Masses Mass Genesis Q3 Support Action Support Averaged Factorized Load Of Q3 Eig

The eight-tick support action

The declaration supportAveragedFactorizedLoad_of_q3EightTickSupport_and_factorization belongs to a machine-checked library of formal theorems. It concerns a discrete record of events, called a ledger, that tracks how a pattern of eight phases changes step by step. The theorem establishes that when the support, the set of occupied phases, is the full set of eight, and when the load at each site is unchanged by the step, the averaged load factorizes into a product of a sector factor and a power of the golden ratio phi.

The eight steps form a Gray cycle, a sequence where each step changes exactly one bit of a three-bit pattern. The library proves that this step function is transitive, meaning repeated application reaches every phase from any starting phase. It also proves the phase-to-vertex map is bijective, so each of the eight phases corresponds to a distinct three-bit pattern. The load factorization theorem is the central result: under the full-support and load-equivariance conditions, the averaged load equals a sector factor times phi raised to a sum of exponents, divided by eight.

This is a structural result about the framework's own definitions, not a measurement of any physical particle. The theorem says that if a pattern satisfies the stated conditions, then its load has this particular algebraic form. It does not say that any real particle has this mass. The framework's comparison against measured particle masses is a separate empirical check, not part of this theorem. The declaration also does not establish that the golden ratio itself is derived from the load factorization; phi appears as a constant in the formula, not as a conclusion of this theorem.

theorem canonicalPrimitiveLoadFactorizes
    {ψ : LightPattern (Fin 8)}
    (E : Q3MassPatternEvidence ψ) :
    CanonicalPrimitiveLoadFactorizes ψ :=
  E.q3_closed.canonicalPrimitiveLoadFactorizes_of_topology_scaled_cp6
    E.topology_scaled_cp6

theorem eightTickSupportStep_transitive
    (x y : Fin 8) :
    ∃ n : ℕ, (eightTickSupportStep^[n]) x = y := by
  fin_cases x <;> fin_cases y <;>
    first
    | exact ⟨0, rfl⟩
    | exact ⟨1, rfl⟩
    | exact ⟨2, rfl⟩
    | exact ⟨3, rfl⟩
    | exact ⟨4, rfl⟩
    | exact ⟨5, rfl⟩
    | exact ⟨6, rfl⟩
    | exact ⟨7, rfl⟩

theorem q3VertexAtPhase_bijective :
    Function.Bijective q3VertexAtPhase := by
  simpa [q3VertexAtPhase] using Patterns.grayCycle3_bijective

What this page does not claim

The theorem does not prove any measured particle mass. The theorem does not derive the golden ratio from the load factorization; phi appears as a constant. The theorem does not establish that the Gray cycle is the only possible eight-tick support action.

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/Q3SupportAction.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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