Masses Mass Genesis Load Rigidity Mass Law Load Realized Of Global Rigidity And

A shortcut to the mass law

The Recognition Science framework models physical objects as recognition events, a discrete record of occurrences. Its mass law states a relationship between a particle's rest mass and a quantity it calls predicted mass. The declaration massLawLoadRealized_of_global_rigidity_and_representatives is a theorem in the framework's machine-checked library of formal theorems. It establishes a sufficient condition for the mass law to hold for every stable closed pattern.

The theorem says: if two properties hold globally on a substrate, then the mass law is realized for every stable closed pattern. The first property is load rigidity: any two stable closed patterns with the same topology have the same integrated neutral load. The second is the existence of a factorized representative: for every stable closed pattern, there exists another stable closed pattern with the same topology whose site density has already been derived in the factorized mass-law form. The theorem then derives that the mass law load is realized for the original pattern.

This is a reduction. It says that to prove the mass law for all patterns, it suffices to prove rigidity and to construct one representative per topology class. The framework's library also derives the equality of rest mass and predicted mass from this same pair of hypotheses. The declaration is a formal theorem, not an empirical measurement or a definitional choice.

What the declaration does not claim is equally important. It does not assert that rigidity or the existence of representatives actually holds for any physical substrate. Those are separate targets, left open. It does not claim that the mass law itself is true; it only establishes a conditional path to it. It does not claim that the topology classes are finite or that the representatives are unique. The theorem is a bridge, not a destination.

theorem massLawLoadRealized_of_global_rigidity_and_representatives
    (hrigid : StableTopologyLoadRigidOn Λ)
    (hreps : FactorizedRepresentativeForEveryStableTopology Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ) :
    MassLawLoadRealized ψ :=
  massLawLoadRealized_of_rigidity_and_factorized_representative
    ψ hψ (hrigid ψ) (hreps ψ hψ)

theorem massLawLoadRealized_of_global_rigidity_and_representatives
    (hrigid : StableTopologyLoadRigidOn Λ)
    (hreps : FactorizedRepresentativeForEveryStableTopology Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ) :
    MassLawLoadRealized ψ :=
  massLawLoadRealized_of_rigidity_and_factorized_representative
    ψ hψ (hrigid ψ) (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 assert that rigidity or representative existence holds for any actual substrate. The theorem does not prove the mass law unconditionally; it only provides a conditional route to it. The theorem does not claim uniqueness or finiteness of topology classes.

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)

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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