The supplied source contains the module IndisputableMonolith.Unification.YangMillsMassGap, which defines multiple theorems establishing the RS Yang-Mills mass gap on the φ-lattice (e.g., exact computation of J(φ), positivity, monotonicity, spectral gap for non-vacuum excitations, gauge bond costs, and sector asymmetry between non-abelian and abelian cases). The module docstring references a 'Complete Yang-Mills Mass Gap Certificate (QG-005)' in §10 and states that all theorems are proved with zero sorry. However, no declaration named yang_mills_gap_cert (or any theorem/def with that exact name) appears in the provided Lean source; the certificate section is truncated after listing high-level points and does not contain a formal statement or proof body for such a named item. Visible related declarations in the source include Jcost_phi_exact, massGap_pos, spectral_gap, gauge_mass_gap, vacuum_unique_zero_cost, mass_gap_asymmetry, and massGap_unfalsified. This specific named theorem is therefore not present.
Explain the Lean theorem `yang_mills_gap_cert` in module `IndisputableMonolith.Unification.YangMillsMassGap`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.
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- declaration named yang_mills_gap_cert
- full formal statement or proof body for the complete Yang-Mills mass gap certificate beyond the truncated docstring
recognition modules consulted
IndisputableMonolith.Foundation.AlexanderDualityIndisputableMonolith.Unification.YangMillsMassGapIndisputableMonolith.Unification.RecognitionBandGeometryIndisputableMonolith.Unification.RecognitionBandwidthIndisputableMonolith.Foundation.RealityFromDistinctionIndisputableMonolith.Mathematics.LanglandsFromRecognitionCostIndisputableMonolith.Measurement.RSNative.Calibration.SingleAnchorIndisputableMonolith.Foundation.RecognitionForcing