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Decomposing Nearby Redshift Mismatches into Endpoint and Path Terms
V33-33.13 · F 证据节 / 显影节 ·
33.13 turns nearby-pair redshift mismatches into an independent-distance-first differential audit: if two objects are genuinely local neighbors, Δ(Δz) should mostly track TPR-side endpoint differences while the matched PER-side path term cancels, and the pattern must survive projected-pair, line-family, and velocity-model nulls; under V08/V09-compatible retain, this remains an object-level nearby redshift ledger rather than a chapter-sized verdict on the full redshift case.
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Keywords: nearby pairs, redshift mismatches, independent distances, Δ(Δz), TPR, PER, ΔJ_end, ΔJ_path, projected-pair control, whole-spectrum shift, invariant ratios, retain boundary
Section knowledge units
thesis
33.13 reframes nearby redshift mismatches as a local differential audit instead of a museum of strange pairs. Once standard distance-based Hubble, peculiar-velocity, local-gravitational, and calibration terms are subtracted under one preregistered order, the remaining residual Δz is split into a TPR-side endpoint baseline and a PER-side path adjustment. The decisive claim is pairwise: if two objects are genuinely part of the same local structure and share nearly the same corridor, then differencing their residuals should largely cancel the path. What should remain is the endpoint contrast. So the chapter is not impressed by a single dramatic redshift offset in isolation; it wants Δ(Δz) to behave like an endpoint ledger after the matched path is removed. Under the V33 guardrail, even that outcome is still an object-level protocol card, not a total redshift settlement.
mechanism
The measurement ledger is deliberately overconstrained. Physical-neighbor status is built from interaction morphology, shared shells or tidal features, common group or cluster membership, and conservative binding limits. Each object also needs at least one distance estimate that does not rely on redshift, plus an upper bound on the true distance difference, so 'it is farther' cannot become the default escape hatch. On top of that the section records z_obs and constructs Δz through one preregistered subtraction chain. Endpoint bookkeeping is carried by compactness, velocity-dispersion, and nuclear-activity proxies together with the Chapter 3 same-source multi-line gate: the source must show a common whole-spectrum shift while preserving invariant ratios. Path bookkeeping is carried by weak-lensing or shear indicators, skeleton-strength or node-distance measures, path-similarity scores, and where possible absorption-system support along the line of sight.
mechanism
The workflow privileges independent distances before any redshift story is allowed to speak. Nearby pairs, triplets, or small groups with clear interaction morphology are constructed in parallel with projected-pair controls drawn from the same depth and redshift range. Distance values and uncertainties are frozen first; then each pair receives Δ(Δz), ΔJ_end, and ΔJ_path. The main rule is simple but harsh: Δ(Δz) should correlate with endpoint differences and correlate materially more weakly with path differences. A two-step fit then makes the logic explicit. Step 1 maps endpoint proxies monotonically into the TPR-side term with the sign convention frozen in advance. Step 2 subtracts that endpoint contribution and checks whether the remaining path terms converge pairwise toward zero. Teams measuring distances and endpoint proxies are blinded from residual labels, while the residual team is blinded from endpoint labels, and part of the sky or sample is held out for final adjudication.
evidence
The controls are designed to prove that the chapter is sensitive to genuine nearby structure and specific against projection, labeling bias, and baseline failures. Projected pairs that are close on the sky but not physically connected must not reproduce the same Δ(Δz)-versus-ΔJ_end pattern. Path-label permutations keep the endpoint ledger fixed while scrambling the path labels; if the endpoint-dominance pattern survives unchanged, the workflow is manufacturing structure. The Chapter 3 multi-line gate is treated as a hard sensitivity and specificity filter: if different line families disagree systematically, the object is not allowed to carry the endpoint baseline. Finally, peculiar-velocity and local-potential subtractions are recomputed under independent model families. If the conclusion lives only inside one subtraction family, or if the same correlation reappears in the projected-pair control, the result belongs back in the artifact ledger.
boundary
The pass line has three linked layers. First, for physically nearby pairs the differential path term must be consistent with zero within uncertainty, so differencing really does cancel the shared corridor. Second, Δ(Δz) must be explained mainly by endpoint differences once independent distances have already bounded the true distance gap, with a stable, reproducible correlation to ΔJ_end that is materially stronger than any correlation to ΔJ_path. Third, the pattern must survive line-family changes, instrument or pipeline swaps, reasonable subtraction standards, the holdout set, and the projected-pair and permutation nulls. Failure is declared as soon as distance explains the mismatch away, path proxies dominate instead of endpoint proxies, the whole-spectrum-shift / invariant-ratio baseline fails, or the pattern only survives in one processing route. The main systematics are distance-ladder instability, misclassified local velocity fields or binding limits, and line-centering or line-shape distortions.
interface
So 33.13 retains a very specific authority and no more. If physically nearby systems keep large redshift mismatches after independent-distance constraints, and pairwise differencing removes the matched path so the residual tracks endpoint proxies while controls separate cleanly, then nearby-pair endpoint dominance survives as one TPR/PER hard ledger. If that chain breaks, the result returns to distance, subtraction-model, or line-family review. Under the compat bridge the chapter is retain, but only as an object-level card inside the broader redshift program. Its proper onward route is into 33.14, where the question is no longer one nearby pair but a fixed sightline and one frozen map. It does not let local mismatches bypass the volume’s protocol-layer court or settle the full redshift ontology by themselves.