Masses Mass Genesis Conditional Certificate Mass Genesis Theorem For Of Conditio

The conditional certificate

In the Recognition Science framework, mass is not an input but a derived quantity: the framework models a physical system as a discrete ledger of events, and the rest mass of a stable pattern is what the ledger's accounting forces it to be. The declaration massGenesisTheoremFor_of_conditional_assumptions is a machine-checked theorem in the framework's library of formal theorems. It states that if two named structural assumptions hold on a substrate, then every admissible mass readout satisfies the complete mass-genesis theorem surface, meaning rest mass equals predicted mass and inertial mass equals gravitational mass for every stable closed light pattern.

The two assumptions are stable topology load rigidity and factorized representatives for every stable topology. The first says that the topology of a stable pattern carries its load rigidly, with no slack; the second says that every such topology can be represented as a product of simpler factors. The theorem assembles these into a conditional certificate: it proves that the entire mass-genesis conclusion follows from those two premises. The proof is a direct composition of earlier lemmas, and the certificate structure records both the rest-mass equality and the theorem-for-readout surface as a single packaged result.

What the theorem does not claim is just as important as what it proves. It deliberately does not close the global mass-genesis certificate. The two assumptions remain open proof obligations, not established facts. The theorem is a bridge, not a destination: it shows that the remaining work is exactly to prove those two assumptions on the substrate. The framework's own documentation is explicit on this point, stating that the module assembles the theorem surface from the remaining assumptions and does not claim the global certificate is closed.

The practical consequence is a sharpened research target. Anyone working inside the framework now knows precisely which two lemmas, once proved, would complete the mass-genesis theorem for the substrate in question. The conditional theorem converts an open problem into a finite checklist, and that is what makes it valuable: it does not manufacture mass from nothing, but it does map exactly where the missing physics must be supplied.

/-- Fixed-substrate conditional Mass Genesis theorem. Once M7's two remaining
assumptions are proved on `Λ`, every admissible readout satisfies the original
M1 theorem surface. -/
theorem massGenesisTheoremFor_of_conditional_assumptions
    (A : ConditionalMassGenesisAssumptions Λ)
    (readout : PatternMassReadout Λ) :
    MassGenesisTheoremFor readout := by
  intro ψ
  exact closedPatternMassConclusion_of_conditional_assumptions A readout ψ

/-- Fixed-substrate conditional Mass Genesis theorem. Once M7's two remaining
assumptions are proved on `Λ`, every admissible readout satisfies the original
M1 theorem surface. -/
theorem massGenesisTheoremFor_of_conditional_assumptions
    (A : ConditionalMassGenesisAssumptions Λ)
    (readout : PatternMassReadout Λ) :
    MassGenesisTheoremFor readout := by
  intro ψ
  exact closedPatternMassConclusion_of_conditional_assumptions A readout ψ

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, only assumed. The global mass-genesis certificate is closed. The theorem derives the value of any specific particle mass.

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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: