Masses Mass Genesis T10 Green To Window Transport Exists Functional Non Source B

The corner transport map

In the Recognition Science framework, a ledger (a discrete record of events) carries signed postings at twenty-seven sites on a three-dimensional torus. A window is a readout of eight complex values, one for each tick of the framework's eight-tick cycle. The declaration exists_functional_nonSourceBlind_sourceWindowRelation proves that there is a map from each posting source to a window that is functional (each source maps to exactly one window) and not source-blind (distinct sources give distinct windows).

The construction uses Fourier modes on the torus. The modes whose exponent is nonzero on every axis with unit magnitude form exactly eight corner characters, and the Gray cube vertex occupied at each tick selects one of them. Reading the posting dipole through the corner character of each tick yields a window. The map is definitional on source data, so the induced relation is functional, and distinct posting axes give distinct windows, so it is not source-blind. This inhabits the exact class the previous wall proved nonempty of obstructions but empty of examples.

The honest negative half: the corner readout of one posting has full support on all eight ticks and is not equal to either gap window. So the corner transport cannot be the gap-one naturality law, and single-posting corner readout cannot supply raw phase-zero/one support. The residual moves to a physical mechanism concentrating the settled octave's readout onto the anchor phases.

The corner transport is a canonical MODEL construction; every property stated about it here is THEOREM. No claim is made that it is the physical readout law.

/-- **The wall's missing class is inhabited.** A functional, non-source-blind
source-window relation exists among current carriers. -/
theorem exists_functional_nonSourceBlind_sourceWindowRelation :
    ∃ relation : SignedSourcePhotonWindowRelation3,
      IsFunctionalSignedSourcePhotonWindowRelation3 relation ∧
        ¬ IsSourceBlindSignedSourcePhotonWindowRelation3 relation :=
  ⟨CornerModeWindowRelation3, cornerModeWindowRelation_functional,
    cornerModeWindowRelation_not_sourceBlind⟩

theorem cornerModeWindowRelation_functional :
    IsFunctionalSignedSourcePhotonWindowRelation3
      CornerModeWindowRelation3 := by
  intro source left right hleft hright
  exact hleft.trans hright.symm

/-- **Positive half.** The corner relation is not source-blind: it reads the
posting axis through the Gray-vertex corner characters. -/
theorem cornerModeWindowRelation_not_sourceBlind :
    ¬ IsSourceBlindSignedSourcePhotonWindowRelation3
      CornerModeWindowRelation3 := by
  rintro ⟨P, hP⟩
  have h0 : P (cornerModeWindowTransport
      (axisSignedPostingPhotonSource3 0)) :=
    (hP (axisSignedPostingPhotonSource3 0) _).mp rfl
  have h1 : CornerModeWindowRelation3 (axisSignedPostingPhotonSource3 1)
      (cornerModeWindowTransport (axisSignedPostingPhotonSource3 0)) :=
    (hP (axisSignedPostingPhotonSource3 1) _).mpr h0
  exact cornerModeWindowTransport_axis_zero_ne_one h1

theorem cornerModeWindowRelation_not_gapOne :
    ¬ CornerModeWindowRelation3
      (phaseSignedPostingPhotonSource3 0) gapOneTwoPhaseMode := by
  intro h
  have h2 := congrFun h 2
  have hzero : gapOneTwoPhaseMode 2 = 0 := by
    simp [gapOneTwoPhaseMode]
  rw [hzero] at h2
  exact cornerModeWindowTransport_phaseSource_ne_zero 0 2 h2.symm

theorem cornerModeWindowRelation_not_gapTwo :
    ¬ CornerModeWindowRelation3
      (phaseSignedPostingPhotonSource3 0) gapTwoTwoPhaseMode := by
  intro h
  have h1 := congrFun h 1
  have hzero : gapTwoTwoPhaseMode 1 = 0 := by
    simp [gapTwoTwoPhaseMode]
  rw [hzero] at h1
  exact cornerModeWindowTransport_phaseSource_ne_zero 0 1 h1.symm

What this page does not claim

The corner transport is not claimed to be the physical readout law. The declaration does not claim that the map is the gap-one naturality law. The declaration does not claim that single-posting corner readout supplies raw phase-zero/one support.

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/T10GreenToWindowTransport.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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