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

3. Results

3.0 Evidence Summary

The evidence is organized by role: L1 is the primary photometric line, L3 is a secondary partial-correlation line, L2 is ancillary, L4 is derived, and L5 is a direct kinematic test. The classification is stated once here and in §1.3; individual results below are reported without repeating it.

3.1 Red Monsters: A No-JWST-Specific-Refit Prediction

The TEP parameterization is applied to galaxies in the Red Monster regime ($z \sim 5$–$6$, $\log M_* \gtrsim 10.5$; Xiao et al. 2024). This is a predictive test: the prespecified canonical TEP magnitude-sector benchmark $\kappa_{\rm gal} = (9.6 \pm 4.0) \times 10^5$ mag from Paper 11 was fixed prior to the high-redshift fit (with Paper 11's independent empirical Cepheid analyses recovering $\kappa_{\rm equiv}^{39} = (1.220 \pm 0.531) \times 10^6$ mag and $\kappa_{\rm Cep}^{44} = (0.665 \pm 0.362) \times 10^6$ mag). The regenerated high-redshift concordance analysis recovers $\kappa = (8.38 \pm 4.11) \times 10^5$ mag from the informative analyses, internally concordant ($p_{\rm concordance}=1.0$) and consistent with the canonical benchmark at $0.21\sigma$ — and equally within $\sim 1.1\sigma$ of the empirical Cepheid values, so the recovery does not discriminate between the canonical and empirical anchors; the concordance reflects the recovery uncertainty rather than agreement on a unique scale. It is therefore classified as a partial, anchor-consistent self-consistency check rather than as the input prior. No parameters are fitted or tuned to the high-redshift observations. The three entries below (S1–S3) use representative parameters spanning the published range (§2.1.1); the predicted correction depends primarily on $R_{\rm ML}$ and is insensitive to the exact input SFE.

Because the sample contains only three objects, the Red Monster calculation is best read as an illustrative no-JWST-specific-refit case study rather than as a standalone statistical test. The primary statistical weight comes from the population-level analyses ($N = 2{,}157$), and the prespecified benchmark prediction is further checked across three surveys ($N = 1{,}254$ at $z > 8$).

The predicted mass bias $R_{\rm ML}^{n} \approx 3.4$ (using the mean $R_{\rm ML} = 5.81$ and $n = 0.7$) reduces the mean corrected SFE to $\sim 0.15$ ($= 0.5/5.81^{0.7} \approx 0.146$); the arithmetic mean of the three individually corrected SFEs is $\sim 0.18$ ($^*$ in Table 3b), reflecting the convexity of the $1/R_{\rm ML}^n$ mapping. Propagating the canonical benchmark (Paper 11, $\kappa_{\rm gal} = (9.6 \pm 4.0) \times 10^5$ mag) uncertainty, the corrected mean spans $\sim 0.12$–$0.26$ across the $1\sigma$ prior: fully resolved at the upper bound ($\kappa_{\rm gal} = 13.6 \times 10^5$ mag, SFE $\sim 0.12$), resolved at the central value ($\sim 0.18$, below the standard $\Lambda$CDM limit of 0.20), and only partially resolved at the lower bound ($\kappa_{\rm gal} = 5.6 \times 10^5$ mag, $\sim 0.26$, above the limit). The resolution is therefore prior-range dependent, secured at and above the central benchmark but not at its lower bound. Per object, the anomaly is fully resolved for the two most massive objects (S1, S2); the third (S3) is 85% resolved, with a residual SFE$_{\rm true} = 0.25$ reflecting the lower halo mass and correspondingly weaker inference-channel response.

3.2 UNCOVER DR4: Mass-sSFR and Mass-Age Correlations

The Red Monster case study establishes that TEP predicts the correct direction and magnitude of the SFE correction for individual extreme objects. The critical question is whether this signal extends to the full galaxy population. In the UNCOVER DR4 sample ($N = 2{,}157$), the mass-sSFR correlation is weak but significant ($\rho = -0.14$, $p = 1.7 \times 10^{-11}$, Cohen's $d = -0.29$). Under the TEP measurement equations, $R_{\rm ML}$ inflates inferred $M_*$ by $R_{\rm ML}^{n_{\rm SPS}}$ ($n_{\rm SPS} \approx 0.7$) and inflates inferred SFR by $R_{\rm ML}^m$ ($m \approx 0.5$), so inferred sSFR $= {\rm SFR}/M_*$ scales as $R_{\rm ML}^{m-n_{\rm SPS}}$. Since $m < n_{\rm SPS}$, the TEP bias lowers sSFR in massive galaxies, deepening the negative mass–sSFR relation rather than canceling it. The observed weak negative correlation is therefore consistent with TEP adding to the intrinsic downsizing trend, not reversing it. The mass-age correlation is positive ($\rho = +0.15$, $p = 2.4 \times 10^{-12}$), consistent with more massive galaxies carrying a larger inference-channel response and therefore appearing older under the standard isochrony mapping. Both correlations are attenuated by the full redshift range; the signal sharpens substantially when the sample is stratified by redshift.

3.3 Redshift Evolution: The High-z Transition

The TEP measurement equations predict $\rho(R_{\rm ML}, {\rm sSFR}) < 0$ at all redshifts, since ${\rm sSFR}_{\rm obs} \propto R_{\rm ML}^{m-n_{\rm SPS}}$ with $m < n_{\rm SPS}$. This is confirmed: the full-sample $R_{\rm ML}$–sSFR correlation yields $\rho = -0.49$ ($p = 7.7 \times 10^{-129}$, $N=2{,}157$), and the partial correlation controlling for $M_*$ and $z$ gives $\rho(R_{\rm ML}, {\rm sSFR} \mid M_*, z) = -0.62$ ($p = 8.2 \times 10^{-29}$, $N=254$) at $z > 8$. The TEP bias deepens the negative mass–sSFR relation in massive halos; it does not predict a sign inversion. The observed redshift evolution of $\rho(M_*, {\rm sSFR})$ — which does invert from negative to weakly positive at $z > 7$ — is an empirical phenomenon that TEP does not claim to generate. It may reflect the weakening of intrinsic downsizing at high redshift, selection effects, or additional physics not captured by the inference-channel response. The TEP-consistent test is the negative $R_{\rm ML}$–sSFR partial correlation, not the mass–sSFR inversion. The redshift stratification is shown for completeness:

Comparing low-$z$ ($4 < z < 6$, $\rho = -0.16$) to high-$z$ ($z > 7$, $\rho = +0.09$): $\Delta\rho = +0.25$ [+0.14, +0.35] (95% CI excludes zero), indicating a statistically significant shift in the mass–sSFR relation. This shift is an empirical observation; the TEP-consistent prediction is the negative $R_{\rm ML}$–sSFR partial correlation, not the mass–sSFR inversion itself.

3.4 Partial Correlation Test

The redshift evolution in §3.3 is consistent with TEP, but by itself it does not eliminate the mass-proxy concern, since $R_{\rm ML}$ depends on halo potential $\Psi \propto M_h^{2/3}$ and correlates with stellar mass. The partial-correlation hierarchy is designed to test exactly that issue. With mass-only control, age-ratio and metallicity remain weakly positive. With joint mass+redshift control they become consistent with zero, so they are classified as mass-proxy-adjacent rather than independent. The high-redshift dust signal behaves differently: at $z > 8$, the dust–$R_{\rm ML}$ correlation survives joint mass+redshift control ($\rho = +0.257$, $p = 1.2 \times 10^{-5}$, Cohen's $d = +0.52$), indicating that $R_{\rm ML}$ carries information about dust beyond mass alone. The clock-level version of the test is stronger again: controlling directly for cosmic time leaves $\rho(t_{\rm eff}, A_V \mid t_{\rm cosmic}) = +0.472$ ($p = 5.0 \times 10^{-17}$), so the signal is not a trivial restatement of redshift ordering.

The key asymmetry: the SUSPENSE kinematic comparison (§3.10) provides the cleanest test. $R_{\rm ML}$ retains residual age information after $M_*$+$z$ control ($\rho = +0.556$, $p = 0.032$), whereas $M_*$ contributes no residual signal once $R_{\rm ML}$+$z$ are controlled ($\rho = +0.031$, $p = 0.91$). A pure mass proxy cannot generically produce that one-way residual structure. If $R_{\rm ML}$ were only a reparameterisation of $M_*$, the relationship would be symmetric and neither predictor would retain residual information once the other was controlled.

A further complication is that if TEP is correct, SED-inferred stellar masses are themselves biased upward by $R_{\rm ML}^{0.7}$. Partial-correlation tests that control for observed $M_*$ would then over-control the true signal by removing TEP-predicted variance, making the reported partial correlations conservative lower bounds. This argument is logically valid but dialectically limited: it cannot be used to dismiss null results, and the cleanest resolution is to seek mass-independent tests. The circularity-breaker tests in §3.4.1 and the dynamical-mass comparison in §3.10 provide that independent route.

Mass-range sensitivity: the partial correlation $\rho(R_{\rm ML}, A_V \mid M_*, z) = +0.31$ is concentrated in the high-mass tail where $R_{\rm ML}$ transitions from screened ($R_{\rm ML} < 1$) to unscreened ($R_{\rm ML} > 1$) values. Restricting to $\log M_* < 9.5$ ($N = 241$, excluding the 13 most massive galaxies) reduces the partial to $\rho = +0.27$ ($p = 2.4 \times 10^{-5}$), and restricting to $\log M_* < 9$ ($N = 228$) gives $\rho = +0.24$ ($p = 3.5 \times 10^{-4}$). The raw mass–dust correlation, by contrast, remains robust at $\rho = +0.49$ ($p = 6.8 \times 10^{-15}$) even for $\log M_* < 9$. This means the TEP-specific residual beyond mass+$z$ is driven by the non-linear $R_{\rm ML}$ transition at the high-mass end, not by a universal linear correlation. This is consistent with the TEP prediction that the signal should emerge where the potential depth crosses the screening threshold, but it also means the partial correlation cannot by itself exclude a generic non-linear mass–redshift interaction. The Steiger comparison (§3.7.5) and the Bayesian model comparison (§3.8) provide the specificity tests that the partial correlation alone cannot.

MIRI-Indicated Mass Recalibration Check: To directly test the vulnerability to SED systematics (such as AGN or emission-line contamination inflating NIRCam-only masses), a systematic mass reduction was applied to the entire high-mass ($>10^{10} M_\odot$) UNCOVER sample, simulating the MIRI-based recalibrations reported by Pérez-González et al. (2024). When all masses are artificially reduced by 0.5 dex, the $R_{\rm ML}$-dust correlation at $z > 8$ remains significant ($\rho = +0.447$, $p = 2.8 \times 10^{-15}$). The signal survives even a full 1.0 dex systematic reduction ($\rho = +0.310$, $p = 9.9 \times 10^{-8}$). The correlation weakens under mass reduction — expected because $R_{\rm ML}$ is a non-linear function of halo mass — but remains statistically significant even under extreme calibration shifts, confirming that the TEP signal is not an artifact of the absolute photometric mass calibration.

3.4.1 Circular Mass-Loop Breaker Tests

The most fundamental structural criticism of the photometric analysis is the circular mass loop: $R_{\rm ML}$ is computed from halo mass, halo mass is estimated from stellar mass via abundance matching, and TEP claims stellar mass is itself biased by $R_{\rm ML}^n$. The $N = 2{,}157$ photometric sample is subject to this loop; the SUSPENSE ($N = 15$) and $\sigma$-expansion ($N = 75$) kinematic tests (§3.10) escape it by measuring potential depth dynamically. Three additional tests directly target this circularity on the full photometric sample (Step 178, step_178_circularity_breaker.json).

Test A — 2D mass-$z$ pairing shuffle: Rather than shuffling mass within narrow $z$-bins (as in step 143, which preserves the $z$-dependence of $R_{\rm ML}$), this test randomly reassigns each galaxy's stellar mass to a different galaxy's redshift, breaking both the mass-$z$ correlation and the $R_{\rm ML}$ functional form simultaneously. At $z > 8$ ($N = 254$), the observed $\rho(R_{\rm ML}, A_V) = +0.646$ collapses to a shuffled mean of $-0.014 \pm 0.058$ ($Z = 11.34$, $p = 5.0 \times 10^{-4}$ over 2,000 shuffles). The signal requires the correct physical mass-$z$ pairing and cannot be reproduced by any arbitrary mass-$z$ combination.

Test B — Placebo $R_{\rm ML}$ (wrong functional form): A placebo predictor with the same mass and redshift dependence but a different functional form — a power-law $(M_h / M_{h,{\rm ref}})^{0.3} (1+z)^{0.5}$ instead of the exponential potential-depth response — is constructed and tested against dust. Evaluated with the canonical bounded, self-consistent $R_{\rm ML}$ used throughout the pipeline, the real response yields $\rho = +0.646$ and the placebo yields $\rho = +0.547$. The bootstrap difference is $\Delta\rho = +0.099$ with 95% CI $[+0.028, +0.174]$: the real response is superior in 99.8% of 2,000 bootstrap draws and the interval excludes zero, so the exponential potential-depth form is statistically distinguished from a generic power-law mass-$z$ interaction on the photometric sample alone.

Test C — Narrow mass-bin subsets and the predicted sign transition: Restricting to 0.5-dex-wide mass bins removes the mass axis of the circularity, leaving $R_{\rm ML}$ to vary only through its redshift dependence. The reference-depth kernel makes a falsifiable sign prediction here: within a bin, $\mathrm{d}\ln R_{\rm ML}/\mathrm{d}z = K_{\rm exp}\sqrt{1+z}\,\mathrm{d}\Psi/\mathrm{d}z + K_{\rm exp}(\Psi - \Psi_{\rm ref})/(2\sqrt{1+z})$ changes sign across a crossover mass set by the competition between the positive stellar-to-halo-mass drift and the $(\Psi - \Psi_{\rm ref})$ term. The observed within-bin correlations execute this transition: $\log M_* \in [8.0, 8.5]$ ($N = 1{,}429$, $\rho = -0.366$, $p = 1.6 \times 10^{-46}$), $\log M_* \in [8.5, 9.0]$ ($N = 491$, $\rho = -0.472$, $p = 1.1 \times 10^{-28}$), $\log M_* \in [9.0, 9.5]$ ($N = 171$, $\rho = -0.0001$, $p = 0.999$, consistent with zero at the crossover), and $\log M_* \in [9.5, 10.0]$ ($N = 47$, $\rho = +0.364$, $p = 0.012$). All four bins match the sign predicted by the kernel derivative at the bin centres ($4/4$, zero discordant at $p<0.05$), with the interpolated crossover at $\log M_* \simeq 9.59$ ($\log M_h \simeq 11.33$, $\Psi \simeq 0.35\,\Psi_{\rm ref}$, shifted below the reference depth by the positive within-bin SMHM drift).

The sign structure is the discriminating content: it is not shared by any uniform-sign monotone-in-$z$ baseline. Raw redshift predicts a positive within-bin correlation in all four bins ($\rho = +0.36$, $+0.50$, $+0.19$, $+0.44$), the power-law placebo likewise ($\rho = +0.28$, $+0.43$, $+0.32$, $+0.45$), and a deliberately inverted monotone baseline $M_*^{0.3}(1+z)^{-0.5}$ predicts a negative correlation in all four ($\rho = -0.29$, $-0.40$, $-0.04$, $-0.21$) — each family fails at least one end of the transition, while raw $M_*$ is consistent with zero in the three lower bins ($\rho = -0.03$, $-0.01$, $+0.15$) and cannot generate the negative branch at all. Only the reference-depth kernel produces the observed negative-to-positive inversion, so the within-bin sign map falsifies every uniform-sign monotone-in-$z$ explanation of the dust signal. The negative sign in the two largest bins is therefore not the ordinary dust–redshift trend read backwards: dust rises with $z$ inside those bins, yet $R_{\rm ML}$ orders anti-correlated with $z$ precisely where $\Psi < \Psi_{\rm ref}$ — the signature of a response anchored to a reference potential depth, not of a generic mass-$z$ correlation.

Assessment: 3 of 3 circularity-breaking tests pass. The 2D shuffle confirms the signal requires the correct mass-$z$ pairing; the placebo comparison resolves the exponential potential-depth form over a generic power-law ($\Delta\rho$ CI excludes zero); and the narrow-mass-bin sign map reproduces the kernel-predicted crossover that no monotone-in-$z$ baseline can generate. The photometric sample therefore does carry TEP-specific functional-form information, complementing — rather than deferring to — the kinematic and cross-survey evidence. The remaining limitations are quantitative: the positive-sign bin is supported by $N = 47$ galaxies, and ordinary linear-model AIC comparison (step 136) finds the $M_* \times z$ interaction and the TEP predictor comparably efficient ($\Delta$AIC $\simeq 2.0$ on UNCOVER $z>8$), so the sign-structure and placebo tests — not single-observable linear regression ranking — carry the discrimination.

3.5 Screening Signatures

A distinctive feature of the TEP framework — one that distinguishes it from any smooth mass-dependent function — is the screening prediction: above a Temporal Topology saturation proximity scale $\rho_T \approx 20$ g/cm³, the scalar field is suppressed and $R_{\rm ML} \to 1$. Paper 10 (TEP-COS) established an effective kinematic screening threshold at $\sigma > 165$ km/s from globular cluster pulsar timing; that boundary belongs to the shear channel $\mathcal{S}_\Sigma$ and does not transfer to the amplitude channel $\mathcal{S}_A$ governing $R_{\rm ML}$ (§2.3.2.2). Under the amplitude-channel suppression of Eq. ($\ref{eq:jwst_kappa_eff}$), all halos in these samples are unscreened — their internal densities sit $\sim 24$ orders below $\rho_T$ — so the predicted column below applies the $\mathcal{S}_A = 1$ kernel, which is the correct limit rather than an approximation. The halo-mass ordering of age ratios is then examined as a screening-adjacent diagnostic:

Environmental contrast. A complementary environmental-screening test splits each sample by local galaxy number density and asks whether the dust–$R_{\rm ML}$ correlation is suppressed in overdense regions, as the ambient-environment dependence of the response predicts (Step 138, step_138_environmental_screening_steiger.json). Whereas an earlier all-epoch 2-D sky projection mixed foreground $z \sim 4$–$6$ galaxies into the neighbour counts of $z > 8$ sources, restricting the 5th-nearest-neighbour density estimator to same-epoch neighbours ($|z_j - z_i| \le 0.5$) isolates the true co-moving environment: at $z > 8$ ($N = 254$), the dust–$R_{\rm ML}$ correlation drops from $\rho_{\rm field} = +0.712$ ($p = 6.2 \times 10^{-21}$) in low-density environments to $\rho_{\rm dense} = +0.484$ ($p = 7.7 \times 10^{-9}$) in overdense environments, yielding a statistically significant contrast $\Delta\rho = +0.227$ (95% CI $[+0.075, +0.376]$, Fisher $Z = +2.85$, $p = 0.0044$), which survives holding the foreground Abell-2744 cluster-centric distance fixed across all three $d_{\rm A2744}$ terciles ($+0.269, +0.184, +0.137$; 3/3 positive, mean $d_{\rm A2744}$-controlled contrast $\Delta\rho = +0.197$). The same-epoch screening contrast is likewise confirmed at $z = 6$–$8$ ($N = 549$, $\Delta\rho = +0.355$, $Z = +4.32$, $p = 1.6 \times 10^{-5}$) and across the full $z = 4$–$10$ sample ($N = 2{,}157$, $\Delta\rho = +0.205$, $Z = +5.15$, $p = 2.6 \times 10^{-7}$), while remaining null in the $z = 4$–$6$ control bin ($\Delta\rho = -0.075$, $p = 0.17$) where the $z > 8$ dust anomaly is absent.

3.5.1 Resolved Core Screening

TEP predicts that deep core potentials screen the scalar field locally while outskirts retain a large response, producing a structurally concentrated, bluer-core signature in massive galaxies. In the JADES DR5 direct-mass morphology sample ($N = 384$, Step 155), after controlling for mass and redshift, the Gini coefficient is strongly supportive (partial $\rho = +0.191$, $p = 1.6 \times 10^{-4}$; replicated in GOODS-S $N = 588$ at $\rho = +0.120$, $p = 3.6 \times 10^{-3}$, Step 156). In the JADES resolved colour-gradient analysis ($N = 277$, Steps 139 and 168), the raw mass-gradient trend is $\rho(M_*, \nabla_{\rm Color}) = -0.166$ ($p = 5.7 \times 10^{-3}$) and the global halo-scale $R_{\rm ML}$ correlation is $\rho(R_{\rm ML}, \nabla_{\rm Color}) = -0.192$ ($p = 1.3 \times 10^{-3}$). While the size-blind global halo predictor $\Gamma_t(M_h, z)$ has no residual variance once $(M_*, z)$ are regressed out ($\rho_{\rm partial} = +0.037$, $p = 0.54$), incorporating the measured inner-to-outer F444W stellar concentration $C_{\rm core} = F_{\rm F444W,CIRC1}/F_{\rm F444W,CIRC4}$ across the exact same apertures defines the resolved radial screening predictor $\Gamma_{\rm rad} = \exp[K_{\rm gal}\Psi_{\rm halo}(M_h)\sqrt{1+z}/C_{\rm core}]$: $\Gamma_{\rm rad}$ correlates with the colour gradient at $\rho = -0.168$ ($p = 0.0050$), retains partial $\rho(\Gamma_{\rm rad}, \nabla_{\rm Color} \mid M_*, z) = -0.179$ ($p = 0.0028$, $2.99\sigma$, exact TEP bluer-core sign; partial $\rho = -0.237$, $p = 6.9 \times 10^{-5}$, $4.0\sigma$ on $C_{\rm core}^{-1}$), outperforms $M_*$ on the Steiger $Z$-test ($Z = 3.02$, $p = 0.0025$, $3.02\sigma$), and produces a statistically significant $(M_*, z)$-residualized bluer-core sign reversal ($58.6\%$ vs $35.7\%$ on $q_{25}/q_{75}$, $\text{OR} = 2.54$, Fisher $p = 0.0054$, $\Delta = -0.273$ mag, 95% CI $[-0.526, -0.035]$; and $57.6\%$ vs $42.4\%$ on $q_{33}/q_{67}$, $\text{OR} = 1.85$, Fisher $p = 0.0275$).

3.6 The z > 8 Dust Anomaly: Correlation Structure

The $R_{\rm ML}$–sSFR partial correlation (§3.3) and the partial-correlation hierarchy (§3.4) show that $R_{\rm ML}$ carries information beyond a simple mass trend. The clearest empirical test is the dust–$R_{\rm ML}$ correlation structure. Under standard physics, the universe at $z \sim 9$ is only $\sim 540$ Myr old, barely enough for the first generation of AGB stars to complete their evolution. The question is not whether the dust budget can be closed under TEP — the inferred-time proxy $t_{\rm eff} = R_{\rm ML} \, t_{\rm cosmic}$ is not a physical proper-time integral (§2.3.2) and cannot be used to compute physical AGB evolution timescales. The question is whether the pattern of dust emergence across the galaxy population is organized by the inference-channel response $R_{\rm ML}$ more strongly than by the simple time-only and mass-only baselines tested here.

3.6.1 Resolution of the Apparent $z = 5$–$7$ Dip via Within-Bin Redshift Control

In unconditioned redshift bins of width $\Delta z = 1$, raw correlations between $R_{\rm ML}$ (or $t_{\rm eff} = R_{\rm ML}\,t_{\rm cosmic}(z)$) and $A_V$ exhibit an apparent dip at $z = 5$–$6$ ($\rho_{\rm raw}(R_{\rm ML}, A_V) = -0.136$, $p = 3.05 \times 10^{-3}$; $\rho_{\rm raw}(t_{\rm eff}, A_V) = -0.19$, $p = 3.3 \times 10^{-5}$) and a null value at $z = 6$–$7$ ($\rho_{\rm raw} = -0.008$, $p = 0.88$), before turning strongly positive at $z > 8$ ($\rho_{\rm raw} = +0.646$, $p = 2.3 \times 10^{-31}$). Decomposing the $z = 5$–$6$ bin ($N = 471$, Step 006) reveals that the physical stellar-mass–dust correlation inside that bin is statistically null ($\rho(M_*, A_V) = -0.031$, $p = 0.50$). The negative unconditioned $\rho_{\rm raw}(R_{\rm ML}, A_V)$ and $\rho_{\rm raw}(t_{\rm eff}, A_V)$ values arise from a within-bin Simpson's paradox across the finite $\Delta z = 1$ bin width: across $z \in [5.0, 6.0)$, $R_{\rm ML}$ and $t_{\rm cosmic}(z)$ decrease steeply with redshift ($\rho(z, R_{\rm ML}) = -0.447$, $\rho(z, t_{\rm cosmic}) = -1.00$) while SED-fitted $A_V$ increases with $z$ ($\rho(z, A_V) = +0.220$), inducing a spurious negative cross-correlation of $(-0.447)\times(+0.220) \approx -0.10$. Controlling for $z_{\rm phot}$ within each redshift bin eliminates the negative dip completely across all intermediate bins while sharpening the $z > 8$ emergence signal: $\rho(R_{\rm ML}, A_V \mid z) = +0.074$ ($p = 0.027$) at $z = 4$–$5$, $-0.043$ ($p = 0.35$, null; with $\rho(t_{\rm eff}, A_V \mid z) = -0.015$, $p = 0.75$) at $z = 5$–$6$, $-0.038$ ($p = 0.48$, null; with $\rho(t_{\rm eff}, A_V \mid z) = +0.022$, $p = 0.68$) at $z = 6$–$7$, $+0.115$ ($p = 0.10$; with $\rho(t_{\rm eff}, A_V \mid z) = +0.195$, $p = 0.0052$) at $z = 7$–$8$, and $+0.658$ ($p = 7.51 \times 10^{-33}$) at $z = 8$–$10$. Physically, at $z = 4$–$7$ the cosmic age ($0.84$–$1.35$ Gyr) already exceeds the $0.3$ Gyr AGB dust-onset threshold for $100\%$ of the sample regardless of halo depth, so dust production is saturated ($\rho \approx 0$); only at $z > 8$ ($t_{\rm cosmic} \approx 0.56$ Gyr) does selective temporal enhancement via $R_{\rm ML}$ govern which galaxies cross the AGB threshold.

The mass-dust correlation was therefore tested across three independent surveys (UNCOVER, CEERS, COSMOS-Web) using different SED fitting codes (Prospector/BEAGLE, EAZY, LePhare) and priors.

3.7 Cross-Survey Replication and Meta-Analysis

3.7.1 Cross-Code Robustness

The $z > 8$ dust-$R_{\rm ML}$ correlation is detected in all three datasets despite differences in methodology:

3.7.2 Meta-Analysis

Combining all three surveys ($N = 1{,}254$ at $z > 8$) yields a fixed-effects meta-correlation of $\rho = +0.635$ with $p = 3.65 \times 10^{-154}$ (Cohen's $d = 1.63$, a large effect). All three surveys independently confirm the positive $\rho$ at $>6\sigma$, and mass-stratification confirms the signal persists at fixed mass. The per-survey effect sizes are $\rho = +0.65$ (UNCOVER, $N = 254$), $\rho = +0.66$ (CEERS, $N = 82$), and $\rho = +0.63$ (COSMOS-Web, $N = 918$). Between-study heterogeneity is negligible ($I^2 = 0\%$, Cochran's $Q = 0.24$, $p_Q = 0.89$), meaning the three surveys agree on a common effect size — as expected if TEP is a universal law with a single coupling constant. This is a non-trivial concordance: the three surveys use different SED fitting codes (Prospector/BEAGLE, EAZY, LePhare), different filter sets, and different selection functions, yet converge on the same $\rho \approx 0.64$. Including the supplementary NIRSpec Balmer-decrement branch raises the combined Fisher $z$ from $25.1\sigma$ to $26.2\sigma$, while the Balmer partial-$\rho$ branch itself is weak after $M_*$+$z$ control ($\rho = 0.136$, $p = 5.9 \times 10^{-15}$ — statistically significant but substantially attenuated relative to the photometric partial $\rho = 0.31$); the COSMOS2025 blank-field dataset is classified as supplementary rather than primary due to its different selection function. A lensing-systematic control specific to the UNCOVER field further isolates the correlation: restricting to unmagnified sources ($\mu_{\rm ML} \le 1.05$, $N = 144$, DR4 v2.0 lens model) leaves $\rho = +0.585$ ($p = 1.34 \times 10^{-14}$), and the correlation is positive in both clustercentric halves ($+0.667$ inner, $+0.580$ outer), with $\rho(\mu_{\rm ML}, A_V) = -0.061$ ($p = 0.33$) — the dust–$R_{\rm ML}$ structure is not carried by the lensing gradient, in contrast to the environmental-density channels audited in §3.8. The magnification-corrected mass diagnostic confirms this: evaluating $R_{\rm ML}$ with $\mu$-corrected stellar masses ($\log M_{*,\rm true} = \log M_{*,\rm obs} - \log_{10}\mu$) strengthens the correlation to $\rho = +0.656$ ($p = 1.30 \times 10^{-32}$, $N = 254$; $\rho = +0.603$ at $\mu \le 1.05$), demonstrating that uncorrected magnification bias does not inflate the primary photometric result. Applying the survey's photometry flag (${\tt use\_phot} = 1$) canonically excludes flagged sources and yields the confirmed headline $\rho = +0.646$ ($N = 254$, $p = 2.3 \times 10^{-31}$; $\rho = +0.585$ on the unmagnified subset, $N = 144$) (step_182).

3.7.3 Inferred-Time Ordering and AGB-Motivated Threshold

A more physically targeted and falsifiable test compares dust against cosmic time ($t_{\rm cosmic}$) versus the TEP-effective inference coordinate ($t_{\rm eff} = R_{\rm ML}\,t_{\rm cosmic}$). Under standard physics, dust should track $t_{\rm cosmic}$; under TEP, dust emergence is organized along $t_{\rm eff}$ and exhibits an empirical step-like transition near the canonical AGB-motivated coordinate threshold ($t_{\rm eff} \gtrsim 0.3$ Gyr).

To test whether the location of the step is being tuned to a particular survey, a leave-one-survey-out holdout validation is performed. The threshold selected on the training surveys has median $t_{\rm eff} = 1.93$ Gyr (range $0.06$–$1.93$ Gyr). Despite this fold-to-fold variation, the held-out results remain strongly inconsistent with the null (Fisher-combined $p = 1.1 \times 10^{-25}$). Using the fixed AGB-motivated threshold $t_{\rm eff} > 0.3$ Gyr yields a Fisher-combined $p = 1.5 \times 10^{-252}$.

In COSMOS-Web, where the dust estimator is zero-inflated, the dust detection fraction is 0.58 above threshold versus 0.07 below threshold (Fisher exact test; p-value $< 10^{-10}$). An independent combined-survey threshold scan ($N = 2{,}971$) confirms the transition. For the fixed theoretical threshold of $t_{\rm eff} \ge 0.3$ Gyr, the combined odds ratio is 9.8 ($p = 2.9 \times 10^{-165}$), with dust detection fraction 0.64 above versus 0.15 below. A step-function AIC comparison against a mass-matched threshold yields $\Delta\text{AIC} = -2.98$ in favour of the $t_{\rm eff}$ step over the mass-matched step (AIC $-367.36$ vs $-364.39$, Step 141), though the continuous polynomial $M_* \times z$ baseline outperforms both two-parameter step models; the $t_{\rm eff}$ step is therefore a threshold-comparison check rather than a standalone functional-form discriminator against continuous models. A secondary unconstrained threshold scan yields a data-selected transition at $t_{\rm eff} = 0.61$ Gyr (bootstrap 16th–84th percentile: $0.52$–$1.37$) that structurally validates the presence of an abrupt temporal step. This cross-survey temporal-ordering behavior tests whether $t_{\rm eff}$ organizes dust emergence and is not a generic "more massive galaxies are dustier" statement.

A dedicated UNCOVER-only validation independently passes all four targeted tests: the AGB threshold gives a 1.60$\times$ dust ratio above versus below $t_{\rm eff} = 0.3$ Gyr; controlling for cosmic time leaves $\rho(t_{\rm eff}, A_V \mid t_{\rm cosmic}) = +0.471$ ($p = 5.0 \times 10^{-17}$); the $t_{\rm eff}$–dust correlation remains positive in the low-mass half ($\rho = +0.42$, $p = 2.0 \times 10^{-7}$) and remains positive but weaker in the high-mass half ($\rho = +0.17$, $p = 0.038$); and the raw mass-dust signal steepens monotonically from $z = 8$–$8.5$ to $z = 9$–$10$ ($\rho = +0.325 \rightarrow +0.716$).

3.7.3.1 AGB Dust Phase Boundary in ($M_*$, $z$) Space

The empirical inferred-time boundary $t_{\rm eff} = 0.3$ Gyr (motivated by the canonical AGB onset timescale but used here as an inference-coordinate threshold, not a physical proper-time integral; see §2.3.2) defines a curve in ($M_*$, $z$) space — not a vertical line (mass-only) or horizontal line ($z$-only). Its shape encodes both the exponential $R_{\rm ML}$ form and the redshift-dependent coupling $\alpha(z) \propto \sqrt{1+z}$. A mass-only threshold cannot replicate this curve.

Using the UNCOVER sample ($N = 2{,}157$) with $A_V > 0.1$ as the dust detection criterion, the TEP phase boundary achieves classification F1 $= 0.859$ (precision $= 0.775$, recall $= 0.964$). A mass-only quantile-matched threshold (1D vertical line in $M_*$ space) yields F1 $= 0.865$ ($\Delta$F1 $= -0.005$), indicating that the TEP boundary does not provide a classification advantage over a simple mass threshold in this single-observable test. This is expected: the TEP boundary is a curve in $(M_*, z)$ space, but dust detection at $z > 4$ is dominated by the mass axis, so a 1D mass threshold captures most of the signal. The TEP boundary's distinctive non-linear shape — curving toward lower masses at higher redshift as $\alpha(z)$ increases — is a qualitative prediction that a mass-only model cannot reproduce, but this shape difference does not translate to a significant F1 improvement. At $z > 8$: 93.1% of galaxies above the TEP boundary are dusty (175/188), while 90.9% below the boundary are also dusty (reflecting that some low-$t_{\rm eff}$ galaxies acquire dust through non-AGB channels such as supernovae). The classification power of the TEP boundary is therefore not a standalone discriminator; the primary evidence for TEP rests on the correlation structure (L1, L3) and the $t_{\rm eff}$-vs-$t_{\rm cosmic}$ Steiger test, not on the F1 classification margin.

3.7.4 The Time-Lens Map: Effective Redshift $z_{\rm eff}$

To express the dust-clock result in a coordinate that is directly comparable across observed redshift, an effective redshift $z_{\rm eff}$ is defined by solving $t_{\rm cosmic}(z_{\rm eff}) = t_{\rm eff} = R_{\rm ML}\,t_{\rm cosmic}(z_{\rm obs})$. In this mapping, galaxies with larger $R_{\rm ML}$ are assigned lower $z_{\rm eff}$ (older effective ages). The key falsifiable prediction is that dust should be more strongly ordered by $z_{\rm eff}$ than by $z_{\rm obs}$.

Across surveys, $|\rho(A_V, z_{\rm eff})| > |\rho(A_V, z_{\rm obs})|$. Critically, UNCOVER and CEERS show zero dust–$z_{\rm obs}$ correlation ($\rho \approx 0$, $p > 0.6$), while the TEP effective-time coordinate yields $|\rho|$ up to $0.62$. Classification performance confirms this: in COSMOS-Web ($N = 2{,}606$), where dust-free galaxies exist, AUC for predicting dusty ($A_V > 0$) vs. dust-poor galaxies is $0.89$ for $t_{\rm eff}$ vs. $0.68$ for $t_{\rm cosmic}$. The combined three-survey AUC is $0.85$ for $t_{\rm eff}$ vs. $0.80$ for $M_*$ vs. $0.72$ for $t_{\rm cosmic}$. (Note: UNCOVER and CEERS $z > 8$ samples have $A_V > 0$ for all galaxies, so binary classification is only possible in COSMOS-Web and the combined sample.)

3.7.5 Functional Form Discrimination

A pure mass proxy makes a specific set of predictions. It should produce dust that increases monotonically with $M_*$ at all redshifts, it should generalize cross-survey because mass is survey-independent, and it should not generate the negative $R_{\rm ML}$–sSFR partial correlation seen in L3. TEP predicts the opposite pattern: little or no dust–mass correlation at $z < 7$, emergence at $z > 8$, and a non-linear inferred-time boundary that curves in ($M_*, z$) space. The tests below are therefore aimed not at asking whether both models can fit one subset of the data, but at asking which set of predictions matches the full activation pattern.

The critical distinction from a mass-only model: a mass proxy that fits the $z > 8$ dust signal would still have to be re-fit survey by survey because survey-specific SED systematics shift the absolute calibration. By contrast, $R_{\rm ML}$, anchored by the prespecified canonical theory benchmark $\kappa_{\rm gal} = 0.960 \times 10^6$ mag, maintains $\rho = 0.63$–$0.66$ across three surveys (fixed-effects meta $\rho = +0.635$) with no retraining. The Steiger tests below therefore compare not just two correlated predictors, but two different claims about what should remain stable across datasets:

• Within-regime ($z > 8$): While the size-blind global halo predictor $t_{\rm eff}(M_h, z)$ does not resolve internal radial structure beyond total mass ($Z = -0.49$, $p = 0.62$), the resolved radial screening predictor $\Gamma_{\rm rad}(M_h, z, C_{\rm core})$ incorporating the measured inner-to-outer F444W stellar concentration $C_{\rm core}$ significantly outperforms $M_*$ on the Steiger test ($Z = 3.02$, $p = 0.0025$, $3.02\sigma$) and retains partial $\rho = -0.179$ ($p = 0.0028$, $2.99\sigma$) after $(M_*, z)$ control.
• Activation pattern test ($z > 8$): $\rho(\text{dust}, t_{\rm eff}) = +0.61$ vs. $\rho(\text{dust}, M_*) = +0.53$ ($Z = 7.4$, $p = 1.7 \times 10^{-13}$, combined three-survey $z>8$ sample). This confirms $t_{\rm eff}$ correctly predicts both the absence of correlation at low $z$ and its emergence at $z > 8$, though the margin over $M_*$ is narrower than for the raw dust–$R_{\rm ML}$ correlation.
• $t_{\rm eff}$ vs. $t_{\rm cosmic}$ per-survey: $t_{\rm eff}$ significantly outperforms raw cosmic time in every survey (per-survey Steiger $Z = +8.1$, $+6.2$, $+30.3$ for UNCOVER, CEERS, COSMOS-Web; Stouffer combined $Z \approx 25.8$).

3.8 Nested Bayesian Model Comparison

The evaluation is structured into three comparison families, distinguished by the conditioning applied to the predictor space:

• TEP-conditioned comparisons (orthogonalized predictors): alternative models are evaluated on the components of mass and redshift orthogonal to $\log R_{\rm ML}$. This isolates whether any explanatory variance lies outside the TEP-predicted direction, but it removes the competitor's access to that direction and is therefore reported as a direction-isolation diagnostic rather than an unconditional Bayes factor.
• Unconditioned comparisons (raw mass + z): the baseline evaluated on observed mass and redshift. Under the TEP measurement model ($M_{\rm obs} = M_{\rm true} + n\log_{10}R_{\rm ML}$), observed mass already contains part of the response, so this conditioning is not neutral either: it grants the baseline access to a channel that carries the TEP signal under the hypothesis being tested.
• Nested augmented comparison: the conditioning-free arbiter. The augmented model (raw mass + z + $\log R_{\rm ML}$) is compared against each reduced model, yielding the marginal evidence for each predictor direction given the other.

The covariance-corrected family, in which the correlated SED outputs are modelled with a joint multivariate Gaussian likelihood using the empirical $K \times K$ covariance matrix of the standardized observables (shared identically across all compared models), exhibits the full conditioning dependence (Table 8). Under TEP conditioning, the 9-parameter theory-fixed predictor ($\ln Z = -1262.6$, 9 parameters, with no separate baseline secular $z$ slope) exceeds the 13-parameter orthogonalized standard model ($\ln Z = -1304.1$, 13 parameters) by $\ln{\rm BF} = +41.5$. When the 9-parameter single-predictor model is compared directly against the 13-parameter unconditioned raw mass+z baseline ($\ln Z = -1248.2$, which fits two free slopes per observable), the difference is $\ln{\rm BF} = -14.4$. The direction-isolation diagnostic quantifies where the signal resides: restoring the $R_{\rm ML}$-aligned direction to the standard predictor is worth $\Delta\ln Z = +55.9$, so essentially all explanatory variance is concentrated in the direction TEP specifies, while the orthogonal complement of mass space is evidentially inert. Crucially, the nested augmented model (mass + z + $R_{\rm ML}$, 17 parameters, $\ln Z = -1243.8$) arbitrates the marginal contributions without conditioning bias: adding $\log R_{\rm ML}$ to raw mass+z yields $\Delta\ln Z = +4.45 \pm 1.09$ ($\text{BF} = 85.4 : 1$, very strong Bayesian evidence on the Jeffreys scale for adding the nonlinear depth predictor $\log R_{\rm ML}$ to the linear mass+$z$ baseline despite the 4-parameter Occam penalty), whereas adding mass+z to the single 9-parameter $R_{\rm ML}$ predictor yields $\Delta\ln Z = +18.9$. The per-observable breakdown shows the conditioned signal is concentrated in dust ($\ln{\rm BF} = +21.1$) and the SED $\chi^2$ statistic ($\ln{\rm BF} = +52.5$), with a positive contribution from sSFR ($\ln{\rm BF} = +49.9$) and a null result for metallicity ($\ln{\rm BF} = +9.9$). Because the SED $\chi^2$ is a fit-quality diagnostic rather than a physical observable, the 3-observable physical subset (dust, sSFR, metallicity) is the primary observable set: it yields $\ln{\rm BF} = +37.4$ under orthogonalized predictors and $\ln{\rm BF} = -20.4$ under raw predictors (7 versus 10 parameters). Two diagnostic audits dissect the remaining covariance-table entries. First, an unconstrained 17-parameter empirical bilinear interaction ($\{1, M_*, z, M_*\times z\}$) attains $\ln Z = -1190.9$ on the full $N=254$ sample ($\Delta\ln Z = -0.9$ when $\log R_{\rm ML}$ is added on top). Dissecting the per-observable $R^2$ (Step 179, step_179_bayes_conditioning_audit.json) reveals why: in the full $N=254$ $z \ge 8$ photometric cut, $204$ of $254$ sources have broad or bimodal photo-$z$ posteriors ($\Delta z_{68} = z_{84} - z_{16} > 5.0$, median $z_{16} = 3.78$) and SED $\chi^2$ values up to $297.7$. Across those broad posteriors, the free bilinear product $M_{\rm std}\cdot z_{\rm std}$ fits Prospector grid-boundary jumps between objects near $z_{\rm phot} \approx 8.1$ pinned at the maximum-sSFR / minimum-metallicity prior boundary ($\log{\rm sSFR} \simeq -7.96$, $\log(Z/Z_\odot) \simeq -1.8$) and high-$\chi^2$ objects near $z_{\rm phot} \approx 9.8$ ($\log{\rm sSFR} \lesssim -10.1$, $\log(Z/Z_\odot) \simeq 0$), inflating $R^2$ on $\log{\rm sSFR}$ ($0.5305$ vs $0.3568$) and metallicity ($0.2727$ vs $0.0774$), whereas on the primary dust observable ($R^2 = 0.5238$ vs $0.5293$) and SED $\chi^2$ ($0.3455$ vs $0.3115$, where TEP is higher) the empirical interaction holds no advantage. When restricted to the clean high-$z$ posterior subset ($z_{16} \ge 7.0$ and $\chi^2 < 50$, $N = 38$, removing low-$z$ secondary photo-$z$ peaks and poor SED fits), the TEP augmented model ($\{1, M_*, z, \log R_{\rm ML}\}$) outperforms the bilinear interaction on dust ($R^2 = 0.8216$ vs $0.8166$), $\log{\rm sSFR}$ ($0.4403$ vs $0.4283$), and $\chi^2$ ($0.3775$ vs $0.3670$), reversing the joint nested-sampling Bayes factor in TEP's favour by $\Delta\ln Z = +2.85 \pm 0.94$ ($\ln Z = -203.19$ vs $-206.05$; and $\Delta\ln Z = +3.68$ for the 9-parameter Cov-TEP model at $\ln Z = -202.36$ over the 17-parameter interaction) on all 4 observables and by $\Delta\ln Z = +3.77 \pm 0.85$ ($\ln Z = -150.34$ vs $-154.11$) on the 3-observable physical subset (Step 179). Independently, any monotone-in-$z$ bilinear interaction is falsified by the narrow-mass-bin sign reversal across the reference potential depth $\Psi = \Psi_{\rm ref}$ ($\log M_* \simeq 9.6$, 4/4 bins; Step 178, §3.4.1) and cannot account for the SED-mass-free velocity-dispersion ($\sigma$) kinematic scaling ($N=75$, Step 171, §3.5). Second, the ambient-proxy audit (Step 182) tests whether adding an additive linear environmental-density column $u_{\rm amb}$ to the 4-observable Gaussian mean model detects ambient screening directly. A naive 3D $k$NN density proxy on (RA, Dec, $\ln(1+z)$) adds $\Delta\ln Z = +16.2$ beyond mass+z ($\ln Z = -1233.0$), but Step 182 shows this gain is carried by the on-sky radial coordinate centered on the foreground Abell 2744 cluster core ($z = 0.308$, ${\rm corr}(u_{\rm amb,sky}, d_{\rm A2744}) = +0.79$). Because a foreground cluster at $z=0.308$ is not part of a $z>8$ galaxy's co-moving ambient environment, $d_{\rm A2744}$ and the DR4 v2.0 lens magnification $\mu_{\rm ML}$ (${\rm corr}(\log\mu_{\rm ML}, d_{\rm A2744}) = -0.85$, ${\rm corr}(\log\mu_{\rm ML}, \chi^2) = +0.46$) act as sightline lensing and mosaic-depth coordinates, gaining $\Delta\ln Z = +34.2$ over $\{M_*,z\}$ ($\ln Z = -1215.0$; $+26.2$ on the 3-observable physical subset). Once $\{M_*, z, d_{\rm A2744}, \mu_{\rm ML}\}$ is controlled in the linear mean model, adding an additive same-epoch mass-weighted density column $u_{\rm amb,mw}$ contributes $\Delta\ln Z = -7.1$ ($-6.0$ on the physical subset). Crucially, this control applies only to an *additive linear shift* in the mean SED outputs; the physical TEP environmental screening prediction is a *multiplicative suppression of the correlation slope* ($\rho_{\rm field}(\text{dust}, R_{\rm ML}) > \rho_{\rm dense}(\text{dust}, R_{\rm ML})$), which is tested directly in §3.6 (Step 138) using same-epoch ($\Delta z \le 0.5$) 5-NN density and confirmed at $\Delta\rho = +0.227$ (Fisher $Z = +2.85$, $p = 0.0044$ at $z > 8$), remaining positive across all three fixed $d_{\rm A2744}$ clustercentric terciles ($+0.269, +0.184, +0.137$) and all five mass-matched quintiles.

The orthogonalized sensitivity analysis provides an additional test under TEP-conditioned levelling. When all alternatives are levelled by orthogonalizing their mass predictor against $R_{\rm ML}$ (preventing circular absorption of the TEP signal through the mass variable), TEP outperforms every tested alternative: $\ln{\rm BF}=+133.0$ versus standard physics (16 parameters), $+129.8$ versus the bursty star-formation model (21 parameters), $+121.2$ versus the M*×sqrt(1+z) interaction model (20 parameters), $+102.6$ versus the AGN-threshold model (18 parameters), $+98.1$ versus the varying-IMF model (20 parameters), and $+77.7$ versus the quadratic baseline (28 parameters). In the joint augmented test, TEP augmented yields $\ln{\rm BF} = +163.1$ versus standard physics (Table 8). The mean $\ln{\rm BF}$ across all eleven alternatives is $+113.8$. TEP achieves this with the fewest parameters (12), leveraging a single theory-fixed predictor across all four observables. The M*×sqrt(1+z) interaction model — the minimal non-linear null that captures the specific mass–redshift interaction TEP encodes through the $\sqrt{1+z}$ factor in $R_{\rm ML}$, without any TEP-specific potential-depth structure — is outperformed by TEP with $\ln{\rm BF} = +121.2$, whereas in the unconditioned covariance family the 17-parameter empirical bilinear interaction $\{1, M_*, z, M_*\times z\}$ attains $\ln Z = -1190.9$ on the full $N=254$ sample by fitting Prospector $\log{\rm sSFR}$ and metallicity prior-boundary trends across the $204/254$ broad photo-$z$ posteriors ($\Delta z_{68} > 5.0$), a preference that reverses in TEP's favour ($\Delta\ln Z = +2.85$ for Cov-Augmented and $+3.68$ for 9-parameter Cov-TEP on all 4 observables, and $+3.77$ on the 3-observable physical subset; Step 179) on the clean high-$z$ posterior subset ($z_{16} \ge 7.0$, $\chi^2 < 50$, $N=38$). The orthogonalized family is reported as a sensitivity analysis because the orthogonalization is TEP-conditioned: alternatives have their mass predictor stripped of $R_{\rm ML}$-correlated variance, while TEP uses raw $R_{\rm ML}$. Two scope limitations apply. First, these alternatives are parametric stand-ins for the labelled mechanisms — linear, quadratic, interaction, sigmoid, and timescale modulations of mass+z — rather than forward-modelled predictions of bursty star formation, IMF variation, or AGN-plus-dust physics, so the comparisons do not test realistic astrophysical models. Second, the results are conditioning-dependent: the covariance-corrected value ($+41.5$) uses orthogonalized predictors, while the unorthogonalized comparison yields $\ln{\rm BF} = -14.4$ (physical subset: $+37.4$ versus $-20.4$). The subsumption driving the flip is deterministic rather than empirical: $\log R_{\rm ML}$ is computed from (mass, z) with ${\rm corr}(M_*, \log R_{\rm ML}) = 0.86$ and $R^2(\log R_{\rm ML}\mid M_*, z) = 0.74$, so orthogonalizing mass against $\log R_{\rm ML}$ removes most of the direction the observables require — the $+41.5$ endpoint measures that structural handicap of the comparator, not independent support. Within the conditioned family the result does carry real information: the standard model stripped of the $R_{\rm ML}$-aligned direction loses $55.9$ ln units of evidence, establishing that the signal direction specified by the theory is where the variance lives.

The residual-space comparisons show the same conditioning split. In the orthogonalized residual space — where observables and competing predictors are residualized against the $R_{\rm ML}$-orthogonal components of mass+z, retaining the $R_{\rm ML}$-aligned direction by construction — TEP outperforms both the residual null model ($\ln{\rm BF} = +157.9$, Table 8) and the constrained AGN model ($\ln{\rm BF} = +104.6$). Under the symmetric conventional residualization, in which the full linear mass+z trend is removed from both observables and predictors, the comparison yields $\ln{\rm BF} = +9.07 \pm 0.93$ ($\text{BF} = 8{,}720 : 1$) in favour of TEP: the nonlinear remainder of $\log R_{\rm ML}$ beyond linear mass+z provides a decisive residual contribution. A log-gamma standardization sensitivity check confirms the joint-space evidence is robust to the scaling choice ($\Delta\ln{\rm BF} = 1.4$ between raw and standardized $\log\Gamma_t$). Additionally, applying the TEP mass correction to conventional astrophysical models yields mixed results (Varying IMF $\ln{\rm BF} = +8.6$, Bursty SF $\ln{\rm BF} = -8.6$, Standard Physics $\ln{\rm BF} = -8.7$, AGN $\ln{\rm BF} = -3.2$; mean $\ln{\rm BF} = -3.0$), with the quadratic IMF model benefiting from the mass-scale correction while linear models absorb the scale shift without improvement.

The L1 observed column reports the three-survey dust–$R_{\rm ML}$ correlation $\rho = +0.635$ across UNCOVER, CEERS, and COSMOS-Web ($N = 1{,}254$; NIRSpec supplementary $N = 3{,}259$), with the partial correlation $\rho = +0.31$ ($p = 4.6 \times 10^{-7}$) surviving mass+redshift control. The fixed AGB step ($t_{\rm eff} = 0.3$ Gyr) yields an odds ratio of 12.7 ($p = 2.1 \times 10^{-159}$) and outperforms the mass-matched step by $\Delta\text{AIC} = -2.98$ (AIC $-367.36$ vs $-364.39$, Step 141), though the continuous polynomial $M_* \times z$ baseline outperforms both two-parameter step models. Dedicated UNCOVER-only validation passes all four prespecified tests, and supplementary DJA-based GOODS-S and Balmer analyses are not part of the primary evidence count.

The L2 morphology and resolved-gradient analyses confirm inside-out core screening once the radial concentration profile is included. In JADES DR5 morphology ($N_{\rm matched}=464$, Step 155), after mass and redshift control, the Gini coefficient is strongly supportive (partial $\rho = +0.191$, $p = 1.6 \times 10^{-4}$; GOODS-S $N=588$ $\rho=+0.120$, $p=3.6\times10^{-3}$, Step 156). In the JADES resolved colour-gradient sample ($N = 277$, Steps 139 and 168), whereas the size-blind global halo predictor $\Gamma_t(M_h, z)$ cannot resolve the internal radial profile after $(M_*, z)$ are regressed out ($\rho_{\rm partial}=+0.037$, $p=0.54$), incorporating the measured inner-to-outer F444W stellar concentration $C_{\rm core} = F_{\rm F444W,CIRC1}/F_{\rm F444W,CIRC4}$ across the same apertures defines the resolved radial screening predictor $\Gamma_{\rm rad} = \exp[K_{\rm gal}\Psi_{\rm halo}(M_h)\sqrt{1+z}/C_{\rm core}]$: $\Gamma_{\rm rad}$ correlates with the colour gradient at $\rho = -0.168$ ($p = 0.0050$), retains partial $\rho(\Gamma_{\rm rad}, \nabla(B-V) \mid M_*, z) = -0.179$ ($p = 0.0028$, $2.99\sigma$, exact TEP bluer-core sign; partial $\rho = -0.237$, $p = 6.9 \times 10^{-5}$, $4.0\sigma$ on $C_{\rm core}^{-1}$), outperforms $M_*$ on the Steiger $Z$-test ($Z = 3.02$, $p = 0.0025$, $3.02\sigma$), and yields a significant $(M_*, z)$-residualized bluer-core sign reversal ($58.6\%$ vs $35.7\%$ on $q_{25}/q_{75}$, $\text{OR} = 2.54$, Fisher $p = 0.0054$, $\Delta = -0.273$ mag, 95% CI $[-0.526, -0.035]$; and $57.6\%$ vs $42.4\%$ on $q_{33}/q_{67}$, $\text{OR} = 1.85$, Fisher $p = 0.0275$).

The L3 replication status: UNCOVER ($N = 2{,}157$) is the primary L3 line, and the COSMOS2025 blank-field follow-up ($N = 49{,}539$ total, $N = 7{,}178$ at $z = 7$–$13$, Step 157) confirms the predicted negative sign across all three high-redshift bins once the positive mass-measurement bias on $M_*$ is debiased (3/3 high-$z$ bins negative: $z = 7$–$8$ debiased $\rho = -0.022$, quality-weighted $\rho = -0.066$, $p = 9.6 \times 10^{-5}$; $z = 8$–$9$ debiased $\rho = -0.016$, quality-weighted $\rho = -0.034$; $z = 9$–$13$ debiased $\rho = -0.103$, $p = 7.2 \times 10^{-5}$, quality-weighted $\rho = -0.070$, $p = 0.027$; combined $z = 8$–$13$, $N = 2{,}588$, debiased $\rho = -0.042$, $p = 0.032$; high-$z$ vs low-$z$ activation shift $\Delta\rho_{\rm debiased} = -0.111$, Fisher $Z = -3.92$, $p = 8.8 \times 10^{-5}$).

Statistical independence: L1 and L3 probe distinct observables (dust and sSFR). The UNCOVER partial $\rho(R_{\rm ML}, {\rm sSFR}|{\rm dust}) = -0.64$ at $z > 8$ ($p = 7.4 \times 10^{-31}$, $N = 254$) confirms that L3 carries information orthogonal to dust. The three-survey L1 Fisher combination is the headline statistic; omnibus multi-test combinations are supportive context.

Supplementary cross-dataset checks: These extend the case without altering the primary evidence count, since they reuse the same predictor families as L1 or L3.

1. COSMOS2025 blank-field: The mass+redshift-controlled dust partial is $\rho = +0.200$ ($p < 10^{-300}$) at $z > 4$. In the sSFR follow-up (Step 157), once the mass-measurement bias on $M_*$ is debiased, all 3 of 3 high-redshift bins recover the TEP-predicted negative sign ($z = 7$–$8$: quality-weighted $\rho = -0.066$, $p = 9.6 \times 10^{-5}$; $z = 8$–$9$: debiased $\rho = -0.016$, weighted $-0.034$; $z = 9$–$13$: debiased $\rho = -0.103$, $p = 7.2 \times 10^{-5}$, weighted $-0.070$, $p = 0.027$, and $z = 9$–$10$ reference-mass-reweighted $\rho = -0.123$, $p = 0.0021$; combined $z = 8$–$13$, $N = 2{,}588$: debiased $\rho = -0.042$, $p = 0.032$; activation Fisher $Z = -3.92$, $p = 8.8 \times 10^{-5}$).
2. Cross-survey temporal ordering: Recovered in UNCOVER, CEERS, and COSMOS-Web with $\Delta\rho_{\rm time} = +0.357$, $+0.609$, and $+0.850$.
3. UNCOVER DR4 MegaScience: The dust signal is null below $z = 7$ and reaches $\rho = +0.631$ at $z = 8$–9. The $z = 9$–12 null reflects compressed dust posteriors and inflated redshift uncertainties; a posterior-broad stack recovers a positive high-$R_{\rm ML}$ reddening contrast.
4. UNCOVER $z > 8$ targeted tests: All four prespecified tests return the predicted sign (AGB threshold, cosmic-time-controlled partial, split-sample persistence, monotonic steepening with redshift).
5. UNCOVER $z = 9$–12 posterior-broad stack: Comparing upper and lower $R_{\rm ML}$ quartiles ($N = 16 + 16$) gives $\Delta \text{dust2} = +0.287$ (95% CI $[+0.103, +0.490]$), with redder rest-frame colours $\Delta(U-V) = +0.354$ and $\Delta(V-J) = +0.365$.
6. JADES DR5 morphology: After mass and redshift control, Gini gives partial $\rho=+0.191$ ($p=1.6\times10^{-4}$); both half-light-radius proxies and $\sigma_\star$ are non-significant. The indication is specific to central concentration.
7. JADES $z = 9$–12 UV-slope: The raw $\rho(R_{\rm ML}, \beta) = +0.259$ ($p = 0.18$, $N = 28$); the quartile split gives $\Delta\beta = +0.941$ (95% CI $[-0.384, +3.299]$). Low power, directionally consistent.
8. Debiased mass control: Correcting for TEP mass bias strengthens O32 and H$\beta$-equivalent-width signals by $\sim 1.5\times$–$1.9\times$.

3.9 TEP Predictions vs Observations Summary

Table 10 is best read as a compact consistency summary rather than as a count of independent confirmations. Several of the 12 listed predictions reuse the same underlying $R_{\rm ML}$ predictor derived from halo mass, so they are not statistically independent. The very high overall correlation ($r = 0.999$) is therefore informative about coherence, but it should not be interpreted as 12 separate demonstrations of the effect.

The strongest evidence rests not on the number of predictions but on the coherence of the evidential structure and its robustness checks (§3.9): the primary empirical line (L1), the secondary $R_{\rm ML}$–sSFR partial correlation (L3), together with the ancillary inside-out core-screening indication (L2) and the derived dynamical-mass comparison (L4). Steiger Z-tests, partial correlations, and non-linear AIC are robustness checks on L1, not additional independent lines. Age-ratio and metallicity correlations do not survive joint mass+redshift control and are not counted as independent evidence.

3.9.1 Adversarial Tests

A genuine physical signal should survive attempts to break it. To test whether the dust–$R_{\rm ML}$ correlation could arise from confounding, selection effects, or artifacts, a set of adversarial tests is applied:

• Randomized mass ordering: Shuffling the stellar-mass ordering that feeds $R_{\rm ML}$ destroys the correlation: over 2,000 shuffles the null distribution is $\langle\rho\rangle = -0.007 \pm 0.067$ ($z$-score $= 9.8$; 0 of 2,000 permutations reach the observed $\rho = 0.646$).
• Within-redshift-bin persistence: The correlation is detected in all three $z > 8$ bins independently: $\rho = 0.41$ ($z = 8$–$8.5$, $N = 102$, $p = 1.7 \times 10^{-5}$), $\rho = 0.55$ ($z = 8.5$–$9$, $N = 62$, $p = 2.9 \times 10^{-6}$), $\rho = 0.77$ ($z = 9$–$10$, $N = 90$, $p = 1.3 \times 10^{-18}$), ruling out a pure redshift-confounding origin.
• $R_{\rm ML}$ vs pure mass: $R_{\rm ML}$ ($\rho = 0.646$) outperforms both $\log M_*$ ($\rho = 0.601$) and $\log M_h$ ($\rho = 0.576$) as a dust predictor, consistent with the redshift-dependent component of $R_{\rm ML}$ carrying additional information beyond mass alone.
• Mass-split persistence: The correlation is detected in both mass halves of the $z > 8$ sample ($\rho = 0.42$ below the median, $p = 8.7 \times 10^{-7}$; $\rho = 0.24$ above, $p = 6.3 \times 10^{-3}$), ruling out a pure mass-confounding origin.

3.9.2 Falsification Tests

A prespecified falsification test set examines six necessary conditions for the TEP framework. All six pass:

• Sign consistency: Dust–$R_{\rm ML}$ ($\rho = +0.65$, $p = 2.3 \times 10^{-31}$) and mass–age ($\rho = +0.15$, $p = 2.4 \times 10^{-12}$) correlations match predicted signs.
• Magnitude scaling: The correlation is positive in all four $R_{\rm ML}$ quartiles and strongest in the highest quartile ($\rho = 0.67$, $p = 2.7 \times 10^{-9}$), as predicted by a real physical effect.
• Redshift evolution: The correlation strengthens at higher redshift, consistent with TEP's $(1+z)$ scaling and weaker cosmological screening.

The full six-condition test set is documented in the supplementary materials.

3.10 Direct Kinematic Test

A fundamental vulnerability of evaluating TEP using purely photometric samples is the mass-proxy circularity: because $R_{\rm ML}$ is computed from halo mass (which in turn is inferred from photometric stellar mass), the observed correlations could in principle be driven by an unmodeled standard-physics process that scales with baryonic mass, rather than by a true temporal dilation tracking the gravitational potential. The circularity-breaker tests in §3.4.1 substantially narrow this concern — the 2D mass-$z$ shuffle confirms the signal requires the correct mass-$z$ pairing, the placebo comparison resolves the exponential potential-depth form over a generic power-law, and the narrow-mass-bin sign map reproduces the kernel-predicted crossover — but they remain anchored to SED-inferred stellar mass at one end of the loop. The kinematic tests in this section provide the mass-independent evidence that closes that loop.

The JWST-SUSPENSE survey of massive quiescent galaxies at $z = 1.2$–$2.3$ ($N = 15$) directly addresses this circularity by employing dynamically measured masses ($M_{\rm dyn}$) from stellar velocity dispersions and spectral ages derived from absorption features. The SUSPENSE analysis tests a dynamical-potential predictor and photometric stellar mass side by side. The central comparison shows that $R_{\rm ML}$ predicts spectral age more strongly than stellar mass, yielding $\rho({\rm Age}, R_{\rm ML} \mid z) = +0.690$ ($p = 4.4 \times 10^{-3}$) compared to $\rho({\rm Age}, M_* \mid z) = +0.493$ ($p = 0.062$). Under joint control of the competing predictor and redshift, $R_{\rm ML}$ retains a residual association with age, $\rho({\rm Age}, R_{\rm ML} \mid M_*, z) = +0.556$ ($p = 3.2 \times 10^{-2}$), whereas stellar mass contributes no residual signal once $R_{\rm ML}$ is controlled, $\rho({\rm Age}, M_* \mid R_{\rm ML}, z) = +0.031$ ($p = 0.912$). Propagating the published asymmetric uncertainties for all 15 galaxies preserves a positive $R_{\rm ML}$ residual in 99.7% of Monte Carlo draws. The direct Steiger comparison remains non-significant ($p=0.253$), so this one-sided residual structure is supportive but still carried with the stated small-sample caveat.

A combined kinematic sample of $N = 75$ galaxies ($z = 1.2$–$7.6$) drawn from six independent surveys (SUSPENSE, Esdaile et al. 2021, Tanaka et al. 2019, de Graaff et al. 2024a, Saldana-Lopez et al. 2025, Danhaive et al. 2025; Step 171, step_171_sigma_kinematic_expansion.json) breaks the SED-mass circularity. By the Virial Theorem ($\sigma^2 \equiv GM_h/R_{\rm vir}$), the gravitational potential depth at velocity dispersion $\sigma$ is identically $\Psi(\sigma) = \Psi_{\rm ref}(\sigma/\sigma_{\rm ref})^2$ (the cosmology-free direct depth map, $\sigma_{\rm ref}=136.3$ km/s). Under this Virial-exact depth map — computed exclusively from measured velocity dispersion $\sigma$ and redshift $z$, with zero dependence on SED-fitted $M_*$ or size $R_e$ — the circularity-free partial correlation controlling for redshift $z$ is strongly positive across all subsamples: $\rho(R_{\rm ML,\sigma}^{\rm dir}, M_{*,\rm obs} \mid z) = +0.463$ ($p = 2.84 \times 10^{-5}$) on the full $N=75$ sample, $\rho = +0.608$ ($p = 8.43 \times 10^{-7}$) on the $N=55$ exact-$M_{\rm dyn}$ subsample, and $\rho = +0.575$ ($p = 0.0080$) on the $N=20$ stellar absorption-line subsample (whereas conditioning simultaneously on both $\sigma$ and $z$ removes the primary $\sigma$ signal by construction, leaving only the nonlinear remainder $\rho = +0.079$, $p = 0.50$). In the primary $M_*$–$\sigma$ residual-evolution test (T1/T6), an earlier virial-map variant had introduced an artificial $(1+z)^{-1}$ decay in $\Psi(\sigma, z)$ by using an expanding-universe $R_{\rm vir}(z)\propto(1+z)^{-1}$ in $\sigma\to M_h$ while using the $z=0$ frozen $R_{\rm vir}(0)$ in $M_h\to\Psi$; under the Virial-exact direct map $\Psi\propto\sigma^2$, all five physical subsamples — pooled ($N=75$, $p=3.0\times10^{-5}$), absorption-line stellar kinematics ($N=20$), emission-line gas kinematics ($N=55$, $p=0.040$), $z\ge4$ ($N=56$, $p=0.020$), and SUSPENSE ($N=15$) — agree in sign with the TEP prediction (5/5), and the TEP mass correction attenuates the absorption-line residual-$z$ trend by $76\%$ ($+0.252 \to +0.062$) and the SUSPENSE trend by $65\%$ ($+0.100 \to -0.035$). Furthermore, when the local $z=0$ reference $\Psi_{\rm ref}$ is held at $z_{\rm ref}=0$ ($\ln R_{\rm ML} = K_{\rm gal}[\Psi(\sigma)\sqrt{1+z}-\Psi_{\rm ref}]$), sign agreement holds across all three $N\ge15$ individual surveys (Danhaive+25, Saldana-Lopez+25, Slob+25) plus the absorption tracer, with the absorption-line residual-$z$ trend reduced by $86.5\%$ ($+0.252 \to +0.034$) and the Fundamental Plane residual scatter reduced by $3.96\%$ ($0.578 \to 0.555$ dex, $N=53$).

3.11 L4 and L5 Future Validation

The cleanest direct kinematic test targets the most massive, brightest galaxies at $z > 7$. Such spectroscopy serves two distinct but complementary purposes: measuring Balmer absorption equivalent widths, and mapping the host galaxy velocity dispersion.

1. Balmer Absorption Physics: The primary photometric signature of TEP is that massive galaxies appear older and dustier than their cosmic age permits. This can be tested spectroscopically via Balmer absorption lines (e.g., H$\delta$), which peak in strength $\sim 300$–$500$ Myr after a starburst as A-type stars dominate the continuum. Under standard physics, a galaxy at $z = 9$ (cosmic age $\sim 540$ Myr) cannot host a dominant $\sim 500$ Myr-old stellar population. Under TEP, even a moderately massive halo ($\log M_* \gtrsim 9.5$) at this redshift exceeds $R_{\rm ML} \approx 3$, the threshold for an effective age of $\sim 1.6$ Gyr — readily allowing for strong Balmer absorption. More massive systems ($\log M_* > 10$) have $R_{\rm ML} \sim 8$–$22$, making the prediction even stronger. Observing H$\delta$ equivalent widths $\gtrsim 4$ Å at $z > 8$ would provide strong confirmation of the older effective stellar age.

2. IFU Kinematics as a Direct Mass Proxy: As discussed in §3.4, the current analysis relies on SED-derived stellar masses to compute $R_{\rm ML}$, creating a potential circularity. A direct resolution requires an independent proxy for the depth of the gravitational potential well. Spatially resolved kinematics (e.g., from JWST NIRSpec IFU) can map the central velocity dispersion ($\sigma$). Using $\sigma$ rather than $M_*$ to predict $R_{\rm ML}$—precisely as was done for the local Cepheid calibration and globular cluster pulsars—directly addresses the photometric mass degeneracy.