Masses Mass Genesis T10 Ledger Photon Bridge Raw Canonical Positive Stationary M

The settled-source theorem

A ledger, in this framework, is a discrete record of events; a recognition is the act of posting one entry. The theorem rawCanonicalPositiveStationaryMode_of_settledSourceData concerns light patterns on eight phases, the basic carriers of the framework's particle model. It states a conditional result: if a light pattern satisfies a package of conditions called T10SettledRawModeSourceData, then that pattern is an AnchorPhaseRawCanonicalPositiveStationaryPrimitiveFactorMode. The package includes a settled ledger octave, support on phases zero and one, a neutral anchor, and a specific phase-zero amplitude. The conclusion is a mouthful, but it names a definite, checkable property of the pattern.

The proof is one line, because it delegates to an earlier theorem about the same property under weaker source data. The new theorem's work is the packaging: it takes the settled-source conditions and shows they imply the earlier theorem's hypothesis. This is a theorem in the machine-checked library of formal theorems, meaning the implication is verified by a proof checker, not by argument. The declaration does not construct any new object. It does not say that any light pattern exists with these properties. It only says that if one exists with the settled-source data, then it has the canonical stationary mode property.

What the theorem does not claim is as important as what it proves. The surrounding module proves two sharp limitations. First, legal posting trajectories do not force the Gray settlement schedule; a legal schedule can fail to settle. Second, even a settled ledger octave paired with a Q3 matter carrier does not force raw photon support onto phases zero and one. The theorem's hypothesis includes that support as an input, so the theorem cannot be used to derive it. The gap-two carrier is an explicit counterexample: it satisfies the ledger and carrier conditions but not the raw anchor support. The bridge from posting to photon transport is therefore not complete; the theorem is a conditional step, not a physical selection law.

In plain terms: the theorem certifies that the settled-source package is sufficient for the canonical mode property, and it leaves the harder direction open. The framework proves a conditional implication, and it proves that the missing premise is genuinely missing. A reader should come away knowing that the ledger-to-photon bridge has a certified conditional step and a named obstacle, and that the obstacle is a concrete counterexample, not a vague gap.

theorem rawCanonicalPositiveStationaryMode_of_settledSourceData
    (ψ : LightPattern (Fin 8))
    (h : T10SettledRawModeSourceData ψ) :
    AnchorPhaseRawCanonicalPositiveStationaryPrimitiveFactorMode ψ :=
  rawCanonicalPositiveStationaryMode_of_t10SourceData
    ψ h.toLocalSourceData

/-- **Trajectory-level settlement wall.** Every step of this run is a legal
atomic post, yet the run does not follow the fixed Q3 Gray settlement. Hence
legality and one-bit parity do not select the schedule. -/
theorem legalPostingTrajectory_does_not_force_q3Settlement :
    ∃ initial : LedgerState 3, ∃ schedule : ℕ → PostInstr 3,
      (∀ t : ℕ,
        LegalAtomicTick
          (run initial schedule t)
          (run initial schedule (t + 1))) ∧
      ¬ Q3FirstOctaveGraySettlementLaw initial schedule :=
  ⟨q3ZeroLedger, offClockPostingSchedule,
    run_step_legalAtomicTick _ _, offClockPostingSchedule_not_settled⟩

/-- **Posting-to-photon support wall.** A settled legal ledger octave together
with a Q3 carrier does not force raw support onto phases zero and one. A new
coupling/readout law must exclude this bare gap-two model. -/
theorem bareSettledLedgerAndQ3Carrier_do_not_force_rawAnchorSupport :
    ¬ ∀ model : BareQ3LedgerPhotonModel,
      RawAnchorPhase01Support model.pattern := by
  intro h
  exact gapTwo_worldline_not_rawAnchorPhase01Support
    (h gapTwoBareQ3LedgerPhotonModel)

What this page does not claim

The theorem does not construct any light pattern with the settled-source data. The theorem does not prove that the Gray settlement schedule is the only legal schedule. The theorem does not complete the ledger-to-photon bridge; the raw anchor support remains an input, not a derived consequence.

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/T10LedgerPhotonBridge.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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