TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ACTUAL-WEAK-CONNECTION-AND-JOINT-SOURCE.txt Original file SHA-256: 705850cdc2e54ccb0edffbaf3c6dfd38446bca31c5bfffda0b21d424ab58cad3 Inclusive original lines: 1-119 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 | ACTUAL WEAK CONNECTION: FAMILY ORIENTATION SURVIVES IN THE JOINT SOURCE 000002 | 30 October 2026. Root calculation on the existing source, with actual v252 data. 000003 | No new action, physical input fit, boundary state, or original-suite edit. 000004 | 000005 | 1. First decisive source operation 000006 | The original continuum connection was previously kept abstract in 000007 | h=A gamma_F-i gamma_F Phi, C22=(1+exp(2ell h))^-1, 000008 | G=[[a,X],[X,1-a]], X=(2cosh(ell h))^-1. 000009 | The full odd-reader dictionary already applies to even, noncommuting A. 000010 | Insert the actual existing charged weak generator into that A, without 000011 | replacing the finite coefficient or deleting the other face. 000012 | 000013 | Let T=pi(0,i sigma_x,0) through v252.rep. The real gauge lift is 000014 | L=T+J_F T J_F^-1, 000015 | Q=-i L=tx-J_F tx J_F^-1, tx=pi(0,sigma_x,0). 000016 | The minus sign in Q follows from antiunitarity. Q is selfadjoint, even, 000017 | and is precisely the Hermitian form of the original weak Lie generator. 000018 | On the existing quarter mode p=1/4, use the formal original field probe 000019 | A(t)=p I+tQ, 000020 | h(t)=(p I+tQ)gamma_F-i gamma_F D_F. (1) 000021 | t is not a selected physical background or fitted interaction constant. 000022 | It records an allowed connection insertion of the given source class. 000023 | At constant Higgs field, [A(t),D_F] need not vanish. In particular 000024 | h(t)^2=A(t)^2+D_F^2-i[A(t),D_F]. (2) 000025 | Deleting the last term would discard the actual coupled response. 000026 | 000027 | 2. Exact calculation with the whole actual finite builder 000028 | Use v252.full_D with 000029 | Yu=diag(1,2,3), Yd=diag(4,5,6), Yd'=P13 Yd. 000030 | All are diagnostic coefficients, not TFPT mass predictions. The separate 000031 | Yu and Yd singular spectra agree in both cases. Keep identical nonzero 000032 | Ye=diag(2,3,4), Ynu=diag(1,3,5), 000033 | MR=[[2,1,0],[1,3,1],[0,1,4]] 000034 | on both sides of the comparison. Retain all96 slots and the actual gamma, 000035 | J_F and gauge lift. No selected quark-only source replaces that matrix. 000036 | 000037 | Exact Gaussian-rational matrix multiplication yields, with Delta=unrotated 000038 | minus left-rotated-down: 000039 | Delta Tr96 h(t)^2=0, 000040 | Delta Tr96 h(t)^4=0, 000041 | Delta Tr96 h(t)^6=5760 t^2. (3) 000042 | The sixth moment is the first distinguishing even moment in this test. 000043 | The coefficient is obtained from (1), not inserted as an allowed invariant 000044 | with an independently chosen weight. The comparison is basis independent 000045 | under a simultaneous transformation of all original operators. 000046 | 000047 | 3. It is visible in the actual common two-face kernel 000048 | For t!=0, equation(3) proves that the eigenvalue multisets of h(t)^2 differ. 000049 | For EVERY given ell>0, u -> 1/(2cosh(ell sqrt(u))) is strictly decreasing 000050 | on u>=0. Therefore the two actual cross-face blocks X have different 000051 | eigenvalue multisets. This is stronger than only finding a permitted word 000052 | in an uncomputed effective action. It follows through the whole existing 000053 | source operation and cannot disappear by a common unitary change of frame. 000054 | 000055 | For a finite p block the Taylor coefficients give a compact scalar check: 000056 | X=I/2-ell^2 h^2/4+5ell^4 h^4/48-61ell^6 h^6/1440+O(ell^8), 000057 | Delta Tr X=-244 ell^6 t^2+O(ell^8), (4) 000058 | Delta logdet X=-128 ell^6 t^2+O(ell^8). (5) 000059 | The last equality uses logcosh z=z^2/2-z^4/12+z^6/45+O(z^8). 000060 | Equations(4)-(5) are finite-mode asymptotics, not interchanges of a small 000061 | ell expansion and the infinite sum over the circle. No whole determinant 000062 | normalization, Pfaffian phase or physical scale is inferred from them. 000063 | Individual scalar traces might agree at isolated widths; the differing 000064 | cross-block eigenvalue multisets persist for every positive width. 000065 | 000066 | The UNLABELLED full G spectra remain0,1 because both are projections of 000067 | the same rank. This does not erase the labelled cross-face information. 000068 | Equivalently, logit(C22)=2ell h retains the sixth-moment distinction. 000069 | The existing CAR source then carries the corresponding different mixed 000070 | two-point functions and its higher products with the given conventions. 000071 | No new Gaussian/state choice was made for this inference. 000072 | 000073 | [OMITTED: non-scientific conversation or execution metadata] 000074 | [OMITTED: non-scientific conversation or execution metadata] 000075 | [OMITTED: non-scientific conversation or execution metadata] 000076 | [OMITTED: non-scientific conversation or execution metadata] 000077 | [OMITTED: non-scientific conversation or execution metadata] 000078 | [OMITTED: non-scientific conversation or execution metadata] 000079 | [OMITTED: non-scientific conversation or execution metadata] 000080 | [OMITTED: non-scientific conversation or execution metadata] 000081 | [OMITTED: non-scientific conversation or execution metadata] 000082 | 000083 | 5. Corrected next origin step 000084 | The source is capable of retaining mixing already with constant Higgs 000085 | through its existing charged weak connection. A new seam derivative is 000086 | not necessary for that capability. Next evaluate the original joint action 000087 | with this SAME actual field dependence, rather than remove the connection 000088 | and infer a theorem from the separate finite spectra. 000089 | 000090 | [OMITTED: non-scientific conversation or execution metadata] 000091 | [OMITTED: non-scientific conversation or execution metadata] 000092 | [OMITTED: non-scientific conversation or execution metadata] 000093 | [OMITTED: non-scientific conversation or execution metadata] 000094 | [OMITTED: non-scientific conversation or execution metadata] 000095 | [OMITTED: non-scientific conversation or execution metadata] 000096 | [OMITTED: non-scientific conversation or execution metadata] 000097 | [OMITTED: non-scientific conversation or execution metadata] 000098 | 000099 | In particular v250:14-17,57-62 explicitly says that the flavor layer 000100 | already fixes charged mass ratios in its stated contract. That framing 000101 | does not establish the common-source dictionary, and no new Yukawa fit 000102 | is required here to replace those old results. Its older NCG obligations 000103 | must be read together with later v252/v254 results. 000104 | 000105 | 6. Reproducibility and original source handles 000106 | check_actual_weak_source_moment.py imports the unchanged v252 constructors, 000107 | converts their diagnostic Gaussian-integer entries exactly, and performs 000108 | polynomial matrix multiplication in SymPy. It keeps p=1/4 and t symbolic. 000109 | actual-weak-source-moment-results.json records every coefficient and check. 000110 | Original v252 full_D:102-116, grading:119-124, Kswap:127-132, rep:139-168; 000111 | the pre-existing reader/graph dictionaries supply the actual source map. 000112 | No original paper, ledger or verification file is modified. 000113 | 000114 | [OMITTED: non-scientific conversation or execution metadata] 000115 | [OMITTED: non-scientific conversation or execution metadata] 000116 | [OMITTED: non-scientific conversation or execution metadata] 000117 | [OMITTED: non-scientific conversation or execution metadata] 000118 | [OMITTED: non-scientific conversation or execution metadata] 000119 | [OMITTED: non-scientific conversation or execution metadata]