— P = e^−S via Cauchy-Ostrowski from A2 + A4 + codomain (A3 proven redundant, August 2026: the system compresses from three axioms to two); machine-verified in Lean 4 (13 August)
— δS = 0 as consequence of P = e^−S
— Born rule P = |ψ|² as third output of the same machine (composition + branching consistency; conditions named explicitly)
— Path integral Z = ∫Dx·e^−S as quantum extension
— Equivalence with Boltzmann, Feynman, Jaynes (structural)

— χ ∈ 24ℤ via Rokhlin's theorem
— χ = 24 via modular invariance (η(τ)²⁴ unique)
— K3 uniqueness via Kodaira-Enriques classification
— Betti numbers K3: (1,0,22,0,1), χ=24 confirmed

— N ≥ 3 via CKM + Jarlskog (CP-violation required)
— N = 3 as K-minimum under CP lower bound (retracted 2026: the K-minimum gives N = 1; the number 3 is address, 10 bits — see testing)
— Higgs stability breaks at N ≥ 4 (I-penalty)

— SM + ν_R unique within the explored universe of finite geometries, under gates frozen in advance and the measurements as referee
— Hypercharges from the consistency requirements themselves
— Theorem S′: the first-order condition forces module maps, embedded leptons force y_d = y_e: Pati-Salam and SU(5) eliminated by the measured bottom-tau ratio
— Seesaw window checks out: M_R from the measured neutrino mass falls mid-window, independently predicted

— E = S + K + I decomposition lemma (orthogonality proven and machine-verified, 13 August; the identification of the terms remains motivated)
— α_K = ln 2 and α_I = ½ forced (Levin maximality resp. Laplace integral; conditions named, 12 August): zero free weight parameters
— Self-consistency f(EE) = EE operational (Einstein-Hilbert + MDL + Hessian are unique choices in their own domain)

— Radiative stability of Λ via 4-form sequestering (structural argument, no numerical meV⁴)
— χ/8 = 3 topological suggestion for N_gen (suggestive, formal closure via ∫c₃ open)

— Observer gates reduced to one core G* (stable rewritable self-representation), self-validating; neutron-star backdoor triple-locked
— Arrow of time as measure preference for compressible initial conditions
— Anarchy reading of the neutrino sector (ordering, mass sum, m_ββ, δ_CP with frozen numbers)
— Local/a-local distinction: the measure weighs a-locally over structures, the law works locally per step; our four misses shared precisely this level confusion

Settled in 2026. The number: not derivable; three pre-registered attempts (unification matching 11% off; selection route wrong gauge group; weight-function route factor 9 off), derivation retracted; α is an address coordinate, typical within the observer window. The structure: stronger than expected; observer-conditioned K-minimisation uniquely selects SM + ν_R, with Majorana neutrinos as the guillotine prediction. Status: number retracted, structure derived; see testing, section 2. Addition (12 August, night): the delegation stake bounds the window from below via local fixed-point consistency (α⁻¹ ≳ 75-90); see the verification page.

Pattern follows from K3 topology: ≤ 42 modes, Casimir ratios, tensor polarization, spectral gap. Absolute frequency depends on stabilization mechanism (KKLT/LVS/uplift), which itself is not a unique EEML prediction. Status: pattern falsifiable, scale scenario-dependent.

— Strict proof of orthogonality in decomposition lemma (completed 13 August: three theorems plus corollary in Lean, Orthogonaliteit.lean; see mathematics, Theorem 4.2)
— Formal dynamics W=0 → W>0 (dissolved August 2026: open problem 11.2 resolved via timelessness + measure preference; see mathematics)
— Exact numerical values α_K, α_I (forced 12 August: ln 2 and ½; see mathematics)
— Machine verification of the core theorem in Lean (completed 13 August: Kern.lean, zero errors; monotonicity derived rather than assumed)
— Explicit calculation of a₆ on Fermat K3 (measured July 2026: a₆ = −0.71 ± 0.02, three seeds, validated curvature engine)
— Yukawa hierarchy: the law-address analysis is done (13 August: ~95 bits as bare address against 39-49 bits for a texture mechanism: the framework bets on structure; see verification page). The concrete texture within K3 stays open: it requires a generation-bundle choice that is not fixed

The living register lives on the verification page: over twenty frozen stakes with failure conditions, including the guillotine (Majorana), the anarchy series (ordering, mass sum, m_ββ, δ_CP with numbers), three structure stakes (no proton decay, no light steriles, no Lorentz violation), the quantum and cosmology stakes, and one meta-stake that makes the law-address boundary itself falsifiable: an accepted first-principles derivation of α would break the address reading. In addition the delegation stake: local fixed-point consistency (asymptotic safety) bounds address coordinates rather than fixing them; for α: α⁻¹ ≳ 75-90, a gain of 0.15-0.27 bits. The two stakes cover each other's flanks.

It comes with an expectation calendar 2026-2030 (per experiment: what EEML says and what the other outcome means) and external verifiability: SHA-256 fingerprints in the changelog plus snapshots at the Internet Archive. The track record counts the misses too: three α falsifications and one Zipf miss stand documented.