Conjecture Alignment UUM8D

Conjecture Alignment with UUM-8D — architectural map

Status: PUBLIC — 2026-08-27
Program: The lattice holds · Shear Studies · Zero Float · Zero Shear · Peer-review bundle · Math Court · Quantum inventory

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.

Live MCP: https://affine.earth/language-invariant/mcp · Registry: earth.affine/math-court
Caller: bash clients/math-court-mcp/prove-live-court.sh
Law: LatticeRender/Sources/LatticeRender/QCCourtLaw.swift + QMACourtLaw.swift

Live tools/list 2026-08-27 is still 23 (HTTP 200, edge nbg-01). QC-001…019 are wired in git (20 named presented-config verifiers). Glama sees them after the cell binary rolls. After deploy, count is 43. Local proof: swift test --package-path LatticeRender --filter QCCourtLaw.

---

Court-exposed algorithms (how researchers call them)

Presented-config verifiers. Unknown grounds are not searched. Decimal strings only. VQE the optimizer and QAOA the pulse schedule are not tools — the court grades the presented energy.

QC	Algorithm	MCP tool	math_court domain	Fixture	Local Lean / prover
11	Ehrhart	math_court	geometry	polytope_id=unit_square dilation=12	gaiaftcl prove conjecture-workload
12	Parallel repetition	math_court	chance	rounds=8	same
13	Connes rigidity	math_court	algebra	word=Z2_a2b	same
22	2-local / VQE problem	execute_2local_hamiltonian · verify_vqe_energy	qma_2local · qc_vqe	constraints=0,1,1,1 config=0,1 → −1/1	QMACourtLaw
23	Spin-glass / QAOA problem	route_spin_glass_manifold · verify_qaoa_energy	qma_spinglass · qc_qaoa	triangle spins → −1	same
24	N-representability	verify_n_representability	qma_nrep	rho2=1/2,0/1|0/1,1/2 n=2	same
25	Permanent	execute_exact_permanent	qma_permanent	all-ones 3×3 → 6	same
QC-001	Shor witness	verify_shor_witness	qc_shor	N=15 halfPow=4 factor=3 cofactor=5	ShorFactor15.lean · ShorWitnessCertifier.lean
QC-001	Period	verify_period	qc_period	a=7 N=15 r=4 proper_divisors=1,2	same
QC-002	Grover	verify_grover	qc_grover	oracle=0001 marked=3	GroverN4.lean
QC-003	QFT phases	verify_qft_phases	qc_qft	n=4 k=1 phases=0/4,1/4,2/4,3/4	QFTN4.lean
QC-004	QPE	verify_qpe_phase	qc_qpe	m=2 k=1 phase=1/4	QPEN4.lean
QC-005	HHL	verify_hhl	qc_hhl	I₂ x = b	HHL2.lean
QC-006	Deutsch–Jozsa	verify_deutsch_jozsa	qc_dj	table=00 class=constant	DeutschJozsa2.lean
QC-007	Bernstein–Vazirani	verify_bernstein_vazirani	qc_bv	hidden=101	BernsteinVazirani4.lean
QC-008	Simon	verify_simon	qc_simon	mask=11 x=00 y=11	Simon8.lean
QC-009	Amp. amp.	verify_amplitude_amplification	qc_ampamp	oracle=0001 iterations=1	AmpAmpN4.lean
QC-010	Amp. est.	verify_amplitude_estimation	qc_ampest	N=4 M=1 fraction=1/4	AmplitudeEstimationMarked.lean
QC-011	Kickback	verify_phase_kickback	qc_kickback	m=1 k=1 phase=1/2	QSVT2.lean
QC-012	Walk C2	verify_quantum_walk	qc_walk	steps=2 start=0 end=0	CTQW2.lean
QC-015	Counting	verify_quantum_counting	qc_count	oracle=0001 count=1	BosonSampling2.lean
QC-016	Teleport	verify_teleport	qc_teleport	alice=01 corrections=00 bob=01	catalog
QC-017	Superdense	verify_superdense	qc_superdense	bits=11 decoded=11	catalog
QC-018	Bell	verify_bell_measurement	qc_bell	ab=00 class=00	catalog
QC-019	Topological word	verify_topological_word	qc_topo	word=Z2_a2b q=0 r=1	Study 13

bash clients/math-court-mcp/prove-live-court.sh
swift test --package-path LatticeRender --filter QCCourtLaw

---

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 — discrete vQbit transitions replace float amplitudes	Study 12	LAW FROZEN — 4/4 WIN
Connes Rigidity	High — group words → Eisenstein linking ((q,r))	Study 13	LAW FROZEN — 5/5 WIN
Riemann Hypothesis	Low — continuous complex plane + float zeta	—	REFUSED — architectural mismatch

---

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

---

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

---

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

---

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)).

---

Peer review

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