TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CALDERON-OPERATION-SOURCE-PROOF.txt
Original file SHA-256: 3e64abb6953af41c27ec47e56f8b01845c485d51856178cbcc0485fd16165213
Inclusive original lines: 121-177
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000121 | Always G_V=V G V*. With E_R the fixed second-face inclusion, always
000122 |  C_V=E_R* V G V* E_R.                                (10)
000123 | For(5), C_V=V_R C V_R*, while its cross block is V_L X V_R*.
000124 | Thus one-face marginals still do not identify the whole lift. The naive
000125 | formula C_V=V C V* is invalid for an arbitrary face-mixing matrix V.
000126 | A given common V=v direct_sum v gives the old common transport, and a
000127 | relative lift I direct_sum v gives the old relative transport. None is
000128 | chosen by this classification. Retain the full source and its determinant,
000129 | central phase, absolute Z0, Ref/Eta/H0 and all ordered word responses.
000130 | 
000131 | The full projector can change under an implementable local operation:
000132 |  (I-G) V G need not vanish even though [G,V] is HS.
000133 | For a bounded A the exact compression defect is
000134 |  G A* A G-G A* G A G=G A*(I-G)A G >=0.               (11)
000135 | Nonzero defect proves failure of multiplicativity for that chosen A*,A;
000136 | it does not mean the inequality is strict for every pair of operators.
000137 | For a proper spatial region O and a field f supported outside O, a
000138 | unitary multiplier equal to I outside O fixes a(f) under its CAR
000139 | automorphism. This is algebraic exterior locality. It does NOT by itself
000140 | prove that a chosen Fock implementer belongs to the given local algebra,
000141 | nor identify the quotient region with a physical3+1 region.
000142 | 
000143 | 6. Consequence at the first original source identification
000144 | R073 classified the color-only part. The given q operation passes color,
000145 | but a nonconstant common q profile changes the actual Cauchy projector
000146 | by(9). This does not disqualify it as an operation: (5) permits its Fock
000147 | implementation. Requiring the state covariance to remain fixed would
000148 | erase these available responses, not derive the physical projector.
000149 | The original physical A/A* reduction is on the reconstructed H_adm,
000150 | not on the occupied Cauchy one-particle subspace. Therefore the literal
000151 | EINTEILCHEN multiplier interpretation of the seam selector collapses to
000152 | C^8, while it has no power to exclude the full OS observable algebra.
000153 | 
000154 | Next execute the actual original field/source correspondence and
000155 | seam/determinant/gap action on those images and whole bounded histories.
000156 | Use the existing Euclidean Green functional, right-action partner and
000157 | bounded thermal RP words where the source actually supplies them. Do
000158 | not demand a new universal isometry of all Fock and OS spaces. Compare
000159 | the original joint functional/cross coherence and admissible operation
000160 | image; state change is allowed. No original Dadm, QTheta or Z_adm measure
000161 | is produced by the analytic norm. Do not impose Padm=G or Gamma(G).
000162 | The old PC=geometric deck error and positive-only carrier collapse are
000163 | already known and are not recounted as new. No new physical milestone.
000164 | F1 remains open with full source, memory, E8/clocks, Y/flavor/alpha and
000165 | R035/R037/R043/R054/R063/R067/R068/R069/R071/R073 retained.
000166 | 
000167 | 7. Sources, validation and limits
000168 | Original geometric/physical distinction: archived boundary source001,
000169 | lines94-174,309-343. Original center/gap definition: QFT source002:12-118.
000170 | Actual graph and source: seam-full-collar-reconstruction-20261015/PROOF.txt
000171 | 63-143; collar-current-source-bridge-20261021/PROOF.md1-145;
000172 | native-arc-charge-source-interface-20261026/PROJECTOR-STATE-RIGIDITY.txt
000173 | 66-108; elliptic-moebius-source-bridge-20261026/two_face_source_20261029/
000174 | PROOF.txt43-135. Existing source reflection and bounded RP are reused.
000175 | Araki1970/71,Publ.RIMS6,385-442,Theorems6/7 atpp430-432:
000176 | https://ems.press/content/serial-article-files/41673
000177 | No new Lean, full-suite run, physical validation or ledger promotion.