33.40 turns time-delay cosmology into an environment-residual translation court: after standard macro modeling plus external convergence κ_ext and external shear γ_ext corrections under frozen light-curve extraction, the normalized residual R_ij must be hit feed-forward by J_env, strengthen in high-filamentarity or high-convergence environments, show stronger sensitivity in saddle-point image pairs, remain near-achromatic across bands and extraction paths, and survive model-family holdouts; under V08/V09-compatible translation, R_ij remains a time-delay readout/interface residual rather than a new potential owner, geometry sovereign, or direct cosmological verdict.
Use this section as a compact machine-readable EFT reference.
33.40 recasts what would normally vanish into time-delay error bars as an admissible residual object R_ij: the point is not to keep decorating the macro model, but to ask whether a stable environment-predictable component remains after standard corrections. Under compat adjudication, this chapter is translate.
The readout package is five-fold: normalized residual R_ij, environment-only hit rate from J_env, image-pair sensitivity with saddle-point emphasis, near-achromatic cross-band consistency, and cross-season or cross-year stability. What matters is not one odd system, but whether these fingerprints line up as one environment-predictable residual ledger.
The workflow keeps two light-curve extraction paths and two lens-modeling paths running in parallel, freezes environment layers before residual inspection, and separates the feed-forward team from the measurement team under held-out environments and image classes. Cadence logs, photometry quality flags, mass-sheet handling, and model-family spread are all published as explicit ledgers rather than hidden tuning knobs.
False predictability must collapse under environment-label permutations, rotated or shifted templates, image-class permutations, observing-window scrambles, and cadence or photometry controls. It also has to survive both band changes and model-family changes with the same sign; otherwise the apparent hit belongs to sampling, microlensing, or modeling ledgers rather than to the environment court.
The pass line requires two extraction paths and two modeling paths to beat chance, stronger environment sensitivity in saddle-point image pairs, near-achromatic behavior across bands, and robustness on held-out environments and held-out image classes. Microlensing time delays, cadence and photometric drift, and mass-sheet or external-field degeneracy remain the three named ledgers that must absorb the effect first.
The chapter ends with one time-delay-cosmology residual ledger only: if R_ij survives as an environment-hit, image-class-sensitive, near-achromatic structure, it sharpens the earlier strong-lens feed-forward court of 33.2 and the wider lens residual chain. If not, it returns to microlensing, cadence, and macro-model ledgers without receiving any free upgrade into geometry or cosmology.