3816 — The Rank-26 Marked Geometry Has Boolean Profile Nine Plus Nine Plus Eight
Question
After ordinary generic-to-physical contiguity is excluded, what is the smallest support-sensitive structure on which the physical half-twist Leray covector must be constructed?
Frozen geometry
On the q_G12 residue surface, the unmarked affine quartic complement has
Euler rank nine. The five marked lines meet the quartic in respectively
(2, 2, 2, 4, 4)
distinct points. Among the ten line pairs, precisely two are parallel:
(g1,g23), (g2,g31).
The other eight pairs meet at distinct affine crossings, and no crossing lies on the quartic at the frozen generic point.
Boolean rank function
For a subset S of marked lines, deletion gives
r(S) = 9 + sum over i in S of (number(K intersect Li)-1)
+ number of nonparallel pairs contained in S.
Möbius inversion on the full five-mark Boolean lattice has grade totals
absolute grade 9
single-mark grade 9
pair-crossing grade 8
triple-and-higher grade 0
Their sum is the established rank 26.
The singleton contributions are (1,1,1,3,3). Every nonparallel pair has
coefficient one; the two parallel pairs have coefficient zero. Every subset
of size at least three has zero Möbius coefficient.
Consequence for the Leray frontier
At the generic marked locus, the support-sensitive associated grade of the physical readout requires only three kinds of input:
- the rank-nine unmarked period packet;
- five source-labelled wall packets of total rank nine;
- eight source-labelled pair-corner packets.
No independent generic triple-mark period generator is predicted by the deletion profile. Higher Čech terms may still supply relations and coherence, but not a new Euler-rank contribution.
This turns the direct physical-half-twist construction into a finite wall-and-corner problem. The next calculation is to derive the residue and orientation maps from the canonical physical Leray germ to these five wall and eight corner packets, then test Čech compatibility. The maps must be source-derived; the rank profile does not select their values.
Scope
This is an Euler/Möbius statement about the deletion filtration. It does not
assert that the rank-26 coefficient object splits canonically as a direct sum
of ranks 9, 9, and 8, nor that every associated-grade class is selected
by the physical chain.
Artifacts
research/benincasa/checkers/check_rank26_boolean_deletion_mobius_profile.pyresearch/benincasa/results/rank26-boolean-deletion-mobius-profile.json
Allocator claim: seqclaim-5a11527ae9bd71ab2e01598d.