TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/paper-source-reconstruction-20261025/SMEARED-OCTIC-ENERGY-BOUND.txt
Original file SHA-256: 9ba6c518b6f254ff1c4152fb27d8525154cbd92b47377c5c59ba597b8823f563
Inclusive original lines: 401-487
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000401 | (Lhat_-1)^8 Omega_d therefore use a finite original CAR word inventory, and
000402 | their microscopic matrix element converges before any infinite mode sum is
000403 | needed.
000404 | 
000405 | ORIGINAL-CAR-WARD-IDENTIFICATION.txt now supplies the direct source-mode
000406 | calculation behind this corollary. With K=Lcal_-8/8 and
000407 | 
000408 |   c(r)=(r+alpha+4)/8,
000409 | 
000410 | the original CAR commutator and sea crossing give exactly
000411 | 
000412 |   [K,h_(k,-n)]=n h_(k,-n-1),
000413 |   K Omega=sum_k delta_k h_(k,-1) Omega.
000414 | 
000415 | Thus the finite energy-64 Ward vector is obtained inside the same original
000416 | CAR representation used above. Its exact nonzero amplitude is
000417 | 
000418 |   <F8;d|(Lcal_-8)^8 Omega>
000419 |     =sqrt(35)(16250979+56071008 i)/128.
000420 | 
000421 | The accompanying checker verifies the current QWZ strip atoms against the
000422 | preserved historical AST and checks 258 bounded source modes. Those finite
000423 | diagnostics corroborate this corollary; the all-energy smeared theorem rests
000424 | on equations (1)--(25), not on the finite diagnostic sample.
000425 | 
000426 | The theorem proves:
000427 | 
000428 |   * the same one-channel QWZ field, state, charge, time and adjoint feed the
000429 |     shifted neutral F8 smearing;
000430 |   * F8(rho) and its adjoint are closable energy-bounded continuum operators on
000431 |     the common finite-energy core;
000432 |   * both the global mode route and the separately mollified local route give
000433 |     transported strong iterated microscopic limits;
000434 |   * the exact energy-64 Ward amplitude is retained.
000435 | 
000436 | The theorem does not prove:
000437 | 
000438 |   * a bounded point field F8(x);
000439 |   * a simultaneous or regulator-independent diagonal N/UV limit;
000440 |   * exact interval support for finite current-mode cutoffs;
000441 |   * selection of the QWZ collar or quotient localization by P1/P2;
000442 |   * an odd E8 root/spinor field, full microscopic field exhaustion or a
000443 |     3+1-dimensional reconstruction.
000444 | 
000445 | 8. Sources
000446 | ----------
000447 | 
000448 | Original microscopic elementary-field theorem:
000449 | 
000450 |   paper-source:7296b452273b7022082ac2e2
000451 |   tex-artefacts/toe_research_20260909.tex:16--96;
000452 | 
000453 |   experiments/theory-contracts/microscopic-charged-car-limit/README.md:
000454 |   41--68,70--117,119--226.
000455 | 
000456 | Folded covariance and current normal ordering:
000457 | 
000458 |   research-source:1a8c7c3f539e779301a7377d
000459 |   experiments/theory-contracts/joint-native-algebra-selection-20261016/
000460 |   FOLD-COVARIANCE-TO-NATIVE-FIELD-RESPONSE.txt:53--152;
000461 | 
000462 |   research-source:9abbdd1d97ecab558a6beb99
000463 |   experiments/theory-contracts/native-octic-seam-origin-20261025/
000464 |   CAR-OCTIC-DICTIONARY.txt:1--109.
000465 | 
000466 | Exact octic normalization and Ward amplitude:
000467 | 
000468 |   experiments/theory-contracts/native-octic-seam-origin-20261025/
000469 |   NATIVE-FOLDED-OCTIC-ORIGIN.txt:22--146;
000470 |   native_folded_octic_origin.py.
000471 | 
000472 | Direct original-CAR stress/current identification and current-source
000473 | diagnostics:
000474 | 
000475 |   experiments/theory-contracts/paper-source-reconstruction-20261025/
000476 |   ORIGINAL-CAR-WARD-IDENTIFICATION.txt;
000477 |   microscopic_octic_composition.py.
000478 | 
000479 | Standard energy-bound framework used only for comparison and terminology:
000480 | 
000481 |   Carpi, Kawahigashi, Longo, Weiner,
000482 |   From vertex operator algebras to conformal nets and back,
000483 |   arXiv:1503.01260;
000484 | 
000485 |   Carpi, Tanimoto, Weiner,
000486 |   Local energy bounds and strong locality in chiral CFT,
000487 |   arXiv:2103.16475.