Masses Mass Genesis Conditional Certificate Closed Pattern Mass Conclusion Of Co

The conditional certificate

The declaration establishes a conditional result in the Recognition Science framework. It proves that if a particular substrate, a collection of patterns, satisfies two structural assumptions, then a complete conclusion about mass follows. The theorem is named closedPatternMassConclusion_of_conditional_assumptions and lives in the framework's machine-checked library of formal theorems.

The two assumptions are precise. The first, stable_topology_load_rigid, states that the stable topology of a pattern carries its load rigidly. The second, factorized_representatives, states that every stable topology has a factorized representative. Together they close the remaining proof burden for the M7 theorem surface on that substrate.

Under these assumptions, the theorem proves that for any admissible readout and any stable closed light pattern, the readout's inertial mass equals its gravitational mass, and both equal the rest mass. It also proves that the rest mass equals the predicted mass from the framework's mass law. This is the full M1 theorem surface, assembled conditionally.

The theorem does not claim the global MassGenesisCertificate is closed. The two assumptions remain unproved in general; the theorem only shows what follows if they hold. The remaining proof burden is the bottom-up derivation of topology-class load rigidity and factorized representatives. The conditional certificate is a scaffold, not the final building.

/-- Conditional assembly of `ClosedPatternMassConclusion` for one pattern. -/
theorem closedPatternMassConclusion_of_conditional_assumptions
    (A : ConditionalMassGenesisAssumptions Λ)
    (readout : PatternMassReadout Λ)
    (ψ : LightPattern Λ) :
    ClosedPatternMassConclusion readout ψ := by
  intro hψ hreads
  exact
    ⟨fun k => integratedMeaningLoad_evolve_invariant ψ k,
     restMass_pos_of_stable ψ hψ,
     phiRungQuantized_of_stable ψ hψ,
     rest_mass_eq_mass_law_from_conditional_assumptions A ψ hψ,
     hreads.1,
     hreads.2⟩

theorem rest_mass_eq_mass_law_from_conditional_assumptions
    (A : ConditionalMassGenesisAssumptions Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ) :
    restMass ψ = predictedMass ψ :=
  restMass_eq_predictedMass_of_global_rigidity_and_representatives
    A.stable_topology_load_rigid
    A.factorized_representatives
    ψ hψ

structure ConditionalCertificateAssemblyCert where
  rest_mass_field :
    ∀ {Λ : Type*} [Fintype Λ] [DecidableEq Λ]
      (_ : ConditionalMassGenesisAssumptions Λ)
      (ψ : LightPattern Λ),
      StableClosedLightPattern ψ →
      restMass ψ = predictedMass ψ
  theorem_for_readout :
    ∀ {Λ : Type*} [Fintype Λ] [DecidableEq Λ]
      (_ : ConditionalMassGenesisAssumptions Λ)
      (readout : PatternMassReadout Λ),
      MassGenesisTheoremFor readout

What this page does not claim

The two structural assumptions are proved in general. The global MassGenesisCertificate is closed. The theorem applies to substrates that do not satisfy the two assumptions.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Masses/MassGenesis/ConditionalCertificate.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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