TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HOLONOMY-E0-SOURCE-REVIEW.txt
Original file SHA-256: 58933c7051e1b008adecf553a607a93be768e0bbcfec17c6a50428a190f0982b
Inclusive original lines: 499-662
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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000499 | 9. The original Z6/Kstr consumer does not supply a rho observable on F5/96
000500 | 
000501 | 9.1 The exact operator chain in the original source
000502 | 
000503 | The original discrete phase section defines
000504 | 
000505 |   omega=exp(2 pi i/3),
000506 |   U6=diag(1,omega,omega^2,-1,-omega,-omega^2),               (18)
000507 |   D_y=y I-delta U6.                                         (19)
000508 | 
000509 | It explicitly identifies U6 with the Fourier form of the one-step shift on
000510 | C6. The structural restriction and kernel are
000511 | 
000512 |   P_str=P_Seam,+ P_sing P_Theta,
000513 |   P_Seam,+=(1+i C)/2,
000514 |   P_Theta=(1+Q_Theta)/2,
000515 |   P_sing=(1+Z_c+Z_c^2)/3,                                   (20)
000516 |   K_f^str=(P_str D_f^dagger D_f P_str)^(-1/2).               (21)
000517 | 
000518 | The same source uses (21) in the flavor amplitude
000519 | 
000520 |   <e_i,Hol_G_D4(nabla_F^star) K_f^str e_j>.                  (22)
000521 | 
000522 | Thus the actual consumer assigned to K_f^str is a positive normalization and
000523 | residue/hierarchy kernel. The source separately assigns the phase observable
000524 | to arg tr(Pi_triangle); it even says that this family-holonomy phase is not an
000525 | additional transport parameter. Equations (18)-(22) do not define a phase
000526 | expectation value of K_f^str.
000527 | 
000528 | Source: documents/archive--tfpt-45--source_extracts--03_em_flavor_source/
000529 | sections/003-subsection-discrete-phase-operator-and-transport-grammar.tex,
000530 | especially lines 3-13, 61-125, SHA256
000531 | 00a2cf1b249b77280dbbf6dfb41c91c77e08aa63e0f30b682d1a8a621f3dd7ec.
000532 | 
000533 | 9.2 Decisive orientation test
000534 | 
000535 | For the explicit bare source (19), with real y and delta,
000536 | 
000537 |   D_y^dagger D_y
000538 |    =(y^2+delta^2)I-y delta(U6+U6^dagger).                    (23)
000539 | 
000540 | Replacing U6 by U6^dagger leaves (23), and therefore every fixed compression
000541 | P_str D_y^dagger D_y P_str and its positive inverse square root, unchanged.
000542 | The source itself writes the corresponding regularized Green kernel as a
000543 | cubic polynomial in
000544 | 
000545 |   C=(U6+U6^dagger)/2.                                       (24)
000546 | 
000547 | Consequently the supplied bare Kstr consumer is even under reversal of the
000548 | Z6 orientation. It cannot distinguish rho=exp(i pi/3) from bar(rho), which a
000549 | CP-odd phase observable must do.
000550 | 
000551 | The un-squared resolvent retains oriented powers in Fourier form,
000552 | 
000553 |   D_y^(-1)= [sum_(m=0)^5 y^(5-m) delta^m U6^m]
000554 |              /(y^6-delta^6).                                (25)
000555 | 
000556 | But in the site basis used for the source's off-diagonal Yukawa amplitudes,
000557 | 
000558 |   <e_i|D_y^(-1)|e_j>
000559 |     =y^(5-k) delta^k/(y^6-delta^6),  k=(i-j) mod 6,          (26)
000560 | 
000561 | which is real. A direct exact replay with the 6 by 6 shift verified both the
000562 | resolvent identity in (25) and the equality of the two Gram matrices under
000563 | U6 <-> U6^dagger. All 36 numerators in the site chart are real polynomials.
000564 | 
000565 | The source later permits D_f=D_0+V_adm, with [P_str,V_adm]=0 and a norm
000566 | bound, but gives no matrix for V_adm. Such an unspecified perturbation cannot
000567 | be used to infer an oriented phase response. The exact conclusion here is
000568 | about the explicitly supplied bare Z6 kernel and its stated positive
000569 | consumer, not about every possible admissible completion.
000570 | 
000571 | Sources:
000572 | 
000573 | * the same original source tree, 004-source.tex:340-389, SHA256
000574 |   107d525221eb816043dbf4fb1a3c7e8244d3e24a5a5bcbfe1c2c34d8ee192f4a;
000575 | * the same original source tree, 005-source.tex:1-230, SHA256
000576 |   786d2619e775775d70adf177794138485b261968042a880b2f0f617bb0111814;
000577 | * documents/tfpt_2_standard_model/sections/
000578 |   011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex:162-178,
000579 |   SHA256 a6ddc0c8bfa566b632b1b3734ea44ab684761310b141bcc05fd895c0c179961b.
000580 | 
000581 | 9.3 What v561 actually proves
000582 | 
000583 | The v561 checker explicitly labels itself a narrowing result. It inserts
000584 | 
000585 |   RHO=exp(i pi/3)                                             (27)
000586 | 
000587 | as a declared constant and checks the arithmetic identity
000588 | 
000589 |   sum_(d in {2,8,12,14,18,20,24,30}) RHO^d = 4 RHO.          (28)
000590 | 
000591 | It then finds two inequivalent scalar diagnostics,
000592 | 
000593 |   P2=arg(sum RHO^d),             character (-1,+1),
000594 |   V5=Im(RHO det)/det,            character (-1,-1).           (29)
000595 | 
000596 | Neither (28) nor (29) is a state, an insertion, an operator on the E8
000597 | adjoint, or an expectation value. The checker says that neither carrier is
000598 | frame-coupled and leaves the physical choice open. In particular, (28) is
000599 | not an E8 adjoint trace merely because the summation indices are E8 degrees.
000600 | 
000601 | Source: verification/v561_cp_channel_identities.py:1-33,65-106,121-124,
000602 | SHA256 79e3552c12978093ec248861c1b8d7288e0f4eb51ba3fd4fbced7bb900e5817d.
000603 | The current Atlas audit classifies RHO in this checker as a declared axiom.
000604 | 
000605 | 9.4 Typing against the actual whole F5/96 source
000606 | 
000607 | The finite source checker fixes
000608 | 
000609 |   H_F=C^96=(particle/antiparticle) x (three generations) x C^16
000610 | 
000611 | and builds the complete D_F from 3 by 3 generation matrices Y and the
000612 | Majorana block, together with the actual J_F, grading and face data. It does
000613 | not define U6, RHO, K_f^str, a representation C6 -> End(H_F), an embedding of
000614 | the six phase sites into the generation/particle slots, or an observable O
000615 | whose expectation is P2 or V5. Its displayed Y matrices are structural test
000616 | inputs; they are not obtained from (18)-(26).
000617 | 
000618 | Therefore the already fixed full source state and time evolution cannot yet
000619 | measure rho: the operator to evolve and the typed consumer to read are
000620 | absent before any state or time question arises. Although C^96 can of course
000621 | host many six-dimensional subspaces, choosing one would be a new phase-fiber
000622 | embedding rather than a consequence of the original source.
000623 | 
000624 | Source: verification/v252_full_finite_triple.py:1-280, SHA256
000625 | 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163.
000626 | 
000627 | There is also a relevant prior exact exclusion. In the original 240-root
000628 | source Hamiltonian a common multiplication of every source ray by one phase
000629 | leaves all ray projectors, reflections, overlaps and the full Hamiltonian
000630 | exactly fixed. Hence inserting rho merely as a common scalar phase cannot
000631 | make it observable. A relative phase between two independently phased
000632 | sources is visible through the already defined overlap quadratures, but that
000633 | is a different, two-source response and does not supply the missing map from
000634 | the Z6 transport fiber into H_F.
000635 | 
000636 | Source: experiments/theory-contracts/
000637 | common-source-gauge-grade-transfer-20260920/phase_operator/PROOF.md,
000638 | SHA256 874f2eb2082c0a90de9d35792d8ab3f377a33c92c204d2ac82522a7c4a0746e6.
000639 | The independent positive-spectrum counterexample in
000640 | experiments/theory-contracts/phase-origin-yukawa-defect-20260919/PROOF.txt,
000641 | SHA256 4d3f9e0b24b445e0d72fc7816e6c5aa860c8c8f957cbd997291e704958a154e0,
000642 | likewise shows that doubled positive data do not select a chiral determinant
000643 | phase.
000644 | 
000645 | 9.5 Verdict and first missing definition
000646 | 
000647 | No original rho-carrying operator insertion or response functional on the
000648 | actual full F5/96 source was found. The explicit Kstr path is a positive,
000649 | orientation-even magnitude consumer. The bare closed v117 triangle remains
000650 | real by Section 8. The v561 identity 4 RHO is a scalar character sum with RHO
000651 | already supplied.
000652 | 
000653 | This is a scoped obstruction, not a universal exclusion of coherent phase
000654 | measurements. The first missing source datum is a typed oriented evaluation
000655 | or coherence map from the Z6 phase fiber into End(H_F), together with an
000656 | observable that distinguishes rho from bar(rho) and is compatible with the
000657 | actual J_F, grading, faces, state and time evolution. The original source
000658 | must supply that map or an equivalent open-leg/interference insertion. It
000659 | cannot be obtained by placing a chosen Z6 scalar into the round product
000660 | Pi_triangle. Until that datum exists, Kstr fixes residue magnitudes while the
000661 | pi/3 phase remains a separate declared phase fiber rather than a measurable
000662 | observable of the given whole source.