33.70 turns redshift decomposition into a retainable joint-fit court: after unified subtraction of z_ΛCDM, z_pec, z_grav, and z_sys, one frozen base-map path integral I(θ, z_s) must support a universal TPR coefficient α across source classes, spectral-line families, and carriers, the baseline-subtracted residual must resolve into a smaller discrete PER family co-located with strong-gradient structures, multi-line and multi-band readouts for the same source must preserve sign and ordering without dispersion-law rescaling, and the whole fit must beat base-map / label / bandwidth / low-z / structure-free nulls in held-out data; under V01/V08/V09-compatible retain, this remains one TPR–PER joint-fit ledger rather than a total redshift verdict.
Use this section as a compact machine-readable EFT reference.
33.70 turns redshift residuals into a two-part court. The admissible claim is that one frozen base map supports both a smooth TPR baseline and a smaller discrete PER family across classes and carriers, rather than each source class receiving its own custom residual rulebook.
The measurement ledger begins with Δz after one unified subtraction of z_ΛCDM, z_pec, z_grav, and z_sys. T(θ, z) and the path integral I(θ, z_s) are frozen under one W(z, z_s) and smoothing scale, one global α is checked across source classes, line families, and carriers, the baseline-subtracted residual is tested for discrete PER clustering, same-source multi-line and multi-band sign/order consistency, and the localization of baseline versus micro-adjustment structure along nearby sightlines.
The workflow freezes decomposition before interpretation. Subtraction models are locked at the full-sample level, the base map and path integral are built first from lensing and structure data only, one full-sample α is fitted and then frozen before any PER family is inferred, held-out sky regions or object sets are reserved for final arbitration, and multi-line or multi-band data for the same source are aligned with one shared calibration chain inside the same co-located window.
Controls are aimed at the decomposition itself. Rotating or permuting the base map must collapse the Δz–I relation, redshift or line-label permutation must destroy α universality and discrete clustering, bandwidth changes must not reveal a standard dispersion law, low-redshift samples should weaken the TPR baseline, and structure-free sky regions with near-zero base map may not preserve a strong coherent bias.
Support requires one α that remains stable across classes and lines, a smaller discrete PER family that survives after α is frozen and stays nondispersive across lines and bands, and held-out replication with null controls that significantly degrade both correlation and clustering. Falsification follows from class-specific α values, dispersive micro-adjustments, no repeatable PER family, comparable null effects, or uncontrolled dependence on velocity-field modeling, calibration chains, or subtraction scope. The named adversaries are velocity-field and local gravitational-redshift errors, line-fitting and wavelength-calibration systematics, and selection-function or mask coupling.
So the chapter closes only one retained TPR–PER joint-fit ledger aligned with the V01/V08/V09 redshift-decomposition lane. TPR may survive only as the frozen baseline color and PER only as the smaller localized refinement family, not as a one-chapter final verdict on total redshift ontology. Its clean onward value is to hand a reusable decomposition grammar into 33.71 and the later summary courts.