TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/direct/WEAKEST-DIRECT-E8-SOURCE-ROUTE.txt
Original file SHA-256: fb13b19762d7e8a327547859a56a335f717d1711f0d4ad3d924c7b26b7ab6583
Inclusive original lines: 401-504
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.

000401 | 
000402 |   raw RP seam state and observables
000403 |       -> the canonical V_E8 vacuum representation.          (7.1)
000404 | 
000405 | This is the active content of SEAM.EQUIV.01.  A physical C3 Cauchy map may
000406 | prove (7.1), but it is one route rather than part of the statement that has
000407 | to be assumed.
000408 | 
000409 | There is already a concrete original operator on the source side.  The old
000410 | ordered CAR winding W1 extends to a unitary finite energy operator W_ext on
000411 | all four D8 Heisenberg modules.  On the common algebraic core it transports
000412 | the lattice fields by
000413 | 
000414 |   W_ext Y(e^lambda,x) W_ext^(-1)
000415 |     =a(lambda) x^(-(R lambda).e0) Y(e^(R lambda),x),          (7.2)
000416 | 
000417 | with the retained cocycle, Klein phases, charge action and quarter Ward
000418 | identities. The vertex representation on 0+s is E8; W_ext maps it to v+c.
000419 | Half-integral powers of x in (7.2) encode the resulting twisted monodromy.
000420 | 
000421 | Equation (7.2) is already the algebraic defect operator required by the
000422 | compiler.  Its exact boundary is locality: W_ext is a global representation
000423 | intertwiner, not yet a point local smeared field on the primitive source
000424 | Hilbert space.  Formal Li transport does not prove a common strong operator
000425 | core or a bounded localized net defect.
000426 | 
000427 | This sharpens (7.1) further.  The smallest sufficient original theorem is a
000428 | local state and adjoint preserving star morphism from the already fixed
000429 | CAR/AIA sector, with its common conformal vector and one nonzero M_h field,
000430 | into the primitive P1 source.  The marked generator theorem then supplies
000431 | the whole E8 field.  Reconstructing W_ext again from a physical genus two
000432 | bulk would duplicate an operator that already exists algebraically.
000433 | 
000434 | 
000435 | 8. SOURCE STATUS
000436 | ================
000437 | 
000438 | Atlas revision checked
000439 | 
000440 |   ab02252b5bdcfccd5fb5cf3d
000441 | 
000442 | Reviewed exact sources
000443 | 
000444 |   experiments/theory-contracts/e-series-source-reconstruction-20261024/
000445 |     SIMPLIFICATION.txt
000446 |     SHA256 51bb029fdaa33e327d2d24d98b47972a19bacf6a5987452a1ea3010be7130dab
000447 | 
000448 |   experiments/theory-contracts/e-series-source-reconstruction-20261024/
000449 |     THEOREMS.txt
000450 |     SHA256 5c0d7328c583cdbc0a8c358445b57821d5b5722540ca372c1d28052b900eb584
000451 | 
000452 |   experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/
000453 |     SPIN-RIGIDIFIED-THETA-MODULE.txt
000454 |     SHA256 4bd17ffbb2be4b31c4eb7a4efe9cd8a1191c9065655889ce189f3b1f6c2499d2
000455 | 
000456 |   research-20261027-boundary-origin/uniqueness/
000457 |     SAME-SPIN-REFERENCE-SIMPLIFICATION.txt
000458 |     SHA256 8a0586c93b371905105d33f04c1deb796c9f603c0fed09c8cc90dbb33bd64481
000459 | 
000460 |   research-20261027-boundary-origin/source/
000461 |     ORIGINAL-BOUNDARY-NORM-ORIGIN.txt
000462 |     SHA256 2a92d7c75aeed3fb09d85de0f9cf8be3c9fb8757b6686cf0c6724cd7b4a977a6
000463 | 
000464 |   research-20261027-source-unification/analytic/
000465 |     C3-CAUCHY-HARDY-ARROW.txt
000466 |     SHA256 3c8c2b55ca3a58469aaaa61be3e2d74b2075cc33d132fef799790fad22c1bdc2
000467 | 
000468 |   experiments/theory-contracts/canonical-seam-fermionization-20261025/
000469 |     SAME-SOURCE-AFFINE-DEFECT.txt
000470 |     SHA256 514356e9ca01f8aa02399020a503f6cd782c879b00220274b7c4377cbbad7255
000471 | 
000472 | Original seam source checked
000473 | 
000474 |   documents/tfpt_research_contracts/sections/005-source.tex
000475 |     SHA256 1b75b77d20cace101afe1a24b682ce2a1022dea797cfdfacea6f47542e93ba19
000476 | 
000477 | It explicitly leaves the unconditional raw seam to holomorphic E8 boundary
000478 | identification open.  Its stronger historical wording about a unique
000479 | fundamental postulate does not alter the later sharper marked generator
000480 | theorem: for the chiral mathematical field, the sufficient premise is (4.8).
000481 | For the physical equality of the raw seam state with that vacuum, the parent
000482 | claim remains open.
000483 | 
000484 | Primary mathematical theorems already used by the accepted contracts
000485 | 
000486 |   Huang, Kirillov and Lepowsky, arXiv:1406.3420, Theorem 3.2.
000487 |   Kirillov and Ostrik, arXiv:math/0101219, Theorems 1.6 and 3.3.
000488 |   Davydov, Mueger, Nikshych and Ostrik, arXiv:1009.2117,
000489 |     Sections 3.3 and 3.4.
000490 |   Carpi, Gaudio, Giorgetti and Hillier, CMP 402 (2023),
000491 |     Theorems 3.9, 4.7, 4.10 and Corollary 4.11.
000492 |   Mumford, On the Equations Defining Abelian Varieties I,
000493 |     Inventiones Mathematicae 1 (1966), Sections 1 and 2.
000494 | 
000495 | 
000496 | CONCLUSION
000497 | ==========
000498 | 
000499 | The unnecessary requirement was the physical C3 bulk identification, not
000500 | the locality premise.  The curve already works as a canonical auxiliary
000501 | splitting and theta space for the finite marks.  The E8 field already follows
000502 | from one marked local generator in the same conformal compiler extension.
000503 | Only the identification of the primitive RP source with that local extension
000504 | and its vacuum remains a physical origin statement.