TFPT scientific source excerpt Original repository path: experiments/theory-contracts/seam-joint-source-origin-audit-20261016/MINIMALITY_SELFCONSISTENCY_PROOF.txt Original file SHA-256: 0db534e0345f8dc1f99a2fba37c22445d1bbeef7257f0b96d8b8fff43dc3689c Inclusive original lines: 26-128 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. 000026 | 2. What original minimality actually minimizes 000027 | 000028 | S1=_archive/tfpt-45/source_extracts/01_boundary_kernel_source.tex: 000029 | 480-497: A_loc is part of every operational seed, together with dynamics, 000030 | reflection, state, seam class and collar generator. 000031 | 523-540: essentialization removes summands on which seam flow, polarization, 000032 | determinant degree and primitive Yukawa type all vanish. 000033 | 543-560: the minimized lexicographic vector is 000034 | 000035 | D(B)=(abs(SF), rank_ess H_prim_fin, c1(L+)+c1(L-), h_red). 000036 | 000037 | 571-594: the proof establishes order preservation and existence of a minimum 000038 | value; it explicitly reduces uniqueness to classification of the final 000039 | minimized stratum. 000040 | 629-644: the bordism itself includes A+, H+, D+, J and Gamma. 000041 | 646-683: uniqueness of B_min is asserted, but the proof does not classify 000042 | the operator/algebra objects having the minimizing defect vector. 000043 | 000044 | An algebra can influence these coordinates indirectly. Merely not listing 000045 | its multiplication as a coordinate is NOT an independence theorem. The precise 000046 | missing result is that, on the ORIGINAL admissible essentialized category, 000047 | the inverse image of the minimum vector is one unitary-equivalence class of 000048 | algebras with their sector actions. Neither well-ordering nor invariance 000049 | under changes of presentation proves that statement. Essentialization does 000050 | not independently prove it either; its definitions already refer to the 000051 | carrier and Yukawa structures whose original selection is under examination. 000052 | 000053 | The previous same-operator A0/A1 control is NOT used as proof that two global 000054 | minimizers exist. Its domain was explicitly smaller than these full original 000055 | conditions. No such new global minimizers are claimed here. 000056 | 000057 | 3. Why the later joint closure does not repair the upstream step 000058 | 000059 | S2=_archive/tfpt-45/source_extracts/02_carrier_source.tex: 000060 | 2814-2994: the joint discrete theorem claims a singleton. Its Step3, 000061 | 2912-2920, imports the compact Higgs rank2 and the actual branch-Yukawa 000062 | theorem yielding rank3. Its rank/occupancy check follows at2931-2944. 000063 | 3020-3063: the projected master functional FIRST fixes d_disc* and P_adm. 000064 | Its continuous variables are xi=(alpha,chi_geo,delta_ph,rho_vac). 000065 | The barrier is0 at B isomorphic to B_min and infinity otherwise. 000066 | 3117-3145: factorization and stationarity are evaluated on that retained 000067 | sector; A_loc and an unmarked carrier representation are not extra 000068 | continuous coordinates optimized by these displayed equations. 000069 | 3148-3171: the common invariant tuple I0 ALREADY contains E3+E2,Y,P_adm. 000070 | 3174-3228: the singleton fiber product starts with Z_disc={d_disc*}. 000071 | 3250-3294: rigid reconstruction cites that same discrete uniqueness and 000072 | downstream sector uniqueness. It does not independently classify all 000073 | upstream algebras in the minimizing defect fiber. 000074 | 000075 | Elementary selection lemma: if q:C->I records upstream invariants and all 000076 | subsequent conditions factor through q, selecting one i* in I leaves the 000077 | source set q^(-1)(i*). A singleton invariant value implies a singleton source 000078 | only when this fiber has independently been shown to be a singleton (up to 000079 | the declared equivalence). A compatible fiber product of downstream singleton 000080 | values cannot prove the upstream singleton it already assumes. This is a 000081 | logical test of the displayed proof, not an assertion that q has nontrivial 000082 | fibers for every possible full TFPT source. 000083 | 000084 | 4. The strongest exact conditional3+2 derivation 000085 | 000086 | Grant total carrier rank g=5 and family multiplicity N=3. IF the two-block 000087 | gauge form is already S(U(b) x U(s)), b,s>0, b+s=5, AND the occupancy equality 000088 | 000089 | N 2^(g-1)=(g-1)(b^2+s^2-1) 000090 | 000091 | is independently known from the source, then 000092 | 000093 | 48=4(b^2+s^2-1), b^2+s^2=13, 000094 | (b+s)^2=25=13+2bs, so bs=6, 000095 | (t-b)(t-s)=t^2-5t+6=(t-2)(t-3). 000096 | 000097 | Hence the UNORDERED pair is{2,3}. The condition b>s used by v14 then labels 000098 | it(3,2); the arithmetic alone does not identify which original sector is 000099 | the positive bosonic block. This conditional lemma is correct. 000100 | 000101 | [OMITTED: non-scientific conversation or execution metadata] 000102 | [OMITTED: non-scientific conversation or execution metadata] 000103 | [OMITTED: non-scientific conversation or execution metadata] 000104 | [OMITTED: non-scientific conversation or execution metadata] 000105 | [OMITTED: non-scientific conversation or execution metadata] 000106 | [OMITTED: non-scientific conversation or execution metadata] 000107 | 000108 | The active text tfpt_1_architecture_e8.tex:1747-1759 ties b^2+s^2=13 to the 000109 | E8 closure AND SM gauge algebra. The actual verification/v14_carrier_uniqueness.py 000110 | states this scope in its header and filters by that equality at42-49; its 000111 | anomaly test at54-60 uses a supplied SM generation list. It is an arithmetic 000112 | check, not a derivation of the internal gauge dimension from family roots. 000113 | We have read and audited it, not rerun its downstream checks as origin evidence. 000114 | 000115 | The universal5/4 quotient offers an even sharper CONDITIONAL rank decoder. 000116 | With the general normalized roots Y=-I_V/b+I_W/s used in S2:378-393, 000117 | gamma=Tr_E Y^2=1/b+1/s=g/(bs), B=b/s, 000118 | B gamma=g/s^2. 000119 | If B gamma=g/(g-1) is independently known on unknown split carriers, then 000120 | s^2=g-1; g=5 forces the ORIENTED ranks s=2,b=3. For the four splits the 000121 | quotients are5/16,5/9,5/4,5. Thus this equality really could separate them. 000122 | But S2:419-448 first computes B,gamma and their product on the already 000123 | minimal3+2 carrier, while1112-1148 explicitly proves equality of ratios 000124 | ON THAT branch using those values and60/48. The independent appearance of 000125 | a5/4 spectral/defect value does not prove its identification with B gamma 000126 | for an unknown carrier. Treating that cross-identification as an upstream 000127 | equation would add a premise, not repair the displayed derivation. This 000128 | does not deny its possible future derivation from a common source.