Masses Mass Genesis T10 Commit Settlement Window Commit Settlement Window Adjace

Settlement windows

In the Recognition Science framework, a commitment is a discrete event that occupies one tick of an eight-tick cycle. The settlement window is the difference between occupying that tick and clearing at the next one. The declaration commitSettlementWindow_adjacentPairSupport proves that this window is supported on exactly the adjacent pair {phase, phase+1}: at every tick except the commit tick and the one after it, the window value is zero. At the commit tick the value is 1, and at the clearing tick it is -1, so the window is a sharp spike followed by an equal and opposite dip.

This is a theorem about a model construction, not a claim about physical reality. The model defines a window as a function from eight ticks to numbers, and the theorem proves a property of that function. The property is neutrality: the sum of all values is zero, meaning the window neither creates nor destroys anything. It is also nontrivial, so it is not the zero window. The theorem establishes the shape of the window, and it does so for every one of the eight phases.

The framework uses this result to supply a missing piece in its account of mass generation. The phase-zero commitment produces exactly the gap-one window, a specific two-phase pattern that earlier work had identified but could not yet produce. The theorem also excludes the gap-two shape: no commitment in the family posts a window with a gap of two ticks between the spike and the dip. These are structural facts about the model, proved in the framework's machine-checked library of formal theorems.

What the theorem does not claim is that the settlement window is determined by the source object that posts the commitment. Phases zero and two post on the same axis and carry the same signed source object, yet their settlement windows differ. The framework proves that no functional relation from source to window contains the settlement family. The physical settlement law reads the clock phase of the commitment, not the source object alone. This is the honest wall: the settlement readout is phase-borne, not source-borne.

theorem commitSettlementWindow_adjacentPairSupport (phase : Fin 8) :
    RawPhotonAdjacentPairSupport phase (commitSettlementWindow phase) := by
  intro t hcommit hclear
  unfold commitSettlementWindow commitOccupationWindow
  have hshift : t - 1 ≠ phase := by
    intro h
    exact hclear (sub_eq_iff_eq_add.mp h)
  rw [if_neg hcommit, if_neg hshift]
  ring

theorem commitSettlementWindow_at_commit (phase : Fin 8) :
    commitSettlementWindow phase phase = 1 := by
  unfold commitSettlementWindow commitOccupationWindow
  have hne : phase - 1 ≠ phase := by
    intro h
    have h1 : phase + 0 = phase + 1 := by
      rw [add_zero]
      exact sub_eq_iff_eq_add.mp h
    exact absurd (add_left_cancel h1) (by decide)
  rw [if_pos rfl, if_neg hne]
  ring

theorem commitSettlementWindow_at_clear (phase : Fin 8) :
    commitSettlementWindow phase (phase + 1) = -1 := by
  unfold commitSettlementWindow commitOccupationWindow
  have hclear : phase + 1 - 1 = phase := by
    rw [add_sub_cancel_right]
  have hne : phase + 1 ≠ phase := by
    intro h
    have h1 : phase + 1 = phase + 0 := by
      rw [add_zero]
      exact h
    exact absurd (add_left_cancel h1) (by decide)
  rw [if_neg hne, hclear, if_pos rfl]
  ring

theorem commitSettlementWindow_zero_eq_gapOne :
    commitSettlementWindow 0 = gapOneTwoPhaseMode := by
  funext t
  fin_cases t <;>
    simp [commitSettlementWindow, commitOccupationWindow,
      gapOneTwoPhaseMode]

theorem commitSettlementWindow_ne_gapTwo (phase : Fin 8) :
    commitSettlementWindow phase ≠ gapTwoTwoPhaseMode := by
  intro h
  have hcommit := congrFun h phase
  rw [commitSettlementWindow_at_commit] at hcommit
  unfold gapTwoTwoPhaseMode at hcommit
  by_cases h0 : phase.val = 0
  · have hval1 : (phase + 1).val = 1 := by
      have hphase : phase = 0 := Fin.ext h0
      subst hphase
      decide
    have hclear := congrFun h (phase + 1)
    rw [commitSettlementWindow_at_clear] at hclear
    unfold gapTwoTwoPhaseMode at hclear
    rw [if_neg (by rw [hval1]; norm_num),
      if_neg (by rw [hval1]; norm_num)] at hclear
    norm_num at hclear
  · rw [if_neg h0] at hcommit
    by_cases h2 : phase.val = 2
    · rw [if_pos h2] at hcommit
      norm_num at hcommit
    · rw [if_neg h2] at hcommit
      norm_num at hcommit

/-- **Interface wall.** No functional source-to-window relation contains the
settlement family: phases zero and two share one source but settle different
windows. The physical settlement law reads the clock phase of the
commitment, not the source object alone, so the source-functional naturality
interface cannot be the settlement law. -/
theorem no_functional_sourceRelation_contains_settlement :
    ¬ ∃ relation : SignedSourcePhotonWindowRelation3,
      IsFunctionalSignedSourcePhotonWindowRelation3 relation ∧
        ∀ phase : Fin 8,
          relation (phaseSignedPostingPhotonSource3 phase)
            (commitSettlementWindow phase) := by
  rintro ⟨relation, hfunctional, hcontains⟩
  have h0 := hcontains 0
  have h2 := hcontains 2
  rw [← phaseSource_zero_eq_phaseSource_two] at h2
  exact commitSettlementWindow_zero_ne_two
    (hfunctional (phaseSignedPostingPhotonSource3 0)
      (commitSettlementWindow 0) (commitSettlementWindow 2) h0 h2)

What this page does not claim

The theorem does not claim that the settlement window is determined by the source object that posts the commitment. The theorem does not claim that the settlement window model is the unique or only possible settlement mechanism. The theorem does not claim that the eight-tick cycle itself is derived from the settlement window construction.

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/T10CommitSettlementWindow.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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