Blowdown Beat Compression Does Not Start
Result
The actual D03 barycentric blowdown
does not factor by the proposed sequence of ring-compatible ordinary beat-point retractions. On the complete 581-cell barycentric carrier, there is no first beat point whose beat neighbour has the same blowdown label.
The executable census is
Thus the proposed length-one-at-each-step costandard compression cannot be used to type .
Exact boundary
This is a falsification of one compression strategy, not a proof that is non-perfect. Ordinary beat-point removal requires the strict upper or lower neighbourhood of the removed point to have a universal comparable neighbour. The barycentric face poset has no compatible point of that kind at its initial state.
A weak-point or discrete-Morse collapse would establish only a topological or chain contraction unless its homotopy is also shown to respect the ringed incidence-module adjunction. It therefore cannot be substituted silently for the missing bounded finite-projective resolution.
The remaining gate is unchanged: compute the actual incidence module , then either exhibit a bounded finite-projective resolution or produce a module-theoretic obstruction. Only after that decision is a supported comparison with Entry 176 meaningful.
Evidence
research/voevodsky/check_d03_blowdown_beat_compression.rs reconstructs the
45 old faces, 51 stellar-blowup faces, and barycentric census
. It tests both upper- and lower-beat conditions in the
full induced order and requires equality of the actual initial-face blowdown
labels. The checker asserts that the removal count is zero.
Worker-delegation run run-e2275878c16b4ac7883dfbb507118c08 was requested
as a low-cognition audit of stronger collapse criteria. It is not evidence
for the result above unless and until it returns a substantive certificate.