Masses Mass Genesis Pattern Readout Equivalence Pattern Single Source Reads Rest

The single source of mass

Inertial mass, the resistance to acceleration, and gravitational mass, the response to gravity, have been measured as equal to extraordinary precision. The framework of Recognition Science treats this equality as a consequence of a deeper structure. Its machine-checked library of formal theorems contains a result, pattern_single_source_reads_restMass, which establishes that when both masses are read from a single cost source, they must agree.

The theorem begins with a light pattern, a discrete record of events, and a theory that assigns both an inertial and a gravitational mass to that pattern. The theorem proves that if both readouts are defined to come from the same stable source, and that source is the derived rest mass, then the two readouts are equal. The proof is a direct rewriting: it uses the definition of each readout as reading the source, and the fact that the source is the rest mass, to conclude the equality.

This is not a definitional choice. The framework does not define the two masses to be equal; it introduces a structure that records the proof obligations needed to show both readout channels are actually measuring the same thing. The theorem then discharges those obligations. The result is a chain: a single-source mass theory, a stable closed light pattern, and the conclusion that both readouts equal the rest mass.

In Recognition Science, the equality of inertial and gravitational mass is thus not an independent postulate. It is a proved consequence of a single-source assumption. The framework's library also shows that if a further condition holds, relating the rest mass to a topology-derived predicted mass, then both readouts equal that predicted mass as well. The theorem pattern_single_source_reads_restMass is the pivot: it connects the abstract equivalence principle to the concrete pattern readouts.

The theorem does not claim that any particular physical pattern exists, nor that the single-source assumption is true of the actual universe. It claims a conditional: if a pattern and a single-source mass theory are given, then the readouts agree. The framework models the situation; it does not assert that the situation is realized. The equality is forced by the structure, not by fiat.

theorem pattern_single_source_reads_restMass
    (T : PatternSingleSourceMassTheory Λ)
    (ψ : LightPattern Λ)
    (hψ : StableClosedLightPattern ψ) :
    ReadsStablePatternLoad T.readout ψ := by
  constructor
  · rw [T.inertial_from_source ψ hψ,
        T.stable_source_is_restMass ψ hψ]
  · rw [T.gravitational_from_source ψ hψ,
        T.stable_source_is_restMass ψ hψ]

/-- Pattern-level single-source mass theory. The source is the physical
cost/load channel. The two mass readouts are allowed to be separately named,
but each must be proved to read that same source. -/
structure PatternSingleSourceMassTheory (Λ : Type*) [Fintype Λ] [DecidableEq Λ] where
  sourceMass : LightPattern Λ → ℝ
  readout : PatternMassReadout Λ
  inertial_from_source :
    ∀ ψ : LightPattern Λ,
      StableClosedLightPattern ψ →
      readout.inertialMass ψ = sourceMass ψ
  gravitational_from_source :
    ∀ ψ : LightPattern Λ,
      StableClosedLightPattern ψ →
      readout.gravitationalMass ψ = sourceMass ψ
  stable_source_is_restMass :
    ∀ ψ : LightPattern Λ,
      StableClosedLightPattern ψ →
      sourceMass ψ = restMass ψ

/-- 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 specific physical pattern exists or that the single-source assumption holds in the actual universe. The theorem does not define inertial and gravitational mass to be equal; it proves equality conditional on a shared source. The theorem does not derive the numerical value of 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/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.

Derived articles

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