Masses Mass Genesis Stable Light Pattern

Stable Light Patterns

A light pattern is a discrete record of events that carries a load, a measure of its content. In the Recognition Science framework, the question is which patterns can persist as stable structures rather than dissolving. The answer, proved in the framework's machine-checked library of formal theorems, is precise: a pattern is stable exactly when it is localized, meaning its support is confined to a finite region, and it carries a nontrivial neutral load, meaning it has content that is not empty. This is the stable light pattern.

The framework models evolution as a cyclic shift, a rotation of the pattern through eight discrete steps or ticks. The central theorem, closedRHatOrbit_period_eight, proves that every light pattern closes after eight ticks: applying the shift eight times returns the pattern to its original state. For a localized, nontrivial pattern, this closure is what makes it stable. The stability is not approximate or asymptotic; it is exact periodicity. The pattern does not decay, spread, or change its character. It simply cycles.

This stability carries through evolution. The framework proves that as a stable pattern evolves through any number of ticks, its support, its topology labels, its sector, its rung, and its integrated load all remain unchanged. Most importantly, its rest mass, the measure of its content at rest, is invariant. A stable pattern keeps its mass exactly, tick after tick. This is the persistent light pattern: a structure that carries its identity and its mass through time unchanged.

The module does not yet derive the phi-rung quantization of masses or the full mass-law identity. Those remain open targets. What it establishes is the structural foundation: a precise, machine-checked characterization of what makes a pattern stable, and the proof that such patterns preserve their defining properties under evolution. This is the first solid step in the Mass Genesis route, showing that stable, mass-carrying structures can exist within the framework's discrete dynamics.

/-- For the concrete eight-tick Rhat, stability reduces to locality plus
nontrivial neutral load. Later Rhat refinements can replace the closure
lemma without changing the downstream API. -/
theorem stable_iff_localized_nontrivial (ψ : LightPattern Λ) :
    StableClosedLightPattern ψ ↔
      LocalizedSupport ψ ∧ NontrivialNeutralLoad ψ := by
  constructor
  · intro hψ
    exact ⟨hψ.1, hψ.2.1⟩
  · intro hψ
    exact stable_of_localized_nontrivial ψ hψ.1 hψ.2

/-- Every light pattern closes after the concrete eight-tick cyclic-shift
Rhat evolution. This is the structural orbit-closure input for M2. -/
theorem closedRHatOrbit_period_eight (ψ : LightPattern Λ) :
    ClosedRHatOrbit ψ := by
  refine ⟨8, by norm_num, dvd_refl 8, ?_⟩
  intro x _hx
  exact cyclicShift_period_8 (ψ.window x)

theorem restMass_evolvePattern_of_stable
    (ψ : LightPattern Λ) (k : ℕ)
    (hψ : StableClosedLightPattern ψ) :
    restMass (evolvePattern k ψ) = restMass ψ := by
  have h_ev := stable_evolvePattern_of_stable ψ k hψ
  rw [restMass_eq_integratedMeaningLoad_of_stable (evolvePattern k ψ) h_ev,
      restMass_eq_integratedMeaningLoad_of_stable ψ hψ,
      integratedMeaningLoad_evolvePattern ψ k]

What this page does not claim

This answer does not claim that the phi-rung quantization of masses is proved. This answer does not claim that the mass-law identity is derived. This answer does not claim that all light patterns are stable, only those that are localized and nontrivial.

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

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