Masses Mass Genesis Pattern Readout Equivalence Pattern Single Source Identity W

The single-source identity

Inertial mass, the resistance of an object to acceleration, and gravitational mass, the strength of its response to a gravitational field, are classically distinct ideas. Their equality in everyday experience is so familiar that it is easy to forget it is a fact about the world, not a definition. In the Recognition Science framework, which treats reality as maintaining a discrete record of recognition events, this equality is not assumed. It is derived from a more basic premise: both kinds of mass are readouts of the same underlying cost.

The declaration pattern_single_source_identity_with_predictedMass is a theorem in the framework's machine-checked library of formal theorems. It states that for any stable, closed light pattern, if the inertial mass readout and the gravitational mass readout both draw from the same source, and if that source's rest mass equals a separately predicted mass, then both readouts equal that predicted mass. In plainer terms: if you have a theory where the two masses are forced to read the same cost channel, and you have a prediction for what that cost should be, then both masses are locked to that prediction. The theorem does not define the two readouts to be equal; it proves they must be, given the single-source structure.

The theorem's proof is a short chain of rewrites. It takes the single-source structure's two properties, that each readout equals the source's rest mass, and then uses the hypothesis that the rest mass equals the predicted mass. The conclusion follows by transitivity. This is not a numerical prediction of any specific particle mass. It is a structural result: it establishes the conditions under which two distinct physical quantities are forced to coincide, and it identifies the predicted mass as the common value they must take.

What the theorem does not claim is just as important. It does not say that any particular particle has any particular mass. It does not say that the predicted mass is correct, or that the single-source structure actually holds for any real pattern. Those are separate, empirical questions. The theorem only says: if the structure holds, then the equality follows. It is a conditional statement, a piece of logical machinery that becomes physically relevant only when its premises are met. The framework's library proves the conditional; it does not, in this declaration, establish the premises.

/-- If M7 is closed for the pattern, the two readouts also equal the
topology-derived MassLaw value. -/
theorem pattern_single_source_identity_with_predictedMass
    (T : PatternSingleSourceMassTheory Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ)
    (hM7 : restMass ψ = predictedMass ψ) :
    T.readout.inertialMass ψ = predictedMass ψ ∧
    T.readout.gravitationalMass ψ = predictedMass ψ := by
  have hreads := pattern_single_source_reads_restMass T ψ hψ
  exact ⟨hreads.1.trans hM7, hreads.2.trans hM7⟩

/-- If M7 is closed for the pattern, the two readouts also equal the
topology-derived MassLaw value. -/
theorem pattern_single_source_identity_with_predictedMass
    (T : PatternSingleSourceMassTheory Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ)
    (hM7 : restMass ψ = predictedMass ψ) :
    T.readout.inertialMass ψ = predictedMass ψ ∧
    T.readout.gravitationalMass ψ = predictedMass ψ := by
  have hreads := pattern_single_source_reads_restMass T ψ hψ
  exact ⟨hreads.1.trans hM7, hreads.2.trans hM7⟩

/-- If M7 is closed for the pattern, the two readouts also equal the
topology-derived MassLaw value. -/
theorem pattern_single_source_identity_with_predictedMass
    (T : PatternSingleSourceMassTheory Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ)
    (hM7 : restMass ψ = predictedMass ψ) :
    T.readout.inertialMass ψ = predictedMass ψ ∧
    T.readout.gravitationalMass ψ = predictedMass ψ := by
  have hreads := pattern_single_source_reads_restMass T ψ hψ
  exact ⟨hreads.1.trans hM7, hreads.2.trans hM7⟩

What this page does not claim

The theorem does not assert that any particular particle has a specific mass value. The theorem does not establish that the single-source structure holds for any real physical pattern. The theorem does not prove that the predicted mass is the correct one.

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/PatternReadoutEquivalence.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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