Masses Mass Genesis Anchor Amplitude Primitive Primitive Factor Norm Of Primitiv

The amplitude norm equivalence

The declaration primitiveFactorNorm_of_primitiveAmplitudeNorm is a proved statement in the Recognition Science framework's machine-checked library of formal theorems. It says that if a certain amplitude norm (a measure of a pattern's total squared size) holds for a light pattern, then a related factor norm (a measure of how that size splits into two multiplicative parts) also holds for the same pattern. In plain terms, the theorem establishes that these two conditions are interchangeable: satisfying one is exactly the same as satisfying the other.

The equivalence rests on a definition. The framework defines a primitive closed pattern amplitude (a single positive number built from a sector load and a phi transport factor) and then shows its square equals a product of two loads. The theorem primitiveAmplitudeNorm_iff_primitiveFactorNorm proves the two norms are logically equivalent, and primitiveFactorNorm_of_primitiveAmplitudeNorm is the one-way direction that converts an amplitude-norm assumption into a factor-norm conclusion. This is a formal bridge: it lets later arguments use whichever formulation is more convenient.

What the declaration does not claim is just as important. It does not assert that any actual light pattern satisfies the amplitude norm; it only says that if one does, then the factor norm follows. It does not derive the chord from Q3/Rhat dynamics, as the framework's own documentation states. It does not prove that the amplitude norm holds for any specific physical pattern, nor does it establish any particle mass value. The theorem is a conditional implication between two formal conditions, not an existence result.

In the broader framework, this equivalence is a stepping stone. The full chain shows that if a pattern has the amplitude condition plus Q3 closed-pattern evidence, then it has positive rest mass, phi-rung quantization, and equal inertial and gravitational masses. But that chain requires the amplitude condition as an input; the theorem here does not supply it. The declaration's role is to keep the formal path clean, letting the framework move between two equivalent descriptions of the same target.

theorem primitiveAmplitudeNorm_iff_primitiveFactorNorm
    (ψ : LightPattern (Fin 8)) :
    AnchorPhasePrimitiveAmplitudeNorm ψ ↔ AnchorPhasePrimitiveFactorNorm ψ := by
  unfold AnchorPhasePrimitiveAmplitudeNorm AnchorPhasePrimitiveFactorNorm
  rw [primitiveClosedPatternAmplitude_sq ψ]

theorem primitiveFactorNorm_of_primitiveAmplitudeNorm
    (ψ : LightPattern (Fin 8))
    (hamp : AnchorPhasePrimitiveAmplitudeNorm ψ) :
    AnchorPhasePrimitiveFactorNorm ψ :=
  (primitiveAmplitudeNorm_iff_primitiveFactorNorm ψ).1 hamp

theorem primitiveFactorNorm_of_primitiveAmplitudeNorm
    (ψ : LightPattern (Fin 8))
    (hamp : AnchorPhasePrimitiveAmplitudeNorm ψ) :
    AnchorPhasePrimitiveFactorNorm ψ :=
  (primitiveAmplitudeNorm_iff_primitiveFactorNorm ψ).1 hamp

What this page does not claim

No actual light pattern is shown to satisfy the amplitude norm. No particle mass value is derived from this theorem alone. The chord is not derived from Q3/Rhat dynamics.

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/AnchorAmplitudePrimitive.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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