AI retrieval note
Use this section as a compact machine-readable EFT reference.
Keywords: Dark Pedestal, Tension Slope, rotation curves, weak lensing closure, a_res, ΔΣ_res, Π, baryonic standard, projection mapping, environment gradient, B-mode null, V08 tightening
Section knowledge units
thesis
33.4 rejects the comfort of telling two different stories about the same galaxy sample. Rotation curves read the system through dynamics, while weak lensing reads the same structure through light deflection. The chapter says that if an extra effect is real, it must not require one hidden structure for dynamics and a different one for lensing. Instead, both channels must close under one smooth Dark Pedestal and Tension Slope profile. The operational order matters: subtract baryons first, fit the residual profile from rotation curves, then ask whether that same profile predicts the lensing residual after one frozen projection mapping. In V33 terms this is a same-map closure court. It is not a license to declare that the dark-sector case is already over.
mechanism
The measurement core has four layers. First is the rotation-curve side: the observed circular speed is compared with the baryon-only prediction to define the dynamical residual acceleration a_res(r). Second is the lensing side: tangential shear or excess surface density is stripped of the same baryonic contribution to define ΔΣ_res(R). Third is the smooth profile itself, compressed into a small preregistered parameter set Π rather than an object-by-object zoo of halo shapes. Fourth is the environment ledger: each system receives both discrete grades and continuous indicators such as filamentness, distance to node, external convergence, external shear, or equivalent skeleton-strength percentiles. The chapter then asks two questions at once: can Π predict the sign and dominant amplitude scale of ΔΣ_res under one frozen mapping, and does Π strengthen with environment in a monotonic or threshold-like way?
mechanism
The workflow is deliberately built to prevent convenient re-fitting. Galaxies are selected for both strong rotation-curve quality and usable weak-lensing information, then stratified by mass and morphology so incompatible populations are not mixed. One frozen baryonic standard covers stellar mass-to-light assumptions, gas corrections, inclination, distance calibration, extinction, and non-circular motions for both channels. The dynamics team fits Π using only v_obs(r) and the frozen baryonic model. Π and the projection mapping are then frozen. The weak-lensing team completes shape measurement, photometric-redshift work, and shear calibration without seeing Π, and the adjudication team scores closure only after both streams are finished. A holdout subset of sky area or environment bins remains untouched until final confirmation. This is the chapter’s operational meaning of “rotation curves first, weak lensing second.”
evidence
The controls are chosen so that apparent closure has to separate cleanly from artifact. In a baryon-dominated subsample, both a_res and ΔΣ_res should become small rather than forcing a negative or oscillatory Dark Pedestal just to save the fit. If environment labels are permuted across systems, any Π-environment trend should collapse. Weak-lensing B-mode checks, random rotations, random-point stacking, and mask perturbations must sharply weaken the residual lensing signal. Small preregistered perturbations of the baryonic standard must not flip the closure verdict. Finally, within narrow mass bins, filament and node systems should still show systematically larger Π than void systems if the environment enhancement is genuine. These are not decorative side tests. They are the filter that prevents selection artifacts, shear systematics, or baryonic bookkeeping from masquerading as same-map closure.
boundary
The pass line is strict. Π inferred from rotation-curve residuals must predict the sign and dominant amplitude scale of ΔΣ_res under a frozen projection mapping, separate fits from dynamics and lensing must agree within combined uncertainty, and the Π-environment relationship must survive holdouts while disappearing under permutation nulls. Failure is declared when weak lensing needs an additional independent halo-profile spectrum, when a_res and ΔΣ_res settle into contradictory sign or shape patterns, when the environment trend exists only in one subsample or one pipeline, or when null tests reproduce the same closure strength. The named risks are baryonic-model bias, weak-lensing calibration and redshift systematics, and selection or mass-correlated artifacts. In other words, 33.4 does not tolerate closure that survives only by secretly giving each channel a different extra structure.
interface
So 33.4 delivers only a first-layer verdict. If one frozen baryonic standard and one frozen projection mapping let Dark Pedestal and Tension Slope parameters close rotation curves and weak lensing together, then the chapter grants a same-map closure card. That result is important, but it is still a tightening result under the compat bridge. It does not settle the full dark-sector ontology, and it certainly does not authorize per-galaxy halo patchwork to be reintroduced on the side. If the channels cannot close without mutually incompatible extra structures, the case is rejected and later background-floor or spectral-floor chapters must not inherit a false win. That is why the chapter hands off narrowly: it opens a controlled route to 33.5 rather than declaring the whole front end already proven.