Conjecture Alignment UUM8D

Conjecture Alignment with UUM-8D — architectural map

Status: PUBLIC — 2026-08-22
Program: Shear Studies · Zero Float · Zero Shear

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Summary

Conjecture	UUM-8D fit	Study	Status
Ehrhart Volume	Native — integer lattice points in scaled polytopes	Study 11	LAW FROZEN — 5/5 WIN
Quantum Parallel Repetition	High — vQbit + Jordan algebras replace float amplitudes	Study 12	CHARTER SEALED — corpus OPEN
Connes Rigidity	Moderate–High — group algebras → discrete topological invariants	Study 13	CHARTER SEALED — corpus OPEN
Riemann Hypothesis	Low — continuous complex plane + float zeta	—	REFUSED — architectural mismatch

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1. Ehrhart Volume Conjecture — NATIVE (WIN SEALED)

System fit: Native.

Integration: Ehrhart theory counts integer lattice points in dilated convex polytopes. UUM-8D is bound to integer-only constraint manifolds and Eisenstein lattice geometry. Polytope boundaries are affine halfspaces; coefficient extraction uses forward differences on the count table — no floating-point operation.

Proof sealed: Study 11 Results — 5/5 primary WIN, 5/5 float-volume adversary MISS.

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2. Quantum Parallel Repetition — HIGH (charter)

System fit: High, leveraging native primitives.

Integration: Standard quantum parallel repetition uses continuous probability amplitudes. The vQbit primitive over the GaiaFTCL substrate discards continuous probabilities. Bipartite entanglement matrices represented through integer-bounded Jordan algebras in the 8D manifold evaluate parallel-repetition bounds as discrete state transitions.

Status: Charter sealed; corpus and frozen law OPEN. See Study 12 and QuantumShearMap.swift transport rows.

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3. Connes Rigidity Conjecture — MODERATE–HIGH (charter)

System fit: Moderate to high via structural translation.

Integration: Connes's conjecture concerns von Neumann operator algebras and structural invariants of groups. Continuous group algebras project into Jordan-bonded linking structures. If group properties isolate as discrete topological invariants on the integer manifold, rigidity tests without continuous domains.

Status: Charter sealed; corpus OPEN. See Study 13.

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4. Riemann Hypothesis — REFUSED

System fit: Low — architectural mismatch.

Reason: Standard evaluation of the Riemann zeta function requires the continuous complex plane and heavy floating-point operations. That violates affine, integer-only constraint on the seal path.

Permitted path (not chartered): Discard the classical zeta entirely; process discrete analogs (Hasse–Weil zeta over finite algebraic curves) mapped to the Eisenstein lattice. No Study is opened on (\zeta(s)) in (\mathbb{C}).

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Recommendation executed

Ehrhart Volume Conjecture was prioritized. Study 11 is LAW FROZEN with publishable results. Studies 12–13 are chartered for the next corpus pulls.