Masses Mass Genesis T10 Settled Origin Decision Settled Origin Commit Settlement

The settled origin

In the Recognition Science account, a settled octave is a completed eight-tick recognition cycle, and each such octave carries an indexing that marks where its run began. The theorem settledOrigin_commitSettlement_eq_gapOne states that, relative to that carried origin, the commitment settlement window of the octave's initial parity phase is exactly the gap-one two-phase mode. In plainer words: the first tick of a settled octave is fixed to be the first gap in the two-phase structure, and this is true for every settled octave in the framework.

The proof is short and direct. A prior theorem, settledOrigin_is_phaseZero, establishes that every settled octave's own origin reads phase zero. Substituting that fact into the definition of the commitment settlement window yields the gap-one result. The machine-checked library of formal theorems records this derivation without gaps or unstated assumptions.

What the theorem does not claim is just as important. It does not say that this phase-zero origin is observer-independent or absolute. The framework's own documentation is explicit: a search for an observer-independent reindexing law that preserves the physical settlement class and forces the same absolute anchor phases did not yield a kernel-checked positive theorem. The final form, Branch B, accepts the carried origin as final. Uniqueness and anchor support are stated relative to the carried run origin, and absolute observer-free phase naming remains outside the closed claim.

This is a deliberate boundary. The theorem pins down the first tick of a settled octave relative to its own carried clock, but it does not pretend to fix an absolute phase for the universe. That distinction matters for anyone reading the framework's claims: the settled origin is a settled relative fact, not a claim about an observer-free absolute frame.

/-- Relative to the carried origin, the run-origin commitment settles exactly
gap-one. -/
theorem settledOrigin_commitSettlement_eq_gapOne
    (octave : Q3SettledLedgerOctave) :
    commitSettlementWindow (q3PhaseOfLedgerParity octave.initial) =
      gapOneTwoPhaseMode := by
  rw [settledOrigin_is_phaseZero octave,
    commitSettlementWindow_zero_eq_gapOne]

/-- Every settled legal octave's own origin reads phase zero. -/
theorem settledOrigin_is_phaseZero
    (octave : Q3SettledLedgerOctave) :
    q3PhaseOfLedgerParity octave.initial = 0 :=
  settledOctave_initial_phase_zero octave

theorem carriedSettledOriginFinalForm :
    CarriedSettledOriginFinalForm where
  every_settled_octave_origin_phase_zero := settledOrigin_is_phaseZero
  run_origin_settlement_is_gap_one :=
    settledOrigin_commitSettlement_eq_gapOne
  claim_scope := trivial

structure T10SettledOriginDecisionCert : Prop where
  branch_b_accepted : CarriedSettledOriginFinalForm
  origin_phase_zero :
    ∀ octave : Q3SettledLedgerOctave,
      q3PhaseOfLedgerParity octave.initial = 0
  origin_settlement_gap_one :
    ∀ octave : Q3SettledLedgerOctave,
      commitSettlementWindow (q3PhaseOfLedgerParity octave.initial) =
        gapOneTwoPhaseMode

What this page does not claim

The theorem does not establish an observer-free absolute phase origin. It does not prove that the carried origin is unique across all possible reindexings. It does not derive the physical masses themselves, only a structural anchor for their rungs.

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/T10SettledOriginDecision.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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