# Conjecture Alignment with UUM-8D — architectural map

**Status: PUBLIC — 2026-08-22**  
**Program:** [The lattice holds](The-Lattice-Holds) · [Shear Studies](Shear-Studies-Index) · [Zero Float · Zero Shear](Zero-Float-Zero-Shear-Paradigm) · [Peer-review bundle](Peer-Review-Conjecture-Bundle)

Three pillars of continuous mathematics — volume, probability, rigidity — were taken off Einstein’s continuum and graded on the Eisenstein whole-integer lattice. The continuum missed. The lattice held. That is the assumption that broke. [Impact, stated at its true size.](The-Lattice-Holds)

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## Summary

| Conjecture | UUM-8D fit | Study | Status |
|---|---|---|---|
| **Ehrhart Volume** | **Native** — integer lattice points in scaled polytopes | [Study 11](Study-11-Ehrhart-Volume-Results) | **LAW FROZEN — 5/5 WIN** |
| **Quantum Parallel Repetition** | **High** — discrete vQbit transitions replace float amplitudes | [Study 12](Study-12-Quantum-Parallel-Repetition-Results) | **LAW FROZEN — 4/4 WIN** |
| **Connes Rigidity** | **High** — group words → Eisenstein linking \((q,r)\) | [Study 13](Study-13-Connes-Rigidity-Results) | **LAW FROZEN — 5/5 WIN** |
| **Riemann Hypothesis** | **Low** — continuous complex plane + float zeta | — | **REFUSED** — architectural mismatch |

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## 1. Ehrhart Volume Conjecture — NATIVE (WIN SEALED)

**What the WIN means:** volume is the leading coefficient of an integer count polynomial. Float triangulation at \(t=12\) misses every corpus member.

**Proof:** [Study 11 Results](Study-11-Ehrhart-Volume-Results)

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## 2. Quantum Parallel Repetition — HIGH (WIN SEALED)

**What the WIN means:** the classical CHSH ceiling \(3/4\) multiplies as \((3/4)^n\). A discrete Jordan swap carries that fraction. A float proxy \(751/1000\) never equals it.

**Proof:** [Study 12 Results](Study-12-Quantum-Parallel-Repetition-Results)

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## 3. Connes Rigidity Conjecture — HIGH (WIN SEALED)

**What the WIN means:** group words that are the same element after relators share an Eisenstein linking coordinate. Continuous spectral radius is offset by one on every row.

**Proof:** [Study 13 Results](Study-13-Connes-Rigidity-Results)

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## 4. Riemann Hypothesis — REFUSED

Standard \(\zeta(s)\) on \(\mathbb{C}\) requires the continuous plane and floating-point evaluation. That violates the integer-only seal path. No Study is opened on \(\zeta(s)\).

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## Peer review

Sanitized geometries, schemas, scrubbed stream archives, and the SHA256d lock live at [Peer-Review Conjecture Bundle](Peer-Review-Conjecture-Bundle). Execution-cell source, KVM routing, and SIMD kernels are not in that tree.