TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/old_source_embedding/CURRENT-LEVEL-CHECK.txt Original file SHA-256: 57b69a7222d16067061cd2c485439069581b903f3dd376ce8515792dea289410 Inclusive original lines: 1-152 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 | REUSE OF THE EXISTING SPINOR-CURRENT LEVEL TEST ON THE ACTUAL v252 MODULE 000002 | 29 October 2026. Independent analytic application; no run or Atlas mutation. 000003 | 000004 | NOT A NEW EXCLUSION 000005 | The Atlas already contains exactly the basic distinction: 000006 | finding:joint-spinor-not-source-coefficient, 000007 | research-source:55e1a01319dc1feaa105883e, 000008 | experiments/theory-contracts/seam-joint-conjugation-20261015/PROOF.txt:189-216. 000009 | That original report explicitly states: ordinary complex CAR fields with 000010 | coefficient S+ give c=16 and Spin(10) current level4, whereas D5_1 uses ten 000011 | REAL VECTOR fermions and its spinor16 is a Ramond/spin-field sector. 000012 | It also records the selfdual-doubling distinction and the old spin-field 000013 | weights 5/8 and 3/8. Those findings remain valid and are REUSED here. 000014 | 000015 | [OMITTED: non-scientific conversation or execution metadata] 000016 | [OMITTED: non-scientific conversation or execution metadata] 000017 | [OMITTED: non-scientific conversation or execution metadata] 000018 | 000019 | 1. Precise comparison and normalization 000020 | 000021 | The preceding review constructs the actual SM gauge lift of v252 and a 000022 | unitary W from its per-generation gamma_F=+1 module to Lambda_even C5, 000023 | intertwining color, weak isospin and the ORIGINAL hypercharge Y. 000024 | At Phi=0 the proposed source quantizes these sixteen labels as sixteen 000025 | independent COMPLEX chiral CAR fields, per generation. This is exactly the 000026 | statistical assignment to which the old level4 finding applies. Changing to 000027 | a selfdual presentation does not turn those fields into ten real vectors. 000028 | 000029 | Normalize D5 roots as alpha=+/-e_i+/-e_j with squared length2. The basic 000030 | invariant form has (H_i,H_j)_bas=delta_ij, (E_alpha,E_-alpha)_bas=1. 000031 | For sixteen complex free fermions in a representation R, their actual 000032 | Noether currents J_X=:psi^* R(X) psi: have 000033 | [J_X,m,J_Y,n]=J_[X,Y],m+n 000034 | +m Tr_R(R(X)R(Y)) delta_(m,-n) I. 000035 | The corresponding Ward action is the actual R(X) on creators and its dual 000036 | on annihilators. This fixes the same Lie generators as the preceding gauge 000037 | dictionary; it leaves no normalization fit for their charges. 000038 | 000039 | 2. All Cartan and root directions have the SAME factor4 000040 | 000041 | On the original exterior-even module let b_i^* be wedge multiplication, 000042 | b_i contraction, n_i=b_i^*b_i, and H_i=n_i-1/2. Its sixteen even occupation 000043 | weights have H_i=+/-1/2. The full invariant trace is 000044 | Tr_S+(H_i H_j)=4 delta_ij. 000045 | For i!=j the parity constraint still leaves the pair signs balanced, so 000046 | the off-diagonal trace vanishes; the diagonal trace is 16/4=4. 000047 | 000048 | This is not only a Cartan-count test. The actual exterior Spin(10) roots are 000049 | E_(e_i-e_j)=b_i^* b_j, E_(e_j-e_i)=b_j^* b_i, 000050 | E_(e_i+e_j)=b_i^* b_j^*, E_(-e_i-e_j)=b_j b_i. 000051 | They satisfy [H_k,E_alpha]=alpha_k E_alpha and 000052 | [E_alpha,E_-alpha]=alpha.H, with their usual consistent root signs. 000053 | For either root type, E_alpha E_-alpha has four occupied even subsets in 000054 | its trace: set the specified pair of occupations, then four of the remaining 000055 | three-bit subsets have the required parity. Hence 000056 | Tr_S+(E_alpha E_-alpha)=4. 000057 | Other non-opposite root traces vanish by their nonzero weight. These matrix 000058 | identities give the entire invariant form, not different adjustable levels 000059 | for its Cartan or charged root currents. 000060 | 000061 | Therefore IF the same full Spin(10) action is transported through W and used 000062 | as these elementary-field Noether symmetries, its affine level is 000063 | k_D5=4 per generation, k_diag=12 for three generations. 000064 | The full Spin(10) action is a stated premise, since v252 itself supplies the 000065 | SM gauge lift rather than all original Spin(10) generator matrices. The 000066 | root calculation checks this premise's consequence; it does not derive that 000067 | larger physical gauge group or its quantum source selection. 000068 | 000069 | For the OLD ten-real vector realization, vector weights are +/-e_i, so 000070 | Tr_vector(H_i H_j)=2 delta_ij. The real-Majorana current has the usual factor 000071 | 1/2 in its trace form. Its coefficient is therefore delta_ij and k_D5=1. 000072 | This is exactly the old report's normalization, not an index-convention 000073 | disagreement. One complex vector would instead supply two real vectors. 000074 | 000075 | 3. Original hypercharge already decides the required SM comparison 000076 | 000077 | The ORIGINAL P2 generator is 000078 | y=(-1/3,-1/3,-1/3,+1/2,+1/2), 000079 | Y=sum_i y_i H_i=sum_i y_i n_i, since sum_i y_i=0. 000080 | Its basic D5 norm is 000081 | (Y,Y)_bas=sum_i y_i^2=5/6. 000082 | This is the documented D5_1 current coefficient in the old construction. 000083 | 000084 | [OMITTED: non-scientific conversation or execution metadata] 000085 | [OMITTED: non-scientific conversation or execution metadata] 000086 | [OMITTED: non-scientific conversation or execution metadata] 000087 | [OMITTED: non-scientific conversation or execution metadata] 000088 | [OMITTED: non-scientific conversation or execution metadata] 000089 | [OMITTED: non-scientific conversation or execution metadata] 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 the free Phi=0 class a common scalar quarter twist does not alter this 000100 | level. The bilinear currents are periodic, and the twist does not change 000101 | their actual local CAR/Ward algebra. A thermal state changes expectations; 000102 | it does not change these operator commutators. A legitimate normal-ordering 000103 | change can shift currents by scalar terms but cannot remove this abelian 000104 | central commutator for commuting smeared hypercharge generators. 000105 | 000106 | 4. Why rescaling is not a charge-preserving repair 000107 | 000108 | For one family, dividing J_Y by2 would change its central coefficient by1/4 000109 | and produce5/6. But its Ward action would then have Y/2: Q would have1/12, 000110 | e_R^c would have1/2, etc. That is not the original P2 gauge dictionary or its 000111 | global group normalization. For three families a division bysqrt(12) has 000112 | the same problem. Rescaling nonabelian generators likewise changes their 000113 | single-pole Lie bracket/Ward coefficient, not just their central term. 000114 | 000115 | This rules out a direct identification preserving BOTH the specified 000116 | Noether current and its original charge action. It is not a theorem against 000117 | every possible extra current from a commutant, a sector-changing field map, 000118 | a different cover, or a different source embedding. Such an alternative must 000119 | provide its actual joint Ward, state and time map. No new such map is assumed. 000120 | 000121 | 5. Relation to the old source and the claimed E8 subnet 000122 | 000123 | The old D5_1+A3_1 to E8_1 construction uses ten plus six REAL vector fields. 000124 | Its internal spinor16 labels a sector, rather than sixteen elementary complex 000125 | fermions. The new exact v252/P2 representation match does not change that 000126 | older distinction. It proves equality of a FINITE representation, not equality 000127 | of its two different current-net realizations. 000128 | 000129 | The c_R=48 count for three proposed complex-spinor families only shows that 000130 | their whole free right-moving theory is not the old c=8 E8 theory. It does 000131 | not establish an E8 subnet's existence. The sharper application here is that 000132 | the SPECIFIED old D5_1 hypercharge current cannot be the SPECIFIED diagonal 000133 | matter Noether current with the same Ward action: their levels already 000134 | disagree. No exclusion of an unrelated E8 subnet with a different current 000135 | embedding is claimed. Opposite movers or two HS faces must not be silently 000136 | added to or subtracted from this one chiral comparison; that would change 000137 | the current dictionary and its Ward action. The previously known vector 000138 | cancellation result remains scoped to its own complete-vector assignment. 000139 | 000140 | The neutral nu_R^c family-fixed scalar line in the preceding review has 000141 | Y=0. Its scalar CAR embedding therefore transports the source clock charge 000142 | but does not by itself transport this nonzero physical hypercharge current. 000143 | This clarifies which connection the scalar selector can and cannot supply. 000144 | 000145 | [OMITTED: non-scientific conversation or execution metadata] 000146 | [OMITTED: non-scientific conversation or execution metadata] 000147 | [OMITTED: non-scientific conversation or execution metadata] 000148 | [OMITTED: non-scientific conversation or execution metadata] 000149 | [OMITTED: non-scientific conversation or execution metadata] 000150 | [OMITTED: non-scientific conversation or execution metadata] 000151 | [OMITTED: non-scientific conversation or execution metadata] 000152 | [OMITTED: non-scientific conversation or execution metadata]