TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ORIGINAL-RELEVANCE.txt
Original file SHA-256: 516d23005f6b55e0471279ab7b1ab85d4f7f8b56282423c0aae4fabf51ef4362
Inclusive original lines: 381-523
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.

000381 | 4. The first additional assumption, stated minimally
000382 | =====================================================
000383 | 
000384 | The missing premise is not "choose the midpoint cut", "choose alpha", or
000385 | "choose tau=i" independently.  It is the single transport assertion (4).
000386 | Written as a checkable tuple, it must provide:
000387 | 
000388 |   I_top:   the original orientable double of the Moebius base is identified
000389 |            with A_+ or A_- as one object in the Q-paired groupoid;
000390 | 
000391 |   I_seam:  the original seam core and its two cut faces are mapped to the
000392 |            corresponding annulus core and traces, rather than merely to a
000393 |            homotopic circle or to the Schottky fixed boundary;
000394 | 
000395 |   I_deck:  the original free Z2 deck maps to delta_A;
000396 | 
000397 |   I_spin:  its genuine order-four Pin lift maps to A_g up to the central
000398 |            real sign, with no independent U(1) phase;
000399 | 
000400 |   I_clock: Q transports the complete field, domain, state and observables
000401 |            between A_+ and A_-, not only the base points;
000402 | 
000403 |   I_metric: if the target is the later fixed flat full Dirac source, the map
000404 |             must derive the elliptic modulus 1/2 from that source or supply
000405 |             an explicit conformal/operator transport from its modulus 1;
000406 | 
000407 |   I_op:    the original B_Sigma, U_Gamma and Calderon or OS operators retain
000408 |            their actual domains and are not replaced by algebraic h, delta
000409 |            or rho merely because the group orders agree.                   (18)
000410 | 
000411 | This is one load-bearing equivariant source map with several preservation
000412 | obligations.  The obligations prevent a structural match from being promoted
000413 | to a physical dictionary without operator action.
000414 | 
000415 | I_metric is vacuous only when the claim is the broad topological A4
000416 | realization.  It is essential for equality with the already fixed full
000417 | two-dimensional flat Pin operator.  A circle-unit conversion does not meet
000418 | that obligation.
000419 | 
000420 | The modulus tau=i is already fixed on the compiler parity cover by the
000421 | harmonic mu4 cross ratio.  It is not an extra continuous fit after (1).
000422 | Nevertheless A4 by itself does not fix that modulus, and tau=i is not
000423 | B_Sigma, a Euclidean time scale or a transfer kernel.  Those identifications
000424 | belong to I_op.
000425 | 
000426 | 5. Smallest decisive test
000427 | =========================
000428 | 
000429 | The complete decision can be compressed to four exact tests:
000430 | 
000431 |   T1  Eight-real-form census:
000432 |       dividing(rho_(a,b)) iff (a,b)=(1,1) or (1,3).
000433 | 
000434 |   T2  Group transport:
000435 |       Q rho_+ Q^-1=rho_-, so {rho_+,rho_-} is canonical but neither member
000436 |       alone is Q invariant.
000437 | 
000438 |   T3  Marked deck:
000439 |       h and Q^2 have fixed points; hQ^2 is the free translation by T and
000440 |       descends to the Moebius glide (8).
000441 | 
000442 |   T4  Spin character:
000443 |       Q invariance gives epsilon_A=epsilon_B; genuine A4 transport and
000444 |       g^2=B give epsilon_B=-1; hence alpha=(-,-) uniquely.                  (19)
000445 | 
000446 | T1 through T4 pass on the displayed existing data.  Full-source identity does
000447 | not: the fixed full annulus moduli are 1 and 1/2.  The abort test is also
000448 | precise.  If no map satisfying (18), including I_metric for the fixed flat
000449 | source, exists, the construction remains a canonical compiler geometry with
000450 | a matching Moebius and RP pattern, not the original physical P1 seam
000451 | realization.
000452 | 
000453 | 6. Relation to the preceding exact audits
000454 | ==========================================
000455 | 
000456 | The parity-cover source already warned that its marked base and all-J
000457 | representation were separately supplied and that physical seam equality
000458 | requires loop and peripheral intertwiners:
000459 | 
000460 |   experiments/theory-contracts/e-series-quarter-clock-20261023/PROOF.txt:
000461 |   177-228
000462 |   SHA256 ac3e95975adb14c82815731b3d8aa0f6e1caf72d25fb749250a5b1bbcd269884
000463 | 
000464 | The earlier base audit likewise states that the algebraic C2 acts on the
000465 | original normal or boundary problem only after an actual same-base cover and
000466 | spin transport are supplied:
000467 | 
000468 |   experiments/theory-contracts/original-admissible-source-closure-20261025/
000469 |   ORIGINAL-BASES-AND-ELLIPTIC-SPIN.txt:25-28,34-65,72-120
000470 |   SHA256 bf6b2336e24a39aef26b9907c24f033a47a8a1318f8f19ae561e4c477680ce67
000471 | 
000472 | The original-spin audit proves the local A4 implication and keeps the
000473 | geometric deck, Pin lift and winding coefficient distinct:
000474 | 
000475 |   experiments/theory-contracts/canonical-seam-fermionization-20261025/
000476 |   ORIGINAL-SPIN-AND-SEAM-DICTIONARY.txt:517-624,740-765
000477 |   SHA256 dfaef864428375b018d0eddcb77a4a5ccd085e996eb1c1b3f1d8db526991cf24
000478 | 
000479 | The new exact geometry and the corrected lift typing are in:
000480 | 
000481 |   research-20261026-fundamental-rethink/geometry/
000482 |   DIVIDING-REAL-FORMS.txt
000483 | 
000484 | It proves T1 through T3, the finite-width Calderon graph, and the central
000485 | commutator on the (-,-) line.  Its anti-linear Real lifts j_rho are kept
000486 | separate from the complex-linear full-Dirac pullbacks U_rho,U_delta,U_g.
000487 | 
000488 | Atlas audit frame: revision 70d8c8e427bd8d29c8610ff3.  No Atlas record was
000489 | changed.
000490 | 
000491 | Final classification
000492 | ====================
000493 | 
000494 | ORIGINAL OR DECLARED:
000495 | 
000496 |   the mu4 marked boundary line, the base quarter action, the Moebius
000497 |   orientable-double axiom, the seam cut and the order-four spin lift.
000498 | 
000499 | EXACT DOWNSTREAM CONSEQUENCE OF SUPPLIED TFPT DATA:
000500 | 
000501 |   the parity cover E, its h,Q,kappa group, j=1728 and tau=i.
000502 | 
000503 | INTRINSIC INSIDE THAT CONSEQUENCE:
000504 | 
000505 |   the unordered dividing orbit {hQkappa,hQ^3kappa}, the Q transport between
000506 |   its two annuli, and the unique free deck delta=hQ^2 among the involutions
000507 |   of the marked h,Q subgroup.
000508 | 
000509 | CONDITIONAL BUT RIGID:
000510 | 
000511 |   after the genuine equivariant transport (18), A4 and Q force the unique
000512 |   spin alpha=(-,-), its nullmode-free property and the order-four glide
000513 |   sectors.  No extra cut or spin character is chosen.  As a realization of
000514 |   broad A4 the elliptic modulus is already fixed by the compiler cover.  As
000515 |   an identification with the later concrete flat full Dirac source, the
000516 |   unresolved modulus transport I_metric remains an additional premise.
000517 | 
000518 | OPEN FIRST BRIDGE:
000519 | 
000520 |   construct I_cover with its seam, deck, spin, domain, state and operator
000521 |   preservation.  This is the first additional assumption.  Until it is
000522 |   derived, the construction is the strongest existing geometric candidate
000523 |   for the original seam, not a completed primitive P1 derivation.