TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/paper-source-reconstruction-20261025/PAPER-PRIMITIVE-SOURCE-SELECTION.txt
Original file SHA-256: c3b3449113e952b4db209b35d2584c5bab3f131f6852250f8febb5d94eac268d
Inclusive original lines: 201-271
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000201 | mass-one, holonomy-r=1 QWZ strip, its negative-energy projector P_N and filled
000202 | sea Omega_N, then proves the charged CAR field, adjoint, charge, support and
000203 | time limit. None of the criticism above changes that theorem.
000204 | 
000205 | Its exact QWZ numbers have two possible roles:
000206 | 
000207 |   A. Fundamental selection claim. P1 uniquely chooses width=8, mass=1 and
000208 |      r=1. No cited original theorem proves this.
000209 | 
000210 |   B. Regulator representative claim. The operational seed already supplies a
000211 |      source, and this QWZ strip is a local quasifree representative of the same
000212 |      polarized collar class. In this role its exact lattice coordinates do not
000213 |      need to be P1 constants. This claim becomes proved once the full graded
000214 |      local source and time embedding is proved on the same reducing subsystem;
000215 |      the ground-state reduction then supplies its covariance.
000216 | 
000217 | The existing paper supports B as the right target but has not completed its
000218 | antecedent. The source audit in PAPER-COLLAR-REFERENCE.txt narrows the missing
000219 | map to a local state, time and reflection covariant *-monomorphism from the
000220 | quotient CAR net into the operational seed, followed by the elliptic
000221 | collar/domain check. The refined test is that this map contains the odd fields
000222 | and both adjoints and intertwines the original reconstructed time with the
000223 | Bogoliubov dynamics of the same gapped K. Positive energy then derives
000224 | 
000225 |   iota_1 P_QWZ = 1_(-infinity,0)(K_seed) iota_1
000226 | 
000227 | or the corresponding covariance identity on the cyclic image. This equation
000228 | is now a consequence and diagnostic, not a separate state premise. The direct
000229 | argument is in GROUND-STATE-SOURCE-REDUCTION.txt. This is the smallest
000230 | decisive test of the actual charged field source and does not ask P1 to
000231 | reproduce a lattice mass value.
000232 | 
000233 | The transverse strip width eight must also not be confused with the later
000234 | eightfold quotient fold. The latter is a unitary residue-class reindexing of
000235 | one continuum CAR channel. Equality of the two integers is not a source
000236 | selection theorem.
000237 | 
000238 | 5. Exact claim hierarchy
000239 | ------------------------
000240 | 
000241 | PROVED:
000242 | 
000243 |   * A fixed gapped one-particle K determines the pure gauge-invariant
000244 |     quasifree ground-state symbol P=1_(-infinity,0)(K).
000245 |   * A supplied complete operational seed contains net, state, time,
000246 |     reflection, seam class and D_coll.
000247 |   * A supplied elliptic D_+ determines its Calderon projector.
000248 |   * The fixed QWZ representative has the charged CAR scaling limit stated in
000249 |     paper-source:7296b452273b7022082ac2e2.
000250 | 
000251 | CONDITIONAL:
000252 | 
000253 |   * QWZ mass, holonomy and finite-width choices are regulator coordinates
000254 |     rather than fundamental P1 data, conditional on the full graded CAR/time
000255 |     intertwiner and collar admissibility.
000256 | 
000257 | NOT PROVED BY THE CITED ORIGINALS:
000258 | 
000259 |   * SF=1 uniquely fixes D_coll or its covariance;
000260 |   * gap, chirality and reflection uniquely fix K;
000261 |   * the archived source establishes the full graded CAR/time embedding needed
000262 |     to conclude that omega equals the spectral-projector quasifree state;
000263 |   * APS or Quillen reconstructs the QWZ source;
000264 |   * P1 selects width=8, mass=1 and r=1.
000265 | 
000266 | The first actual additional premise is therefore not a numerical QWZ
000267 | parameter and no longer an independent state choice. It is the full graded
000268 | CAR operator-and-time identification on the actual local boundary subsystem.
000269 | Positive energy then forces the covariance. Passing that test would make QWZ
000270 | a genuine regulator representative of the original seed and would remove the
000271 | demand to derive its microscopic coordinates as new P1 constants.