Encyclopedia Masses Masses Mass Genesis T10 Double Entry Mass Quantum Bridge Commit Occupation Windo

ARTICLE 5 claims 5 theorems

Masses Mass Genesis T10 Double Entry Mass Quantum Bridge Commit Occupation Windo

In the framework's ledger, a committed mass quantum occupies exactly two of the eight recognition ticks, a fact that bounds how much any two masses can differ.

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The two-valued occupation

The declaration ledger, a discrete record of recognition events, pins down a specific property of how a mass quantum posts its presence. The theorem commitOccupationWindow_settlementLoad_eq_two states that for any of the eight phases in a recognition cycle, the settlement load of the committed occupation window equals 2. In plain terms: when a mass quantum commits to a phase, it occupies exactly two of the eight ticks in the window, no more and no less.

This two-valued occupation is not an isolated curiosity. The framework's machine-checked library of formal theorems proves that the ledger-carried occupation readout is two-valued at posting unit 1, meaning each tick in the window is either fully occupied or not occupied at all. From this, a chain of consequences follows. The settlement load equals the cut count, the number of occupied ticks, and that cut count is always even. Because the load is exactly 2, the ratio of settlement loads between any two non-zero occupied windows is bounded by 4. This is the mass ratio bound: in the framework, no two masses can differ by more than a factor of four in their settlement load.

In Recognition Science, this result is part of the bridge between the double-entry mass quantum and the carried commit settlement. The theorem shows that the general settlement theory specializes cleanly to the tree's existing commit settlement window and to the ledger-carried occupation. The canonical octave, the standard reference case, is inhabited and its occupation is two-valued with settlement load 2, so the result is not vacuous.

The declaration does not claim that actual particle masses in nature obey this factor-of-four bound. It is a theorem about the framework's internal ledger structure, not a prediction about measured masses. It also does not claim that the two occupied ticks are adjacent or that they have any particular position within the window; the theorem holds for any phase. It does not assert that the settlement load is always 2 for every possible occupation, only for the committed occupation window defined in the framework.

THEOREM commitOccupationWindow_settlementLoad_eq_two · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean
commitOccupationWindow_settlementLoad_eq_two · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean:54 
theorem commitOccupationWindow_settlementLoad_eq_two (phase : Fin 8) :
    settlementLoad (commitOccupationWindow phase) = 2 := by
  have h0 : settlementLoad (commitOccupationWindow (0 : Fin 8)) = 2 := by
    change settlementLoad booleanLoadTwoWitness = 2
    exact booleanLoadTwoWitness_settlementLoad
  have hsw : ∀ t,
      settlementWindow (commitOccupationWindow phase) t =
        settlementWindow (commitOccupationWindow 0) (t - phase) := by
    intro t
    simpa [settlementWindow, commitSettlementWindow] using
      commitSettlementWindow_eq_shifted phase t
  rw [← h0]
  unfold settlementLoad
  rw [neutralize_settlementWindow, neutralize_settlementWindow]
  exact Fintype.sum_equiv (Equiv.subRight phase)
    (fun t => Complex.normSq
      (settlementWindow (commitOccupationWindow phase) t))
    (fun t => Complex.normSq
      (settlementWindow (commitOccupationWindow 0) t))
    (fun t => by
      change Complex.normSq
          (settlementWindow (commitOccupationWindow phase) t) =
        Complex.normSq
          (settlementWindow (commitOccupationWindow 0) (t - phase))
      rw [hsw])
THEOREM ledgerOccupationWindow_twoValued · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean
ledgerOccupationWindow_twoValued · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean:82 
/-- **R13.** The ledger occupation readout is two-valued at posting unit `1`. -/
theorem ledgerOccupationWindow_twoValued
    (octave : Q3SettledLedgerOctave) (phase : Fin 8) :
    TwoValuedOccupation 1 (ledgerOccupationWindow octave phase) := by
  rw [ledgerOccupationWindow_eq_commitOccupation]
  exact (commitOccupationWindow_booleanOccupation phase).twoValued
THEOREM ledgerOccupationWindow_settlementLoad_eq_cutCount · ledgerOccupationWindow_cutCount_even · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean
ledgerOccupationWindow_settlementLoad_eq_cutCount · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean:89 
theorem ledgerOccupationWindow_settlementLoad_eq_cutCount
    (octave : Q3SettledLedgerOctave) (phase : Fin 8) :
    settlementLoad (ledgerOccupationWindow octave phase) =
      (cutCount (ledgerOccupationWindow octave phase) : ℝ) := by
  have := twoValuedOccupation_settlementLoad_eq_normSq_mul_cutCount
    (1 : ℂ) _ (ledgerOccupationWindow_twoValued octave phase)
  simpa [Complex.normSq_one] using this
ledgerOccupationWindow_cutCount_even · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean:97 
theorem ledgerOccupationWindow_cutCount_even
    (octave : Q3SettledLedgerOctave) (phase : Fin 8) :
    Even (cutCount (ledgerOccupationWindow octave phase)) :=
  twoValuedOccupation_cutCount_even 1 _
    (ledgerOccupationWindow_twoValued octave phase)
THEOREM ledgerOccupationWindow_mass_ratio_le_four · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean
ledgerOccupationWindow_mass_ratio_le_four · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean:103 
theorem ledgerOccupationWindow_mass_ratio_le_four
    (octave₁ octave₂ : Q3SettledLedgerOctave) (phase₁ phase₂ : Fin 8)
    (hpos₁ : settlementLoad (ledgerOccupationWindow octave₁ phase₁) ≠ 0)
    (hpos₂ : settlementLoad (ledgerOccupationWindow octave₂ phase₂) ≠ 0) :
    settlementLoad (ledgerOccupationWindow octave₁ phase₁) ≤
      4 * settlementLoad (ledgerOccupationWindow octave₂ phase₂) :=
  twoValuedOccupation_mass_ratio_le_four (1 : ℂ) (by norm_num)
    _ _ (ledgerOccupationWindow_twoValued octave₁ phase₁)
    (ledgerOccupationWindow_twoValued octave₂ phase₂) hpos₁ hpos₂
THEOREM canonicalLedgerOccupation_twoValued_load_two · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean
canonicalLedgerOccupation_twoValued_load_two · IndisputableMonolith/Masses/MassGenesis/T10DoubleEntryMassQuantumBridge.lean:113 
/-- Non-vacuity: `Q3SettledLedgerOctave` is inhabited, and the canonical
octave's occupation is two-valued with settlement load 2. -/
theorem canonicalLedgerOccupation_twoValued_load_two (phase : Fin 8) :
    TwoValuedOccupation 1
        (ledgerOccupationWindow canonicalQ3SettledLedgerOctave phase) ∧
      settlementLoad
          (ledgerOccupationWindow canonicalQ3SettledLedgerOctave phase) = 2 := by
  refine ⟨ledgerOccupationWindow_twoValued _ phase, ?_⟩
  rw [ledgerOccupationWindow_eq_commitOccupation,
    commitOccupationWindow_settlementLoad_eq_two]

What this page does not claim

The theorem does not predict or constrain measured particle masses in nature. The theorem does not specify which two ticks are occupied or their position within the window. The theorem does not apply to every possible occupation, only to the committed occupation window.

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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/T10DoubleEntryMassQuantumBridge.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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