Masses Mass Genesis Conditional Certificate Conditional Certificate Assembly Cer

The conditional certificate

In physics, a certificate is a formal guarantee: a machine-checked proof that a set of assumptions leads to a stated conclusion. The declaration ConditionalCertificateAssemblyCert is exactly that, but with a condition attached. It assembles, from a specific set of assumptions, the full theorem surface of the Mass Genesis framework: the equality of rest mass and predicted mass, the identity of inertial and gravitational mass, and the quantization of mass on a phi-power ladder. The certificate is a structure, a formal object that packages these results together, and it is built from two component theorems.

The first component theorem, rest_mass_eq_mass_law_from_conditional_assumptions, proves that for any stable closed light pattern, the rest mass equals the predicted mass, given the assumptions. The second, massGenesisTheoremFor_of_conditional_assumptions, extends this to any admissible readout, establishing the full MassGenesisTheoremFor surface. The certificate itself, conditionalCertificateAssemblyCert, is the definition that combines these two theorems into a single package. It is a proof that the framework's mass theory is internally consistent, but only under a specific, named condition.

The condition is the key. The certificate requires two assumptions, collected in ConditionalMassGenesisAssumptions: stable topology load rigidity and factorized representatives for every stable topology. These are the remaining pieces of the M7 proof burden. The certificate does not prove these assumptions; it takes them as input. It deliberately does not claim that the global MassGenesisCertificate is closed. The certificate is a bridge that is complete, but it spans a gap that is still open on one side.

What this means in plain terms: the framework has a fully worked-out theory of mass, but it is not yet unconditional. The certificate shows that if two specific structural properties of the substrate hold, then the entire mass theory follows. The remaining work is to prove those two properties from first principles. The certificate is a precise statement of what is known and what is not, a map of the remaining proof burden rather than a claim of completion.

def conditionalCertificateAssemblyCert : ConditionalCertificateAssemblyCert where
  rest_mass_field := rest_mass_eq_mass_law_from_conditional_assumptions
  theorem_for_readout := massGenesisTheoremFor_of_conditional_assumptions

/-- Fixed-substrate assumptions that close M7 on this substrate. -/
structure ConditionalMassGenesisAssumptions (Λ : Type*) [Fintype Λ] [DecidableEq Λ] where
  stable_topology_load_rigid : StableTopologyLoadRigidOn Λ
  factorized_representatives : FactorizedRepresentativeForEveryStableTopology Λ

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 certificate does not prove the two assumptions it depends on. The certificate does not establish the global MassGenesisCertificate as a closed theorem. The certificate does not provide a physical derivation of mass from first principles; it only shows a conditional logical consequence.

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.

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