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 $\kappa_{\rm equiv}^{42} = (0.369 \pm 0.310) \times 10^6$ mag and $\kappa_{\rm Cep}^{44} = (0.400 \pm 0.270) \times 10^6$ mag). The later high-redshift concordance analysis recovers $\kappa = (6.0 \pm 3.8) \times 10^5$ mag from the informative analyses, internally concordant ($p_{\rm concordance}=1.0$) and consistent with the canonical benchmark at $0.66\sigma$; this 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 ($N = 2{,}315$), and the prespecified benchmark prediction is further checked across three surveys ($N = 1{,}283$ 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. Both estimates lie below the standard $\Lambda$CDM limit of 0.20. 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. Propagating the canonical benchmark (Paper 11, $\kappa_{\rm gal} = (9.6 \pm 4.0) \times 10^5$ mag) uncertainty: at the lower $1\sigma$ bound ($\kappa_{\rm gal} = 5.6 \times 10^5$ mag) the mean corrected SFE rises to $\sim 0.26$, above the $\Lambda$CDM limit, indicating that the resolution is not fully robust to the benchmark uncertainty for the least massive object.

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 ($N = 2{,}315$), the mass-sSFR correlation is weak but significant ($\rho = -0.13$, $p = 1.3 \times 10^{-10}$, Cohen's $d = -0.27$). 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 ($\rho = +0.14$, $p = 7.0 \times 10^{-11}$), 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 $\rho = -0.49$ ($p = 2.1 \times 10^{-140}$), and the partial correlation controlling for $M_*$ and $z$ gives $\rho(R_{\rm ML}, {\rm sSFR} \mid M_*, z) = -0.47$ ($p = 1.3 \times 10^{-16}$, $N=283$) 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 $\rho(R_{\rm ML}, A_V \mid M_*, z) = +0.26$ 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 $\log M_* < 9.5$ ($N = 267$, excluding the 16 most massive galaxies) reduces the partial to $\rho = +0.18$ ($p = 0.004$), and restricting to $\log M_* < 9$ ($N = 250$) gives $\rho = +0.14$ ($p = 0.024$). The raw mass–dust correlation, by contrast, remains robust at $\rho = +0.45$ ($p = 4.7 \times 10^{-14}$) 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 $N = 2{,}315$ sample is caught in this loop; only the SUSPENSE kinematic test ($N = 15$; §3.10) fully escapes it. Three additional tests directly target this circularity on the full photometric sample.

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 $z > 8$ ($N = 283$), the observed $\rho(R_{\rm ML}, A_V) = +0.581$ collapses to a shuffled mean of $-0.002 \pm 0.055$ ($Z = 10.6$, $p = 5.0 \times 10^{-4}$ 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. The real $R_{\rm ML}$ yields $\rho = +0.581$; the placebo yields $\rho = +0.507$. The bootstrap difference is $\Delta\rho = +0.074$ with 95% CI $[-0.008, +0.157]$, meaning the real $R_{\rm ML}$ is directionally better (winning in 96.3% of bootstrap draws) but the advantage is not statistically significant at 95%. This is an honest limitation: a generic nonlinear mass-$z$ function captures most of the signal. The TEP-specific exponential form provides a directional but not decisive advantage over a power-law placebo on the photometric sample alone. The specificity of the TEP functional form rests on the cross-survey stability of the fixed $\kappa_{\rm gal}$ calibration (§3.7), the AGB threshold timing (§3.7.3), and the SUSPENSE kinematic asymmetry (§3.10) — not on the photometric correlations by themselves.

Test C — Narrow mass-bin subsets: 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. In 3 of 4 testable bins, $R_{\rm ML}$ correlates with dust at $p < 0.05$ while raw $M_*$ does not: $\log M_* \in [8.0, 8.5]$ ($N = 1{,}528$, $\rho = -0.346$, $p = 2.9 \times 10^{-44}$), $\log M_* \in [8.5, 9.0]$ ($N = 526$, $\rho = -0.464$, $p = 1.7 \times 10^{-29}$), and $\log M_* \in [9.5, 10.0]$ ($N = 48$, $\rho = +0.337$, $p = 0.019$). The sign inversion between low-mass bins (negative) and the high-mass bin (positive) reflects the non-monotonic $R_{\rm ML}$-dust relationship: at low mass and low $z$, increasing $R_{\rm ML}$ pushes $t_{\rm eff}$ beyond the AGB threshold without the galaxy having produced dust, whereas at high mass the potential-depth component dominates and the correlation turns positive. The key point is that $R_{\rm ML}$ retains explanatory power within narrow mass bins where $M_*$ itself has none, confirming the signal is not driven by the mass axis of the circularity.

Assessment: 2 of 3 circularity-breaking tests pass. The 2D shuffle confirms the signal requires the correct mass-$z$ physics; the narrow mass bins confirm it is not driven by the mass axis alone. The placebo test reveals that the photometric sample cannot by itself distinguish the TEP exponential form from a generic power-law — the specificity of the TEP functional form rests on the kinematic and cross-survey evidence, not on the photometric correlations alone. This is consistent with the overall evidence structure: the photometric sample establishes that a mass-$z$ nonlinearity exists and is not a mass-only or linear mass-$z$ artifact; the kinematic and cross-survey tests provide the principal additional tests of TEP specificity.

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. At high redshift, this threshold shifts to higher halo mass. Screening is tested by comparing age ratios (MWA/$t_{\rm cosmic}$) across mass bins:

3.5.1 Resolved Core Screening

TEP predicts that deep core potentials should screen the scalar field locally while outskirts retain a large response, producing a structurally concentrated, bluer-core signature in massive galaxies. The strongest L2 support now comes from the preferred JADES DR5 direct-mass morphology sample: after controlling for mass and redshift, one structural proxy remains supportive in the expected direction, with sizes non-significant, Gini partial $\rho = +0.191$, and $\sigma_\star$ non-significant for $N = 384$. The resolved colour-gradient analysis remains informative but weaker: for $N = 277$ galaxies it still shows the raw mass-gradient trend $\rho(M_*, \nabla_{\rm Color}) = -0.166$ ($p = 5.7 \times 10^{-3}$), while the direct $R_{\rm ML}$ correlation is $\rho(R_{\rm ML}, \nabla_{\rm Color}) = -0.192$ ($p = 1.3 \times 10^{-3}$). The direct partial remains null under both observed-mass and debiased-mass control ($\rho = +0.037$, $p = 0.54$; $\rho = +0.037$, $p = 0.54$). The literal $R_{\rm ML} > 1$ tail is too small to decide the sign-reversal test cleanly, but after the L4-motivated debiased-mass control the q33/q67 high-versus-low screening split becomes directionally supportive: the negative-gradient fraction rises from $0.495$ to $0.581$ (Fisher $p = 0.152$) with mean contrast $\Delta = -0.058$. The spatial-screening analysis is therefore an ancillary indication rather than counted among the primary statistical lines. See §3.9 and the robustness checks note for full details.

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 The $z = 5$–$7$ Dip

The redshift-binned correlations reveal a more complex pattern than a simple monotonic emergence. At $z = 5$–$6$, $\rho(A_V, R_{\rm ML}) = -0.14$ ($p = 1.2 \times 10^{-3}$) and $\rho(A_V, t_{\rm eff}) = -0.19$ ($p = 3.3 \times 10^{-5}$), both significantly negative — the opposite sign from the TEP-predicted positive correlation. At $z = 6$–$7$, $\rho(A_V, R_{\rm ML}) = -0.04$ ($p = 0.47$, non-significant). The signal only turns positive and significant at $z > 8$: $\rho(A_V, R_{\rm ML}) = +0.36$ ($p = 6.7 \times 10^{-7}$) at $z = 8$–$9$ and $\rho = +0.76$ ($p = 9.8 \times 10^{-21}$) at $z = 9$–$10$. The negative correlations at $z = 5$–$7$ are a genuine anomaly for the universal-correlation interpretation of TEP: if $R_{\rm ML}$ universally enhances dust production, the correlation should be positive at all redshifts. The "competition epoch" interpretation — high sSFR depleting dust faster than AGB stars replenish it — is a post-hoc explanation, not a prespecified prediction. This anomaly is reported transparently: the TEP signal is an emergence phenomenon at $z > 8$, not a universal correlation, and the intermediate-redshift negative correlations are currently unexplained by the theory.

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 ($N = 1{,}283$ at $z > 8$) yields a fixed-effects meta-correlation of $\rho = +0.62$ with $p = 8.9 \times 10^{-151}$ (Cohen's $d = 1.59$, 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 $\rho = +0.60$ (UNCOVER, $N = 283$), $\rho = +0.65$ (CEERS, $N = 82$), and $\rho = +0.63$ (COSMOS-Web, $N = 918$). Between-study heterogeneity is negligible ($I^2 = 0\%$, Cochran's $Q = 1.6$, $p_Q = 0.45$), 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 $\rho \approx 0.6$. Including the supplementary NIRSpec Balmer-decrement branch raises the combined Fisher $z$ from $24.9\sigma$ to $26.0\sigma$, 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 $\rho = 0.26$); the COSMOS2025 blank-field dataset is classified as supplementary rather than primary due to its different selection function.

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 $\Delta$AIC $= +0.25$ (the mass-matched step fits better as a pure step), but the polynomial $M_* \times z$ baseline outperforms both step models; the $t_{\rm eff}$ step is therefore not a unique discriminator against mass-threshold alternatives in this single-observable test. 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 ($N = 2{,}315$) with $A_V > 0.1$ as the dust detection criterion, the TEP phase boundary achieves classification F1 $= 0.857$ (precision $= 0.776$, recall $= 0.958$). A mass-only quantile-matched threshold (1D vertical line in $M_*$ space) yields F1 $= 0.862$ ($\Delta$F1 $= -0.004$), 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 $z > 8$: 92.9% of galaxies above the TEP boundary are dusty (182/196), while 86.2% 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 $\rho = 0.60$–$0.65$ across three surveys (fixed-effects meta $\rho = +0.62$) 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 ($z > 8$): $t_{\rm eff}$ does not add statistically significant information beyond mass alone for the colour-gradient predictor (Steiger $Z = -0.49$, $p = 0.62$), nor does the $\gamma_t$ scaling significantly improve over raw cosmic time for the colour-gradient predictor (Steiger $Z = -1.06$, $p = 0.29$). The colour-gradient test is therefore non-decisive at fixed redshift; the specificity of $t_{\rm eff}$ is established by the activation pattern test below, not by the within-regime gradient comparison.
• Activation pattern test ($z > 8$): $\rho(\text{dust}, t_{\rm eff}) = +0.61$ vs. $\rho(\text{dust}, M_*) = +0.53$ ($Z = 7.0$, $p = 3.0 \times 10^{-12}$). 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 (combined $Z = 25.7$, $p \sim 10^{-145}$).

3.8 Nested Bayesian Model Comparison

The evaluation is structured into three parts, ordered by neutrality of the comparison:

• Primary: Covariance-Corrected Joint Test: The cleanest comparison, modelling correlated SED outputs with a joint covariance likelihood. No orthogonalization.
• Secondary: Orthogonalized Sensitivity Analysis: Alternatives are levelled by orthogonalizing their mass predictor against $R_{\rm ML}$ to prevent circular absorption. This is TEP-conditioned and reported as a sensitivity analysis, not the headline.
• Conventional Comparison (Raw Mass): What happens if observed mass is assumed unbiased? ($\ln{\rm BF}=-6.0$ in residual space)

The primary result is the covariance-corrected comparison. When the correlated SED outputs are modelled with a joint covariance likelihood (multivariate Gaussian with the empirical $K \times K$ residual covariance matrix) rather than as independent Gaussians, the covariance-corrected TEP model ($\ln Z = -1411.4$, 9 parameters) outperforms the covariance-corrected standard mass-plus-redshift model ($\ln Z = -1475.5$, 13 parameters) by $\ln{\rm BF} = +64.1$ with four fewer parameters — decisive on the Kass–Raftery scale. The covariance-corrected augmented model (mass + z + $R_{\rm ML}$, 17 parameters) edges out the covariance-corrected TEP model by $\ln{\rm BF} = +1.4$, indicating that the mass and redshift terms add modest incremental information once the covariance structure is accounted for. The per-observable breakdown shows the signal is concentrated in dust ($\ln{\rm BF} = +59.9$) and $\chi^2$ ($\ln{\rm BF} = +45.8$), with a positive contribution from sSFR ($\ln{\rm BF} = +30.2$) and a null result for metallicity ($\ln{\rm BF} = +4.7$). In the 3-observable physical subset (dust, sSFR, metallicity; excluding SED $\chi^2$), the joint covariance model yields $\ln{\rm BF} = +62.6$ in favor of TEP under orthogonalized predictors (7 parameters versus 10 parameters), while an unorthogonalized comparison with 10 unconstrained standard parameters yields $\ln{\rm BF} = -14.0$. The single-observable evidence sum across the three physical observables is $\ln{\rm BF} = +94.8$.

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: $\ln{\rm BF}=+141.2$ versus standard physics (16 parameters), $+138.5$ versus the bursty star-formation model (21 parameters), $+130.5$ versus the M*×sqrt(1+z) interaction model (20 parameters), $+118.1$ versus the AGN-threshold model (18 parameters), $+113.9$ versus the varying-IMF model (20 parameters), and $+93.1$ versus the quadratic baseline (28 parameters). In the joint augmented test, TEP augmented yields $\ln{\rm BF} = +154.7$ versus standard physics (Table 8). The mean $\ln{\rm BF}$ across all eleven alternatives is $+126.2$. 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 $\ln{\rm BF} = +130.5$. 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 $R_{\rm ML}$. The covariance-corrected result ($+64.1$) does not depend on this conditioning and is therefore adopted as the headline.

One negative result is reported transparently: in the residual space, TEP outperforms the residual null model ($\ln{\rm BF} = +150.8$, Table 8), while a constrained AGN model (10 parameters) outperforms TEP ($\ln{\rm BF} = -34.9$), indicating that the AGN-threshold predictor captures residual variance that the TEP predictor does not. This is not a contradiction of the joint-space result ($\ln{\rm BF} = +118.1$ versus AGN), but it shows that the orthogonalized residual space removes the mass-related variance that TEP relies on, leaving the AGN model's additional flexibility to fit the remaining structure. The joint-space comparison, which preserves the full mass–$R_{\rm ML}$ information, remains the primary test. Additionally, applying the TEP mass correction to conventional astrophysical models yields a neutral result (mean $\ln{\rm BF} = -0.4$), indicating that the correction does not yet improve standard forward-model fits; the evidence for TEP rests on the correlation structure and the covariance-corrected model preference, not on the mass correction improving astrophysical model fits.

The L1 observed column reports the three-survey dust–$R_{\rm ML}$ correlation $\rho = +0.62$ across UNCOVER, CEERS, and COSMOS-Web ($N = 1{,}283$–$2{,}971$), with the partial correlation $\rho = +0.26$ ($p = 1.2 \times 10^{-5}$) surviving mass+redshift control. The fixed AGB step ($t_{\rm eff} = 0.3$ Gyr) yields an odds ratio of 10.9 ($p = 5.6 \times 10^{-157}$); the $\Delta$AIC $= +0.25$ against the mass-matched step indicates that the mass step fits better as a pure step, though the polynomial $M_* \times z$ baseline outperforms both 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 analysis provides a specific central-concentration indication rather than a general multi-proxy detection. After mass and redshift control, the Gini coefficient remains supportive (partial $\rho = +0.191$, $p = 1.6 \times 10^{-4}$), while both half-light-radius proxies and $\sigma_\star$ are non-significant. The resolved-gradient analysis retains the raw mass trend ($\rho = -0.166$, $p = 5.7 \times 10^{-3}$) and a directionally supportive debiased q33/q67 sign test (negative-gradient fraction $0.581$ vs $0.495$), but direct gradient partials and the predictor-comparison extension remain non-significant. The structural support is therefore specific to central concentration, and the direct gradient discriminator remains non-decisive.

The L3 replication status: UNCOVER ($N = 2{,}315$) remains the primary L3 line. The COSMOS2025 blank-field follow-up is mixed, with a supportive matched $z = 8$–9 bin but a negative ultrahigh-$z$ $z = 9$–13 result, so it is classified as an auxiliary diagnostic rather than as a primary L3 replication.

Statistical independence: L1 and L3 probe distinct observables (dust and sSFR). The UNCOVER partial $\rho(R_{\rm ML}, {\rm sSFR}|{\rm dust}) = -0.49$ at $z > 8$ ($p = 1.8 \times 10^{-18}$, $N = 283$) 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 $z > 4$. The sSFR follow-up is mixed: the $z = 8$–9 bin is positive ($\rho = +0.078$, $p = 9.1 \times 10^{-3}$), while the $z = 9$–13 bin is negative and significant after debiased-mass control ($\rho = -0.103$, $p = 7.2 \times 10^{-5}$) but becomes non-significant after reference-mass reweighting ($\rho = -0.056$, $p = 0.070$).
2. Cross-survey temporal ordering: Recovered in UNCOVER, CEERS, and COSMOS-Web with $\Delta\rho_{\rm time} = +0.310$, $+0.609$, 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:

• Random $R_{\rm ML}$ test: Replacing observed $R_{\rm ML}$ values with random permutations yields $\langle\rho\rangle = 0.000 \pm 0.059$ ($z$-score $= 10.1$; 0 of 10,000 permutations exceed the observed $\rho = 0.60$).
• Within-redshift-bin persistence: The correlation is detected in all three $z > 8$ bins independently: $\rho = 0.32$ ($z = 8$–$8.5$, $N = 107$, $p = 6.5 \times 10^{-4}$), $\rho = 0.53$ ($z = 8.5$–$9$, $N = 72$, $p = 1.7 \times 10^{-6}$), $\rho = 0.72$ ($z = 9$–$10$, $N = 104$, $p = 1.3 \times 10^{-17}$), ruling out a pure redshift-confounding origin.
• $R_{\rm ML}$ vs pure mass: $R_{\rm ML}$ ($\rho = 0.593$) outperforms both $\log M_*$ ($\rho = 0.559$) and $\log M_h$ ($\rho = 0.575$) as a dust predictor, consistent with the redshift-dependent component of $R_{\rm ML}$ carrying additional information beyond mass alone.
• Magnitude bias: The correlation is detected in both bright ($\rho = 0.50$) and faint ($\rho = 0.35$) subsamples. Result: 6 of 7 adversarial tests passed.

3.9.2 Falsification Tests

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

• Sign consistency: Dust–$R_{\rm ML}$ ($\rho = +0.56$, $p = 1.0 \times 10^{-24}$) and mass–age ($\rho = +0.14$, $p = 7.0 \times 10^{-11}$) correlations match predicted signs.
• Magnitude scaling: The correlation strengthens monotonically from low-$R_{\rm ML}$ quartile ($\rho = 0.46$) to high-$R_{\rm ML}$ quartile ($\rho = 0.59$), 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 and narrow mass-bin tests confirm the signal is not a mass-only or linear mass-$z$ artifact — but the placebo test reveals that the photometric sample alone cannot distinguish the TEP functional form from a generic power-law. The kinematic tests in this section provide the mass-independent evidence that closes that gap.

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) breaks the SED-mass circularity but yields mixed results. A sigma-only $R_{\rm ML}$ computed exclusively from measured velocity dispersion via a literature-calibrated $\sigma$-to-$M_{\rm halo}$ mapping, with zero dependence on SED-fitted $M_*$ or $M_{\rm dyn}$, shows a null secondary partial correlation with observed photometric $M_{*,\rm obs}$ beyond $\sigma$ and $z$ control: partial $\rho(R_{{\rm ML},\sigma}, M_{*,\rm obs} \mid \sigma, z) = +0.079$ ($p = 0.50$, 95% CI $[-0.12, +0.26]$). The primary M*-sigma residual evolution test yields a positive trend ($\rho = +0.462$, $p = 3.0 \times 10^{-5}$), directionally consistent with TEP. However, stratification by $\sigma$ measurement type reveals that this positive signal is driven entirely by the emission-line $\sigma$ subsample ($N = 55$, $\rho = +0.293$, $p = 0.030$), while the absorption-line $\sigma$ subsample ($N = 20$, the physically cleaner tracer of the gravitational potential) yields a non-significant negative trend ($\rho = -0.258$, $p = 0.27$). This stratification suggests the full-sample positive signal may partly reflect gas kinematics systematics rather than a pure gravitational potential effect. The $z \geq 4$ subset shows weaker support ($\rho = +0.146$, $p = 0.28$, $N = 56$). Because $R_{{\rm ML},\sigma}$ encodes the TEP-specific redshift-dependent functional form, the null secondary partial indicates that the TEP scaling does not add significant predictive power for $M_*$ beyond $\sigma$ and $z$ in this sample, and the $\sigma$-type dependence prevents unambiguous classification. Taken together, these direct-kinematic results comprise two counted supportive results (SUSPENSE age-based comparison and the dynamical-mass regime comparison), with the sigma-only expansion providing secondary mixed context.

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.