Masses Mass Genesis T10 Double Entry Mass Quantum Bridge Canonical Ledger Occupa

The canonical ledger occupation

A ledger, in the Recognition Science framework, is a discrete record of events, here a window of eight positions that a mass quantum can occupy. The declaration canonicalLedgerOccupation_twoValued_load_two proves a fact about the framework's canonical ledger octave, the standard reference instance of such a record. The theorem states that for any of the eight phases, the occupation readout is two-valued at unit amplitude, and its settlement load equals 2.

Two-valued at unit amplitude means each position in the ledger is either fully occupied or fully empty, never partially filled. The settlement load is the total count of occupied positions. The theorem therefore establishes that the canonical ledger always has exactly two occupied positions, no matter which phase one examines. This is a structural fact: it says the simplest mass quantum in the framework is represented by a ledger with precisely two filled slots out of eight.

The proof is short and direct. It first shows that the occupation window is boolean, meaning each position is 0 or 1. From that, the theorem derives both the two-valued property and the settlement load of 2. The result is part of a larger bridge certification, T10DoubleEntryMassQuantumBridgeCert, which connects the general settlement theory to the ledger-carried occupation used in the framework's mass genesis module.

In Recognition Science, this fact matters because it gives a concrete, non-vacuous instance of the ledger structure. The canonical octave is inhabited, and its occupation is two-valued with load 2, so the abstract definitions have a real model to work with. This is not a claim about any particular measured particle mass; it is a claim about the internal consistency of the framework's own construction.

/-- 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]

theorem commitOccupationWindow_booleanOccupation (phase : Fin 8) :
    BooleanOccupation (commitOccupationWindow phase) := by
  intro t
  unfold commitOccupationWindow
  by_cases ht : t = phase <;> simp [ht]

/-- 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]

/-- 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

This theorem does not assign a numerical mass value to any particle. It does not claim that all possible ledgers in the framework are two-valued with load 2. It does not derive the fine-structure constant or any coupling constant.

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/T10DoubleEntryMassQuantumBridge.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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