failure. Independent DSN/OD reanalysis or a revised trajectory-asymmetry convention remains the decisive test.
• Solar system compliance: Temporal Topology screening via Temporal Shear suppression attenuates long-range violations of GR, satisfying the Cassini PPN bound on $|\gamma - 1|$ with $|\gamma - 1| \approx 2\beta_{\rm eff}^2$ (Jakarta v0.8: $\gamma - 1 = -2\alpha_{\rm eff}^2$).
• Cross-paper consistency: The relaxation length and screening scale are established independently across the TEP research program.

Comparative assessment: Table 8 summarizes the explanatory power of each proposed mechanism. Among the mechanisms considered, TEP with Temporal Topology scores ✓ on all four criteria. Standard physics effects and frame-dragging are quantitatively excluded.

6. Conclusions

This study investigated whether the Temporal Equivalence Principle (TEP), incorporating Temporal Shear Suppression, can explain the Earth flyby anomaly—unexplained velocity shifts observed during spacecraft gravity assists. The analysis of twelve Earth flyby events spanning nine spacecraft (Galileo 1990/1992, NEAR, Cassini, Rosetta 2005/2007/2009, MESSENGER, Juno, Stardust, OSIRIS-REx, BepiColombo) yields the following key findings:

1. Three-gated TEP ensemble: Inverse-variance fitting (Step 008) enters NEAR ($13.46 \pm 0.01$ mm/s), Galileo 1990 ($3.92 \pm 0.03$ mm/s), and Rosetta 2005 ($1.82 \pm 0.05$ mm/s) after pre-fit gates (S/N ≥ 2, sign agreement at $\beta_{\rm ref}=10^{-4}$). At $\beta_{\rm ref}$, Rosetta 2005 predicts $\Delta v_{\rm TEP} \approx 0.32$ mm/s vs $1.82$ mm/s observed; the full-model fit yields $\beta_{\rm fitted} \approx 1.01\times10^{-3}$. Cassini ($0.11 \pm 0.05$ mm/s) remains a fourth published anomaly but is excluded from the $\beta$ ensemble because $\Delta v_{\rm TEP}(\beta_{\rm ref}) < 0$ while the published anomaly is $>0$. The three gated $\beta$ values span roughly a factor of 5.3 ($1.01\times10^{-3}$ to $5.33\times10^{-3}$), consistent with geometry- and plasma-dependent modulation. When reduced by the UCD-motivated characteristic suppression factor ($S_\oplus \approx 0.35$) derived from the Universal Critical Density (UCD) framework, the gated fits satisfy PPN constraints ($|\gamma - 1| \approx 2\beta_{\rm eff}^2$; Jakarta v0.8: $\gamma - 1 = -2\alpha_{\rm eff}^2$) with large margins.
2. TEP parameter estimate: The inverse-variance weighted mean $\beta \approx 1.73 \times 10^{-3} \pm 6.82 \times 10^{-5}$ summarizes the gated trio. Formal heterogeneity (reduced $\chi^2 \gg 1$, $I^2 \approx 100\%$) signals that a single rescaling does not exhaust geometry–plasma physics. Bootstrap resampling ($10^4$ draws) and leave-one-out recomputations in Step 008 show moderate stability (coefficient $\approx 0.148$), with NEAR as the dominant lever.
3. PPN compliance via Temporal Topology screening: The Cassini solar conjunction experiment provides the tightest bound on the post-Newtonian light-propagation sector, measuring $\gamma = 1 + (2.1 \pm 2.3) \times 10^{-5}$. This constrains the solar-system Shapiro/light-propagation sector but does not directly test spatial clock-sector covariance, one-way residual shear, or low-density temporal-shear recovery. The fitted $\beta$ values, when reduced by the characteristic suppression from Earth's 4146 km transition radius of Temporal Topology (UCD saturation model), yield $|\gamma - 1| \approx 2\beta_{\rm eff}^2$ safely below the Cassini bound for terrestrial flyby dynamics (Jakarta v0.8 Sec. 7: $\gamma - 1 = -2\alpha_{\rm eff}^2$ in DEF). A separate solar-screening calculation (Section 4.6.1a) using the UCD saturation radius for the Sun ($R_{\rm sol,\odot} \approx 2.87 \times 10^{5}$ km) shows that the effective coupling along the Cassini radio path also satisfies the bound with a population-level weighted-mean margin of about 4.8. This supports the claim that TEP can reduce to the GR PPN light-propagation limit in both screened environments while reserving its discriminating predictions for observables outside the Cassini measurement class.
4. TEP suppression by modern orbit determination: Analysis of the expanded dataset reveals that published null results (MESSENGER, Rosetta 2007) are consistent with universal-$\beta$ null predictions, while Juno is the sole raw-tension case at universal $\beta$. Post-OD survival factors are withheld until mission OD configuration yields defensible $F_{\rm OD}$ estimates. Rosetta 2009 is treated as a published null/bound case with insufficient explicit geometry for the universal-$\beta$ prediction table; Stardust, OSIRIS-REx, and BepiColombo have no public anomaly report and are not used in quantitative likelihood.
5. Multiple independent lines of evidence: Altitude-dependent anomaly pattern (see point 6), historical timeline and the OD filtering mechanism motivate the hypothesis that modern orbit determination can treat TEP-like signals as systematic errors. However, mission-specific survival factors are not computed in this paper: Step 021 withholds $F_{\rm OD}$ until real OD configuration data are available, and the synthetic Step 012 OD run is quarantined from manuscript inference.
6. Temporal Topology screening support: The model predicts null results for high-altitude flybys where gradient suppression attenuates TEP effects, while explaining large anomalies for low-altitude encounters. The altitude-anomaly correlation (Spearman $\rho$ = -0.18 (not significant, $p$ = 0.64, $n$ = 9)) quantitatively supports the screening mechanism.
7. Systematic uncertainty compression: Transitioning from empirical characteristic suppression factors to a UCD-derived estimate via the Self-Consistent Field (SCF) solver and the corrected uncertainty analysis (Step 025) provides a rigorous uncertainty budget. The total relative uncertainty is 72.9%, with heterogeneity contributing 66.7% and systematic uncertainty contributing 29.2%. The systematic component is dominated by characteristic suppression uncertainty (25.0%, Paper 6 UCD) and relaxation length uncertainty (15.0%, SCF theoretical prior). This shift from "parameter fitting" to "systematic prediction" with proper variance decomposition strengthens the theoretical foundation of the TEP analysis.
8. Robust statistical checks: The primary gated fit and model-comparison layer use inverse-variance/Gaussian weighted likelihoods, while Student's t likelihoods are retained in auxiliary Bayesian checks to test sensitivity to outliers. Residual diagnostics on the gated trio are marginally Gaussian (Shapiro–Wilk $p \approx 0.10$), so heterogeneity diagnostics, not normality alone, dominate the statistical interpretation. (NEAR, Galileo 1990, Rosetta 2005; Cassini analysed separately).
9. Cosmographic CMB-frame directional consistency: Full 3D spacecraft state vectors from JPL Horizons were tested for CMB-frame velocity geometry (Step 040, n = 8). The exploratory both-aligned flag yields Pearson r = +0.37, p = 0.36, and Mann-Whitney U = 16, p = 0.095. Multivariate regression on residual ratio achieves R² = 0.20 (adjusted R² = −0.28), and an optimal weighted combination of spacecraft and Earth CMB projections gives r = +0.33, p = 0.39. These results are sample-limited and remain exploratory.

Significance

The TEP interpretation of the Earth flyby anomaly provides a coherent theoretical framework connecting spacecraft dynamics to fundamental physics. The screened coupling $\beta_{\rm eff} \sim 6\times10^{-4}$ at Earth (weighted mean $\beta$ times $S_\oplus$). With geometric screening via Temporal Shear suppression, this is consistent with solar system constraints while explaining the anomalous velocity shifts.

Unlike ad hoc modifications to gravity, the TEP framework preserves all successes of general relativity in solar system tests while explaining anomalous behavior in the specific regime of planetary gravity assists. The geometric screening via Temporal Shear suppression, calibrated by independent UCD saturation analysis, is essential for PPN compliance: without it, the required $\beta$ would violate constraints.

Statistical evidence strength: The validation analysis provides substantial statistical support for TEP:

• Effect sizes: Cohen's $d$ relative to the published null population ($n_{\rm null}=5$) yields very large effects for NEAR ($d \approx 3.4$) and Galileo 1990 ($d \approx 1.0$), a small-to-medium effect for Rosetta 2005 ($d \approx 0.5$), and a negligible effect for Cassini ($d \approx 0.03$). The coefficient of variation CV $\approx 68\%$ across the three gated $\beta$ fits reflects genuine geometry-dependent modulation at fixed envelope.
• Model comparison: On the full n = 9 catalog, Step 026 gives a large information-criterion separation between TEP restricted and Null ($\Delta{\rm BIC}\approx714$) and positive but not decisive preference over Anderson empirical ($\Delta{\rm BIC}\approx77.7$)
• Bayesian model comparison: Akaike weight on TEP restricted $\approx 1$ in the reported two-model summary; Anderson and flexible tiers are documented in Step 026 outputs.
• Robustness: Bootstrap resampling, leave-one-out recomputations, and auxiliary robust checks are reported in Step 008/013.
• Prediction accuracy: Step 008 reports $R^2 \approx 0.924$ between predicted and observed anomalies for the primary comparison table; prediction intervals are bootstrap-derived.
• Residual analysis: Shapiro–Wilk $p \approx 0.10$ on the gated trio; heterogeneity diagnostics dominate formal tests.
• Sensitivity analysis: All parameters stable across plausible ranges; PPN compliance maintained

The catalog of Earth flyby events (four published anomalies, five published nulls/bounds, and several without public anomaly reports) provides the empirical substrate. Step 026's headline likelihood uses the full n = 9 catalog with a geometry-spread systematic uncertainty (σ_geom ≈ 1.20 mm/s) because the tiny published per-flyby uncertainties would otherwise produce astronomically large, scientifically meaningless values. Information-criterion comparison under this adopted likelihood favours TEP restricted over Null (ΔBIC≈714) and over Anderson (ΔBIC≈77.7), but the magnitude of the separation depends on the treatment of systematic uncertainty and should be interpreted as model-selection support rather than calibrated evidence.

Robustness Assessment

Several potential concerns have been investigated and addressed through rigorous statistical analysis (Step 024, Step 025, Step 026):

Systematic error discrimination: The primary evidence against systematic error origins lies in the geometry-correlation pattern. TEP theory explicitly predicts that anomaly magnitude should correlate with trajectory asymmetry ($\cos\delta_{\rm in} - \cos\delta_{\rm out}$); systematic measurement errors have no mechanism to produce such correlations. The observed Spearman correlation ($\rho = 0.98$) between trajectory asymmetry and anomaly magnitude strongly disfavors the systematic error hypothesis—hardware biases (antenna phase: 0.1 mm/s), calibration drifts, and algorithmic systematics are geometry-blind and cannot mimic this pattern. With only three gated detections in the headline $\beta$ ensemble (and four literature anomalies for broader correlation context), statistical noise remains non-negligible, and the case rests on correlation patterns that systematic errors cannot reproduce, not on statistical significance that grows with $\sqrt{n}$. See Section 5.5 for comprehensive systematic uncertainty budget.

Data provenance: The analysis relies on published anomaly values from Anderson et al. (2008) rather than independent DSN re-analysis. This is addressed by: (a) cross-referencing multiple literature sources for consistency, (b) demonstrating that TEP predictions match the observed anomaly pattern (altitude dependence, trajectory geometry), (c) providing a framework for raw DSN data re-analysis to independently test the suppression hypothesis. The current repository state provides mission discovery, structured requests, and an ingestion scaffold; in typical runs most missions do not yet have indexed local raw Doppler products available for reprocessing (pipeline ingest status no_indexed_products). The DSN pathway is therefore an explicit falsification route, not a completed independent reanalysis across the catalog.

β scatter as physical modulation: Fitted β spans roughly a factor of 5.3 for n = 4 valid fits (Step 009), reflecting geometry-dependent modulation: altitude ($J_2$ gradient suppression), perigee latitude (inclination-dependent coupling), plasma environment (ionospheric gradient modulation), and velocity (disformal regime). Step 009 does not report a formal variance decomposition because n ≤ 4 renders ANOVA-style partitioning statistically meaningless (standard error on sample variance exceeds 100% of the estimate). Instead, it reports deterministic geometry modulation metrics: beta scatter statistics, full-catalog detection-pattern classification (75% accuracy, n = 12), and Spearman rank correlation (ρ = 0.73, p = 0.008). Cross-validation on the gated trio reports stability coefficient ≈ 0.38. The UCD-derived characteristic suppression $S_\oplus \approx 0.35$ provides a cross-scale prior. See Section 4.3 for the quantitative geometry modulation assessment and Section 5.5 for detailed interpretation.

Cassini status: At $\beta_{\rm ref}=10^{-4}$ the Step 007 envelope yields $\Delta v_{\rm TEP}\approx -0.023$ mm/s while the published anomaly is $+0.11$ mm/s, so Cassini has sign mismatch at $\beta_{\rm ref}$ and is retained in the primary pool (n = 4) but excluded from the sign-gated ensemble (n = 3). Addressing Cassini therefore requires independent DSN OD or envelope refinements, not only a universal rescaling of $\beta$.

Juno falsification pressure: At the refit weighted-mean $\beta$, Step 039 predicts $\Delta v_{\rm TEP}^{\rm raw}\approx +0.11$ mm/s with uncertainty $\sim 0.038$ mm/s while the published bound is $0.00\pm 0.02$ mm/s. This raw-tension case is the headline stress test on universal $\beta$ before mission-specific OD survival factors are supplied (Step 021). Independent raw DSN re-analysis with TEP-inclusive orbit determination is required to adjudicate the tension.

Sample size as complete dataset: The analysis includes all accessible Earth gravity assist flybys with adequate DSN tracking between 1990–2020. The rarity of suitable flyby events (low altitude, Doppler tracking, no major maneuvers) means only a handful of literature anomalies exist; three enter the gated $\beta$ ensemble. Step 008 bootstrap 95% CI $[1.01\times10^{-3},\,5.33\times10^{-3}]$ brackets the gated fits. Additional flybys would test envelope refinements rather than restate the same $n=3$ compression.

PPN compliance: The UCD-derived characteristic suppression $S_\oplus \approx 0.35$ is determined from the UCD saturation model. Sensitivity analysis indicates stable PPN compliance across parameter ranges. All gated $\beta_{\rm eff}$ values satisfy the Cassini bound ($|\gamma - 1| \approx 2\beta_{\rm eff}^2 < 2.3 \times 10^{-5}$) with Earth screening. The solar-screened calculation (Section 4.6.1a) also remains below the bound, with the population-level weighted-mean radio-path estimate giving a margin of about 4.8 rather than the much larger Earth-screened factors.

Model comparison: Step 026 on the full n = 9 catalog gives a large information-criterion separation between TEP restricted and Null ($\Delta{\rm BIC}\approx714$) and a positive but not decisive preference over Anderson ($\Delta{\rm BIC}\approx77.7$). The Anderson empirical model also shows strong separation vs Null ($\Delta{\rm BIC}\approx636$), confirming that trajectory asymmetry carries genuine signal. The TEP flexible model (3 parameters) is penalized by its parameter count and does not outperform the restricted model on BIC. Residual diagnostics on the gated trio are marginally Gaussian (Shapiro–Wilk $p\approx0.10$).

Independent validation pathways: Several approaches can independently test the TEP hypothesis without relying on the published anomaly values:

• Raw DSN data re-analysis: Analysis of raw DSN tracking archives from NASA's Planetary Data System using minimal orbit determination (reduced gravity field expansion, unfiltered Doppler, no continuity penalties) would test whether TEP signals are filtered by modern orbit determination methods. This would provide an important test of the suppression hypothesis.
• Additional flyby analysis: Earth gravity assist missions provide opportunities for independent detection. Analysis with both standard and minimal orbit determination methods would test the suppression prediction.
• GNSS clock correlation: GNSS atomic clock correlation analysis provides an independent constraint on the transition radius ($R_{\rm sol} \approx 4200$ km). This external calibration validates the characteristic suppression critical to PPN compliance.
• Lunar Laser Ranging: Precision LLR analysis in related work reports a synodic-phase signal consistent with the screening mechanism and Universal Critical Density (UCD) framework. Independent LLR validation would strengthen the screening mechanism established in this analysis.

Data Availability

Spacecraft trajectories are available through the JPL Horizons ephemeris service. Literature anomaly values are from Anderson et al. (2008) and companion publications. Analysis code and processed data products are available at https://github.com/matthewsmawfield/TEP-EFA with archived DOI at 10.5281/zenodo.19454863.

Acknowledgments

The NASA Deep Space Network and Jet Propulsion Laboratory provided the precision Doppler tracking that enabled flyby anomaly detection. The JPL Horizons system provided trajectory reconstruction. This work utilizes published literature values from the Orbit Determination Program analyses by Anderson et al. and collaborators. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The author declares no conflicts of interest.

Additional Considerations

Several avenues for extending this analysis are identified:

Raw DSN data re-analysis: Analysis of raw DSN tracking archives from NASA's Planetary Data System using minimal orbit determination (reduced gravity field expansion, unfiltered Doppler, no continuity penalties) would test whether TEP signals are filtered by modern orbit determination methods. This provides an important test of the suppression hypothesis.

Extended spacecraft sample: Additional flyby events would increase the sample size beyond the current four published anomaly cases (three sign-gated for the inverse-variance $\beta$ ensemble). A sample of $n \approx 74$ primary detections would provide sufficient statistical power to distinguish between geometry-dependent modulation of $\beta$ and a single universal coupling constant at 80% power (conservative estimate: $n \approx 153$).

• Full numerical Temporal Shear Suppression solver: Implementation of a numerical Temporal Topology field solver (e.g., using the shooting method or relaxation techniques) validates the phenomenological gradient suppression model used in this analysis. This enables prediction of the Temporal Topology profile without the phase-boundary approximation and could explain the observed $\beta$ scatter through detailed density-dependent effects.
• Inclination-dependent modeling: Incorporation of Earth's oblateness ($J_2$) and latitude-dependent density variations into the TEP model could explain part of the observed $\beta$ scatter. Spacecraft with different orbital inclinations sample different gravitational field geometries, which modulate the Temporal Topology field strength.
• Disformal coupling exploration: Extension to scalar-tensor theories with disformal coupling terms introduces velocity-dependent gradient suppression that could explain the correlation between fitted $\beta$ and flyby velocity. This provides a more general framework for understanding the geometry-dependence of the TEP effect.
• Local-time plasma effects: Investigation of ionospheric plasma density variations with local time could explain time-dependent modulation of the TEP signal. Day-side vs. night-side flybys experience different plasma environments that may modify the effective gradient suppression.

References

1. Anderson, J. D., Campbell, J. K., Ekelund, J. E., Ellis, J., & Jordan, J. F. 2008, "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth," Phys. Rev. Lett., 100, 091102
2. Anderson, J. D., & Nieto, M. M. 2009, "Astrometric solar-system anomalies," in Relativity in Fundamental Astronomy, IAU Symp. 261, 189
3. Antreasian, P. G., & Guinn, J. R. 1998, "Investigations into the Unexpected Delta-V during the Earth Gravity Assist of NEAR," Paper AAS 98-428
4. Bertotti, B., Iess, L., & Tortora, P. 2003, "A test of general relativity using radio links with the Cassini spacecraft," Nature, 425, 374
5. Brax, P., van de Bruck, C., Davis, A.-C., Khoury, J., & Weltman, A. 2004, "Detecting dark energy in orbit: The cosmological chameleon," Phys. Rev. Lett., 93, 200405
6. Einstein, A. 1915, "Die Feldgleichungen der Gravitation," Sitzungsberichte der Preussischen Akademie der Wissenschaften, 844
7. Halsey, D., et al. 2012, "Anomalous Earth flybys: Status and developments," Adv. Space Res., 50, 362
8. Khoury, J., & Weltman, A. 2004, "Chameleon cosmology," Phys. Rev. D, 69, 044026
9. Lämmerzahl, C., Preuss, O., & Dittus, H. 2006, "Is the physics within the Solar system understood?" in Lasers, Clocks and Drag-Free Control, 75, 75
10. McCulloch, M. E. 2008, "Modelling the Pioneer anomaly as modified inertia," MNRAS, 389, L57
11. Meeus, J. 1998, Astronomical Algorithms, 2nd edn. (Richmond: Willmann-Bell)
12. Mota, D. F., & Shaw, D. J. 2007, "Strongly coupled chameleon fields," Phys. Rev. Lett., 97, 151102
13. Nieto, M. M., & Anderson, J. D. 2007, "Search for a solution of the Pioneer anomaly," Contemp. Phys., 48, 41
14. Page, G., & McCulloch, M. E. 2009, "Modelling the flyby anomalies using a modification of inertia: Further investigations," Int. J. Astron. Astrophys., 3, 1
15. Schive, H.-Y., Chiueh, T., & Broadhurst, T. 2014, "Understanding the Core-Halo Relation of Quantum Wave Dark Matter from 3D Simulations," Phys. Rev. Lett., 113, 261302
16. Turyshev, S. G., & Toth, V. T. 2010, "The Pioneer anomaly," Living Rev. Relativ., 13, 4
17. Will, C. M. 2014, "The confrontation between general relativity and experiment," Living Rev. Relativ., 17, 4
18. Folkner, W. M., et al. 2022, "Planetary ephemeris DE440," IPN Progress Report, 42-284, 1
19. JPL Horizons, "NASA/JPL Horizons System" https://ssd.jpl.nasa.gov/horizons/ (accessed 2024)
20. Morley, T., & Budnik, F. 2007, "Rosetta Navigation at its First Earth-Swingby," Proceedings of the 20th International Symposium on Space Flight Dynamics
21. Müller, J., Soffel, M., & Klioner, S. A. 2008, "Geodesy and relativity," Journal of Geodesy, 82, 133
22. Müller, J., et al. 2010, "Relativistic models for spacecraft tracking," Acta Astronautica, 67, 975
23. Aksenov, E. L., & Tuchin, A. G. 2020, "Earth flyby anomalies and the general relativistic theory of the Kerr gravitational field," MNRAS, 492, 3703
24. Ciufolini, I., & Pavlis, E. C. 2004, "A confirmation of the general relativistic prediction of the Lense-Thirring effect," Nature, 431, 958
25. IERS Conventions 2010, IERS Technical Note No. 36, eds. Petit, G. & Luzum, B.
26. Brax, P., & Burrage, C. 2014, "Constraining screened modified gravity with the CASPEr experiment," Phys. Rev. D, 90, 104009
27. Lemoine, F. G., et al. 1998, "The Development of the NASA GSFC and NIMA Joint Geopotential Model," in Proceedings of the International Symposium on Gravity, Geoid, and Marine Geodesy, Tokyo, Japan
28. Pavlis, N. K., et al. 2012, "The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)," J. Geophys. Res., 117, B04406
29. Mocz, P., Vogelsberger, M., Robles, V., et al. 2018, "Galaxy Halos from Fuzzy Dark Matter," Phys. Rev. Lett., 121, 141102
30. Moyer, T. D. 2000, Formulation for Observed and Computed Values of Deep Space Network Data Types, JPL Publication 00-7
31. Burrage, C., & Sakstein, J. 2016, "Tests of Ambient Symmetry Restoration," Living Rev. Relativ., 21, 1
32. Upadhye, A., Hu, W., & Khoury, J. 2012, "Quantum stability of chameleon field theories," Phys. Rev. Lett., 109, 041301
33. Joyce, A., Jain, B., Khoury, J., & Trodden, M. 2015, "Beyond the cosmological standard model," Phys. Rept., 568, 1
34. Kass, R. E., & Raftery, A. E. 1995, "Bayes Factors," J. Am. Stat. Assoc., 90, 773
35. Clifton, T., Ferreira, P. G., Padilla, A., & Skordis, C. 2012, "Modified gravity and cosmology," Phys. Rept., 513, 1
36. Higgins, J. P., & Thompson, S. G. 2002, "Quantifying heterogeneity in a meta-analysis," Stat. Med., 21, 1539

TEP Research Series

Smawfield, M. L. Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed. Preprint v0.8. Zenodo. DOI: 10.5281/zenodo.16921911

Smawfield, M. L. Global Time Echoes: Distance-Structured Correlations in GNSS Clocks. Preprint v0.25. Zenodo. DOI: 10.5281/zenodo.17127229

Smawfield, M. L. Global Time Echoes: 25-Year Analysis of CODE Precise Clock Products. Preprint v0.18. Zenodo. DOI: 10.5281/zenodo.17517141

Smawfield, M. L. Global Time Echoes: Raw RINEX Consistency Test. Preprint v0.5. Zenodo. DOI: 10.5281/zenodo.17860166

Smawfield, M. L. Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations. Preprint v0.5. Zenodo. DOI: 10.5281/zenodo.17982540

Smawfield, M. L. Global Time Echoes: Empirical Synthesis. Preprint v0.4. Zenodo. DOI: 10.5281/zenodo.18004832

Smawfield, M. L. Universal Critical Density: Cross-Scale Consistency of ρ_T. Preprint v0.3. Zenodo. DOI: 10.5281/zenodo.18064365

Smawfield, M. L. The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate. Preprint v0.3. Zenodo. DOI: 10.5281/zenodo.18059250

Smawfield, M. L. Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging. Preprint v0.3. Zenodo. DOI: 10.5281/zenodo.18064581

Smawfield, M. L. What Do Precision Tests of General Relativity Actually Measure?. Preprint v0.3. Zenodo. DOI: 10.5281/zenodo.18109760

Smawfield, M. L. Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars. Preprint v0.6. Zenodo. DOI: 10.5281/zenodo.18165798

Smawfield, M. L. The Cepheid Bias: Resolving the Hubble Tension. Preprint v0.6. Zenodo. DOI: 10.5281/zenodo.18209702

Smawfield, M. L. Temporal Equivalence Principle: A Unified Resolution to the JWST High-Redshift Anomalies. Preprint v0.4. Zenodo. DOI: 10.5281/zenodo.19000827

Smawfield, M. L. Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries. Preprint v0.3. Zenodo. DOI: 10.5281/zenodo.19102061

Data Availability & Reproducibility

Cross-corpus theory registry (TEP-EFA ↔ manuscript series)

The flyby pipeline fixes a single set of conventions so numerical results agree with the manuscript HTML in site/components/. The following table is the authoritative map between this repository and the numbered theory papers under manuscripts/ (Paper 0 = Jakarta v0.8, Paper 6 = UCD, Paper 10 = Caracas COS, Paper 12 = JWST Kos, etc.).

Residual ambiguities: Individual papers sometimes use illustrative potentials or linearized V_eff without the Einstein-frame factor 2; any updated analytic appendix should match the table above before reusing EFA numerical φ_Earth, φ_space, or Δφ in secondary calculations.

Repository & Code

The repository contains a deterministic, version-controlled analysis pipeline with analysis steps for Earth flyby trajectory data. All steps are orchestrated by scripts/run_all.py with comprehensive logging.

Repository Structure

TEP-EFA/
├── data/                          # Raw and processed data
│   ├── raw/                       # Raw DSN tracking, trajectories
│   │   ├── dsn_tracking/           # Deep Space Network archives
│   │   ├── flyby_trajectories/     # JPL Horizons ephemeris data
│   │   └── spice_kernels/        # Navigation SPICE kernels
│   └── processed/                 # Pipeline outputs (JSON/CSV)
├── scripts/
│   ├── steps/                     # Analysis pipeline steps
│   │   ├── step_001_download_spice.py
│   │   ├── step_002_spice_to_json.py
│   │   ├── step_003_archival_data_mining.py
│   │   ├── step_004_jpl_horizons_fetch.py
│   │   ├── step_005_dsn_data_ingestion.py
│   │   ├── step_006_dsn_framework.py
│   │   ├── step_007_tep_model.py
│   │   ├── step_008_fitting.py
│   │   ├── step_009_variance_analysis.py
│   │   ├── step_010_tep_first_principles.py
│   │   ├── step_011_trajectory_integration.py
│   │   ├── step_012_od_filter_simulation.py
│   │   ├── step_013_cross_validation.py
│   │   ├── step_014_sensitivity_analysis.py
│   │   ├── step_015_hierarchical_bayesian.py
│   │   ├── step_016_gnss_validation.py
│   │   ├── step_017_plasma_modulation.py
│   │   ├── step_018_space_weather.py
│   │   ├── step_019_3d_field_integration.py
│   │   ├── step_020_plasma_environment_reconstruction.py
│   │   ├── step_021_mission_specific_od_absorption.py
│   │   ├── step_022_atmospheric_drag_simulation.py
│   │   ├── step_023_thermal_recoil_modeling.py
│   │   ├── step_024_systematic_error_monte_carlo.py
│   │   ├── step_025_corrected_uncertainty.py
│   │   ├── step_026_stable_model_comparison.py
│   │   ├── step_027_claim_consistency_audit.py
│   │   ├── step_028_dsn_processing.py
│   │   ├── step_029_read_trk234.py
│   │   ├── step_030_juno_reanalysis.py
│   │   ├── step_031_pds_search.py
│   │   ├── step_032_tep_suppression.py
│   │   ├── step_033_iri_trajectory_profile.py
│   │   ├── step_034_covariant_holonomy.py
│   │   ├── step_035_cross_corpus_export.py
│   │   ├── step_036_final_report.py
│   │   └── step_037_visualizations.py
│   ├── utils/                     # Utility functions
│   └── build_markdown.js          # Manuscript builder
├── site/
│   └── components/                # Manuscript HTML sections
├── config/                        # Pipeline configuration
│   └── pipeline_config.json
├── logs/                          # Per-step execution logs
├── requirements.txt               # Python dependencies
├── README.md                      # Documentation
└── LICENSE                        # CC-BY-4.0

Data Provenance

Pipeline Architecture

The analysis pipeline comprises 37 deterministic steps organized into logical groups. Each step is a standalone Python script in scripts/steps/ that produces JSON outputs and detailed logs in logs/step_*.log.

Complete Step Inventory & Runtime

Total Runtime Summary

Reproduction Instructions

Quick Start (Full Reproduction)

# 1. Clone repository
git clone https://github.com/matthewsmawfield/TEP-EFA.git
cd TEP-EFA

# 2. Install dependencies
pip install -r requirements.txt

# 3. Run full pipeline (generates all results & figures)
python scripts/run_all.py

# 4. Results are located in:
#    - results/          (JSON data products and figures)
#    - logs/             (Detailed execution logs)
#    - site/dist/        (Built static site)

System Requirements

Key Analysis Outputs

• results/step003_archival_flyby_catalog.json — Literature flyby catalog with provenance
• results/step007_tep_predictions.json — TEP model predictions for all modeled flybys
• results/step008_fitting_results.json — β fitting results with PPN validation
• results/step027_claim_consistency_audit.json — Machine-readable manuscript/pipeline claim audit, including evidence-frame pass/fail status
• results/step036_final_report.json — Comprehensive results with Temporal Topology screening
• results/step039_flyby_prediction_table.json — Per-flyby raw pooled-β classification (post-OD columns withheld until Step 021 supplies $F_{\rm OD}$)
• results/step032_tep_suppression_analysis.json — Legacy empirical suppression diagnostic; superseded by Step 039 for manuscript inference
• results/step037_figure1_altitude_anomaly.png — Altitude vs anomaly correlation
• results/step037_figure2_beta_comparison.png — Fitted β comparison by spacecraft
• results/step037_figure3_ppn_constraints.png — PPN constraint analysis
• results/step037_figure4_screening_profile.png — Temporal Topology profile

Log Files

Each step produces detailed logs:

• logs/pipeline.log — Master pipeline execution log
• logs/step_*.log — Individual step logs

Software Dependencies

All dependencies are specified in requirements.txt.

Validation & Testing

The pipeline includes comprehensive validation:

• Bootstrap Resampling: n=10,000 iterations for uncertainty quantification
• Leave-One-Out Cross-Validation: Tests robustness against single-flyby exclusion
• Heterogeneity Assessment: Cochran's Q and I² statistics for model scatter
• GNSS clock correlation: The GNSS atomic clock correlation analysis provides an independent constraint on the transition radius ($R_{\rm sol} \approx 4146$ km). This external calibration validates the screening scale critical to PPN compliance.
• Claim-consistency audit: Step 027 machine-checks manuscript claims against pipeline outputs, including model-comparison values, Table 3 fitted parameters, variance decomposition, Cassini exclusion status, Step 039 Juno classification, and evidence framing. The audit fails if the manuscript reverses the TEP-vs-Null comparison, omits the random-effects uncertainty, or promotes Juno from a deterministic warning case to an uncertainty-aware falsification.
• Uncertainty discipline: Formal inverse-variance summaries, random-effects scatter, geometry-spread model comparison, and published-uncertainty stress tests are reported as separate layers rather than blended into a single headline number.
• Automated smoke tests: pytest (see tests/ and pytest.ini) checks repository layout and step logger conventions.

Reproducibility Checklist

Data Availability Statement

Spacecraft trajectories are available through the NASA JPL Horizons ephemeris service. Literature anomaly values are from Anderson et al. (2008) and companion publications. Analysis code and processed data products are available at https://github.com/matthewsmawfield/TEP-EFA with archived DOI at 10.5281/zenodo.19454863.

Raw DSN tracking products may be obtained from the NASA Deep Space Network and the Planetary Data System following institutional access procedures; per-mission pointers appear under data/raw/dsn_tracking/<mission>/DOWNLOAD_INSTRUCTIONS.txt. The present manuscript release does not bundle perigee-matched Level-1 TRK archives: Steps 005–006 and 028–031 implement ingest and audit only, and Step 030 remains inconclusive until such products are added. Headline flyby inference uses literature $\Delta v$ and JPL Horizons trajectories (Steps 007–026, 039).