Masses Mass Genesis T10 Sourced Channel Emission Channel Tick Current Eq Origin

The ledger current

A ledger, a discrete record of events, is the core image of Recognition Science. The declaration channelTickCurrent_eq_originLocalSettlement_at_phase is a proved theorem inside the framework's machine-checked library of formal theorems. It states a precise identity: for any octave and any phase of the eight-tick cycle, the current flowing through a posted photon channel equals the amplitude of a local settlement readout computed from the ledger occupation difference between consecutive ticks. In plainer words, the theorem says that the signal carried by an emitted photon is not an independent quantity; it is exactly the change in the ledger's occupation number from one tick to the next, read through a specific settlement function.

This identity is the core of what the framework calls a sourced channel. The theorem channelTickCurrent_eq_commitSettlementWindow first shows that the tick current equals a commit settlement window. Then, using a settlement law, the theorem proves that this window is exactly the amplitude of the difference settlement readout applied to consecutive ledger occupations. The consequence is that the photon's window, the shape of its signal over the eight ticks, is definitionally tied to the ledger, not a free field. The theorem EmittedPhotonState.window_eq_localSettlementImage extends this to the emitted state: the window of any emitted photon is that same local settlement image. This is a structural result about how the framework models photon emission, not a claim about any specific measured photon.

What the declaration does not claim is equally important. It does not say that the framework derives the fine-structure constant, nor that it proves the Riemann Hypothesis. It does not claim that the ledger is a physical object in the conventional sense; the ledger is a modeling choice within the framework. The theorem does not assert that all photons arise this way, only that in the sourced channel model, the window is the settlement readout. It also does not claim that the gap-two mode, a specific two-phase pattern, can be an emitted window; a separate theorem proves it cannot. The declaration is a proved identity inside the framework, with its scope limited to the sourced channel model it defines.

/-- Equivalent form: sampling equals the origin-style local settlement
readout at this phase under the difference readout. -/
theorem channelTickCurrent_eq_originLocalSettlement_at_phase
    (octave : Q3SettledLedgerOctave) (phase : Fin 8) :
    channelTickCurrent octave phase =
      (fun t =>
        differenceSettlementReadout.amplitude
          (ledgerOccupationWindow octave phase t)
          (ledgerOccupationWindow octave phase (t - 1))) := by
  rw [channelTickCurrent_eq_commitSettlementWindow,
    settledLedger_settlement_law octave differenceSettlementReadout phase]

theorem window_eq_localSettlementImage (e : EmittedPhotonState) :
    e.window =
      (fun t =>
        differenceSettlementReadout.amplitude
          (ledgerOccupationWindow e.octave e.phase t)
          (ledgerOccupationWindow e.octave e.phase (t - 1))) :=
  channelTickCurrent_eq_originLocalSettlement_at_phase e.octave e.phase

/-- Gap-two cannot arise as any emitted-photon window. -/
theorem gapTwo_not_emittedPhotonWindow :
    ¬ ∃ e : EmittedPhotonState, e.window = gapTwoTwoPhaseMode := by
  rintro ⟨e, he⟩
  exact e.window_ne_gapTwo he

What this page does not claim

The framework derives the fine-structure constant or proves the Riemann Hypothesis. The ledger is a physical object in the conventional sense; it is a modeling choice. All photons in the framework arise from a sourced channel; the theorem covers the sourced model only.

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/T10SourcedChannelEmission.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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