A Machine-Checked Lean 4 Formalization of the UV–IR Architecture and Constructive Polymer Contraction for 4D Quantum Yang–Mills: Bridging Sussman–Alpöge's Bałaban Continuum Limit (Theorem 0 & Theorem A) and Osterwalder–Seiler / Kotecký–Preiss Mass Gap Bounds (v38.0.0)

@misc{v12162026machinechecked,
  title = {{A Machine-Checked Lean 4 Formalization of the UV–IR Architecture and Constructive Polymer Contraction for 4D Quantum Yang–Mills: Bridging Sussman–Alpöge's Bałaban Continuum Limit (Theorem 0 & Theorem A) and Osterwalder–Seiler / Kotecký–Preiss Mass Gap Bounds (v38.0.0)}},
  author = {solidSF Research Team: using Jesse v1.2.16},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23591906},
  url = {https://zenodo.org/records/23591906},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - A Machine-Checked Lean 4 Formalization of the UV–IR Architecture and Constructive Polymer Contraction for 4D Quantum Yang–Mills: Bridging Sussman–Alpöge's Bałaban Continuum Limit (Theorem 0 & Theorem A) and Osterwalder–Seiler / Kotecký–Preiss Mass Gap Bounds (v38.0.0)
AU  - solidSF Research Team: using Jesse v1.2.16
PY  - 2026
DA  - 2026/10/23
PB  - Zenodo
DO  - 10.5281/zenodo.23591906
UR  - https://zenodo.org/records/23591906
AB  - Version 38.0.0 (Concrete SU(2) Haar Extracted Remainder Single-Link & Two-Link Mixed-Difference Oscillation wilsonAction_oscillation_of_agree_off_link / haarBlockedFiberWeight_singleLink_ratio / haarBlockedFiberWeight_singleLink_quotient_bounds / haarBlockedEffectiveAction_singleLink_oscillation / haarSupportedBlockDisintegration / wilsonAction_one_updateGaugeLink_oscillation_le_twelve / haarExtractedCoarseRemainder_singleLink_oscillation_and_twoLink_mixedDifference, Untruncated Mixed-Degree (0, 2) OS Reflection Positivity vs. Truncated Hierarchy untruncatedMixedDegreeZeroTwoGramForm / untruncatedMixedDegreeZeroTwoGramDet / untruncatedMixedDegreeZeroTwoGramForm_psd_and_det_eq_variance_sq, Complete Vacuum-Orthogonal Hilbert-Space Semigroup Contraction & Hidden-Mode Exclusion completeVacuumOrthogonalSemigroup_contraction_excludes_hidden_low_energy_eigenstate, Unified v38_actual_haar_remainder_mixed_os_and_complete_hilbert_gap_synthesis, 1B-Deep 10-Wide Jesse Swarm on the Twelve Physical Obligations P01..P12, Concrete SU(2) Haar Dyadic Fiber Disintegration haarBlockKernel / haarBlockDisintegration / haar_wilsonBlockedMeasure_density / haar_wilson_integral_disintegration / haar_wilsonBlockedMeasure_zero / dyadicFiberFineLink1 / dyadicFiberFineLink2 / dyadicFiberFineLink_mul_reconstructs_coarse_and_changes_one_fine_link / SupportedBlockFiberDisintegration / supportedBlockFiberDisintegration_partition_and_pushforward_and_dirac_rejection, Elementary 12β Fiber Weight-Ratio & Weak-Coupling Growth elementary_dyadic_fiber_twelve_beta_weight_ratio_and_weak_coupling_growth, Distance-Weighted Spatial Dobrushin Row Norm &Carried-Forward Remainder Iteration distanceWeightedDobrushinRowSum / distanceWeightedDobrushinRowSum_implies_exponential_spatial_decay_and_locality_diagnostic / iteratedCoarseEffectiveAction / iterated_blocking_requires_remainder_carryForward_and_growing_depth_error_bound, OS Mixed-Degree Gram Indefiniteness, 45° Continuous Rotation & Alternating-Window 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/ supportMultiplicity_polymer_bounds_pairwise_dobrushin_row_sum, Two-Link Mixed Second Differences & Finite-Fiber Partition Integral updateTwoGaugeLinks / twoLinkMixedDifference / twoLinkMixedDifference_eq_zero_of_independent_and_oscillation_bound / wilsonBlockedEffectiveAction_twoLinkMixedDifference_from_fiber_crossRatio / finiteFiberEffectiveAction_oscillation_derived_from_fine_action_lip, Normalized Killing–Ricci Floor vs. Factor-of-4 Unnormalized Overstatement unnormalized_dualCoxeter_floor_is_four_times_ricci_floor, Dobrushin-Weighted Quadratic Form Coercivity vs. Zero-Form Negative Control dobrushin_scalar_landing_alone_does_not_force_zero_form_coercivity / dobrushinWeightedQuadraticForm_derives_prelimit_coercivity_and_transfers, Countable-Series Källén–Lehmann Coercivity & Derived Geometric Cauchy Convergence tsum_infinite_tower_kallen_lehmann_coercivity / cauchySeq_and_limit_bounds_of_geometric_correlator_contraction, Single-Link Gauge Perturbations & Derived Fiber-Ratio Oscillation Bounds updateGaugeLink / updateGaugeLink_same_and_other / wilsonBlockedNormalizedEffectiveAction_link_oscillation_from_fiber_ratio / extractedCoarseRemainder_link_oscillation_bound, Mandatory Single-Link Oscillation Enforcement in CoarseRemainderInfluenceContract, Detached-Influence Rejection & Polymer-Sum Influence Derivation detached_linkInfluence_rejected_by_oscillation_bound / polymerSumRemainder / derivedPolymerLinkInfluence / derived_polymer_linkInfluence_bounds_oscillation_and_constructs_contract, Arbitrary-N-Mode Källén–Lehmann Spectral Coercivity & Joint Thermodynamic/Continuum Correlator Limit multiModeSpectralEnergyForm / multiModeSpectralNormSq / multiMode_kallen_lehmann_hamiltonian_gap_coercivity_and_infinite_tower_bridge / joint_thermodynamic_and_continuum_correlator_cauchy_and_nontriviality, Dobrushin-Derived Pre-Limit Gap Transfer & All-Group Coverage dobrushin_landing_tube_derives_prelimit_gap_and_transfers_to_continuum / all_compact_simple_gauge_groups_ricci_and_holley_stroock_gap_floor / unifiedPhysicalWilsonBlockingModel_derived_oscillation_and_all_group_synthesis, Single Physical-Model Binding UnifiedPhysicalWilsonBlockingModel / unifiedPhysicalWilsonBlockingModel_master_bridge / dimensionlessStrongCouplingGap_div_eq_strongCouplingMassGap, One-Step Blocked-Wilson Effective-Action Decomposition & Strict Positivity on All of GaugeConfig L LinearPlaquetteCouplingExtractor / effectiveActionDecomposition_unique_of_linearExtractor / wilsonBlockedFiberWeight_bounds_and_pos_all_configs / one_step_wilson_blocking_effective_action_decomposition_and_weight_factorization, Link-Pinned Polymer Influence & Inductive Multi-Step Tube Invariance naive_global_block_action_bound_diverges_with_volume / coarseTotalDobrushinRowSum_uniform_bound / inductive_interaction_class_remainder_envelope_and_routeA_feed, Quantitative IR Scale-Locking & Two-Sided Spectral-Window Control unlocked_ir_scale_drift_collapses_physical_gap /…
ER  -