TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/C58-ORIGINAL-APS-AND-SEWING-REVIEW.txt Original file SHA-256: 6efaea0323cd55e250bec2d1423151fb9bc05555c139907fd5944dcd525da34a Inclusive original lines: 1-127 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. 000001 | C58: THE ACTUAL APS CHOICE, WHOLE CALDERON SOURCE AND SEWING 000002 | 30 October 2026. Independent targeted original-source review. 000003 | No new source, state, domain choice, checker run, original edit or Atlas change. 000004 | 000005 | Verdict 000006 | The original provisional APS theorem supplies a fixed-domain perturbation 000007 | contract once its geometric anchor and adapted boundary operator are given. 000008 | It does not set that operator equal to the Phi=0 kinetic operator and does 000009 | not call a reference-sea boundary vector in Z_adm. C58's asserted unique 000010 | old P0 therefore does not follow. Moreover the original full D_+ Calderon 000011 | construction PRECEDES the relative split, so a degeneracy of the later 000012 | D_rel upgrade cannot eliminate the already existing whole Cauchy source. 000013 | The established fixed-cap amplitude remains a valid comparison under its 000014 | stated exterior/CAR sewing contract; it is not selected by the APS theorem. 000015 | 000016 | 1. Exact original source handles 000017 | B1 = documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/ 000018 | sections/001-section-primitive-core-and-carrier-interface-handoff.tex 000019 | SHA256 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79 000020 | paper-source:8027564739689dd02e02f11c, lines58-377; 000021 | research-source:666f49c8dea3f8819e27c103, lines353-377. 000022 | B2 = same directory, 002-section-intrinsic-closed-branch-and-canonical-rigid- 000023 | obje.tex, SHA256 1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e 000024 | research-source:0c3af591ac78ed8332145c62, lines33-84; 000025 | research-source:38b1537329d8bec338b1b1a2, lines100-119. 000026 | Q2 = documents/archive--tfpt-45--source_extracts--04_qft_source/sections/ 000027 | 002-section-closure-theorems-from-the-admissibility-complex.tex 000028 | SHA256 61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c 000029 | research-source:9ce95751dc72a6922f3bd238, lines167-198. 000030 | These three registered original intervals were read, not inferred from 000031 | their titles or the earlier review. B1's earlier definitions were reread. 000032 | 000033 | 2. First actual domain call, and the missing equality in C58 000034 | B1:353-377 takes a finite compact geometric cutoff, D_geo, an ADAPTED 000035 | boundary operator A_partial, and CHOOSES a modified APS boundary condition 000036 | B_sa=H^(1/2)_-(A_partial), 000037 | with a chosen kernel Lagrangian when needed. Its perturbation realization 000038 | is D_geo,B_sa+D_rel on the same domain. B2:33-42 explicitly calls this an 000039 | analytic starting representative; it distinguishes the later closed 000040 | domain and the subsequently induced family pairing. The original symbol 000041 | guide 01/003:121-122 repeats that distinction. 000042 | 000043 | The displayed source does not contain A_partial=p gamma_F, a Phi=0 anchor, 000044 | or P0=P_-(p gamma_F). To obtain precisely the old source cap one must 000045 | identify this actual adapted operator, including both endpoint normal 000046 | orientations, with that old kinetic one. The word FIXED says what remains 000047 | constant under the subsequent perturbation. It does not specify which 000048 | anchor was fixed, and it is not a quantum boundary-state preparation rule. 000049 | An adapted operator is principally prescribed; its name alone also does 000050 | not remove permitted zero-order boundary terms. 000051 | 000052 | The existing actual constant Phi perturbation is bounded zero order and 000053 | satisfies the needed same-domain theorem. The already reviewed generic 000054 | first-order relative-bound-zero error is not rediscovered here; reuse 000055 | finding:order-one-infinitesimal-bound-inference-fails and 000056 | finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair. 000057 | 000058 | 3. The original whole Calderon call survives the later split question 000059 | B1:72-81 starts with a FULL D_+=gamma_n(partial_n+B_Sigma) on a 000060 | reflection-regular collar. B1:101-107 defines P_C from the boundary problem 000061 | for D_+. Only afterwards, at122-129, are D_ref and D_rel defined using 000062 | the actual geometric deck pullback. These are distinct operator calls. 000063 | 000064 | Q2:167-198 subsequently asserts an APS upgrade through the canonical 000065 | double D_b of D_rel. If a proposed particular split makes this D_rel=0, 000066 | the zero operator does not meet the usual Dirac-type elliptic Calderon 000067 | construction used in that proof sketch. This challenges that substitution 000068 | in the LATER upgrade, not the earlier full D_+ Cauchy-data construction. 000069 | It yields no exhaustive theorem that only the old reference APS cap remains. 000070 | Nor is D_rel=0 for every constant field a consequence of these original 000071 | formulas: the deck includes base and spin/domain transport. The existing 000072 | deck-vs-fiber split findings are reused, not rederived here. 000073 | 000074 | The smallest positive whole-source check is already exact. For the given 000075 | constant full collar, mode h and R=exp(-ell h), its Cauchy graph has 000076 | G(h)=[[A,X],[X,I-A]], 000077 | A=(1+exp(-2ell h))^-1, X=(2cosh(ell h))^-1. 000078 | At finite ell and each finite eigenvalue X>0, and G is a nonzero projector. 000079 | Even Phi=0 leaves this whole source. No replacement state or new Calderon 000080 | problem is required. The earlier proof applies on its actual graph domain. 000081 | This is reuse of the completed whole-source construction, not a new one. 000082 | 000083 | 4. The actual fixed-cap sewing call and its unavoidable energy factor 000084 | Reuse finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction, 000085 | APS-DOMAIN-AND-STATE.txt and FIXED-CAP-DETERMINANT.txt:14-35,82-97. 000086 | For the specified old endpoint spaces P=P_-(h0), h0=p gamma_F, the 000087 | already proved fixed inverse and exterior sewing are available. At one 000088 | existing odd pair h=p sigma_z+m sigma_y, E=sqrt(p^2+m^2), they give 000089 | M=P exp(-ell h)P=cosh(ell E)+|p|sinh(ell E)/E, 000090 | C=exp(-ell E)M=a+(1-a)exp(-2ell E), 000091 | a=(1+|p|/E)/2. 000092 | The reference old-sea exterior amplitude is exp(ell|p|). Thus the ACTUAL 000093 | ratio to that reference is 000094 | A_fixed/A_ref=exp(ell(E-|p|)) C. 000095 | It is C only after a COUPLED sea-energy subtraction, or when the moving 000096 | coupled exterior amplitude rather than the old reference is divided out. 000097 | In many slots this retains exp(ell sum(E-|p|)) times det_F C; the known 000098 | bulk renormalization and common source scalar are not removed by the 000099 | finite boundary determinant. No new calculation or cutoff extrapolation 000100 | is required for this already established sewing identity. 000101 | 000102 | Therefore C58's ratio-to-old-reference step cannot itself identify the 000103 | primitive Z_rel with the H_exc-normal-ordered cap. Actual boundary data 000104 | plus a fermionic sewing/quantization rule could supply a cap insertion; 000105 | the closed elliptic realization alone does not supply that second call. 000106 | 000107 | 5. Stronger actual original quantum consumer, retained rather than erased 000108 | B2:103-119 already defines the full operational Seed with A_loc, tau_t, 000109 | Theta, omega, seam class and elliptic collar. Its omega/time are not to be 000110 | chosen again from an APS realization. The later original QFT4:111-155 has 000111 | an actual different full transfer consumer: T_V is built from the given 000112 | local C6 kernels, diagonal admissibility weights and P_adm; its stated 000113 | primitive Perron construction supplies the finite-volume vacuum v_V^*. 000114 | Reference: research-source:29a6b485f10379ecc3c34ec6, QFT/004-source.tex, 000115 | SHA256 a5d1cc26f80d2f1d5af3d89b94cf8ff8912b572040614d4e1c27f1fe3b747126. 000116 | On that stated original consumer the direct vacuum call is exactly 000117 | =||v_V^*||^2. 000118 | This uses its original Perron equation, not an independently selected sea. 000119 | The previously reviewed producer/weight scope remains unchanged; no new 000120 | T_V, normalization convention or equivalence with F5 is introduced here. 000121 | 000122 | The concrete source comparison is consequently to transport the actual 000123 | original boundary insertions/reference through this existing whole source 000124 | or its stated OS caller. C58 supplies no original equality doing that with 000125 | the specific old P0, so its exclusivity and completed-origin claims fail. 000126 | The valid fixed-domain cap, whole graph and existing original quantum 000127 | consumer all remain available. None is eliminated by a constant split.