Energy Filament Theory · EFT Full KB
Four-Dimensional Tomography of Cosmic-Scale Path Redshift: Sky Region, Redshift, Environment, and a Common Component
V33-33.27 · F 证据节 / 显影节 ·
33.27 turns cosmic path redshift into a four-dimensional tomography card: after unified references, source-end calibration, and standard subtraction, Δz_path(θ, z, env) must stay non-dispersive across lines and bands, increase monotonically from voids to filaments to nodes, remain continuous across sky pixels and adjacent redshift slices, and beat environment-only feed-forward cards on blinded holdouts across pipelines and facilities; under V08/V09-compatible retain, this remains a TPR / PER-compatible path-level tomography ledger rather than a finished verdict on the first cause of total redshift.
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Keywords: Δz_path, θ, z, environment, κ_ext, γ_ext, κ_weak, void/filament/node, skeleton strength, feed-forward cards, endpoint controls, template rotation, TPR, PER, path redshift
Section knowledge units
thesis
33.27 refuses to let path redshift survive as a handful of disconnected anomalies. If a line-of-sight term is real, it should organize into a reproducible cube across sky region, redshift, environment, and common-component strength. It should stay non-dispersive across lines and bands, grow with environment, and remain continuous across neighboring sky pixels and redshift slices. That is why the section is compat-adjudicated as retain. It may preserve one cosmic-scale path-level tomography card, but it may not let one cube settle the first cause of all redshift.
mechanism
The ledger is explicitly four-dimensional. For each sky-pixel and redshift-slice unit, the chapter assigns a common-component direction and graded strength, then compares that indicator across multiple spectral-line families and neighboring sub-bands to enforce non-dispersive consistency. Each unit is also stratified by void, filament, and node classes together with continuous environment measures such as κ_ext, γ_ext, κ_weak, galaxy density, distance to the nearest node, and skeleton-strength quantiles. Correlation length, anisotropy, and continuity are then tracked across smoothing scales and across adjacent thin and thick redshift slices so that environment ranking can be separated from radial mixing.
mechanism
Execution is endpoint-first and template-first. Source-end consistency screening is completed before any environment labels are opened, and at least two independent pipelines produce the residual cube using different line-fitting and calibration conventions. Environment skeletons and κ_ext / γ_ext / κ_weak templates are frozen without using the redshift residuals, then sealed feed-forward cards predict the sign and strength of each pixel–slice unit before measurement outputs are seen. Holdout sky blocks and redshift intervals form the adjudication set, and at least two independent facilities or surveys must reproduce direction agreement under the same pixel, slice, and environment definitions.
evidence
The null court is broad because tomographic maps are easy to over-read. Environment-label and redshift-slice permutations should drive monotonicity and continuity toward random. Template rotations or phase randomizations should break co-location while preserving global template statistics. Sub-band and line-family permutations should break directional agreement if the indicator is truly non-dispersive rather than pipeline-locked. Footprint and mask-boundary controls test whether the apparent structure follows observing geometry instead of path structure. Endpoint permutations then ask whether source-population drift, rather than a path term, is carrying the environment ranking.
boundary
A pass requires the whole cube to clear multiple gates at once. At least two pipelines and two independent facilities or surveys must reproduce a cross-line and cross-band common component with stable direction, environmental strength must rise from voids to filaments to nodes under blinding and beat the sealed feed-forward cards again on holdouts, and the sky–redshift structure must keep reproducible correlation length and scale dependence while template rotations and label permutations break it decisively. Failure is declared if the residual behaves dispersively, tracks wavelength calibration or footprint boundaries, collapses under slicing or masking, or disappears once endpoint controls are applied. Wavelength calibration, velocity-field leakage, and environment-template error with radial mixing remain the named systematics.
interface
The chapter’s one-sentence success line is preserved as a retain-level tomography card. A pass means one non-dispersive, environment-ranked, sky–redshift continuous path cube has reproduced across systems and survived feed-forward blinding plus nulls. It does not mean the first cause of total redshift has been settled. The section therefore remains on the protocol layer and routes onward to 33.28, 33.29, and 33.31, where the path and residual windows continue under the same TPR / PER-compatible discipline.