TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/ROLE-AUDIT.txt Original file SHA-256: e0d2041a68f53d499844f88d732469afc3ad493a0c7f997ac83a9584c035c270 Inclusive original lines: 1-153 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 | E8, E7, E6: ACTUAL ACTIONS, COMPLETE SOURCES AND TYPED RESTRICTIONS 000002 | 29 October 2026. Original-source review with three decisive exact tests. 000003 | 000004 | 1. The answer depends on the object, not merely the exceptional name 000005 | 000006 | The native E8 root lattice, its248-dimensional weight-one Lie algebra, 000007 | its infinite lattice VOA/net, the finite Weyl/G31 actions and a physical 000008 | gauge group are different objects. The first four have concrete existing 000009 | relations and actions. A physical E8/E7/E6 gauge group or breaking history 000010 | does not follow by renaming those objects. Likewise a lattice root direction 000011 | is not a spacetime dimension, and an internal spinor-type current is not 000012 | already a physical spacetime Grassmann field. 000013 | 000014 | The existing reconstruction theorem is POSITIVE and complete in its class: 000015 | e-series-source-reconstruction-20261024/THEOREMS.txt:6-46,197-386 fixes 000016 | V_E8 from the marked C4 extension of V_D5 tensor V_A3, including vacuum, 000017 | local products, positive form, radial adjoint/reflection, all vacuum 000018 | correlators and L0. These are not independent open choices of this already 000019 | given source. Membership of the primitive physical source in that class is 000020 | a different question. No new arbitrary measure is demanded for the given VOA. 000021 | 000022 | 2. E8 has an explicit operational field meaning in the supplied source 000023 | 000024 | With the actual invariant form and cocycle, its currents satisfy 000025 | [J^a_m,J^b_n]=J^[a,b]_(m+n)+m k kappa(a,b)delta_(m+n,0), k=1. 000026 | The248 directions are the weight-one generators, not the whole state space. 000027 | Charges, products and cocycle signs determine their joint action and all 000028 | descendants. The D5+A3 splitting is 000029 | 248=(45,1)+(1,15)+(16,4)+(10,6)+(16bar,4bar). 000030 | The complete source is generated by these currents. Actual mixed(10,6) 000031 | actions and the resulting full Clifford response were already checked in 000032 | E8-CLIFFORD-RESPONSE.txt; this review does not call them new dynamics. 000033 | 000034 | 3. The four E6 and six E7 share one precise tetrahedron 000035 | 000036 | Fix the original D5 and its three-coordinate A3 complement. For the four 000037 | axes (+++),(+--),(-+-),(--+), the E6 root sets consist of40 D5 roots and32 000038 | half roots each. Every pair intersects in exactly D5. There are six E7 000039 | cuts retaining this D5, one per unoriented A3 root line. 000040 | 000041 | check_roles.py uses the unchanged original root builder to verify that 000042 | EACH pair of these E6 sets generates precisely its unique E7 under the 000043 | actual ambient root-addition closure:104 union roots close to126. All six 000044 | edges are distinct. Thus four E6 vertices, six E7 pair envelopes and one 000045 | common D5 genuinely form a tetrahedral incidence dictionary inside E8. 000046 | This is an explicit application of the old complete cut/incidence theory, 000047 | not a discovered temporal evolution E8 -> E7 -> E6. The full lattice contains 000048 | 120 E7 and1120 regular E6; this picture is the fixed-D5-compatible subset. 000049 | 000050 | The other important E7, neutral for the supplied source Q=sum a_j, has 000051 | normal q/2=(1/2)^8. It is in the64 half-root-normal class, not one of these 000052 | six edges. Different E7 roles must not be merged by their common label. 000053 | 000054 | 4. Complete E6 and E7 field windows retain their complements and glue 000055 | 000056 | The true level-one conformal inclusions are 000057 | E7_1 x A1_1 subset E8_1, central charges7+1=8, 000058 | E6_1 x A2_1 subset E8_1, central charges6+2=8, 000059 | and the original D5_1 x A3_1 window has5+3=8. 000060 | The lattice quotients are C2,C3,C4 respectively, as already proved in 000061 | e-series-quarter-clock-20261023/PROOF.txt:165-175,232-269. 000062 | The standard primary classification is also listed in Adamovic et al., 000063 | Finite vs infinite decompositions in conformal embeddings, 000064 | arXiv:1509.06512, section6.6; no new conformal inclusion is claimed here. 000065 | 000066 | At weight one the actual branchings include 000067 | 248=(133,1)+(1,3)+(56,2), 000068 | 248=(78,1)+(1,8)+(27,3)+(27bar,3bar). 000069 | The associated FULL lattice Hilbert/VOA module is a DIRECT SUM of matched 000070 | glue-module tensor products. It is not a tensor product of two independently 000071 | chosen complete theories. With the canonical conformal dynamics the stress 000072 | tensor and L0 add, but a complete thermal trace sums over the correlated 000073 | glue labels. Dropping a complementary factor or correlated sectors changes 000074 | the object and its source response. Total c remains8 in each complete window. 000075 | 000076 | 5. Two important old E6 results were present before this review 000077 | 000078 | compiler-e6-seam-readout-20260918/PROOF.txt:140-198 uses the ORIGINAL root 000079 | operators to identify E6 and A2 as mutual commuting centralizers and to 000080 | prove the closed charged-current module 000081 | (27,3), 27=16_1+10_-2+1_4. 000082 | The old48=(16,3) currents require30+3 further directions for E6 closure. 000083 | The charges1,-2,4 are the named internal U1, not hypercharges or spins. 000084 | The fixed physical carrier-Y values are retained on each16 component. 000085 | 000086 | compiler-vacuum-current-cubic-20260918/PROOF.txt:20-105 computes the actual 000087 | affine grade-one248 Gram and the common vacuum correlation 000088 | =kappa(a,[b,c]) 000089 | C_(A,i)(B,j)(C,k)=d_ABC epsilon_ijk 000090 | on(27,3). The E6 cubic is symmetric, with45 signed source-basis monomials; 000091 | its Ward matrix has rank44 on45 candidates. This fixes its relative 000092 | coefficients; source normalization supplies the overall factor. These are 000093 | completed source-level tensor identifications, not mere numerical branching. 000094 | They were present as resolved_results of old Atlas contracts with empty 000095 | supporting_findings; historical PARTIAL was not mathematical openness here. 000096 | 000097 | The same old proof explicitly corrects I4/4: it is a normalized CURRENT 000098 | RESPONSE GRAM, not a partial trace of the grade-zero vacuum. Equal current 000099 | norms do not select physical populations, particle numbers or masses. 000100 | Likewise d times epsilon is not already a4D fermion Yukawa functional. 000101 | 000102 | 6. Inclusion and projection have different algebraic functions 000103 | 000104 | An E6/E7 current subalgebra is a valid closed inclusion. The orthogonal 000105 | root/Cartan cut projector FROM e8 ONTO it is not a Lie homomorphism. 000106 | For example in the (+++) E6 chart remove alpha=e0+e5 and its negative. 000107 | Both root currents project to0, but their bracket is a nonzero signed 000108 | coroot. Its retained Cartan component is 000109 | e0+(e5+e6+e7)/3, norm squared4/3. 000110 | For neutral E7 choose alpha=e0+e1. Its retained Cartan component is 000111 | e0+e1-q/4, norm squared3/2. 000112 | Both witness P[a,b] != [Pa,Pb]. The exact checker verifies these witnesses. 000113 | 000114 | Consequently deleting root labels and continuing E8 multiplication is not 000115 | the same operation as restricting all fields/observables to the actual 000116 | subalgebra. The rank16/48 half-root filters also do not define full E6 000117 | invariant modules; their explicit escape brackets are in E6-REVIEW.txt. 000118 | The ratio64/48=4/3 remains exact for equal-norm response counting. It is 000119 | neither an identity I=(4/3)(I-P) nor a new universal evolution/readout law. 000120 | 000121 | 7. Source charge neutrality and source-time symmetry are distinct 000122 | 000123 | Reuse the existing ACTUAL source identity 000124 | H8=8L0-rho_A7.a0+(2a-1)Q/2, 000125 | [H8,J_(alpha,n)]=[-8n-rho_A7.alpha+(2a-1)Q(alpha)/2]J_(alpha,n). 000126 | The126 Q-neutral roots form E7, but alpha=e0-e1 is neutral and its ORDINARY 000127 | horizontal mode obeys[H8,J_(alpha,0)]=-J_(alpha,0). Thus the whole E7 000128 | horizontal symmetry does not preserve this supplied time generator. 000129 | 000130 | The new small direct check finds precisely8 ordinary n=0 root modes 000131 | commuting with H8 in either quarter. Their roots form4 mutually orthogonal 000132 | A1 pairs, rank4. Adding all8 Cartan zero modes gives a16-dimensional 000133 | horizontal centralizer, not the full E7 or E8 horizontal algebra. 000134 | This is explicitly NOT a classification of all AFFINE conserved modes: 000135 | the old p* modes at n=-1,+1 already give another conserved sl2. The old 000136 | source color-center restriction removes the extra p* ground state and 000137 | retains Omega; no new vacuum ambiguity is posed. Physical OS time and 000138 | the primitive source map are not derived by this finite commutator check. 000139 | 000140 | 8. Functional verdict 000141 | 000142 | E8 supplies the common product/charge/current framework and its completed 000143 | conditional field source. E7 supplies root-normal windows, actual paired 000144 | Gaussian operations and a genuine given-source neutral-sector dictionary. 000145 | E6 supplies compatible carrier/family reorganizations, closed27 modules 000146 | and an actual unique cubic vacuum-correlation tensor. Their full conformal 000147 | windows preserve complements, glue, state and L0; the distinct original H8 000148 | grading and native transported clocks must be checked rather than equated. 000149 | These concrete functions are well understood in the stated source class. 000150 | What is not established is a universal physical gauge-breaking history, 000151 | the identification of every internal current as a spacetime particle, or 000152 | the common primitive P1 physical insertion/time map. No extra E7 numeric 000153 | coupling law follows from rank alone, and no such law is used in this review.