TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-CHARGE-CLOCK-FILTER-20261102.txt Original file SHA-256: e043f0f2a243e0ea45d205fab259e82edb6350671d54ae3fb83d05abc2fdcbef Inclusive original lines: 1-82 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 | Original whole Higgs-family charge filter; 2 November 2026 000002 | 000003 | Question and fixed source 000004 | ------------------------- 000005 | Which proposed fixed diagonal charge generators commute simultaneously with the 000006 | actual finite grading and the whole constant real Higgs family with its given 000007 | Majorana block? Use v252_full_finite_triple.py:63-121 and the four original 000008 | real one-form directions constructed in check_dynamical_higgs_source.py:24-56. 000009 | We preserve arbitrary supplied 3x3 Yukawa and Majorana matrices. No value, 000010 | Higgs weight, local algebra, clock mechanism or physical state is selected. 000011 | 000012 | The 96 indices are particles and conjugates, with grading gamma_F = +1 on 000013 | particle L, -1 on particle R, and the opposite on conjugates. A real diagonal 000014 | particle charge is extended with the opposite charge on conjugates, as required 000015 | by the v252 real structure. We use integer-normalized generators 3B, L, 000016 | 3Q_em, 6Y, and the two diagonal colour generators diag(1,-1,0), diag(0,1,-1). 000017 | Their exponentials exp(i theta lambda) are 2pi periodic. This normalization 000018 | is a mathematical test convention, not the established TFPT time map. 000019 | 000020 | Exact general conclusion in this stated six-generator real linear span 000021 | ----------------------------------------------------------------------- 000022 | Assume at least one Yukawa entry and at least one Majorana entry are nonzero. 000023 | Let lambda = a(3B)+b L+c(3Q_em)+d(6Y)+e C1+f C2. Require [lambda,V(H)]=0 000024 | for every H in the original whole Higgs family, keeping the fixed Majorana 000025 | term, and [lambda,gamma_F]=0. Then b=c=d=0, and the admissible generators 000026 | in this class are exactly a(3B)+e C1+f C2. Their weighted trace is zero: 000027 | 000028 | tr_96(lambda gamma_F) = 0. 000029 | 000030 | Proof. On an allowed nonzero neutral Yukawa link the B, L, Q and colour 000031 | charges are identical on the connected L/R entries, whereas 6Y differs. 000032 | Thus d=0. An original charged Higgs direction connects the corresponding 000033 | weak partners; the Q_em eigenvalues differ by one unit, while B, L and each 000034 | colour charge still agree. Thus c=0. The original Majorana block connects 000035 | nu_R to its charge-conjugate nu_R. Its 3B and colour charges vanish and its 000036 | L charges differ, so b=0 when that block is nonzero. Conversely the explicit 000037 | one-form construction is colour-diagonal and connects equal B charges, and 000038 | the Majorana block is neutral under both. This proves sufficiency for all 000039 | given Yukawa matrices, all four real H components and arbitrary MR. 000040 | 000041 | The weighted trace vanishes by pairing each left particle of a given species, 000042 | colour and generation with the corresponding right particle of the same 000043 | surviving charge; the antiparticle block cancels in the same way. This result 000044 | holds also when Yukawa matrices have kernels: no invertibility assumption is 000045 | used. For any Hermitian odd V and commuting lambda, the kernel-weighted trace 000046 | equals tr(lambda gamma_F), because V pairs nonzero eigenvalues across chirality 000047 | within each lambda eigenspace. Thus in the selected class the weighted kernel 000048 | trace is 0, subject to those joint commutation conditions. An index of any 000049 | particular boundary operator or a relative determinant additionally requires 000050 | its own domain, seam, covariance, orientation and implementability proof. 000051 | 000052 | Key scope distinctions 000053 | ---------------------- 000054 | L and B-L commute with the Higgs family but not a nonzero fixed Majorana 000055 | block. Electromagnetic charge commutes with a neutral H direction yet not 000056 | with both charged H directions. Hypercharge does not commute even with the 000057 | neutral Yukawa link. These are fixed-H internal commutators: the full gauge 000058 | action simultaneously transforms H, so the Q/Y result is not a claim that 000059 | electroweak gauge invariance is broken by the underlying field theory. 000060 | 000061 | The six-generator span is not the entire commutant. Chiral or flavour 000062 | generators supported on Yukawa/Majorana null spaces, non-diagonal colour, 000063 | field-dependent transformations, and clocks from the seam or E8 are not 000064 | excluded. The matrix theorem does not give a dynamical original clock nor 000065 | physical masses. It does not replace the nonzero selected 18-channel index 000066 | or the full96 unweighted index: those use their own domains and restrictions. 000067 | 000068 | Reproduction and result 000069 | ----------------------- 000070 | Run from repository root: 000071 | OPENBLAS_NUM_THREADS=1 python3 -B experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_original_charge_filter_20261102.py 000072 | 000073 | PASS. The script calls the actual v252 operator/representation constructors; 000074 | all four original one-form matrices are built from them. Exact comparisons 000075 | are performed with integer/complex-integer constructor-control matrices, not 000076 | floating-point approximations of unknown physical Yukawa parameters. It 000077 | tests all original source blocks and both Cartan generators. For example, 000078 | 3Q_em has 288 nonzero commutator entries for each charged Higgs direction and 000079 | zero for neutral directions; L has 14 in this selected Majorana control and 000080 | zero in the Higgs directions. These counts depend on the selected nonzero 000081 | control entries; the charge-difference argument above establishes the stated 000082 | class result generally under its nonzero premises.