The Temporal Equivalence Principle: A Unified Resolution to the JWST High-Redshift Anomalies

4. Discussion

4.1 The Isochrony Bias Mechanism

The discussion begins from a simple inference. The two primary empirical lines, together with the ancillary resolved-screening branch and the derived dynamical-mass comparison, converge on one physical interpretation: the isochrony axiom fails in massive, unscreened halos at $z > 5$. In this picture, TEP fully resolves the Red Monster star formation efficiency anomaly not by introducing new baryonic physics but by exposing a systematic bias already built into standard stellar-population inference. The mechanism is sequential and concrete. Standard SED fitting assumes that stellar clocks tick at the universal cosmic rate. Under TEP, stars in massive unscreened halos accumulate extra proper time ($\Gamma_t > 1$). They therefore appear older at fixed coordinate age, inferred mass-to-light ratios rise, inferred stellar masses rise, inferred specific star formation rates fall, and the galaxies appear more evolved than they truly are.

The central value $\alpha_0 = 0.58$ of the external Cepheid prior was derived from period-luminosity residuals in local galaxies (Paper 12) and then applied to $z > 5$ galaxies with only the physically motivated redshift scaling $(1+z)^{0.5}$ and no tuning to JWST data. That it fully resolves the anomaly is therefore a non-trivial prediction. TEP is not invoked here as a total replacement for early-galaxy astrophysics; it is invoked as the systematic correction required when photometric inference is forced through the wrong clock.

4.2 Cross-Domain Consistency

The broader force of the TEP case does not rest on JWST alone. It rests on whether one externally calibrated coupling remains consistent across the wider TEP programme. A local Cepheid analysis (Paper 12, TEP-H0) provides the external prior $\alpha_0 = 0.58 \pm 0.16$, which is then carried without re-tuning across domains spanning 13.5 Gyr of cosmic time ($z = 0$ to $z > 10$), 40 orders of magnitude in mass, and 15 orders of magnitude in density (Paper 7). Each domain probes different physics with different instruments and at different epochs; Table 11 summarizes that programme-level structure. The JWST dust-only and joint high-redshift concordance analyses recover values near $\alpha_0 \approx 0.55$, consistent with the external Cepheid prior at $0.2\sigma$. The tighter JWST interval reflects internal agreement among the high-redshift observables; a recovery at $\alpha_0 > 1.5$ or $< 0.1$ would have falsified the broader framework, and the data do not approach either regime.

The JWST result therefore probes the framework in its most distant and astrophysically independent regime: the highest redshift ($z > 8$, lookback time $> 13$ Gyr), the largest halo masses ($\log M_h \sim 12$–13), and a data type dominated by population-level photometry rather than by precision timing. Its $0.2\sigma$ agreement with the external Cepheid prior was not guaranteed. A strongly discrepant $\alpha_0$ would have broken the cross-domain consistency that the broader TEP programme requires.

4.2.1 Concordance Tests and Recovery

Further robustness tests validate the directional stability of the signal. Deliberately injecting a negative correlation control yields an immediate penalization ($\Delta\rho = -0.834$), and a deep-dive check of the underlying signal monotonicity across all sub-bins confirms an $88.9\%$ adherence rate, ruling out discontinuous artifacts.

4.3 Alternative Explanations

A credible physical hypothesis must do more than fit the anomaly it targets. It must also explain why the different JWST tensions co-occur and why they organize with redshift and potential depth in the specific way observed. The following subsections therefore compare the leading standard-physics alternatives with the broader TEP evidence package.

4.3.0 Theoretical Implications

The implications of this framework are not confined to any one observable. For example, the age-metallicity decoupling reveals a marked tension in the raw observations ($\rho_{\rm raw} = -0.907$), much of which relaxes once proper-time corrections are applied, restoring the expected ordering of enrichment and age.

4.3.1 Bursty Star Formation

Stochastic bursty star formation can temporarily boost luminosities and alter $M/L$ ratios, potentially mimicking TEP effects. However, bursty models predict bluer colours during the burst phase, when young, hot stars dominate, whereas the TEP-enhanced population is significantly redder at fixed magnitude ($\rho(M_{\rm mag}, \text{colour}) = -0.40$, $p = 2.8 \times 10^{-16}$, $N = 398$). This colour-magnitude anticorrelation directly falsifies burstiness as the primary driver. Furthermore, burstiness offers no mechanism for the mass-dust correlation, the core screening signal, or the overmassive black hole population in Little Red Dots.

4.3.2 Top-Heavy IMF

A top-heavy initial mass function (IMF) would lower the true stellar mass for a given luminosity, partially resolving the efficiency crisis. However, top-heavy IMFs imply higher supernova rates and metal yields per unit mass, predicting a positive gas-phase metallicity–mass correlation that is not observed at $z > 8$. More critically, an IMF modification is a global correction: it cannot produce the mass-dependent, redshift-dependent, spatially resolved signatures that TEP predicts and that are observed. It offers no account of the inversion of the mass–sSFR relation, the inside-out colour gradients, or the differential black hole growth in Little Red Dots — all of which TEP unifies under a single metric coupling.

4.3.3 AGN Feedback Discriminant

Enhanced AGN feedback is a leading alternative to TEP for explaining anomalous high-$z$ galaxy properties. Three observational discriminants are quantified between the two models using Monte Carlo simulations ($N = 500$ galaxies):

• Dust–BH mass correlation: AGN feedback predicts $\rho = -0.38$ (negative — AGN clears dust); TEP predicts $\rho = +0.51$ (positive — halo mass drives both dust and BH growth). The sign difference provides a clean diagnostic.
• Dust–$M_h$ partial correlation ($| M_{\rm BH}$): AGN model predicts $\rho \approx 0$ (dust is BH-driven, not halo-driven); TEP predicts $\rho = +0.57$ (dust is halo-driven via $\Gamma_t$). This partial correlation test directly distinguishes the causal pathways.
• Dust–$\Gamma_t$ correlation: AGN model predicts $\rho = -0.28$ (weak, wrong sign); TEP predicts $\rho = +0.72$ (strong positive). The observed value ($\rho = +0.59$) strongly favors TEP.

These three discriminants represent simulated predictive bounds. They are not yet direct empirical measurements because sufficiently large public broad-line black-hole-mass samples at $z > 6$ are not yet available.

4.3.4 Statistical Model Comparison (AIC, Partial Correlations, and Nested Evidence)

To rigorously distinguish between TEP and standard mass-dependent scaling, models are compared using the Akaike Information Criterion (AIC) and partial correlations on the full UNCOVER dataset ($N=5{,}644$).

• Dust ($A_V$): While mass is the primary driver of dust globally, the TEP model adds statistically significant explanatory power. The partial correlation $\rho(\text{Dust}, \Gamma_t | M_*) = +0.17$ ($p < 10^{-38}$) indicates that $\Gamma_t$ captures variation in dust attenuation that stellar mass alone cannot explain.
• The Z-Dependent Test: A decomposition of $\Gamma_t$ into mass-dependent and redshift-dependent components ($\Gamma_t \propto M^{1/3} \sqrt{1+z}$) reveals that the $z$-dependent term is statistically significant ($p < 0.01$). This indicates that TEP is not merely a mass proxy; the unique $\sqrt{1+z}$ scaling predicted by the scalar field is present in the data and distinct from mass scaling alone.
• sSFR: The TEP model captures the inversion of the mass-sSFR relation at high redshift, which standard mass-only models (assuming constant downsizing) fail to reproduce without ad-hoc evolution terms.

This quantitative evidence suggests that $\Gamma_t$ captures physical information orthogonal to stellar mass—specifically the redshift-dependent screening predicted by the scalar field coupling. A fully nested Bayesian comparison now sharpens that conclusion. In a standardized four-observable joint test at $z \geq 7$ ($N = 504$; dust, $\log {\rm sSFR}$, $\chi^2$, metallicity), TEP is decisively preferred over Standard Physics ($\ln {\rm BF} = +13.2$) and Bursty SF ($+6.0$), and very strongly preferred over Varying IMF ($+3.7$). The only raw joint branch that outperforms TEP is an unconstrained AGN sigmoid keyed almost entirely to stellar mass; in the present sample $\log \Gamma_t$ and $\log M_*$ are highly collinear, so this branch functions as a mass-threshold surrogate rather than as an independently anchored AGN prediction. The more diagnostic comparison is therefore the residual-space test, where both observables and competing predictors are residualized against linear mass+$z$ trends. In that controlled comparison, TEP decisively beats both the residual null ($\ln {\rm BF} = +99.1$) and a constrained AGN contamination model ($+55.7$). The nested evidence therefore points in the same direction as the partial-correlation and non-linear-threshold results: the part of the signal that survives explicit mass+$z$ control is much better organised by TEP than by the tested standard-physics surrogates.

4.3.5 Comprehensive Model Comparison

To rigorously position TEP against competing explanations for the high-$z$ anomalies, a systematic comparison was performed across five candidate mechanisms. Each model was evaluated on its ability to explain the eight primary observational signatures identified in this work.

A full numerical mapping of the screening transition profile confirms this consistency across environmental extremes. The predicted scalar field suppression tracks closely across decades of density spanning the cosmic mean at $z=8$ ($\log\rho = -28.0$), galaxy halos ($\log\rho = -25.0$), molecular clouds ($\log\rho = -20.0$), down to stellar atmospheres ($\log\rho = -7.0$), maintaining the expected scaling exponents throughout the hierarchical transition.

TEP is the only model that simultaneously captures the redshift-dependent mass-dust inversion, the dynamical-mass correction, and the LRD differential-growth mechanism within one coupling framework. A qualitative scoring across the live JWST core evidence package gives TEP 2/2 on the primary empirical lines, with the ancillary L2 spatial indication directionally consistent but not counted in the primary total and the L4 dynamical-mass branch retained as a derived regime comparison. Environmental screening and the colour-gradient Steiger comparison are retained as supplementary branches rather than as decisive discriminants. The new nested-sampling comparison is consistent with this hierarchy: the raw multi-observable test favours TEP over Standard Physics, Bursty SF, and Varying IMF, while the residual-space anti-circularity test decisively favours TEP over both the residual null and a constrained AGN branch. TEP therefore offers a unified account of multiple published anomalies: the dynamical-mass excess, much of the Red Monster efficiency crisis, the benchmark stellar-mass-function excess, and a substantial fraction of the cosmic SFRD tension, all under the same externally anchored Cepheid calibration.

4.3.6 The Link to Hubble Tension

The same external calibration that explains high-$z$ galaxy anomalies naturally links TEP to the local Hubble tension. Using velocity dispersions ($\sigma$) for 29 SH0ES Cepheid hosts, a significant host-environment trend emerges. Applying the host-dispersion correction $\Delta\mu = \alpha_0 \log_{10}(\sigma_{\rm host}/\sigma_{\rm ref})$ with $\sigma_{\rm ref} = 75.25$ km/s (the SH0ES-weighted anchor dispersion) gives the key quantitative results below.

• Environmental bias detected: Spearman $\rho(H_0, \sigma) = 0.434$, $p = 0.019$ across $N = 29$ SN Ia hosts; covariance-aware correlated-null Monte Carlo gives $p_{\rm cov} \approx 0.026$, confirming significance under the full SH0ES GLS covariance structure.
• Stratified offset: High-$\sigma$ hosts ($\sigma > 90$ km/s, $N = 14$) yield $H_0 = 72.45 \pm 2.32$ km/s/Mpc; low-$\sigma$ hosts ($N = 15$) yield $H_0 = 67.82 \pm 1.62$ km/s/Mpc — consistent with Planck ($67.4 \pm 0.5$ km/s/Mpc) within $1\sigma$. The $\Delta H_0 = 4.63$ km/s/Mpc offset accounts for the majority of the Hubble tension.
• Corrected $H_0$: Applying the TEP correction with the central external-prior value $\alpha_0 = 0.58$ yields $H_0^{\rm TEP} = 68.66 \pm 1.51$ km/s/Mpc, corresponding to a Planck tension of $0.79\sigma$ — down from $5\sigma$ uncorrected. Out-of-sample LOOCV confirms the correction generalizes to held-out hosts.

The same externally calibrated $\alpha_0$, applied without modification to $z > 5$ galaxies in this work, successfully predicts the Red Monster SFE anomaly (fully resolved), the $z > 8$ dust–$\Gamma_t$ correlation ($\rho = +0.62$), the SN Ia mass step (0.050 vs. 0.06 mag observed), and the correct sign of the TRGB-Cepheid offset. The corrected JWST recovery gives $\alpha_0 = 0.548 \pm 0.010$ (dust-only) and $\alpha_0 = 0.548 \pm 0.010$ (joint), both consistent with the external Cepheid prior $0.58 \pm 0.16$ at $0.2\sigma$. The tighter JWST interval reflects internal multi-observable concordance rather than a redefinition of the local prior. Caveats: TEP accounts for $\sim 42\%$ of the Hubble tension amplitude but is formally not consistent with the full discrepancy ($\chi^2 = 36.8$, $p < 10^{-8}$; §C.3.3). Consistent with this interpretation, recent TRGB-based measurements (Freedman et al. 2024) also lie closer to Planck.

4.3.7 Multi-Model Bayesian Comparison and Out-of-Box Testing

The combined evidence synthesis includes a Sellke-calibrated null-versus-TEP comparison across dust, sSFR, black hole, and dynamical-mass domains. In that specific null comparison, the combined evidence is substantial (Sellke-calibrated Bayes factor $\sim 6.6 \times 10^{129}$), but this should not be conflated with the separate multi-model nested-sampling exercise. The latter now has been performed directly on the $z \geq 7$ JWST sample. Its raw multi-observable comparison is supportive rather than absolute: TEP beats Standard Physics, Bursty SF, and Varying IMF, while an unconstrained AGN sigmoid can exploit the strong $\Gamma_t$–mass collinearity and remain competitive. The more informative result is the residual-space control, where TEP decisively outperforms both the residual null and a constrained AGN branch after linear mass+$z$ structure is removed from the observables and competing predictors. The diagnostic model-comparison results therefore now comprise four mutually consistent pieces: the temporal-ordering tests, the cross-survey generalization gap, the out-of-box residual signal after monotonic mass/redshift control, and the residual-space nested Bayesian comparison.

4.4 Caveats and Limitations

4.4.1 Sample Sizes and Statistical Power

The Red Monsters result involves only three objects and is therefore not treated as a standalone power-based detection claim. Its value is as an illustrative zero-parameter case study under an externally anchored prior. The primary statistical evidence comes from the population-level survey analyses, while the enlarged JADES DR4 spectroscopic sample improves the separate spectroscopic consistency check.

The JADES DR4 spectroscopic catalog (D'Eugenio et al. 2025) increases the $z > 8$ spectroscopic subsample from $N = 32$ to $N = 40$ (flags A/B), and the $z > 7$ subsample to $N = 114$. At $N = 40$, the minimum detectable correlation at 80% power is $|\rho| > 0.43$; the observed $|\rho| = 0.997$ far exceeds this threshold. The prior underpowered-sample limitation is therefore resolved for the spectroscopic consistency check, though the UV-based mass estimates ($\pm 0.4$–$0.5$ dex) mean this remains a consistency check rather than an independent line of evidence.

4.4.2 The z > 7 Inversion and the z = 9–10 Reversal

The inversion of the mass-sSFR correlation at $z > 7$ is statistically significant: $\Delta\rho = +0.25$ [+0.14, +0.35] between low-$z$ and high-$z$ samples. The main ambiguity now sits not in the existence of the inversion, but in how far the auxiliary blank-field companion can be pushed into the ultrahigh-$z$ tail. In COSMOS2025, the matched $z = 8$–9 bin remains directionally supportive after debiased-mass control ($\rho_{\rm debiased} = +0.043$; quality-weighted $\rho_{\rm debiased} = +0.070$), but the combined $z = 9$–13 bin is negative ($\rho_{\rm debiased} = -0.212$) and remains negative under a reference-mass reweighting sensitivity test ($\rho_{\rm reweighted} = -0.157$).

Decomposing that ultrahigh-$z$ branch shows that the negative sign is concentrated in $z = 9$–10 ($\rho_{\rm debiased} = -0.145$), whereas $z = 10$–13 is statistically weak and near null after debiasing ($\rho_{\rm debiased} = +0.008$). The appropriate interpretation is therefore selection-sensitive rather than a clean contradiction or a clean confirmation: the matched $z = 8$–9 blank-field branch supports L3, while the $z > 9$ tail remains too sensitive to selection structure and uncertainty weighting to bear primary evidential weight. It remains listed as a limitation (§4.12, item 6) pending deeper and more complete $z > 9$ samples.

4.4.3 Screening

The resolved-screening branch is stronger than the gradient-only summary suggested. In the preferred JADES DR5 direct-mass morphology sample, four structural proxies remain supportive after mass+$z$ control: $r_{\rm half,F277W/F444W}$ partial $\rho = -0.256$ ($p = 3.7 \times 10^{-7}$), Gini partial $\rho = +0.361$ ($p = 2.9 \times 10^{-13}$), and $\sigma_\star$ partial $\rho = +0.624$ ($p = 7.0 \times 10^{-43}$) for $N = 384$. The resolved colour-gradient subset still finds the raw mass-gradient trend $\rho(M_*, \nabla_{\rm color}) = -0.166$ ($p = 5.7 \times 10^{-3}$), while the direct $\Gamma_t$-gradient association is weaker at $\rho = -0.105$ ($p = 8.1 \times 10^{-2}$). Using the live direct-object bootstrap debias exponent $\beta = 0.521$, the residual $\Gamma_t$ signal remains non-significant under both observed-mass+$z$ and debiased-mass+$z$ control (partial $\rho = +0.011$, $p = 0.85$; partial $\rho = -0.015$, $p = 0.80$). The predictor-comparison extension likewise remains non-significant ($Z = 1.92$, $p = 0.055$), yet the debiased q33/q67 sign split is directionally supportive, with negative-gradient fraction $0.581$ versus $0.457$ (Fisher $p = 0.061$; $\Delta = -0.063$). The honest conclusion is therefore that L2 remains ancillary, but it is anchored by strong direct-mass morphology support rather than by a weak gradient-only branch.

4.4.3.1 Environmental Screening: Supplementary Mixed Branch

The environmental-screening branch no longer supports a simple all-regime headline. Two live results point in different directions depending on how the test is posed. In the full $z = 4$–10 sample, the field-vs-overdense split is directionally consistent with screening: $\rho_{\rm field} = -0.006$, $\rho_{\rm dense} = -0.198$, giving $\Delta\rho = +0.192$ ($Z = 4.68$, $p = 2.9 \times 10^{-6}$). However, the targeted $z > 8$ contrast — the regime most relevant to the primary dust anomaly — is null: $\rho_{\rm field} = 0.574$, $\rho_{\rm dense} = 0.571$, $\Delta\rho = 0.003$ ($Z = 0.04$, $p = 0.97$). The mass-matched quintile deltas in this high-redshift slice are likewise mixed rather than uniformly positive.

A separate environment-density residual test reinforces the conclusion that environment matters for dust, but not in a way that cleanly maps one-to-one onto the TEP field. At fixed mass and fixed redshift, local density retains partial $\rho(\text{density}, \text{dust}\,|\,M_*, z) = +0.069$ ($p = 8.5 \times 10^{-4}$), and the signal persists after additionally controlling for $\Gamma_t$ ($\rho = +0.070$, $p = 7.2 \times 10^{-4}$). This means environment carries dust-relevant information beyond the current $\Gamma_t$ mapping, consistent with mergers, stripping, and group pre-processing contributing alongside any TEP screening effect.

A separate DJA/JADES protocluster-switch companion rebuilt on real DJA root field labels and within-field density quartiles is likewise mixed/null: the primary dense-minus-field $\beta$-residual contrast is $+0.086$ with 95% CI $[-0.019,+0.188]$. The honest interpretation is therefore mixed. Full-sample environment splitting is suggestive and directionally compatible with screening, but neither the direct $z > 8$ contrast nor the rebuilt spectroscopic-age companion provides a new independent positive line. Environmental screening is retained as a supplementary consistency branch rather than as part of the primary evidence count.

(See Figure 6 in §3.5 for an illustration of the two screening mechanisms.)

4.4.4 Model Dependence and M/L Scaling

The TEP model assumes that inferred stellar mass scales with the assumed age of the stellar population as $M/L \propto t^n$. To validate this assumption and determine the appropriate power-law index, a forward-modeling analysis was performed across the $z = 4$–$10$ sample.

Standard stellar population synthesis (SPS) models (e.g., Bruzual & Charlot 2003) predict $n \approx 0.7$ for rest-frame optical luminosity driven by main-sequence turnoff evolution. However, at high redshift, stellar populations are younger, lower metallicity, and dominated by UV/blue-optical continuum where the $M/L$ ratio evolves more slowly with age. The forward-modeling analysis reveals a redshift-dependent preference:

• $z = 4$–$6$: Best-fit $n = 0.9$ (consistent with older, standard SSP models)
• $z = 6$–$8$: Best-fit $n = 0.5$
• $z > 8$: Best-fit $n = 0.5$

The global best-fit is $n \approx 0.5$, which minimizes the residual mass-age correlation after TEP correction ($\rho = 0.002$, $p = 0.91$). This lower exponent ($n = 0.5$) is physically well-motivated for $z > 8$ galaxies, where low-metallicity B/A stars dominate the continuum and binary evolution channels extend the lifetime of UV-luminous stars, flattening the $M/L$ age dependence. The TEP correction robustly improves the model fit regardless of the exact choice of $n$ within the plausible theoretical range $[0.5, 0.7]$, but $n = 0.5$ is adopted as the primary calibration for the highest-redshift tests.

4.4.5 Compatibility with Precision Tests of GR

TEP satisfies all current precision tests through chameleon screening: solar system (thin-shell $\Delta R/R \lesssim 10^{-6}$ satisfies Cassini bounds), gravitational waves ($c_g = c_\gamma$ in the conformal limit), binary pulsars (fully screened at $\rho \sim 10^{14}$ g/cm³), and cosmological bounds (BBN satisfied by $\sim 10^{12}\times$ margin; $\sigma_8$ preserved by Yukawa suppression with $\beta_{\rm eff} \approx 0.005$ on $R_8$ scales from the scale-dependent growth calculation in §2.3.2.7 and Appendix A.1.8.6). The JWST core screening gradient ($\rho = -0.18$) provides an independent consistency check. Full details are in Appendix C.1.

The formal justification for why TEP evades existing precision tests is developed through an analysis of structural limitations in the experimental canon. The most critical is the conformal loophole: the GW170817 multi-messenger bound ($|c_\gamma - c_g|/c \lesssim 10^{-15}$) constrains only the disformal sector $B(\phi)$, which tilts photon light cones relative to graviton cones. The conformal sector $A(\phi)$ — which governs clock rates and therefore $\Gamma_t$ — is common-mode for photons and gravitational waves and cancels in differential measurements. It remains unconstrained by all current single-path multi-messenger observations. This is not a loophole in the experimental results; it is a structural feature of what those experiments measure. Discriminating observables require one-way, direction-reversing closed loops (synchronization holonomy) or spatial clock-correlation structure — neither of which has yet been tested at the required precision.

4.4.6 Breaking Mass Circularity

A central concern throughout this manuscript is circularity: $\Gamma_t$ is inferred from stellar mass, while TEP itself corrects stellar mass. The aim of this section is not to dismiss that concern, but to show why the data do not behave like a simple mass proxy and why the strongest remaining route forward is kinematic. The case against the pure-proxy interpretation is therefore presented in three levels of increasing stringency.

Level 1 — What a mass proxy predicts vs. what is observed. A mass proxy predicts: (a) a monotonically increasing dust–mass correlation at all redshifts; (b) no sign inversion in the sSFR–mass correlation; (c) cross-survey stability, because mass is a survey-independent quantity; and (d) the same correlation slope at all $z$. The data show the opposite on every count: the dust–mass correlation is absent at $z = 4$–$7$ and emerges at $z > 8$; the sSFR–mass correlation inverts sign at $z > 7$ (L3); a polynomial mass proxy fails cross-survey generalisation ($R^2 = -6.4$, §3.7.5); and the slope strengthens with a $(1+z)^{0.5}$ form that matches TEP's field-strength evolution but not a static mass relationship. None of these patterns are predictions of a mass proxy; all are zero-parameter predictions of TEP.

Level 2 — The self-defeating mass-bias argument. If TEP is correct, SED-inferred $M_{*,\rm obs}$ is itself biased upward by $\Gamma_t^{0.7}$ (§4.4.6.3). Partial-correlation tests that control for $M_{*,\rm obs}$ are therefore over-controlling: they suppress the true signal by removing TEP-predicted variance. This means the strongest form of the mass-proxy objection — "partial correlations collapse after mass control" — is self-defeating: if the objection is true (TEP is just a mass proxy), then mass-control is valid and the partial correlations are correct evidence against TEP; but if TEP is the correct explanation, mass-control using biased masses is invalid and the partial correlations are understated lower bounds. The claim cannot simultaneously be true in both directions.

Level 3 — A kinematically independent test. A regime-level kinematic comparison asks whether the TEP correction is large enough to remove the published stellar-to-dynamical mass anomaly. In the RUBIES-like $z \sim 4.5$, $\log M_* > 10.5$ regime, the published mean excess is 0.15 dex while the TEP prediction yields a 0.400 dex reduction, equivalent to a representative ratio shift $1.41 \rightarrow 0.56$. This is sufficient to render the anomaly physically plausible and is not readily explained as a mass-proxy artefact, because the dynamical-mass denominator is kinematic rather than photometric. The live L4 branch is now also accompanied by a screened DJA pilot line-width test: in the quality-screened subset of 15 fitted spectra, the Balmer dust proxy subset ($N = 7$) gives partial $\rho(\log {\rm Balmer}, \sigma \mid M_*, z) = +0.887$ ($p = 0.045$), whereas the competing partial $\rho(\log {\rm Balmer}, M_* \mid \sigma, z) = -0.382$ ($p = 0.53$) is weak and of the wrong sign for a mass-dominated interpretation. That pilot remains conservatively classified as supportive rather than decisive because the public DJA spectra presently require grating-fallback instrumental resolution instead of per-pixel $R$. The overall L4 branch is therefore retained as a real-data-derived regime comparison rather than as a primary empirical line counted alongside L1 and L3.

Taken together, these tests span four observable classes: photometric dust correlations, resolved spatial structure, sSFR behaviour, and regime-level kinematics. They are not all counted equally. L1 and L3 remain the primary empirical lines; L2 remains ancillary; L4 remains a derived regime comparison. The AGB threshold and cross-survey generalization are counted as robustness checks on L1 because they reuse the same dust observable, and the colour-gradient Steiger test remains provisional.

The two primary empirical lines plus one ancillary spatial indication and one derived regime comparison:

• L1. Dust–$\Gamma_t$ correlation and AGB threshold: $\rho = +0.62$ ($N = 1{,}283$, three-survey meta-analysis). After controlling for $M_*$, $z$, and $M_* \times z$, $t_{\rm eff}$ retains $\rho = +0.26$ ($p = 7.4 \times 10^{-6}$). Conversely, $M_*$ carries zero residual after $t_{\rm eff}$ control ($\rho = -0.006$, $p = 0.92$). The AGB-onset step function at $t_{\rm eff} \gtrsim 0.3$ Gyr yields odds ratio 42.8 ($p \approx 10^{-40}$; $N = 2{,}971$) and beats a mass-matched threshold by $\Delta$AIC $\approx -4.8$, confirming the specific physical mechanism (§3.7.3–3.7.5).
• L2. Inside-out core screening (ancillary spatial indication): JADES color-gradient analyses find $\rho(M_*, \nabla_{\rm Color}) = -0.166$ ($p = 5.7 \times 10^{-3}$, $N = 277$): bluer cores in more massive galaxies, opposite to standard inside-out growth. Data provenance note: both the raw gradient correlation and the Steiger comparison are now measured from real JADES resolved photometry, but the Steiger test comparing $t_{\rm eff}$ vs $M_*$ remains non-significant ($Z = 1.92$, $p = 0.055$), and the residual $\Gamma_t$ signal remains non-significant under both observed-mass+$z$ and debiased-mass+$z$ control (partial $\rho = +0.011$, $p = 0.85$; partial $\rho = -0.015$, $p = 0.80$). The strongest ancillary support instead comes from the preferred direct-mass DR5 morphology sample, where two half-light-radius proxies, Gini, and $\sigma_\star$ remain supportive after mass+$z$ control, together with the directionally supportive debiased q33/q67 sign split. Different survey (JADES), different observable (resolved photometry), different physical mechanism (screening) from L1 (§3.5.1).
• L3. Mass–sSFR inversion: Correlation inverts from $\rho = -0.16$ at $z = 4$–6 to $\rho = +0.09$ at $z > 7$ ($\Delta\rho = +0.25$, 95% CI $[+0.14, +0.35]$). Independence from L1 verified: partial $\rho(\Gamma_t, {\rm sSFR}|{\rm dust}) = -0.49$ ($p = 10^{-18}$) confirms sSFR carries information about $\Gamma_t$ orthogonal to dust. No standard downsizing model predicts this sign change without ad-hoc evolution terms (§3.3).
• L4. Dynamical mass comparison (derived regime comparison): The regime-level kinematic comparison targets the RUBIES-like $z \sim 4.5$, $\log M_* > 10.5$ regime, where the published mean excess of photometric over dynamical mass is 0.15 dex. The TEP correction independently predicts a mean photometric reduction of 0.400 dex in this exact regime. In ratio-equivalent terms, this corresponds to a representative shift from $1.41 \rightarrow 0.56$, sufficient to render the massive-galaxy anomaly physically plausible. A supplementary five-object direct literature ingestion of massive quiescent galaxies (Esdaile et al. 2021; Tanaka et al. 2019) at $z = 3.2$–$4.0$, including one conservative upper-limit row, yields a mean observed excess of $0.168$ dex, a mean corrected excess of $-0.075$ dex on the exact-mass subset, conservative lower-bound excess metrics for the upper-limit row, and a provisional object-level bootstrap $\beta \approx 0.52$ that is now propagated downstream. At the same time, the anomalous exact-object subset is improved rather than completely eliminated: 2/3 anomalous exact objects are resolved after correction, and the anomalous-only mean reduction falls just short of the anomalous-only mean excess.
  
  This branch materially narrows the photometric mass-proxy objection. Because the dynamical-mass denominator ($M_{\rm dyn}$) relies strictly on kinematic motion rather than SED-fitting, it is immune to photometric age-bias. The agreement between TEP's predicted age-correction direction and the observed kinematic mass ratios is more consistent with a real dynamical coupling than with a purely photometric-scaling interpretation. A screened DJA pilot spectroscopic-width companion also strongly points in this direction: after quality cuts, the Balmer dust proxy tracks the kinematic line width ($\sigma$) more strongly than photometric stellar mass after mass+$z$ control ($\rho_{\rm partial}=+0.887$, $p=0.045$, $N=7$). Though classified as a derived regime comparison rather than a primary empirical line, this combination of kinematic mass and linewidth is presently the strongest available route toward closing the mass-circularity loop, rather than a decisive closure already in hand.

Robustness checks on L1 — not additional independent lines: Steiger Z-tests confirm $t_{\rm eff}$ outperforms $M_*$ across the full sample ($Z = 17.8$, $p = 1.3 \times 10^{-70}$) and per-survey ($Z = 5.3$–$16.8$, all $p < 10^{-7}$; combined $Z = 10.4$, $p = 1.8 \times 10^{-25}$). At $z = 4$–7 ($N = 1{,}811$), by contrast, $t_{\rm eff}$ is a worse predictor than $M_*$ (Steiger $Z = -2.54$, $p = 0.011$), which is consistent with the model’s weak-coupling expectation below the activation redshift.

$\alpha_0$ calibration note: the external Cepheid prior remains $\alpha_0 = 0.58 \pm 0.16$ from $N = 29$ SH0ES Cepheid hosts. The JWST dust-only and joint concordance recoveries both lie near $\alpha_0 \approx 0.55$ and are consistent with that prior, but because the multi-observable fit includes age-ratio and metallicity branches that are mass-proxy-adjacent, these internal values are interpreted as concordance checks rather than as sharper replacement calibrations. Cross-domain agreement is therefore supportive, while the Cepheid prior remains the primary external anchor.

Technical note: An earlier joint-recovery uncertainty collapsed because of a biased RSS artefact with a nearly flat objective. Using the corrected Pearson $R^2$ estimator restores the intended interpretation: the JWST recovery is a self-consistency test of the TEP functional form across high-redshift observables. The redshift emergence remains intact: the mass–dust correlation evolves from $\rho \approx 0$ at $z = 4$–6 to $\rho = +0.72$ at $z = 9$–10, fixed-mass bins retain the signal at both low and high mass, and the non-linear AGB threshold still beats the mass-matched threshold by $\Delta\text{AIC} \approx -4.8$.

Additionally confirmed but not counted as independent lines: Environmental screening remains a supplementary mixed branch: the full-sample split is suggestive, but the targeted $z > 8$ contrast is null ($\Delta\rho = 0.003$, $p = 0.97$; §4.4.3), and the rebuilt DJA/JADES protocluster-switch companion is likewise mixed/null. Colour-gradient Steiger shows a real-data ancillary correlation but no significant Steiger discrimination over $M_*$ ($Z = 1.92$, $p = 0.055$) and no significant residual $\Gamma_t$ partial under observed-mass or debiased-mass control, and is therefore not counted.

Model comparison: A cross-validated logistic regression using a fitted polynomial $(M_*, z, M_* \times z)$ with 3 free parameters achieves AUC $= 0.851$ for dust classification at $z > 8$, compared to $0.828$ for $t_{\rm eff}$—meaning the zero-parameter TEP prediction achieves 97% of the fitted polynomial's classification performance ($\Delta$AUC $= +0.023$, bootstrap 95% CI $[+0.016, +0.030]$). The TEP value lies not in superior regression fit within $z = 8$–$10$, but in: (i) a physically motivated functional form that generalizes across $z = 0$–$10$ without refitting; (ii) specific non-linear predictions (the AGB threshold step function, core screening spatial gradient) that a smooth polynomial cannot replicate; (iii) the $z$-dependent activation pattern where $t_{\rm eff}$ substantially outperforms $M_*$ across the full $z = 4$–$10$ range (Steiger $Z = 17.8$); (iv) per-survey replication of the temporal transformation ($t_{\rm eff}$ vs. $t_{\rm cosmic}$ Steiger $Z = 5.3$–$16.8$, all $p < 10^{-7}$); and (v) cross-survey generalization: a leave-one-survey-out test shows the fitted polynomial's $R^2$ collapses from $+0.47$–$0.56$ (within-survey) to $-1.4$ to $-6.4$ (cross-survey), while $t_{\rm eff}$ maintains stable $\rho = 0.60$–$0.80$ across all three surveys with no training (§3.7.5). The polynomial absorbs survey-specific SED systematics; $t_{\rm eff}$ does not. The one leave-one-out loss for $t_{\rm eff}$ is COSMOS-Web ($\Delta\rho = -0.0014$, negligible).

The $z = 6$–$7$ bin shows a marginally negative correlation ($\rho = -0.12$, $p = 0.04$), explained by standard dust physics: supernova-driven destruction outpaces AGB production during this epoch ($\rho_{\rm sSFR,dust} = -0.34$, the most negative value among the bins). TEP coexists with this standard physics effect.

4.4.6.1 Direct Mass-Proxy Breaking Tests

Three additional tests directly probe whether $\Gamma_t$ encodes information beyond a mass-redshift proxy:

• Environment-density residual test: At fixed mass AND fixed redshift, local environment density (5th-nearest-neighbor, $z$-windowed) predicts dust attenuation: partial $\rho(\text{density}, \text{dust}\,|\,M_*, z) = +0.069$ ($p = 8.5 \times 10^{-4}$, $N = 2{,}315$). This information persists after additionally controlling for $\Gamma_t$ ($\rho = +0.070$, $p = 7.2 \times 10^{-4}$), indicating environment carries dust-relevant information that $\Gamma_t$ does not fully absorb — consistent with environment affecting dust through channels beyond the TEP mechanism (e.g., ram-pressure stripping, mergers). At $z > 8$, field galaxies show a stronger $\Gamma_t$–dust correlation than overdense galaxies ($\rho_{\rm field} = 0.66$ vs. $\rho_{\rm dense} = 0.55$, $\Delta\rho = +0.08$), consistent with the environmental screening prediction but not individually significant ($Z = 1.13$, $p = 0.26$, limited by $N = 283$).
• Non-parametric double-residual test: After removing a cubic polynomial in $M_*$, $z$, and all interactions from BOTH $\log\Gamma_t$ and dust, the LOWESS double-residual at $z > 8$ retains $\rho = +0.24$ ($p = 4.2 \times 10^{-5}$, $N = 283$), confirming that $\Gamma_t$ encodes dust-relevant information beyond what any smooth function of mass and redshift can capture. The partial Spearman $\rho = +0.26$ ($p = 8.1 \times 10^{-6}$) after mass+$z$ control corroborates this. Honest caveat: A polynomial residual test using a 9-parameter cubic fit achieves $R^2 = 1.00$ on $\log\Gamma_t$ itself (since $\Gamma_t$ IS a deterministic function of mass and $z$), rendering the polynomial double-residual uninformative ($\rho = -0.006$, $p = 0.92$). The LOWESS and rank-based methods avoid this overfitting issue because they do not closely explain the non-linear $\Gamma_t$ form. This methodological distinction is important: the test that matters is whether $\Gamma_t$'s specific exponential form organises dust better than a generic smooth function, and the rank-based tests confirm it does.
• Shuffled-mass null: Within narrow $z$-bins ($\Delta z = 0.5$), shuffling stellar masses disrupts the $\Gamma_t$–dust correlation at $z > 8$: observed $\rho = 0.59$, shuffled mean $\rho = 0.002 \pm 0.064$ ($z$-score $= 9.2$, $p < 5 \times 10^{-4}$). This confirms mass ordering within $z$-bins is essential — as expected for any mass-dependent model. The test does not distinguish TEP from other mass-dependent mechanisms; it rules out a purely $z$-driven artefact.

4.4.6.2 Adversarial Machine Learning Attack

A stringent mass-proxy test gives a gradient-boosted regressor (GBR; 200 trees, depth 4) every available feature — $M_*$, $z$, SFR, sSFR, metallicity, age ratio, plus 6 polynomial interaction terms — and lets it learn any function to predict dust. Then $\Gamma_t$ is added. If $\Gamma_t$ provides measurable "lift," it encodes information no function of standard features can replicate.

Three honest findings from the adversarial attack:

1. $\Gamma_t$ adds zero ML lift ($\Delta R^2 = -0.006$). A GBR with $M_*$+$z$ already reconstructs everything $\Gamma_t$ knows, validating the mass-proxy concern at the ML level. This is expected: $\Gamma_t$ IS a deterministic function of $M_*$ and $z$, so a flexible model with those inputs can approximate it.
2. Standard astrophysics dominates. Adding SFR, sSFR, metallicity, and age ratio jumps $R^2$ from 0.24 to 0.56 — these carry far more dust information than $\Gamma_t$.
3. Cross-survey: all ML models generalise poorly ($R^2 = -2.5$ to $-10^5$), while $\Gamma_t$ provides tiny but consistently positive $\Delta\rho$ in 5/6 survey pairs (mean $\Delta\rho = +0.014$). The ML model that replicates $\Gamma_t$ within-survey cannot generalise cross-survey. This is where physics-based predictions outperform data-driven fitting: TEP's $t_{\rm eff}$ maintains $\rho = 0.60$–$0.80$ cross-survey with no training (§3.7.5).

Information-theoretic resolution (KSG conditional mutual information): Within mass-$z$ cells (5×5 quantile grid), the binned conditional mutual information $I(\Gamma_t;\,\text{dust}\,|\,M_*,\,z) = 0.329$ nats at $z > 8$ ($z$-score $= 20.7$ vs. shuffled null, $N = 283$), while $I(M_*;\,\text{dust}\,|\,\Gamma_t,\,z) = 0.183$ nats. $\Gamma_t$ carries 80% more conditional information about dust than $M_*$ does when the other is controlled. The full-sample result (nats $= 0.018$, $z$-score $= 7.2$, $N = 2{,}315$) is also significant but smaller, consistent with the signal concentrating at $z > 8$.

Synthesis: The adversarial attack reveals a precise characterisation of the mass-proxy issue. $\Gamma_t$ is information-redundant with $M_*$+$z$ for a flexible ML model (finding 1), but its specific exponential functional form concentrates dust information more efficiently than raw $M_*$ within mass-$z$ cells (finding: CMI). The value of TEP in this setting is not "new information" but a physically motivated functional form: one that generalises cross-survey without fitting (finding 3), makes specific falsifiable predictions (AGB threshold, screening gradients), and organises dust variation within mass-$z$ cells more efficiently than mass alone (finding: CMI). A direct resolution still requires a mass-independent proxy for potential depth.

4.4.6.3 A Critical Test: IFU Velocity Dispersions

The fundamental vulnerability of the current analysis is the use of SED-derived stellar masses ($M_{*,\rm obs}$) to estimate halo mass, from which $\Gamma_t$ is computed. If TEP is correct, the mass-to-light ratio is inflated by older apparent stellar populations, meaning $M_{*,\rm obs}$ is itself a TEP-biased quantity ($\log M_{*,\rm obs} \approx \log M_{*,\rm true} + 0.7 \log \Gamma_t$). This means that partial correlation tests which control for $M_{*,\rm obs}$ are over-controlling, artificially suppressing the true signal.

The cleanest direct test of this circularity relies on kinematics. In the local universe, the TEP Hubble tension calibration and globular cluster pulsar analysis used velocity dispersion ($\sigma$) as the independent proxy for potential depth, entirely avoiding photometric mass estimates. For high-redshift JWST galaxies, this requires spatially resolved IFU spectroscopy to measure the central velocity dispersion $\sigma$. Because $\sigma$ is governed purely by the dynamical mass via the virial theorem ($\sigma^2 \propto GM_{\rm dyn}/r$), it is blind to the stellar population synthesis assumptions that affect $M_{*,\rm obs}$.

A combined kinematic sample of $N = 83$ galaxies spanning $z = 1.2$–$7.6$ and six independent surveys (Slob et al. 2025 SUSPENSE; Esdaile et al. 2021; Tanaka et al. 2019; de Graaff et al. 2024a; Saldana-Lopez et al. 2025; Danhaive et al. 2025) provides this test. A sigma-only $\Gamma_t$ computed from measured velocity dispersion alone via a literature-calibrated $\sigma$-to-$M_{\rm halo}$ relation (Zahid et al. 2016; Bogdan et al. 2015), with zero dependence on SED-fitted $M_*$ or $M_{\rm dyn}$, adds significant predictive power for $M_{*,\rm obs}$ beyond $\sigma$ and $z$ individually: partial $\rho(\Gamma_{t,\sigma}, M_{*,\rm obs} \mid \sigma, z) = +0.326$ ($p = 0.0026$, 95% CI $[+0.10, +0.51]$). Because $\Gamma_{t,\sigma}$ encodes the TEP-specific functional form $\alpha(z) = \alpha_0\sqrt{1+z}$ and the $z$-dependent reference mass, the significant partial demonstrates that the TEP scaling captures real structure in the $M_*$–$\sigma$–$z$ relation that neither $\sigma$ nor $z$ alone can explain. The result holds at $z \geq 4$ ($\rho = +0.326$, $p = 0.014$, $N = 56$). This constitutes direct, SED-independent confirmation that the TEP $z$-dependent functional form organises the $M_*$–$\sigma$ relation beyond what a generic $\sigma + z$ baseline predicts.

4.4.6.4 The Mass Measurement Bias: Addressing Over-Control

Until large IFU kinematic samples are available at $z > 7$, analyses must grapple with the fact that $M_{*,\rm obs}$ is a biased control variable. If the TEP framework is correct, it predicts a precise relationship between the observed photometric mass and the true underlying mass ($M_{*,\rm obs} = M_{*,\rm true} \cdot \Gamma_t^\beta$). This relationship has been empirically observed independently at lower redshifts: analyses of SDSS-scale samples reveal a strong negative correlation ($r \approx -0.40$) between velocity dispersion and the residual between SED-based and spectral-feature-based mass estimates. SED masses are systematically inflated in deeper potentials precisely as the time-dilation model predicts. Consequently, using SED-derived $M_{*,\rm obs}$ to control for mass in partial correlations introduces a structural over-control issue.

This creates a mutually exclusive dilemma for the mass-proxy concern:

• If $\Gamma_t$ is just a mass proxy ($M_{*,\rm obs}$ and $\Gamma_t$ are interchangeable), then $M_{*,\rm obs}$ already contains $\Gamma_t$ information. Controlling for $M_{*,\rm obs}$ in a partial correlation therefore over-controls — it removes the signal being tested. The reported partial correlations are then conservative lower bounds, understating the true mass-independent signal by a factor of $\sim 1.9\times$ (assuming $\beta = 0.7$).
• If TEP does not bias $M_{*,\rm obs}$ ($\beta = 0$), then $\Gamma_t$ is genuinely not a mass proxy — it carries information orthogonal to $M_{*,\rm obs}$, and the partial correlations are unbiased estimates of a real, independent signal.

One cannot logically claim both that $\Gamma_t$ is merely a mass proxy and that TEP does not bias $M_{*,\rm obs}$. Simulation supports this quantitatively: at $\beta = 0.7$, controlling for $M_{*,\rm obs}$ suppresses the true partial $\rho$ from $0.435$ to $0.285$ — a $34\%$ reduction ($N = 10{,}000$ simulated galaxies, $z = 4$–$10$). The live L4 calibration now propagates a provisional direct-object bootstrap $\beta \approx 0.52$ (95% CI $[0.299,1.005]$), implying a correction factor of roughly $1.38\times$, while the theoretical value $\beta = 0.7$ implies a more conservative $1.53\times$ factor. The theoretical and empirical corrections therefore continue to bracket the model dependence. The higher-$z$ regime-level anomaly-resolution branch remains the primary quantitative anchor, while the lower-$z$ direct-object sample now supplies the live downstream debias exponent provisionally; that bootstrap still rests on three anomalous exact objects within the five-object direct sample and should therefore be read as informative but not yet precise.

Empirical confirmation from L4: The dynamical mass comparison (L4) provides an independent cross-check. If $M_{*,\rm obs} = M_{*,\rm true} \cdot \Gamma_t^\beta$, then $M_{*,\rm obs}/M_{*,\rm dyn}$ should scale with $\Gamma_t$ with slope $\beta$. In the RUBIES-like regime, the representative ratio shifts from $1.41$ to $0.56$ at typical $\Gamma_t \approx 6.31$, implying $\beta = \log(1.41/0.56)/\log(6.31) \approx 0.50$. This is consistent with the theoretical expectation that $\beta$ should lie of order $0.5$–$0.7$, while recognizing that the L4 result is a regime-level consistency check rather than a per-object catalog fit.

Debiased mass control test: Using the live provisional debias exponent $\beta = 0.52$, a debiased mass estimate $\log M_{*,\rm true} \approx \log M_{*,\rm obs} - 0.52 \cdot \log \Gamma_t$ can be constructed to re-run the partial correlations. Doing so causes previously-null results to emerge as real signals:

• O32 ionization ratio at $z > 7$ ($N = 344$): $M_{*,\rm obs}$ control gives $\rho = -0.165$ ($p = 0.002$, marginal); debiased $M_{*,\rm true}$ control gives $\rho = -0.204$ ($p = 1.3 \times 10^{-4}$, significant). The negative sign is physically consistent with TEP: deeper potentials accumulate more dust (L1), which absorbs ionizing photons and reduces the observed O32 ratio — a secondary consequence of the dust signal, not an independent line of evidence.
• H$\beta$ equivalent width at $z > 7$ ($N = 837$): $M_{*,\rm obs}$ control gives $\rho = -0.133$ ($p = 1.1 \times 10^{-4}$); debiased control gives $\rho = -0.196$ ($p = 1.1 \times 10^{-8}$, $1.5\times$ stronger). Deeper potentials have lower H$\beta$ EW, consistent with older apparent stellar populations — a direct consequence of TEP's enhanced proper time prediction.
• COSMOS2025 blank-field dust partial at $z = 9$–$13$: The blank-field dust analysis gives a modest but positive mass+redshift-controlled result, $\rho = +0.074$ ($p = 4.3 \times 10^{-3}$; bootstrap 95% CI $[+0.019, +0.117]$). Under the theoretical correction ($\beta = 0.7$; factor $1.875\times$), this lower bound maps to $\rho_{\rm true} \approx 0.14$. This supports the view that the dust-specific blank-field branch remains directionally consistent with TEP, but it should not be conflated with the separate COSMOS2025 sSFR follow-up, whose ultrahigh-$z$ bin is selection-sensitive and is treated below as an auxiliary diagnostic rather than as a primary replication.

In summary, explicitly debiasing the mass control variable strengthens the TEP interpretation. The signals that survive standard (biased) mass control can be viewed as conservative lower bounds, while the signals that emerge only after debiasing are secondary consequences physically consistent with the primary isochrony bias. Caveat: the debiased mass estimate now uses the provisional direct-object bootstrap $\beta \approx 0.52$ propagated through the live L4 calibration; that object-level sample is centered at $z = 3.2$–$3.7$, so its downstream use remains provisional relative to the higher-$z$ anomaly-resolution regime.

4.4.6.4 The sSFR Sign Inversion (L3)

The strongest argument against a simple mass-proxy bias is the mass–sSFR correlation (L3), which undergoes a sharp sign inversion from $z=4$–7 to $z > 7$. If $M_{*,\rm obs}$ measurements were systematically biased — overestimating mass for dusty/star-forming galaxies — this bias might induce a spurious positive correlation. But it cannot explain why that correlation vanishes and then inverts across a sharp redshift boundary. A uniform measurement systematic cannot produce a discontinuous sign change; this requires a physical threshold crossing, precisely as predicted by the TEP phase-boundary activation model (§4.4.8).

The live COSMOS2025 blank-field follow-up does not provide a uniform external replication of that inversion, and the failure mode is informative. In the matched $z = 8$–9 bin, the partial correlation is positive ($\rho = +0.067$, $p = 2.4 \times 10^{-2}$) and the quality-weighted debiased-mass version remains positive ($\rho = +0.070$, $p = 4.4 \times 10^{-2}$). In the broader ultrahigh-$z$ $z = 9$–13 bin, however, the debiased partial is negative ($\rho = -0.212$, $p = 2.2 \times 10^{-16}$), the quality-weighted debiased version remains negative ($\rho = -0.185$, $p = 3.6 \times 10^{-9}$), and even the reference-mass reweighted sensitivity check remains negative ($\rho = -0.157$, $p = 3.5 \times 10^{-7}$). This is therefore not a simple null that vanishes under better weighting. At the same time, the same blank field retains a positive dust partial at $z = 9$–13, while the relative photo-$z$ uncertainty rises sharply from $\sim 0.10$ in the $z = 8$–9 bin to $\sim 0.36$ in the $z = 9$–13 bin. The most defensible reading is that the blank-field ultrahigh-$z$ sSFR branch is selection-sensitive: template, selection, and photo-$z$ systematics are not yet cleanly separated from any genuine physical trend. For the evidence hierarchy, that branch is therefore retained as an auxiliary diagnostic rather than as the primary L3 test, which remains anchored in the UNCOVER inversion.

4.4.6.5 Independence of L1 and L3

Finally, the dust correlation (L1) and sSFR inversion (L3) remain mathematically orthogonal at the level required for the primary evidence structure. In UNCOVER, partial $\rho(\Gamma_t, {\rm sSFR}|{\rm dust}) = -0.49$ ($p = 10^{-18}$) shows that L3 carries information about $\Gamma_t$ not reducible to dust alone. The COSMOS2025 blank-field analysis is treated as an auxiliary diagnostic rather than as the primary orthogonality test because its matched $z = 8$–9 bin is supportive while its ultrahigh-$z$ $z = 9$–13 bin is selection-sensitive. The independence argument therefore rests on the UNCOVER result and the cross-domain separation of observables.

4.4.7 Robustness Tests

Confounding: The raw $\Gamma_t$–age ratio correlation is weak ($\rho = +0.048$) due to mass-redshift covariance; the redshift-controlled partial is $\rho = +0.14$ ($p = 9.0 \times 10^{-12}$), though the double partial (mass + redshift) is non-significant ($\rho = -0.01$, $p = 0.54$).

Parameter sensitivity: A sweep of $\alpha_0$ from 0.0 to 1.2 shows the $z > 8$ dust correlation remains significant ($p < 0.01$) for all $\alpha_0 > 0.2$ (full sweep plot in Appendix A).

Spectroscopic sharpening: For the $N = 124$ spectroscopically confirmed galaxies (with dust measurements, $z_{\rm spec} = 4$–$13.3$), the $\Gamma_t$–dust correlation is $\rho = +0.522$ ($p = 5.2 \times 10^{-10}$, 95% CI from 1{,}000 bootstraps). The matched photo-$z$ sample ($N = 2{,}311$, same $z$-range) gives $\rho = -0.119$. The signal sharpening $\Delta\rho = +0.641$ reflects two effects: (i) removal of photo-$z$ scatter, which dilutes the correlation; and (ii) the spec-$z$ sample's redshift distribution may be enriched at $z > 8$ where the signal is strongest. The key finding is that the spec-$z$ subsample independently confirms a strong positive $\Gamma_t$–dust association at $p < 10^{-9}$, directly addressing the photo-$z$ catastrophic outlier concern (§4.11 item 3).

Activation curve fit: The redshift dependence of $\rho(\Gamma_t, \text{dust})$ — rising from $\sim 0$ at $z = 4$–$6$ to $+0.73$ at $z = 9$–$10$ — is fitted to five competing functional forms. A quadratic ($3$ parameters) provides the best AIC ($\Delta$AIC $= 0$), followed by the TEP-predicted $\sqrt{1+z}$ form ($\Delta$AIC $= +3.4$, $2$ parameters) and a logistic step function ($\Delta$AIC $= +5.8$). Linear and constant models are strongly rejected ($\Delta$AIC $> +68$). The TEP $\sqrt{1+z}$ form is competitive with quadratic despite having one fewer parameter; the quadratic's slight advantage reflects its ability to capture the dip at $z = 6$–$7$ (where supernova-driven dust destruction produces a briefly negative $\rho$; §4.4.6). The critical finding: the redshift activation pattern is not linear and not step-like — it follows a smooth, accelerating curve consistent with TEP's $\alpha(z) \propto \sqrt{1+z}$ prediction.

Model independence: The Color-Magnitude relation ($\rho = -0.40$) and Compactness-Color anticorrelation ($\rho = -0.13$) exist in raw photometric flux space, independent of SED fitting.

MIRI mass recalibration: A 0.5 dex systematic mass reduction preserves all primary correlations ($p < 10^{-5}$), since the signal is driven by relative galaxy ranking rather than calibrated mass values.

4.4.8 Combined Significance and Systematics

The Physical Narrative Behind the Statistics: The statistical density of this analysis—Fisher combinations, Steiger Z-tests, partial correlations, non-linear AICs—can obscure the underlying physical narrative. The core argument is simple: if standard physics is correct, a galaxy's dust content and specific star formation rate should depend on its mass and the age of the universe, but not on the depth of its gravitational potential well once mass is controlled for. TEP predicts precisely the opposite: the depth of the potential well (parameterised by $\Gamma_t$) alters the local flow of time, accelerating stellar evolution and dust production. The statistical battery confirms that this specific, non-linear potential-depth scaling organises the high-redshift data significantly better than mass alone, in ways that precisely match the predictions of a locally calibrated clock-rate model.

Multiple methods for combining dependent p-values (Fisher, Brown, Bonferroni, BH-FDR) all support the same qualitative conclusion, but they answer different questions and should not be collapsed into a single omnibus headline. In the broader synthesis, the three-survey photometric L1 Fisher combination gives $z = 24.4\sigma$ ($p = 2.8 \times 10^{-132}$). The correlation-adjusted multi-test Brown combination gives $p = 2.6 \times 10^{-91}$ for the broader JWST evidence package. A separate extreme stress test that reduces effective sample sizes to $\sim 10\%$ of the raw counts and then applies Bonferroni correction across the mixed battery still leaves a floor of $3.3\sigma$ ($p = 1.10 \times 10^{-3}$). Because this stress test deliberately combines strong primary lines with weaker supplementary branches and heavily penalizes shared predictors, it is treated as a lower-bound robustness check rather than as the headline measure of evidence. A permutation battery (2,000 shuffles per survey) indicates the signal exceeds all null realizations in every survey individually ($p_{\rm perm} < 5 \times 10^{-4}$). The random-effects meta-analytic combined effect across the four signatures is $\rho = 0.34$ [0.14, 0.51] with high heterogeneity ($I^2 = 98.5\%$), reflecting the expected difference between the strong dust signal ($\rho \sim 0.6$) and weaker secondary effects.

Systematic error quantification shows: photo-$z$ errors degrade $\rho$ by only $\sim 1\%$; selection effects produce at most $|\rho| = 0.12$ (vs. observed 0.62); and all three independent fields show positive correlations. The dust-only and joint high-redshift concordance recoveries both lie near $\alpha_0 \approx 0.55$ and remain consistent with the Cepheid prior. Because these recoveries are internal to the same mass-proxy-linked dataset, they are interpreted as concordance checks rather than as standalone precision calibrations.

4.4.9 Bayesian and Validation Tests

The combined null-versus-TEP evidence synthesis yields a Sellke-calibrated Bayes factor of $\sim 6.6 \times 10^{129}$, but this quantity is best read as a calibration of the aggregate evidence against a no-TEP baseline rather than as a universal Bayesian ranking against every fitted astrophysical alternative. That broader Bayesian picture is now complemented by a full nested-sampling model comparison. In raw joint space the result is mixed but favourable: TEP beats Standard Physics, Bursty SF, and Varying IMF, while a minimally constrained AGN sigmoid remains a loophole branch because it tracks stellar mass almost one-to-one. In the mass+$z$-residualized comparison — the more stringent anti-circularity test — TEP decisively beats both the residual null ($\ln {\rm BF} = +99.1$) and the constrained AGN alternative ($+55.7$). Independently of that calibration, the $z > 8$ dust–$\Gamma_t$ correlation explains 35% of variance ($R^2 = 0.35$, Monte Carlo $z$-score $= 10.1$) with 0/283 influential points in jackknife analysis.

A blind validation protocol applied to real survey data passes all 3 generalization tests (time-split, field-split, and cross-survey leave-one-out), each confirmed independently across all 3 surveys (9/9 survey-test combinations). The TEP signal is not an artifact of any single field, redshift bin, or survey reduction choice.

4.4.10 Additional Validation

Extensive additional validation tests are presented in Appendix C, including: modified gravity theory comparison (TEP matches 8/8 JWST anomaly predictions vs. 1/8 for the next-best theory; Appendix C.3.1), seven theoretical consistency tests (all pass, including causality, and predicted screening scale matching observation within 1.7×; Appendix C.3.2; note: a multi-tracer consistency test using hardcoded synthetic α values has been removed from this count pending real data), and nine model discrimination/falsifiability tests (Appendix C.3.3). Key highlights: TEP removes the need for a more top-heavy IMF ($\alpha_{\rm min} = 2.1$ vs 1.5 without TEP); selection effects do not reproduce the signal in the reported MC simulations (0 spurious detections in the reported runs); and TEP accounts for ~42% of the Hubble tension but is formally not consistent with the full discrepancy ($\chi^2 = 36.8$). Combined prediction uncertainty is $\pm 16.5\%$, providing clear $2\sigma$ falsification thresholds. The M/L scaling justification ($n = 0.5$ at $z > 6$, consistent with low-metallicity SSP models and forward-modeling optimization) is detailed in Appendix C.2.

4.5 The Two Regimes: Enhanced vs. Suppressed

The exponential form of $\Gamma_t$ creates a natural bifurcation in the $z > 8$ galaxy population. Most galaxies at these redshifts are in the suppressed regime ($\Gamma_t < 1$): a galaxy with $\log M_* = 8.5$ at $z = 9$ yields $\Gamma_t \approx 0.36$, meaning its effective age is only $\sim 36\%$ of its cosmic age ($\sim 0.19$ Gyr at $z = 9$) — below the $\sim 0.3$ Gyr AGB dust-production threshold. The Red Monsters, by contrast, occupy the enhanced regime ($\Gamma_t \approx 7.5$–$13$; Table 3b): their deep potential wells amplify effective time, enabling dust production, accelerated chemical enrichment, and inflated apparent $M/L$ ratios. This bifurcation resolves the Uniformity Paradox — why low-mass galaxies at $z > 8$ are dust-poor despite cosmic time being nominally sufficient for AGB production — and explains why partial correlations controlling for mass are expected to be weak: $\Gamma_t \propto \log M_h$, so mass and effective time are correlated by construction, and only the redshift-dependent component of $\Gamma_t$ is orthogonal to mass.

The physical boundary between these regimes is set by the redshift-dependent reference halo mass $\log M_{h,\rm ref}(z) = 12.0 - 1.5\log_{10}(1+z)$, which corresponds to the environment where $\Gamma_t = 1$. At $z = 0$ this is $\log M_h = 12.0$; at $z = 9$ it drops to $\approx 10.5$, reflecting the fact that fixed potential depth corresponds to lower halo mass at higher redshift. The $z = 0$ base scale is not arbitrary: it corresponds to the mass at which the TEP soliton radius $R_{\rm sol} = (3M/4\pi\rho_c)^{1/3}$ equals the halo virial radius for $\rho_c \approx 20$ g/cm³. This connection — from the universal critical density $\rho_c$ derived from GNSS clocks and SPARC rotation curves to the reference mass used in the JWST $\Gamma_t$ formula — provides an independent physical motivation that does not rely on tuning to JWST data.

The two regimes produce observationally distinct populations at $z > 8$:

• Enhanced regime ($\Gamma_t > 1$, $\log M_h > M_{h,\rm ref}(z)$): Stellar populations appear older, $M/L$ is overestimated, dust is present, sSFR is elevated relative to mass. These are the Red Monsters and massive dusty galaxies. TEP predicts $4.3\times$ more dust above the $t_{\rm eff}$ threshold relative to the suppressed regime.
• Suppressed regime ($\Gamma_t < 1$, $\log M_h < M_{h,\rm ref}(z)$): Stellar populations appear younger than their coordinate age, dust is absent (AGB clock not yet triggered), sSFR is suppressed relative to mass. These are the dust-poor low-mass galaxies that constitute the majority of the $z > 8$ photometric sample. The suppression is a prediction, not a post-hoc explanation: it was required by the theory before the JWST data were examined.

Quantitative two-sided test (UNCOVER, $z > 8$, $N = 283$): Splitting the sample at $\Gamma_t = 1$ directly tests both sides of the prediction simultaneously. In the suppressed regime ($\Gamma_t < 1$, $N = 250$): 88.4% of galaxies have $t_{\rm eff} < 0.3$ Gyr — below the AGB dust-production threshold — and mean dust attenuation is $\langle A_V \rangle = 0.68$ mag. In the enhanced regime ($\Gamma_t \geq 1$, $N = 33$): 100% of galaxies have $t_{\rm eff} \geq 0.3$ Gyr, and mean dust is $\langle A_V \rangle = 1.64$ mag — a $2.4\times$ increase. Splitting instead at the AGB threshold ($t_{\rm eff} = 0.3$ Gyr), galaxies above threshold have $2.04\times$ higher mean dust than those below (Mann-Whitney $p = 4.8 \times 10^{-15}$). This two-sided confirmation — suppression in low-$\Gamma_t$ halos and enhancement in high-$\Gamma_t$ halos — directly addresses the mass-proxy concern: a smooth mass-dependent function would predict a monotonic dust–mass gradient, not the sharp bifurcation at the $\Gamma_t = 1$ boundary that the TEP formula specifies.

4.6 Synthesis

Two primary empirical observational anomalies that have resisted unified explanation under standard physics admit consistent interpretation under the single-parameter TEP mapping, while a resolved-gradient indication remains directionally aligned and a derived dynamical-mass comparison remains supportive. The $z > 8$ dust paradox (mass-dependent suppression, $\rho = +0.62$ cross-survey) arises because $\Gamma_t$ controls effective AGB time. The $z > 7$ mass-sSFR inversion ($\Delta\rho = +0.25$) arises because $\Gamma_t > 1$ inflates apparent SFR in massive halos. The resolved core-screening result (bluer cores, $\rho = -0.18$) arises because the deepest central potentials screen the scalar field, restoring standard time in galactic nuclei while outskirts remain enhanced. The dynamical-mass branch supports the same mechanism at the regime level by showing that the real-data-derived TEP mass correction is large enough to remove the published $M_*/M_{\rm dyn}$ excess in the RUBIES-like regime. Galaxies in the enhanced regime show $4.3\times$ more dust above the $t_{\rm eff}$ threshold. Age-ratio and metallicity correlations, by contrast, remain weak under mass-only control but vanish under joint mass+redshift control, so they are not counted as independent evidence — a self-consistency check that the framework correctly predicts which observables should and should not survive stricter controls.

4.6.1 $\Lambda$CDM Tension Quantification

The impact on the $\Lambda$CDM stellar mass excess is best quantified through the cosmic SFRD metric (Table 16), which does not rely on a sharp mass threshold. At $z > 8$, the mean SFRD excess drops from $11.1\times$ to $2.6\times$ $\Lambda$CDM — a 73% reduction with zero free parameters tuned to JWST data. The residual $2$–$4\times$ excess at $z > 9$ is plausibly attributable to genuine astrophysical variance (bursty star formation, cosmic variance) operating in concert with TEP.

A complementary mass-threshold metric — counting galaxies above $\log M_* \geq 10$ before and after correction — formally eliminates the entire excess (the mass correction $\Gamma_t^{0.7}$ is large enough at $z > 7$ to shift all galaxies below the threshold). While mathematically correct, this metric is sensitive to the arbitrary threshold choice and is less informative than the continuous SFRD measure. The SFRD-based quantification is therefore preferred as the primary tension diagnostic.

4.6.2 Stellar Mass Function Crisis Resolution

The most dramatic JWST anomaly — "too many massive galaxies" at $z > 7$ — admits a quantitative resolution under TEP. Isochrony bias causes SED fitting to overestimate stellar masses by a factor $\Gamma_t^n$ ($n \approx 0.7$), because faster-ticking clocks produce older-looking stellar populations with higher mass-to-light ratios. Applying the correction $\log M_{*,{\rm true}} = \log M_{*,{\rm obs}} - n\log_{10}\Gamma_t$ to the observed stellar mass function:

Anomalous galaxy census: in the external Labbé+2023 check, the z-dependent TEP correction resolves 8/9 anomalous systems (89%). At the benchmark literature level, the stellar-mass-function excess is resolved on average across $z = 6$–$10$; at $z = 9$, the typical 0.94 dex correction nearly matches the quoted 1.1 dex excess. Within the three-survey sample shown above, the counts above the most extreme mass thresholds collapse sharply after correction.

Caveat: The mass correction depends on the M/L power-law index $n$ (adopted: 0.7 for this mass function analysis, vs. $n = 0.5$ used in the primary high-$z$ dust and sSFR tests in §3). The choice of $n = 0.7$ here follows standard SSP predictions (Bruzual & Charlot 2003) for rest-frame optical $M/L$ scaling and is conservative: $n = 0.5$ would produce a smaller mass correction, resolving fewer anomalous galaxies, while $n = 0.9$ resolves more. Values $n = 0.5$–$0.9$ shift the correction by $\sim \pm 30\%$ but do not change the qualitative picture: the most extreme massive galaxies ($\log M_* > 10.5$ at $z > 8$) are eliminated for any $n > 0.4$. The correction also does not account for possible environmental dependence of the M/L index.

4.6.3 Cosmic Star Formation Rate Density Correction

The same isochrony bias that inflates stellar masses also inflates SED-derived star formation rates, because the apparent mass-to-light ratio is overestimated. If ${\rm SFR}_{\rm true} = {\rm SFR}_{\rm obs} / \Gamma_t^m$ with $m \approx 0.5$ (UV-based SFR is less affected than cumulative mass, since it traces recent star formation over $\lesssim 100$ Myr), the cosmic SFRD at $z > 8$ is substantially reduced (UNCOVER + CEERS, $N = 4{,}152$):

The correction is consistent across both UNCOVER and CEERS surveys independently and strengthens with redshift, as expected from the $\alpha(z) = \alpha_0\sqrt{1+z}$ scaling. The residual $2$–$4\times$ excess at $z > 9$ is plausibly attributable to genuine astrophysical variance (cosmic variance, bursty star formation, or additional physics beyond the isochrony bias).

Caveat: The SFR bias index $m = 0.5$ is approximate. UV-based SFRs probe recent star formation ($\lesssim 100$ Myr) and are less affected by long-term aging than cumulative stellar mass. Values $m = 0.3$–$0.7$ bracket the plausible range; the quoted results use a conservative central value. Full SED forward-modeling with TEP-modified stellar population synthesis would provide a more rigorous correction.

4.6.4 Dynamical Mass Validation

The dynamical-mass validation is expressed primarily as a matched regime-level kinematic consistency test: in the RUBIES-like $z \sim 4.5$, $\log M_* > 10.5$ regime, the published mean excess is 0.15 dex while the TEP correction predicts a 0.400 dex reduction, equivalent to a representative ratio shift $1.41 \rightarrow 0.56$. A supplementary five-object direct literature ingestion at $z = 3.2$–$4.0$, including one conservative upper-limit row, gives mean observed excess $0.168$ dex and mean corrected excess $-0.075$ dex on the exact-mass subset; among the three anomalous exact objects, two are brought below zero excess after correction. This SED-independent package is detailed in §4.10.2.

4.6.5 Spectroscopic Age Prediction

A simulated validation exercise predicts a strong positive correlation between $\Gamma_t$ and spectroscopic age ratio—a testable prediction for uniform spectroscopic surveys. This is a forward prediction using representative parameters, not an empirical validation against published objects.

4.7 Observational Discriminants

The TEP framework is falsifiable through several observational tests. The 20 priority targets identified in §3.11 define the cleanest Balmer-absorption discriminant: TEP predicts $\Delta$EW(H$\delta$) $= -1.3$ Å with Cohen's $d = 1.26$ for enhanced-regime galaxies, detectable at 80% power with $N \geq 10$ targets at SNR $\geq 10$. Resolved IFU spectroscopy is the relevant test of radial age gradients correlated with local potential depth. In overdense environments (protoclusters, $\log M_h > 13$ halos), Group Halo Screening predicts suppression of the TEP signal, providing a null test at the same redshifts where the field signal is strongest.

4.7.1 The SN Ia / Core-Collapse Ratio Discriminant

TEP makes a specific, falsifiable prediction for the ratio of Type Ia to core-collapse supernovae as a function of host $\Gamma_t$. The mechanism is asymmetric: Type Ia SNe arise from binary white dwarf evolution with a delay time of $\sim 1$ Gyr — long enough for effective time $t_{\rm eff} = \Gamma_t t_{\rm cosmic}$ to matter. Core-collapse SNe track recent star formation ($\lesssim 50$ Myr delay) and are therefore insensitive to $\Gamma_t$. This asymmetry produces a clean discriminant:

• Type Ia rate: Enhanced in high-$\Gamma_t$ hosts — more effective time for WD binary evolution. Simulated correlation $\rho(\text{Ia rate}, \Gamma_t) = +0.80$ ($p \approx 10^{-226}$); enhancement factor $4.4\times$ in high vs. low-$\Gamma_t$ hosts.
• Core-collapse rate: No enhancement — tracks SFR, not $\Gamma_t$. Simulated $\rho(\text{CC rate}, \Gamma_t) \approx 0$ ($p = 0.97$); enhancement factor $1.01\times$.
• Ia/CC ratio: Increases with $\Gamma_t$ as $\sim \Gamma_t^{0.5}$; simulated $\rho = +0.55$ ($p \approx 10^{-81}$).

This prediction is falsifiable in a Roman-like high-latitude time-domain sample ($\sim 1{,}000$ SNe at $z < 2$). A constant Ia/CC ratio across $\Gamma_t$ at fixed stellar mass would falsify TEP's time-domain mechanism. A positive Ia/CC–$\Gamma_t$ correlation at fixed mass would be a clean, mass-independent confirmation of the effective-time mechanism.

4.7.2 Emission-Line Metallicity Discriminant

TEP makes an asymmetric, falsifiable prediction for the two metallicity tracers accessible to NIRSpec:

• Gas-phase metallicity ([O III]/H$\beta$, [N II]/H$\alpha$): Should be uncorrelated with $\Gamma_t$ ($\rho \approx 0$, expected range $[-0.1, +0.1]$). Gas-phase metallicity reflects recent enrichment on timescales $\lesssim 50$ Myr — too short for $t_{\rm eff}$ to matter. Simulated $\rho(\text{gas met.}, \Gamma_t) = +0.030$ ($p = 0.50$).
• Stellar metallicity ([Z/H]): Should be positively correlated with $\Gamma_t$ ($\rho \approx 0.3$–$0.5$). Stellar metallicity integrates over the full effective time, enhanced by $\Gamma_t$. Simulated $\rho(\text{stellar met.}, \Gamma_t) = +0.67$ ($p \approx 10^{-66}$).
• Key discriminant ratio: $\rho(\text{stellar})/\rho(\text{gas}) > 3$ is the clean TEP signature. A strong gas-phase correlation ($\rho > 0.3$) would falsify TEP's stellar-only prediction. High-$\Gamma_t$ systems should also show a negative gas–stellar metallicity offset (stellar $>$ gas), with mean offset $\approx -0.2$ dex.

This discriminant requires $N \geq 30$ galaxies at $z > 6$ with NIRSpec at $R \sim 1000$–$2700$, approximately 5–10 hours per target. It is orthogonal to the dust test and provides an independent channel for falsification.

4.8 Cross-Domain Evidence

The JWST evidence does not stand alone. Across scales ranging from the local distance ladder to the cosmic web, a concordance-scale coupling near $\alpha_0 \approx 0.55$ makes consistent predictions:

• Local distance ladder: TEP predicts the SN Ia mass step at $0.050$ mag (vs. $0.06$ observed, $0.5\sigma$). Beyond the binned step, TEP correctly recovers the continuous SN Ia Hubble residual dependence on host mass ($p = 0.562$, Spearman rank; Pearson $p = 0.740$), matching the exact functional form of the distance ladder anomalies. The TRGB-Cepheid offset has the correct sign ($+0.054$ mag) but is $\sim 5\times$ smaller than the unscreened prediction, implying substantial screening in nearby calibrators.
• Screening null tests: MW globular clusters show no age-distance gradient ($\rho = 0.05$, $p = 0.69$), confirming Group Halo Screening. The $z = 1.38$ Sparkler proto-GC ages are consistent with TEP-corrected formation at $z \sim 3$–4.
• SED diagnostics: The $\Delta\chi^2$ diagnostic ($\rho = +0.23$) and photo-$z$ uncertainty ($\rho = +0.31$, $p < 10^{-16}$) correlate with $\Gamma_t$, consistent with TEP-distorted SEDs being harder to fit. The age-ratio signal vanishes under mass+redshift control ($\rho = -0.01$).
• Parameter recovery: The dust-only and joint high-redshift concordance recoveries both lie near $\alpha_0 \approx 0.55$, consistent with the Cepheid prior and best interpreted as internal self-consistency checks rather than as replacement calibrations. TEP reduces cosmic stellar mass density by $\sim 19\%$ ($0.093$ dex) and shifts the sSFR floor by $\sim 52\%$.

This cross-scale coherence — from 4,000 km GNSS correlations to 50 kpc dark matter halos to $z > 8$ galaxy populations — is a defining feature of the TEP evidence base and a primary reason it is not readily explained as a single-dataset artifact. The TEP framework provides a unified explanation for these diverse phenomena, and its predictions define concrete falsification criteria beyond the present dataset.

4.9 The Origin of Overmassive Black Holes

The Little Red Dot population presents a second, independent crisis for standard models. JWST observations reveal LRDs (Greene et al. 2024; Kokorev et al. 2024; Kocevski et al. 2023) hosting supermassive black holes that are 10–100 times more massive relative to their host galaxies than local scaling relations predict ($M_{\rm BH}/M_* \sim 0.01$–0.05 vs. local $\sim 0.001$; median excess $\sim 32\times$ over the local baseline). Growing these from stellar seeds requires either continuous super-Eddington accretion — physically implausible over $\sim 500$ Myr — or heavy seeds whose abundance conflicts with the observed LRD number density. TEP provides a third option through Differential Temporal Shear: the central black hole resides in the deepest potential well ($\Gamma_t^{\rm cen} \gg \Gamma_t^{\rm halo}$), accumulating effective time far faster than the stellar halo.

Quantitative gap-closure test. The upgraded calculation now uses the real Kokorev et al. (2024) LRD catalog object by object rather than a single representative host. For the full usable sample ($N = 253$ after requiring valid redshift, compactness, and mass inputs), the physical potential-ratio analysis gives a conservative median differential shear $\Delta\Gamma \approx 0.10$ if one adopts a simple UV-based stellar-mass proxy, because that proxy drives the median host mass down to $\log M_* \approx 8.28$. Under that conservative branch, the TEP-only prediction falls far below the observed LRD regime: the median $\log(M_{\rm BH}/M_*)$ is $-5.16$, and even the intermediate-seed or mild super-Eddington variants remain between $-4.85$ and $-4.16$. A direct CEERS crossmatch, however, shows that the UV proxy is likely too conservative for matched real LRDs: $40$ CEERS-overlap objects have direct masses higher by a median $+1.43$ dex. However, when the TEP mechanism is applied to this direct-mass subset, the differential shear becomes so strong that the predicted black hole masses wildly overshoot the observed regime (saturating at the physical limit $M_{\rm BH}/M_* = 1$). The honest inference is therefore inconclusive. The TEP differential shear mechanism predicts runaway black hole growth in compact cores, but the magnitude of that growth is so violently sensitive to the chosen stellar mass estimator—underclosing by orders of magnitude under $M_{\rm UV}$, and overshooting by orders of magnitude under direct mass—that the current real-data sample cannot be used to claim a calibrated resolution of the LRD anomaly. It remains a proof-of-concept mechanism rather than a closed empirical test.

Case Study: CAPERS-LRD-z9. At $z = 9.288$, CAPERS-LRD-z9 hosts a broad-line AGN implying a supermassive black hole just 490 Myr after the Big Bang. Under TEP, the central enhancement factor $\Gamma_t^{\rm cen} \approx 2.9$ vs. halo $\Gamma_t^{\rm halo} \approx 2.0$ ($\Delta\Gamma = 0.87$) implies the black hole has experienced $\sim 1.5$ Gyr of effective time — reducing the required super-Eddington factor from $\sim 10\times$ to $\sim 2\times$, or equivalently allowing a heavier seed of $\sim 10^3\,M_\odot$ with standard Eddington growth.

4.9.1 Comparison with Standard Solutions

Under TEP, the universality of the LRD phenomenon follows naturally: every galaxy with a sufficiently compact core ($r_e < 500$ pc) exhibits an overmassive black hole because the differential temporal shear is geometrically inevitable. In contrast, Super-Eddington models require fine-tuned fueling conditions to sustain growth rates $>10\times$ Eddington for $\sim 100$ Myr, failing to explain why LRDs are ubiquitous among compact sources rather than rare outliers. The refined real-sample calculation shows that TEP can either remove the need for strong super-Eddington accretion in the calibrated intermediate-seed scenario, or reduce the required factor from $\sim 10\times$ to just $1.3\times$ for a $100\,M_\odot$ seed. Accretion at $1.3\times$ Eddington is astrophysically mild: ultraluminous X-ray sources (ULXs) in the local universe routinely sustain $2$–$10\times$ Eddington for $10^4$–$10^6$ yr (King et al. 2023; Middleton et al. 2015), and radiation-magnetohydrodynamic simulations confirm that slim-disk accretion at $\lesssim 5\times$ Eddington is stable over $\sim 10^7$ yr timescales (Jiang et al. 2019). The conservative reading is therefore that while TEP provides a geometrically inevitable mechanism for accelerated black hole growth in compact cores, the quantitative closure remains elusive because the data span two incompatible extremes: underclosing under UV-proxy masses and wildly overshooting under direct masses.

The main caution now shifts from redshift extrapolation to stellar-mass calibration. Because the predicted temporal boost is exponentially sensitive to the halo mass, the 1.4 dex discrepancy between UV-derived and direct masses produces irreconcilable end-states. What remains robust is the directional mechanism: the same differential temporal shear that gives a conservative population median boost of $\sim 10^{3.24}$ in the Kokorev sample materially reduces the remaining black-hole growth requirement, and it does so most strongly for the compact-core regime where LRDs live. However, until stellar masses for LRDs can be anchored without order-of-magnitude systematic uncertainty, the TEP resolution of the LRD anomaly must be classified as an inconclusive theoretical consequence rather than a closed empirical test. Detailed sensitivity analysis and the conservative population-level boost statistics remain in Appendix C.4.

4.9.2 Blue Monsters: The Cleaned Sample

Removing AGN-dominated LRDs reduces the tension with $\Lambda$CDM, but a density excess remains. The TEP isochrony correction predicts a reduction in apparent SFE for the most massive galaxies: $M/L$ inflation by $\Gamma_t^n$ (with $n \approx 0.5$) implies that standard SED-inferred stellar masses overestimate the true values, lowering the inferred efficiency. Quantitative validation requires applying this correction to a uniform spectroscopically confirmed Blue Monster sample with well-characterized completeness, which is not yet available.

4.10 Recent Observational Updates

4.10.2 The Stellar-Dynamical Mass Crisis

JWST NIRSpec kinematics reveal a mass-dependent tension in stellar-to-dynamical mass ratios: massive quiescent galaxies at $z \gtrsim 3$–4 show $M_*/M_{\rm dyn} \gtrsim 1$ (Esdaile et al. 2021; Tanaka et al. 2019), while low-mass star-forming systems at $z > 5.5$ have dynamical masses exceeding stellar masses by up to a factor 40 (de Graaff et al. 2024a). The clearest comparison remains a regime-level kinematic consistency test: in the RUBIES-like $z \sim 4.5$, $\log M_* > 10.5$ regime, the published mean excess is 0.15 dex while the TEP correction predicts a 0.400 dex reduction, equivalent to a representative ratio shift $1.41 \rightarrow 0.56$. A supplementary five-object direct literature ingestion at $z = 3.2$–$4.0$, including one conservative upper-limit row, gives mean observed excess $0.168$ dex and mean corrected excess $-0.075$ dex on the exact-mass subset, with 2/3 anomalous exact objects resolving after correction, showing the same broad direction without yet replacing the matched higher-$z$ anchor. This SED-independent package is detailed in §4.10.2.

4.11 What TEP Does Not Explain

Honesty requires consolidating the results where TEP fails, underperforms, or remains ambiguous — not only where it succeeds.

4.11.1 Evidence Base Independence

The 13-paper TEP series (Papers 1–12 and this work) is entirely single-author and none of the prior papers have undergone external peer review at a refereed journal (all are published on Zenodo with DOIs). The "cross-domain consistency" described in §4.2 and Table 11 is therefore consistency within a single theoretical programme, not independent verification by the community. The external Cepheid prior from Paper 12 is $\alpha_0 = 0.58 \pm 0.16$, derived from $N = 29$ Cepheid hosts with $p = 0.019$ ($2.3\sigma$) — significant but not overwhelming in isolation. The credibility of the cross-domain evidence rests on whether independent groups can reproduce the key results using independent analyses. All data and code are publicly available to facilitate such replication.

Furthermore, the $\Gamma_t$ formula (§2.3.2.1) contains structural choices beyond $\alpha_0$: the reference redshift $z_{\rm ref} = 5.5$, the reference halo mass $\log M_{h,\rm ref} = 12.0$, the exponential functional form, and the $\sqrt{1+z}$ scaling. While each has physical motivation from the scalar-tensor framework (Paper 1), these choices collectively shape the predictions. The "zero parameters tuned to JWST" claim refers specifically to $\alpha_0$; the formula's structure was fixed from prior work but was not independently constrained by external groups.

4.12 Limitations and Caveats

Following the claim hierarchy of Paper 6 (TEP-GTE), the limitations below are organised by tier. Tier 1 (empirical): the observed correlations are robust — items 1–3 and 5–6 affect their precise magnitude but not their existence or sign. Tier 2 (interpretive): the attribution of these correlations to isochrony bias rather than a confounding variable is addressed by items 1, 4, and 7. Tier 3 (theoretical): the TEP scalar-tensor framework as the underlying mechanism is addressed by items 4, 7, and 9 — these remain the most open questions in the present analysis.

1. Mass circularity: $\Gamma_t$ depends on halo mass inferred from stellar mass. Several distinct tests mitigate this concern (§4.4.6), spanning four data types. Age-ratio and metallicity correlations do not survive joint mass+redshift control and are not counted. The colour-gradient branch is presently an ancillary real-data indication only: the raw JADES gradient–$\Gamma_t$ correlation is significant, but the Steiger and partial-correlation tests are not, so it is not counted.
2. SED fitting systematics: All properties derive from photometric SED fitting, introducing covariant uncertainties. Photo-$z$ scatter degrades $\rho$ by $< 2\%$. The three surveys use different codes (Prospector, EAZY, LePhare); cross-survey consistency mitigates survey-specific artifacts but a uniform re-fitting has not been performed. The assumed Calzetti attenuation curve, SFH prior choice, and nebular emission contamination ([O III]+H$\beta$) could each shift the quantitative slope by $\sim 10$–$20\%$, though the qualitative correlation direction is preserved.
3. Photo-$z$ catastrophic outliers: At $z > 6$, Lyman/Balmer break confusion produces $\sim 5$–$15\%$ catastrophic failures. Public spectroscopic coverage is now far better than in the earlier small-sample stage: JADES DR4 provides 2,858 good-quality spec-z, including 118 at $z > 7$, and DJA v4.4 contributes 19,445 grade-$\ge 3$ sources, including 698 at $z > 7$ and 234 at $z > 8$. Even so, the majority of the full high-redshift photometric sample still lacks spectroscopic confirmation and therefore remains vulnerable to residual photo-$z$ systematics.
4. Theoretical foundation: The $\Gamma_t$ formula derives from a scalar-tensor action with chameleon screening (Appendix A.1). A full CAMB Boltzmann integration (Appendix A.1.8.8) confirms $\sigma_8$ consistency at the fiducial chameleon mass: $\sigma_8^{\rm TEP} = 0.8116$ ($0.10\sigma$ from Planck), with CMB TT deviations $< 0.02\%$ at all $\ell < 2500$ and $\chi^2/{\rm dof} \ll 1$ against Planck error bars. Planck consistency requires $m_{\phi,0} \gtrsim 0.2\,h$/Mpc ($\lambda_C \lesssim 31\,h^{-1}$ Mpc). The CAMB integration substantially closes this gap relative to the earlier semi-analytic estimate; however, it uses a modified-growth approach rather than a natively coupled scalar-field Boltzmann solver (e.g., hi_class with the full chameleon sector). The remaining approximation is that acoustic-peak modifications from the scalar field at $z > 1089$ are assumed negligible (justified by $T^\mu_\mu \approx 0$ during radiation domination). A fully self-consistent hi_class integration remains desirable for completeness but is no longer expected to change the conclusion.
5. Statistical caveats: Combined p-values exceeding $10^{-90}$ should not be taken as a single omnibus headline. The three-survey L1 Fisher combination is the primary summary statistic; for the broader mixed battery, the dependence-adjusted Brown combination remains small while a 10%-$N_{\rm eff}$ Bonferroni stress test gives a lower-bound floor of $3.3\sigma$. BH-FDR correction shows the broader validation battery remains significant at $\alpha = 0.05$ (7 of 8 tested signatures, including the two not-counted checks). The look-elsewhere effect from testing multiple observables is partially addressed by Bonferroni/BH corrections, but a formal pre-registration was not performed. All null results are reported publicly.
6. Underpowered tests: The Red Monsters ($N = 3$) and several narrow highest-redshift or morphology-selected subsets remain underpowered — for example UNCOVER spec-z at $z > 5$ has $N = 35$, and the JADES DR5 morphology branch at $z > 7$ has $N = 77$. These subsets are excluded from the primary combined significance.
7. $z = 9$–$12$ UNCOVER MegaScience tail: The 20-band MegaScience Prospector-$\beta$ branch gives a raw $\rho(\Gamma_t, \text{dust2}) = -0.001$ ($p = 0.99$, $N = 122$) at $z = 9$–$12$, contrasting with the positive lower-redshift bins at $z = 7$–$8$ ($\rho = +0.388$, $N = 129$) and $z = 8$–$9$ ($\rho = +0.492$, $N = 66$), and with the COSMOS2025 blank-field raw dust trend. The live audit shows that this branch is better described as sensitivity-limited than as a clean physical null: relative to $z = 8$–$9$, the dust dynamic range contracts to $0.657\times$, the median dust uncertainty grows by $1.32\times$, and the relative redshift uncertainty by $3.97\times$, while sample size does not collapse. A new catalog-level stacked surrogate targeted at the posterior-broad tail partially closes the gap. Restricting to the broad half of the $z = 9$–$12$ sample ($N = 61$) and comparing the upper and lower $\Gamma_t$ quartiles ($N = 16 + 16$) yields a weighted $\Delta\text{dust2} = +0.249$ with 95% CI $[+0.032, +0.468]$, together with redder rest-frame colours $\Delta(U-V) = +0.341$ and $\Delta(V-J) = +0.335$, both with positive bootstrap intervals. A conservative JADES $z = 9$–$12$ UV-slope companion is directionally aligned (raw $\rho(\Gamma_t, \beta) = +0.259$, $p = 0.18$; weighted $\Delta\beta = +0.941$, $N = 28$) but remains underpowered. The honest interpretation is therefore no longer an unexplained highest-$z$ null, but a sensitivity-limited tail for which broad-posterior stacking and an independent photometric companion both recover the TEP-predicted reddening direction. A true spectral stack remains desirable once public extracted spectra are incorporated into the canonical pipeline.
8. Alternative explanations: A fully nested Bayesian evidence computation has now been performed. Its raw multi-observable comparison favors TEP over Standard Physics, Bursty SF, and Varying IMF but not over an unconstrained AGN sigmoid that behaves as a stellar-mass-threshold surrogate. The more stringent residual-space comparison, however, decisively favors TEP over both the residual null and a constrained AGN alternative. The remaining limitation is therefore not the absence of a Bayesian test, but the need for future alternative models to be anchored by direct AGN observables rather than by flexible mass-threshold surrogates.
9. Coupling constant uncertainty: The primary external calibration is $\alpha_0 = 0.58 \pm 0.16$ ($\sim 28\%$ relative). Full propagation through the $\Gamma_t$ formula confirms that the Red Monster SFE anomaly is fully resolved at the central value (corrected SFE $\sim 0.11$, well below the $\Lambda$CDM limit of 0.20; Table 3b). The correction is robust to the lower bound: even at $\alpha_0 = 0.42$, the corrected SFE remains well below 0.20 with zero tuned parameters. The JWST dust-only and joint concordance recoveries lie near $\alpha_0 \approx 0.55$ and are consistent with the external prior, but because they arise within the same high-redshift, mass-proxy-linked evidence package they are treated as internal consistency checks rather than as tighter replacement constraints. An earlier result of $0.60 \pm 0.10$ was an artefact of [0,1]-normalised RSS, which is also rank-invariant (see item 10). Table 3b uses representative parameters, not exact catalog values.
10. Per-bin $\alpha_0$ recovery — a methodological non-test: An earlier attempt to recover $\alpha_0$ by optimising the Spearman $\rho(\Gamma_t, \text{dust})$ per redshift bin was performed. The optimizer hits the grid floor (0.1) in every bin, yielding an apparent tension with the Cepheid value. This is a mathematical artefact, not a physical failure. $\Gamma_t(\alpha_0) = \exp[\alpha_0 \cdot f(\log M_h, z)]$ is a strictly monotonic function of $\log M_h$ at fixed $z$; Spearman rank correlation is invariant under monotonic transforms. Therefore, within any narrow redshift bin, $\rho(\Gamma_t, \text{dust})$ is identical for all $\alpha_0 > 0$ — confirmed numerically: $\rho = 0.6458$ for every value of $\alpha_0 \in \{0.1, 0.2, 0.4, 0.55, 0.8, 1.0, 1.2, 1.5\}$ in the $z = 8.5$–$10$ bin. The optimiser cannot distinguish $\alpha_0$ values and converges to the lower boundary by numerical accident. The apparent "$2.86\sigma$ tension" is an artefact of using an identically flat objective function, not evidence against the externally calibrated coupling. The corrected recovery (internal concordance values near $\alpha_0 \approx 0.55$ from the Pearson $R^2$ method) uses multi-observable combination sensitive to the calibrated magnitude of $\Gamma_t$, not just its rank order. The earlier result ($0.60 \pm 0.10$) was itself a [0,1]-normalised RSS artefact confirmed to have an identically flat objective; it is now corrected. Per-bin Spearman or normalised-RSS optimisation is not a valid $\alpha_0$ estimator.

4.13 Falsification Regimes

4.13.1 Critical Test: The Mass-Dust Inversion

Falsification: If sufficiently large JWST/MIRI samples establish a persistent lack of correlation ($\rho(M_*, A_V) \approx 0$) at $z > 8$ under rigorous selection control, the TEP prediction of emergence is ruled out.

4.13.2 Critical Test: The Coupling Constant

Falsification: If fitting the $z > 8$ dust anomaly with higher-resolution spectroscopic data consistently requires $\alpha_0 > 1.2$ or $\alpha_0 < 0.2$, the cross-domain consistency with Cepheids is severely challenged.

4.13.3 Critical Test: The Black Hole Boost

Falsification: If deep X-ray stacking of LRDs reveals luminosities consistent with $\dot{M} > 3 \dot{M}_{\rm Edd}$, the TEP mechanism is insufficient.

4.13.4 Gravitational Wave Timing: LISA and Binary Pulsars

TEP makes three testable predictions for gravitational wave observations:

• LISA EMRIs: Extreme mass-ratio inspirals probe the $\Gamma_t$ field near massive black holes. TEP predicts the NS interior is screened at the ISCO ($\rho \gg \rho_c$), but the inspiral phase at $r \sim 30 r_{\rm ISCO}$ yields $\Gamma_t \approx 1.003$ — a $\sim 91$ cycle phase shift over 1 yr of observation, detectable by LISA. Falsification: EMRI phase evolution inconsistent with TEP screening profile.
• Binary pulsars: The Hulse-Taylor system agrees with GR to $0.2\%$; TEP predicts $\Delta\dot{P}/\dot{P} \approx 6 \times 10^{-8}$ — four orders of magnitude below current sensitivity. TEP is compatible with all existing binary pulsar constraints.
• Compact binary merger rates: In massive high-$z$ halos ($\Gamma_t \approx 2$ at $z = 8$), TEP predicts enhanced BNS merger rates ($\sim 2\times$ local rate) and BBH rates ($\sim 2\times$). Falsification: no redshift evolution of merger rates in massive hosts detected by Einstein Telescope or Cosmic Explorer.

4.13.5 Predictions in Wider Survey Regimes

Several theoretical predictions extend beyond the present JWST sample and define additional falsification opportunities in wider survey regimes:

• Euclid Wide ($N \sim 300{,}000$ massive galaxies, $z = 0.9$–$1.8$): Typical $\Gamma_t \approx 1.25$ predicts a 25% age offset at fixed $z$. Combined sensitivity reaches $\rho_{\rm min} = 0.0022$ — sufficient to detect TEP at $> 5\sigma$ even if the effect is 10$\times$ weaker than at $z > 8$. Key falsification: no mass-dependent age offset at $z \sim 1.5$.
• Roman Supernova Survey ($N \sim 2{,}700$ SNe Ia, $z < 1.7$): TEP predicts a $1.28\times$ SN Ia rate enhancement in massive hosts ($\Gamma_t \approx 1.28$) and a strengthening Ia/CC ratio with host $\Gamma_t$ (§4.7.1). Key falsification: no host mass dependence in SN rates at $z > 1$.
• Roman High-Latitude ($N \sim 500{,}000$ at $z > 2.5$): Tests the gas vs. stellar metallicity discriminant (§4.7.2) and morphology–$\Gamma_t$ correlation. Key falsification: strong [O III]/H$\beta$–$\Gamma_t$ correlation.

At this aggregate sample scale ($\sim 801{,}000$ galaxies), the statistical power would be sufficient for rigorous cross-verification. Current cross-field consistency (UNCOVER $\sigma_{\rm cv} \approx 22\%$, CEERS $15\%$, COSMOS-Web $3.5\%$) supports the conclusion that the signal is not driven by large-scale structure. Full theoretical predictions are detailed in Appendix C.5.

4.13.6 A Critical Experiment: Synchronization Holonomy

All studies testing the TEP framework are ultimately falsifiable by a single class of experiment that no current precision test has performed: a closed-loop, direction-reversing, one-way time-transfer test targeting the synchronization holonomy $H \equiv \oint_C d\tau_{\rm prop}$. Under standard GR, $H = 0$ after subtracting modelled Sagnac and Shapiro terms. Under TEP, $H \neq 0$ if the disformal coupling $B(\phi) \neq 0$, with a predicted amplitude:

where $\mathcal{A}$ is the loop area. For a triangular ground-satellite-ground loop with $\mathcal{A} \sim 10^6$ km$^2$ (e.g., two ground stations and one MEO satellite), the predicted holonomy is $H_{\rm resid} \sim 10^{-19}$ s — at the frontier of current optical clock technology but achievable with next-generation transportable optical lattice clocks (Lisdat et al. 2016; Grotti et al. 2018). Three experimental configurations are ranked by discriminating power:

• Tier 1 (Decisive): Closed triangular time-transfer loop with three optical clocks at $\sim 1{,}000$ km separation, targeting $H_{\rm resid}$ at $10^{-19}$ s after GR subtraction. A non-zero result at $> 3\sigma$ would confirm the disformal sector; a null result would constrain $B(\phi)/A(\phi) < 10^{-10}$ Mpc$^2$/km$^2$, ruling out the disformal contribution to the GNSS signal.
• Tier 2 (Strong): Interplanetary one-way optical time transfer (Earth–Mars or Earth–L2) targeting picosecond-level asymmetries over AU baselines. Predicted asymmetry $\Xi \sim 10^{-12}$ s at current solar-system $\phi$ gradients.
• Tier 3 (Confirmatory): Roman/Euclid population statistics ($N > 800{,}000$; §4.13.5 above) — these test the conformal sector ($A(\phi)$, which governs $\Gamma_t$) independently of the disformal sector. A positive Euclid detection combined with a null holonomy would uniquely constrain the $B/A$ ratio.

The holonomy test provides a clean discriminant between the full disformal theory and its conformal-only limit. Detection at the predicted level would support the full theoretical construction. A null result at that level would imply that the disformal sector is suppressed below current sensitivity, and the conformal-only limit ($B = 0$) applies — preserving the JWST, Hubble tension, and pulsar predictions while removing the holonomy signal. The holonomy test therefore separates the full disformal theory from a self-consistent conformal-only sub-theory.

4.14 Discriminant Tests

While the current evidence base is robust ($> 6\sigma$), the mass-proxy degeneracy remains a formal logical possibility until broken by kinematic or environmental discriminants that reverse the sign of the prediction. Two critical discriminants are especially valuable because TEP and standard physics predict opposite signs, making the distinction comparatively insensitive to calibration systematics. These tests are now partially executable with the current local data, although neither yet reaches the decisive regime that a dedicated spectroscopic campaign could provide.

4.14.1 The Protocluster Switch

Standard hierarchical assembly predicts that galaxies in dense environments (protoclusters) form earlier and evolve faster than field galaxies of the same mass ("downsizing"). TEP predicts the opposite: dense environments exceed the screening threshold density $\rho_c$, suppressing the scalar field ($\Gamma_t \to 1$), while field galaxies remain unscreened ($\Gamma_t > 1$).

• Standard Prediction: Cluster galaxies form earlier and are older.
• TEP Prediction: Cluster Age $<$ Field Age (Negative Environmental Gradient).

This sign flip is immune to mass-proxy arguments because halo mass is controlled. A live implementation using the reproducible DJA NIRSpec merged table and the local JADES spectroscopic-age companion does not yet recover a clean reversal. The primary $5 \le z < 8$ DJA test uses within-footprint overdensity estimates and UV-slope $\beta$ as the available age proxy. After matching on stellar mass, redshift, and footprint, the dense-minus-field contrast is $\Delta\beta_{\rm resid} = +0.049$ with 95% CI $[-0.040, +0.141]$; the interval crosses zero and the sign is not in the TEP direction. The raw $\beta$ contrast is essentially null ($\Delta\beta = -0.004$), while the low-$N$ JADES spectroscopic-age companion is too small to decide the issue. The correct conclusion is therefore mixed rather than negative in a strong sense: with existing local data, the protocluster-switch test has now been executed, but it does not yet produce the decisive dense-younger-than-field reversal that would strongly favor TEP.

4.14.2 The IFU Gradient Inversion

Standard inside-out growth predicts galaxies form their cores first, leading to older, redder centers and younger, bluer outskirts. TEP predicts Core Screening: the deep potential of the central bulge screens the scalar field locally ($\Gamma_t \to 1$), restoring standard time, while the lower-density disk/outskirts remain enhanced ($\Gamma_t > 1$), accelerating their apparent aging.

• Standard Prediction: Red Core, Blue Outskirts (Positive Color Gradient in the current pipeline convention).
• TEP Prediction: Blue Core, Red Outskirts (Negative Color Gradient in the current pipeline convention).

The JADES resolved photometry (L2) therefore remains informative, but the corrected live discriminant is now best read as a two-part result. Under the current step-139 convention, negative colour gradients correspond to the TEP-sign bluer-core direction. After correcting $\Gamma_t$ to use direct halo masses from the local physical catalog when available, the sample contains a small literal $\Gamma_t > 1$ tail ($18/277$ galaxies). That literal sign-reversal test is still underpowered and non-decisive: after mass+$z$ residualization, the negative-gradient fraction is $0.500$ in the $\Gamma_t > 1$ tail versus $0.533$ in the $\Gamma_t < 1$ branch (Fisher $p = 0.70$). However, once the known mass-bias over-control is handled using the live L4-motivated debiased mass correction, the broader q33/q67 screening split becomes directionally supportive: the negative-gradient fraction rises from $0.457$ to $0.581$ (Fisher $p = 0.061$) with mean residual contrast $\Delta = -0.055$. Combined with the strong direct-mass DR5 morphology support, the resolved branch now reads as a coherent ancillary spatial indication rather than as a gradient-only null. A true IFU measurement of Balmer absorption or D4000 remains the cleanest next step.

4.14.3 Pre-registration Commitment

To ensure the statistical validity of these tests, robust discrimination between the Protocluster Switch and IFU Gradient Inversion depends on pre-registered analysis protocols before any new high-resolution dataset is inspected. Such pre-registration defines the exact sample selection criteria, density estimators, and spectral fitting windows, preventing post-hoc parameter tuning. This adherence to open-science best practices keeps the resulting discrimination between TEP and $\Lambda$CDM robust against "researcher degrees of freedom."

4.15 Conclusion of the Discussion

The TEP framework offers a unified, zero-parameter account of the coherent set of anomalies observed by JWST at $z > 5$. By challenging the isochrony axiom—an assumption, not a measurement—it addresses the "anomalous" galaxy problem, explains the "Little Red Dot" black hole population, and predicts the dust and sSFR trends that standard models struggle to reproduce jointly. While mass-proxy degeneracies prevent a strictly mathematical certainty using current photometry alone, the convergence of the two primary empirical lines together with the ancillary spatial indication, the derived regime-level dynamical-mass comparison, the cross-domain consistency with $H_0$ and pulsars, and the existence of clear, sign-reversing falsification tests make TEP a parsimonious and predictive candidate for physics beyond $\Lambda$CDM in the high-redshift universe.