UGP/GTE Lean formalization

Lean 4 software archive for the UGP Physics / GTE program: Lean Ugp. This Zenodo record bundles a pinned Git snapshot of the formalization (382 modules — all CatAL results independently machine-verifiable; named axioms: rcc_physics_ax, rule110_simulates_computable, simultaneous_dual_tape_ax, which appear only in CatAD chains, not in any CatAL proof chain). All core modules zero sorry; named axioms: rcc_physics_ax, rule110_simulates_computable, simultaneous_dual_tape_ax. Exact file scope and revision policy appear in the repository manifest shipped with the archive. June 2026 completions (Rounds 81–83D): FKTT eta_B baryon asymmetry CatAL (6.109e-10, +0.15 sigma); pion mass m_pi = 139.57 MeV CatAL (GOR+condensate, -0.001% from PDG); all three PMNS mixing angles closed CatAD (sin^2 theta_12=4/13, sin^2 theta_23=19/42, sin theta_13=11/73); m_tau structural prediction v_H/(98*sqrt(2)) disclosed (-2.42 sigma). Additional CatAL theorems: phimdl_potential_su2l_invariant (SU(2)_L weak force, zero named axioms — all four forces CatAL); mdl_tower_bundle; particles_computation_spacetime_trinity (PCT Trinity); gte_polynomial_five_roles_k_extra_zero (Single-Source Principle); psc_enumeration_forces_ngen_3 (exhaustive 34,560-universe PSC scan, native_decide); incompleteness_implies_nonzero_omega_lambda (PSC→Omega_Lambda > 0). Z7InvariantSubsets graduation (10 theorems, zero sorry): p_poly invariant subset classification (exactly {0}, {0,1}, Z_7), Rule 110 unique maximal proper invariant sub-CA, QNR Binary Floor — N_fam=5 being a quadratic non-residue mod 7 uniquely explains {0,1} as the binary floor. Round 98 graduation (2026-06-09, 8702 build jobs, zero sorry): GTECausalTree.lean (8 theorems — perfectTree_numNodes, gte_rulegte_ten_generations certifying 1023 events at depth 10, perfectTree_horton_ratio, gte_causal_tree_summary); PolyExplorations.lean (35 theorems — poly_p_uniform_gs_roots, poly_p_diagonal_factorization, period_475_is_minimal, four_object_GTE_pairwise_distinct, T_b_output_not_determined_by_mod7, poly_p_vacuum_basin_card_eq_52, and others); NgenThreeMechanismsUnified.lean (N_gen=3 three-mechanism unified certificate); CUP3DUniqueness.lean additions (gen2_outer_positions_constant, gen3_outer_positions_constant, gen2_gen3_topology_degenerate). Round 100 graduation (2026-06-09, zero sorry): MDLThreeLevelUnification.lean — P51 OP3 closed: three-level MDL Tower non-circularity machine-certified; polynomial p connects Level 1 theory selection, Level 2 PMDL dynamics, and Level 3 Born-rule adjudication in a single non-circular derivation. Wave-2 graduation (2026-06-11, commit d989f57, 8728 build jobs, zero sorry): TriangleLiftTheorem.lean + TriangleLiftStructural.lean — Direct-Interpolation Lift (ugp_orbit_interpolation_lift): the GF(7) rule is uniquely determined from UGP orbit data alone; sparsity floor CatAL; chirality census (orbit_chirality_census): exactly {Rule 110, Rule 124} survive ordering-by-chirality, CatAL. SpinSevenWallSpectroscopy.lean (14 theorems — directed wall/bump spectroscopy, exact gap law). CMCAPhysicalPoint.lean (8 theorems — tape spacing a=hbar*c/Lambda_GTE derived, xi_kink=|Z_7|=7, Boundary Equivalence Theorem). tape_saturation_theorem (Tape Saturation Theorem CatAD | CSC, criterion proven minimal via Boundary Equivalence). ParityProjectionBattery, ParityProjectionForcing (777-form + 16807-recoding censuses). gte_trajectory_two_tile_containment + gte_two_tile_compilation_theorem. planck_eft_blocking_ratio + hosting_boundary_csc_equivalence. pmdl_carrier_pricing_chain (TemporalVoxelCC). GTECompilation (register-machine trajectory containment). Total: 334 modules. Wave-3 graduation (2026-06-13, commit ef22e9d, 8764 build jobs, zero sorry): PSL(2,7) algebraic unification suite — f21_is_borel_psl27, pgl27_generated_by_singer_and_borel, psl27_is_aut_fano, f21_regular_on_fano_flags (F_21 as Borel subgroup and flag-transitive group of the Fano plane); A4/Eisenstein suite — eisenstein_a4_from_inert_2, gte_manifest_flavor_is_s3_in_a4 (A4 from inert prime 2 in Z[omega], S3 <= A4 as leading-order neutrino flavor group); klein_quartic_genus_eq_n_gen (Klein quartic genus = N_gen = 3, CatAL); va_op6_bundle (g_A/g_V = -1 exactly from F_21 -> SU(2)_L doublet structure, CatAL); C2 selector closure — d1_d5_forces_gibbs_family, c2_selector_member_independent (D4+D5 pin selector to Born-rule state, member-independent over [D], CatAL); golden_universality_class_theorem (golden-fiber taxonomy, CatAL); lambda_all_order_zero_pure_phi (Lambda=0 all-order in pure-phi sector, CatAL); spin7_soft_spectrum_converges_kink (spectral continuum limit, CatAL); landauer_heat_floor_transputation (Landauer heat floor, CatAL); and others. Total: 361 modules. Wave-4 graduation (2026-06-14, zero sorry): VacuumGHConvergence.lean — OQ-QG-1a CLOSED CatAL: vacuum CMCA spatial causal graph converges in Gromov-Hausdorff distance to flat R^3 (vacuum_cmca_gh_converges_to_flat_space, quantitative bound ghDist(FinGrid L, UnitCube) <= 1/L, proven via grid_coord_error, unit_cube_near_grid_point, fin_grid_gh_dist_bound using ghDist_le_of_approx_subsets); MatterGHPrecompactness.lean — single-kink flat-limit theorem CatAL (single_kink_gh_converges_to_flat: isolated kink GH-converges to R^3, finGrid_family_totally_bounded); SU2LDoubletHilbert.lean — SU(2)_L doublet Hilbert space CatAL (su2l_doublet_hilbert_certified: DoubletSpace = EuclideanSpace C (Fin 2), orthonormal neutrinoState/electronState doublet partners, SU(2)_L generators T_1/T_2/T_3 certified as Pauli/2 representation). Total: 364 modules. EPIC_091 graduation (2026-06-15, commits 4afbf1a + 213d5a6, zero sorry): GTE arithmetic fully derived from Z_7×Z_3 algebraic structure — ridge constant 16 = 2^(1+ord_7(2)) derived via CRT (gt001_gt009_ridge_closed); quotient gap 13 = F_7 where index k*=ord_7(2)+N_c+1 from field structure (gt012_gap_from_z7_z3); Fibonacci lift uniquely forced by quotient-gap constraint (gt011_ridge_offset_eq_pisano_7); a-values {1,9,5} as orbit projections not hardcoded (semantic_floor_a_condition_from_cascade); even-step c-prime = 2^(n+2Nc)−1 uniquely selected by double-Fibonacci minimality (mersenne_ladder_uniqueness_proved); N_c=3 → b_1=73 as theorem (gt013_psc_nc_bundle); circle closure — PSC+ridge (Chain A) and MDL+Z_7×Z_3 (Chain B) independently derive the same polynomial p (ugp_orbit_interpolation_lift extended). Five new modules: GTE/RidgeDerivation.lean, GTE/FibonacciDerivation.lean, GTE/SemanticFloorDerivation.lean, GTE/MersenneLadder.lean, GTE/PSCColorRankBundle.lean. Total: 368 modules. Round 7 graduation (2026-06-15, commits ea84a74 + dc6cf79, zero sorry): 8 new modules certified — UgpLean.Gravity.ClassicalLambda (classical_lambda_zero: phimdl_vacuum_energy = 0, zero sorry); UgpLean.Universality.EWRhoCorrectedMZ (m_Z_rho_corrected_interval, CatAD, ρ-parameter EW correction, pole mass 91.2±0.1 GeV); UgpLean.Universality.AlphaEMArchivalIdentities; UgpLean.Universality.Phi7UnificationTheorem; UgpLean.GTE.MobiusTripleClassification; UgpLean.GTE.PolynomialLipschitz; UgpLean.QM.BilinearNeutrinoNoGo; UgpLean.QM.KahlerStateManifold; UgpLean.Spacetime.EntanglementAreaLaw; UgpLean.Spacetime.LorentzianCausalityNecessity; UgpLean.Universality.IMTStructuralPair. Wolfenberg → Weinberg theorem rename (m_Z_gte_from_weinberg); 20 CatAL certifications graduated from exp to canonical. Total: 382 modules. Octonion certificate cluster graduation (2026-07-05, commit 7a7dc20, zero sorry): 10 new modules formalizing the P55 octonionic shadow — OctonionShadowInterface.lean, HurwitzCosetCertificate.lean, G2StabilizerCertificate.lean, TrialityInterface.lean, OctonionColorFlavorDisambiguation.lean, KinkSigmaParityAction.lean, KinkSectorTrialityAction.lean, PhiMDLZeroModeIndex.lean, BraidAtlasPhaseEquivariance.lean, SeesawTrialityPinning.lean; plus pre-existing SeesawNumericalCerts.lean (11 modules certified by P55 Appendix B); 174 theorems, zero sorry; Assumption C9 (Cartan-Killing classification) added; formalization paper updated to 145 pages. Total: 392 modules. Every CatAL result independently reproducible via: lake build. Cite using the Zenodo DOI after publication.