TFPT scientific source excerpt Original repository path: experiments/theory-contracts/e-series-joint-source-20261023/SELECTION.txt Original file SHA-256: eaf46bcdc3ae40faded8b33bb100e5a6625cc3f71bdc07a4d696e49bd6705e7d Inclusive original lines: 1-110 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 | MATH.SEAM.JOINT.SELECTION.05 000002 | 23 October 2026 000003 | 000004 | Exact remaining selection symmetry 000005 | 000006 | 1. Fixed object and scope 000007 | 000008 | Retain the native E8 chart, H=W(D5)xW(D3), J, sigma, c=J sigma and 000009 | Y=(-2,-2,-2,3,3,0,0,0)/6. Retain the native quartic subspace P5 and its 000010 | actual equivariant erasure map into the neutral cubic20. Morphisms preserve 000011 | these subspaces and maps with their actual component representations. They 000012 | do not fix each individual quartic vector pointwise. Morphisms here are the 000013 | native lattice isometries in H that stabilize the named marks and maps. 000014 | They preserve the compiler root factors setwise; they need not commute with 000015 | every labelled element of H. A separately selected 000016 | field ray, preparation or cut would be extra marking. 000017 | 000018 | Question: do these data already distinguish one of the four E6 cuts 000019 | containing the given D5? This is a necessary check before declaring a 000020 | uniquely selected common E6 source. 000021 | 000022 | 2. Complete stabilizer calculation 000023 | 000024 | Inside H each matrix is a signed permutation preserving the two coordinate 000025 | blocks, with even sign parity separately in each. Commutation with J forces 000026 | source coordinate pairs to map to target pairs. Complete enumeration gives 000027 | 000028 | C_H(J): order64, 000029 | image on the four family axes: cyclic order4, transitive, 000030 | C_H(J) intersect Stab(Y) = {I,d}, 000031 | d=diag(1,1,1,1,1,1,-1,-1). 000032 | 000033 | The last equality also has an immediate analytic proof. Fixing Y permits 000034 | only ordinary permutations within its three color and two weak coordinates. 000035 | J couples color coordinate2 to weak3 and weak4 to zero-family5, so both 000036 | weak coordinates and color2 are fixed individually. Commuting with J then 000037 | fixes color0 and1 as well. Only the last family pair6,7 can move. Its even 000038 | family sign condition leaves I or simultaneous reversal of6,7. 000039 | 000040 | The matrix d commutes with sigma and c. The projective family axes can be 000041 | written(1,+/-1,+/-1). It acts by 000042 | 000043 | (1,a,b) -> (1,-a,-b), 000044 | 000045 | which has two two-cycles and no fixed vertex. 000046 | 000047 | 3. Actual quartic and erasure compatibility 000048 | 000049 | In the native complex chart, d sends(z0,z1,z2,z3) to(z0,z1,z2,-z3). 000050 | On the literal five native quartics its matrix is 000051 | 000052 | diag(1,1,1,1,-1). 000053 | 000054 | This is checked against the actual sparse supports of process._code_basis. 000055 | On each derivative g_(i,j)=partial_j f_i it gives the actual chain-rule 000056 | factor epsilon_i d_j. Thus d preserves the original4/5/20 diagram as an 000057 | equivariant diagram. No charged current20 or replacement erasure is used. 000058 | 000059 | 4. Exact nonselection conclusion and positive meaning 000060 | 000061 | If a rule selects one E6 vertex equivariantly from precisely these marked 000062 | data, every automorphism of the data must fix that selected vertex. The 000063 | explicit automorphism d fixes the data but no vertex. Hence no such unique 000064 | selection rule exists in this category. 000065 | 000066 | The obstruction is not resolved by adding the already supplied J, sigma, 000067 | c, Y or whole quartic/erasure spaces: all are preserved by d. It is not a 000068 | no-go for a separately marked quartic ray or any different input category. 000069 | The complete covariant mathematical object therefore carries the family 000070 | and its transport. It must not manufacture a preferred vertex. Existing 000071 | individual E6 charts remain exact conditional charts. 000072 | 000073 | 5. The full-field phases also preserve the obstruction 000074 | 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 | 000082 | 8,9,40,41,94,95,126,127,128,129,160,161,214,215,246,247. 000083 | 000084 | [OMITTED: non-scientific conversation or execution metadata] 000085 | 000086 | 126,127,128,129. 000087 | 000088 | They form an affine torsor under the difference subgroup{0,1,254,255}. 000089 | The first two have squareI. The last two have square D_1 and order4. 000090 | Therefore the two INVOLUTIVE full lattice-VOA automorphisms with masks126 000091 | and127 are actual automorphisms of the fixed associated source and its 000092 | compiler clock, not just transitions to another lift choice. Their neutral 000093 | action is d and their E6 vertex action is still fixed-point-free. 000094 | 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 | [OMITTED: non-scientific conversation or execution metadata] 000099 | [OMITTED: non-scientific conversation or execution metadata] 000100 | [OMITTED: non-scientific conversation or execution metadata] 000101 | 000102 | Executable certificate: 000103 | python3 -B experiments/theory-contracts/e-series-joint-source-20261023/stabilizer_selection.py 000104 | 000105 | Native sources retained without changes: 000106 | verification/v634_st31_structure.py:J_vec,SIGMA_IDX 000107 | tfpt_explorer/process.py:_code_basis 000108 | ../e-series-compiler-closure-20261023/CUTS.txt:125-155,207-324 000109 | 000110 | Verdict: PASS, complete in the fixed marked-data category above.