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 |
| Full Stack 2026 FineStructure.lean (root) |
Master aggregator imports all 26 modules: E7 + killed paths + QEC + Music + Prime/Landauer + Electroweak + Cancer + Gravity + Bio/Proton/2O + Reversible + Grace + Cross-domain. One lake build for the complete regime. 3,315 jobs. Clean. |
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. 26 modules total. 3,315 jobs. Clean. | VERIFIED |
git clone https://github.com/LacobusGump/music2.0
cd music2.0/fine_structure
lake build
# Build completed successfully — 3,315 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.