IndisputableMonolith.Holography.PixelGluedPlaquette
Defines glued 2×1 domino plaquettes on a 2×3 vertex grid, packing six recognition bits into Fin 64. Introduces sector representatives, the domino stabilizer action, and admissible-sector counting with a super-additivity lemma. Cited by anyone deriving the integer factor in the recognition-pixel area from discrete holography. The module is mostly definitions plus finite enumeration and stabilizer orbit arguments.
claimA glued domino configuration is a 6-bit assignment on the vertices of a $2\times 3$ grid (top $0,1,2$, bottom $3,4,5$), encoded in $\mathrm{Fin}\,64$. The module defines the closed configurations, the stabilizer action, sector representatives, the set of admissible sectors, and proves that the glued sector count is super-additive under gluing.
background
Recognition Science holography splits the pixel area $a_{\mathrm{pix}}=4\cdot H\cdot\ell_P^2$ into three separately forced pieces. The entropy $H=(\varphi+2)\log\varphi$ is already a theorem; the Planck area is blocked by a scale-invariance no-go. The remaining integer $4$ is attacked on the forced discrete substrate: $D=3$ spatial dimensions and the eight-tick octave $2^3$ (forcing chain T7–T8).
Upstream PixelLocal sets the local recognition-pixel counting problem on that lattice. This module enlarges the local picture to a glued $2\times 1$ domino: two adjacent plaquettes sharing an edge, with one recognition bit per vertex of the resulting six-vertex graph. Configurations live in the low six bits of $\mathrm{Fin},64$.
The combinatorial objects are the closed bit patterns, a stabilizer group acting by vertex symmetries compatible with the domino, sector representatives under that action, and the admissible-sector set used for counting.
proof idea
Definition-heavy module with finite combinatorial proofs. DominoCfg packs six bits; vbit and closed select vertex values and closed patterns. dominoStabilizer and actBy implement the symmetry action; isSectorRep and admissibleSectors carve out orbit representatives. Sector cardinality identities (glued_sector_count, admissibleSectors_eq) are by direct Finset enumeration on Fin 64. Super-additivity (glued_super_additive) compares admissible counts before and after gluing via injection or inclusion of representatives.
why it matters in Recognition Science
Feeds RecognitionMultiplicity, the next holography layer that encodes a selector as a T-1 ledger and performs a rank-consistency check. That downstream module was retagged conditional (not a pure derivation) after an adversarial panel: the Bekenstein $1/4$ selector is no longer claimed as forced solely from the ledger floor. The glued-plaquette count still supplies the discrete multiplicity input those ledger arguments consume when relating local sector counts to the integer prefactor in $a_{\mathrm{pix}}$.
In the broader RS chain this sits under holography on the T7 eight-tick / T8 $D=3$ substrate, supporting the integer $4$ in the pixel-area formula once local and glued counts are assembled. It does not by itself close the $\ell_P^2$ no-go or force the Bekenstein factor.
scope and limits
- Does not derive the Bekenstein 1/4 factor or claim it is forced from the ledger alone.
- Does not resolve the Planck-area scale-invariance no-go blocking $\ell_P^2$.
- Does not treat continuous geometry; only finite 6-bit domino configurations on Fin 64.
- Does not count sectors on larger lattices or non-domino gluings beyond the 2×1 case.
- Does not assert unconditional holography; downstream multiplicity remains modeling-conditional.