Masses Mass Genesis Load Rigidity Rest Mass Eq Predicted Mass Of Global Rigidity

Mass from topology

In the Recognition Science framework, a ledger is a discrete record of recognition events, and a stable closed pattern is a self-consistent arrangement of such events. The theorem restMass_eq_predictedMass_of_global_rigidity_and_representatives states that if every stable pattern in a topology class is load-rigid, and if each such topology has a representative whose site density is already known in a factorized form, then for any stable pattern the rest mass equals the predicted mass. The proof is a chain of two implications: rigidity plus a representative yields the mass-law load, and that load realization closes the rest-mass equality.

The two assumptions are named StableTopologyLoadRigidOn and FactorizedRepresentativeForEveryStableTopology. The first says that any two stable patterns with the same topology have the same integrated neutral load. The second says that for every stable pattern, there exists another stable pattern with the same topology whose site density has already been derived in the factorized MassLaw form. Together they allow the theorem to conclude that the rest mass of any stable pattern equals its predicted mass, without ever referring to a measured mass value.

This is a reduction result, not a numerical prediction. It does not say which topologies are load-rigid, nor does it construct the factorized representatives. Those are separate targets. The theorem only establishes that if those two conditions hold, then the mass equality follows. The proof is machine-checked in the framework's library of formal theorems, with no unverified axioms beyond the standard ones of the ambient type theory.

What this means in practice is that the difficult work of deriving particle masses is shifted to two cleaner problems: proving rigidity for each topology class, and constructing one factorized representative per class. The theorem guarantees that solving those two problems is sufficient. It does not claim that the problems are solved, nor that the framework has already predicted any specific particle mass.

theorem restMass_eq_predictedMass_of_global_rigidity_and_representatives
    (hrigid : StableTopologyLoadRigidOn Λ)
    (hreps : FactorizedRepresentativeForEveryStableTopology Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ) :
    restMass ψ = predictedMass ψ :=
  restMass_eq_predictedMass_of_load_realized ψ hψ
    (massLawLoadRealized_of_global_rigidity_and_representatives
      hrigid hreps ψ hψ)

/-- Global substrate-level version of the rigidity target. -/
def StableTopologyLoadRigidOn (Λ : Type*) [Fintype Λ] [DecidableEq Λ] : Prop :=
  ∀ ψ : LightPattern Λ, StableTopologyLoadRigidAt ψ

/-- Global substrate-level representative target. -/
def FactorizedRepresentativeForEveryStableTopology
    (Λ : Type*) [Fintype Λ] [DecidableEq Λ] : Prop :=
  ∀ ψ : LightPattern Λ,
    StableClosedLightPattern ψ →
      FactorizedSameTopologyRepresentative ψ

theorem restMass_eq_predictedMass_of_global_rigidity_and_representatives
    (hrigid : StableTopologyLoadRigidOn Λ)
    (hreps : FactorizedRepresentativeForEveryStableTopology Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ) :
    restMass ψ = predictedMass ψ :=
  restMass_eq_predictedMass_of_load_realized ψ hψ
    (massLawLoadRealized_of_global_rigidity_and_representatives
      hrigid hreps ψ hψ)

What this page does not claim

The theorem does not prove that load rigidity holds for any specific topology. The theorem does not construct factorized representatives for any topology. The theorem does not predict a numerical value for any 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/LoadRigidity.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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