Masses Mass Genesis T10 Posting Photon Readout Phase Bearing Coherence Scaled Ev

The source attachment theorem

In the Recognition Science account, a posting transaction is a discrete record of an event, and a phase event is one of the eight steps in the cycle that builds such a record. The theorem phaseBearingCoherenceScaledEventOperator3_source_attachment states that every phase event constructs an operator whose event carries a signed source attachment: a formal link back to the posting source that produced it, with a sign and a reference field. The proof is by reduction to a more basic lemma, unitPosting_source_attachment, which says the same for a single posting step. This is a theorem in the machine-checked library of formal theorems: it is proved, axiom-clean, and establishes a structural fact about how phase events are anchored to their sources.

The theorem does not claim that the source attachment determines which photon window the event reads out. The library proves the opposite: the current posting-to-photon compatibility relation is not functional, meaning one and the same posting input can be compatible with two distinct photon windows. Concretely, the canonical phase-zero input is compatible with both the gap-one window and the gap-two window, and those two windows are distinct. Even an actual source-attached phase posting, paired with a bridge-compatible physical photon and a matching Q3 pattern, does not force phase-zero or phase-one support. The wall is sharp: the current compatibility relation is not a source-to-window function, and the missing premise is a target-blind source-window naturality that would select a unique window from the signed posting source.

What the theorem does establish is a necessary condition, not a sufficient one. Every phase event is source-attached, so any future account of photon readout must respect that attachment. But the attachment alone does not resolve which window the photon takes. The library names two missing premises: a source-window naturality relation derived from the signed posting source, and a pattern-anchor readout equality. Neither is defined here to return the desired gap-one answer. The consequence is a precise boundary: the framework has not yet derived the posting-to-photon readout rule, and the theorem certifies that boundary rather than crossing it.

theorem phaseBearingCoherenceScaledEventOperator3_source_attachment
    (phase : Fin 8) :
    SignedPostingSourceAttachment3 1
      (phaseBearingCoherenceScaledEventOperator3 phase).event
      (Equiv.refl (Fin 3))
      (signedRealGreenField3 1
        (phaseBearingCoherenceScaledEventOperator3 phase).event) :=
  unitPosting_source_attachment
    (phaseBearingCoherenceScaledEventOperator3 phase)

/-- Coherence-scaled event operator carried by the actual posting at one Gray
phase. The operator remains a MODEL physical carrier; its source attachment is
a theorem. -/
def phaseBearingCoherenceScaledEventOperator3
    (phase : Fin 8) : CoherenceScaledEventOperator3 where
  event := (phaseBearingPostingEvent3 phase).1
  event_realized := (phaseBearingPostingEvent3 phase).2

/-- **First readout wall.** Current posting/photon compatibility is not
functional: the same actual posting source, Maxwell/DEC channel, and zero-J
carrier admit the distinct gap-one and gap-two windows. -/
theorem currentPostingPhotonCompatibility_not_functional :
    ¬ IsFunctionalPostingPhotonRelation3
      CurrentPostingPhotonCompatibility3 := by
  intro hfunctional
  exact gapOneTwoPhaseMode_ne_gapTwoTwoPhaseMode
    (hfunctional
      (canonicalPhasePostingPhotonInput3 0)
      gapOneTwoPhaseMode
      gapTwoTwoPhaseMode
      gapOne_currentPhysicalPhotonWindowCompatible
      gapTwo_currentPhysicalPhotonWindowCompatible)

theorem gapObservations_same_posting_photon_input :
    gapOnePhasePostingPhotonObservation3.input =
      gapTwoPhasePostingPhotonObservation3.input :=
  rfl

theorem gapObservations_distinct_windows :
    gapOnePhasePostingPhotonObservation3.window ≠
      gapTwoPhasePostingPhotonObservation3.window :=
  gapOneTwoPhaseMode_ne_gapTwoTwoPhaseMode

/-- **Physical readout wall.** Actual source attachment, a valid physical
photon, a matching raw pattern anchor, and the Q3 carrier still do not force
phase-zero/one support. The missing premise must relate the signed posting
source to the physical photon window. -/
theorem actualPostingPhysicalPhotonQ3_does_not_force_rawAnchorSupport :
    ¬ ∀ model : PhasePostingPhysicalPhotonQ3Model3,
      RawAnchorPhase01Support model.pattern := by
  intro h
  exact gapTwo_worldline_not_rawAnchorPhase01Support
    (h gapTwoPhasePostingPhysicalPhotonQ3Model3)

What this page does not claim

The theorem does not claim that the source attachment selects a photon window. This answer does not claim that the posting-to-photon readout rule has been derived; it remains open. The framework does not claim that gap-one is the physically realized window, only that the current compatibility relation admits both.

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/T10PostingPhotonReadout.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.

Derived articles

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