Lean 4 formalizations of GUMP claims. Executed. Logged. No hand-waving.
| Package | Key results | Status |
|---|---|---|
| E7 Uniqueness E7Uniqueness.lean |
S(E7) = dim + max Kac = 137, unique among all ADE algebras. Gaussian norm 4²+11²=137. Pythagorean triple (105, 88, 137). McKay data. See theorem → | THEOREM |
| Quantum / ALE QuantumErrorCorrection.lean ALESpectralConjecture.lean |
Surface code qubit counts (d3=17, d5=49, d7=97). Willow 0.14% below 1% threshold. ALE spectral conjecture target. Kuramoto-QEC mapping. See page → | VERIFIED |
| Prime / Landauer / Alpha PrimeBounceDispatch.lean ComputationFloor.lean AlphaFixedPointHierarchy.lean |
M4 hardware factorizations (10=2×5, 6=2×3, 32=2&sup5;). 9.12× trampoline theorem. 224,000× grokking cost ratio. Alpha fixed point at 210 GeV (14.7% gap documented). Prime → Landauer → | VERIFIED |
| MC1R: DNA Coupling DNACouplingGraph.lean |
DNA at the MC1R locus as a weighted contact graph (Thakur melanocyte Hi-C). Fiedler value R = 0.7001 (WT). Weyl bound proved: |ΔR| ≤ 2δ for single-edge perturbation. rs3212363 ΔR = +0.0066 inside window (< 0.01). rs3212361 ΔR = +0.0035 inside window. Anesthesia reduction: lidocaine >25%, bupivacaine >18% (norm_num). Regime detector empirical (negative K-damage corr → retuner). Open: MC1R-TUBB3 splice-ratio experiment. See page → | VERIFIED |
| Full Stack 2026 FineStructure.lean (root) |
Master aggregator imports all 29 modules (corrected 2026-07-10 from a stale “30” that disagreed with this same page's own count below): E7 + killed paths + QEC + Music + Prime/Landauer + Electroweak + Cancer + MC1R/DNA + Gravity + Bio/Proton/2O + Reversible + Grace + Cross-domain + Shroud kills + Gravity kills + 2O three-term conjecture. One lake build for the complete regime. |
VERIFIED |
| Flush Round — Bio / Proton / 2O BioMisfolding.lean ProtonDecayPrediction.lean TwoOCharacterData.lean |
Bio misfolding inverse rule across ALS-FUS, Alzheimer’s Aβ42, Parkinson’s α-synuclein: add charge to sticky surfaces reduces aggregation. 798 mutations screened (10/10 top stabilizers add charge). K-decay 0.85→0.40 aging model. Proton decay p→e¹π° at ~1.1×10&sup4;° yr with explicit falsifiers. 2O group data: 48 elements, 8 conjugacy classes, McKay ↔ affine E7(1). E7/2O ALE spectral det explicitly OPEN. | VERIFIED |
| Flush Round — Reversible / Grace / Cross-domain ReversibleLandauer.lean GraceConsciousnessGate.lean CrossDomainPredictions.lean |
Reversible computing: 224,000× grokking advantage, lysozyme 87 bits = 150 kJ/mol exact, 408× adiabatic sweet spot at 840 ps, theoretical combined 3,721×. Grace gate: R = 1/φ as consciousness threshold. Cross-domain ledger: Ngen=3 as best Λ match, 315-culture convergence, electroweak vev α8 fixed point. | VERIFIED |
| Flush Round — Killed Claims + 2O Cycle 9 ShroudKilledMechanisms.lean GravityKilledClaims.lean ThreeTermConjecture.lean |
Shroud killed mechanisms: 13 explicit energy shortfalls (108× to 1072×) — the largest single explicit graveyard list on the site. Gravity kills: frame-dragging-as-Kuramoto and dark matter as Landauer heat. Three-term conjecture: Cycle 9 decomposition of the 2O spectral determinant into resolution (G/h = 48/18) + orbifold (full McKay char proj) + intrinsic cross-term. 29 modules total. 3,317 jobs. Clean. | VERIFIED |
git clone https://github.com/LacobusGump/music2.0
cd music2.0/fine_structure
lake build
# Build completed successfully — 3,317 jobs
curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh — then lake build handles the rest. Real numericals (ℝ literals) are validated via gump + mpmath cross-checks documented in the package logs. Source: github.com/LacobusGump/music2.0/tree/main/fine_structure
Lean verifies logical and arithmetic structure: that 133 + 4 = 137, that no An or Dn algebra achieves S = 137, that the surface code formula gives the right qubit counts. It does not verify the physical interpretations (that primes actually avoid GPU collisions, that the ALE geometry maps to α). Those claims are backed by measurement and the killed-ideas ledger. Machine verification applies to the math. The physics is documented separately.