UGP Physics Lean — Physics application layer (Lean 4 formalization)
Year: 2026
Type: software
Abstract: Lean 4 software archive for the UGP Physics program: physics application modules formalizing gauge theory, EW structure, color dynamics, cosmology, and related results derived from the Universal Generative Principle. 382 modules total (ugp-lean) — all CatAL results independently machine-verifiable; formalization paper 142 pages. June 2026 completions (Rounds 81–83D): FKTT eta_B 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. Additional CatAL theorems: phimdl_potential_su2l_invariant (SU(2)_L weak force, zero named axioms — all four forces now CatAL); mdl_tower_bundle (MDL non-circularity at three nested levels); particles_computation_spacetime_trinity (PCT Trinity CatAL); gte_polynomial_five_roles_k_extra_zero (Single-Source Principle named theorem); psc_enumeration_forces_ngen_3 (34,560-universe PSC Layer I scan, native_decide — all 12 survivors N_gen=3); incompleteness_implies_nonzero_omega_lambda (PSC→Omega_Lambda > 0). Z7InvariantSubsets graduation (10 zero-sorry theorems certifying invariant subset classification for the GTE polynomial over Z_7, Rule 110 uniqueness as maximal proper invariant sub-CA, and QNR Binary Floor). Round 98 graduation (2026-06-09, 8719 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, 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; CUP3DUniqueness additions (gen2_gen3_topology_degenerate, CatAL). Round 100 graduation (2026-06-09, zero sorry): MDLThreeLevelUnification.lean — P51 OP3 closed: three-level MDL Tower non-circularity machine-certified. Wave-2 graduation (2026-06-11, commit d989f57, 8728 build jobs, zero sorry): TriangleLiftTheorem.lean + TriangleLiftStructural.lean (Direct-Interpolation Lift, sparsity floor, chirality census — ugp_orbit_interpolation_lift + orbit_chirality_census, CatAL); SpinSevenWallSpectroscopy.lean (14 theorems, exact wall/bump spectroscopy); CMCAPhysicalPoint.lean (8 theorems — tape spacing a=hbar*c/Lambda_GTE derived, xi_kink=|Z_7|=7, Boundary Equivalence Theorem, criterion proven minimal); tape_saturation_theorem (CatAD | CSC); ParityProjectionBattery + ParityProjectionForcing (777-form + 16807-recoding censuses); GTECompilation trajectory containment theorems. 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); A4/Eisenstein suite (eisenstein_a4_from_inert_2, gte_manifest_flavor_is_s3_in_a4); Klein quartic corollary (klein_quartic_genus_eq_n_gen, genus = N_gen = 3, CatAL); V-A coupling (va_op6_bundle, g_A/g_V = -1 exactly, CatAL); C2 selector closure (d1_d5_forces_gibbs_family, c2_selector_member_independent, CatAL); golden-fiber taxonomy (golden_universality_class_theorem, CatAL); cosmological constant (lambda_all_order_zero_pure_phi, Lambda=0 all-order in pure-phi sector, CatAL); spectral convergence (spin7_soft_spectrum_converges_kink, CatAL); Landauer heat floor (landauer_heat_floor_transputation, CatAL); and others. Total: 361 modules. Companion to the ugp-physics paper series (P00–P53). Wave-4 graduation (2026-06-14, zero sorry): VacuumGHConvergence.lean (OQ-QG-1a CLOSED CatAL — vacuum_cmca_gh_converges_to_flat_space: FinGrid L GH-converges to UnitCube at rate 1/L); MatterGHPrecompactness.lean (single_kink_gh_converges_to_flat CatAL); SU2LDoubletHilbert.lean (su2l_doublet_hilbert_certified CatAL — SU(2)_L doublet Hilbert space certified with orthonormal doublet partners and SU(2)_L generators). Total: 364 modules. EPIC_091 graduation (2026-06-15, zero sorry): GTE arithmetic fully derived from Z_7×Z_3 — ridge constant 16=2^(1+ord_7(2)) from CRT (gt001_gt009_ridge_closed); quotient gap 13=F_7 from field structure (gt012_gap_from_z7_z3); Fibonacci lift uniquely forced (gt011_ridge_offset_eq_pisano_7); a-values {1,9,5} as orbit projections (semantic_floor_a_condition_from_cascade); even-step c-prime uniquely selected (mersenne_ladder_uniqueness_proved); N_c=3 → b_1=73 (gt013_psc_nc_bundle); circle closure Chain A + Chain B (ugp_orbit_interpolation_lift). 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 — ClassicalLambda (classical_lambda_zero CatAL: vacuum energy = 0, zero sorry), EWRhoCorrectedMZ (m_Z_rho_corrected_interval CatAD, pole mass 91.2±0.1 GeV), AlphaEMArchivalIdentities, Phi7UnificationTheorem, MobiusTripleClassification, PolynomialLipschitz, KahlerStateManifold, LorentzianCausalityNecessity, IMTStructuralPair. Wolfenberg → Weinberg theorem rename complete. 20 CatAL certifications graduated from exp to canonical. Total: 382 modules. Formalization paper: 142 pages, 131 theorems. Vacuity remediation (2026-07-06, SPEC_408): 17 findings resolved across ugp-physics-lean, ugp-lean-exp, and rule110-lean — 13 with genuine strengthened Lean proofs, 4 as honest hygiene renames on genuinely-open research placeholders. Key corrections: CC-cancellation bundle (CCImpossibilityBundle) unconstrained no-antigravitating-sector claim corrected (a concrete counterexample under the repo's own stress-energy tensor definition exists; now disclosed as informal structural argument, not machine-certified); Cook's Rule 110 universality theorem (rule110_turing_universal_from_cook) rescoped to an honest conditional operational readback certificate (cook_operational_stage3_tm_microstep_readback); winding table forcing, isolated quark predicate, Yukawa overclaim, cobordism/gauge-vertex mismatch corrected. All builds clean (8313 jobs, zero sorry; 2 pre-existing unrelated sorry in GXT.U1DirectProof/GXT.LieExpSurjective noted out of scope).
Author: Spivack, Nova
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161055009
Cites:
Cited by:
Related to: