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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

E6 E7 E8 operator roles, tetrahedral envelopes and actual horizontal time centralizer

In the question: Active mathematical program: marked seam monodromies and lattice lifts

Exactly the fixed native root chart and the given eight-channel time operator. The tetrahedron covers four of1120 E6 and six of120 E7. The Q-neutral E7 has a half-root normal and is not one of those six; Q is not automatically Y. Only ordinary horizontal n=0 modes are classified, not all affine conserved modes. Existing shifted p* sl2 modes and the solved color-center-neutral vacuum selection remain valid. The projector counterexample does not exclude genuine subalgebra inclusions, state restrictions or separately justified physical reductions.

Read the exact result, assumptions and evidence

Result

In the fixed original D5+A3 cut, each of the six pairs among the four E6 systems generates precisely its unique E7:104 union roots close to126, with a common40-root D5. Orthogonal root/Cartan projectors onto E6 and E7 are not Lie homomorphisms, as removed opposite-root pairs with nonzero projected coroot show. For the existing H8=8L0-rho_A7.a0+(2a-1)Q/2, Q-neutral E7 membership is not full horizontal energy symmetry: [H8,J_(e0-e1,0)]=-J_(e0-e1,0). At a=1/4 and3/4 exactly8 ordinary n=0 root modes commute, of type4A1; with8 Cartan modes this horizontal centralizer has dimension16. Complete conformal E7+A1 and E6+A2 windows retain their complements and glued modules. A cut sequence is not a derived physical breaking or time history.

Required assumptions

  • Original D5+A3 compiler split and established seed

    Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.

  • Exact local reconstruction class of the marked C4 glue

    Mathematical object class Ext_H(U): U=V_D5 tensor V_A3 with fixed embedding and sector chart, H=<(s,f)>=C4. Objects are connected local unitary conformal VOA extensions with the same conformal vector and underlying labelled U module exactly the sum of M_h for h in H, each once. Isomorphisms fix U and sector labels. This is an explicit mathematical reconstruction class; membership of primitive P1 is neither assumed nor derived.

  • Four D8 source modules with fixed affine time

    Mathematical parent of the four D8*/D8 modules 0,v,s,c with eight identical Heisenberg oscillators, source charge chart p and N≥0. H=8(N+|p|²/2+delta.p),delta_j=(j+a)/8−1/2,0<a<1,Q=sum p_j. Original quarter cases are a1/4,3/4. Conformal L0, individual Cartan charges and totalQ remain distinct. This mathematical completion does not assume a physical P1 realization of the Ramond space or a local field map.

Original evidence

  • ROLE-AUDIT.txt lines 1–153

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/ROLE-AUDIT.txt

    e0d2041a68f53d499844f88d732469afc3ad493a0c7f997ac83a9584c035c270

  • check_roles.py lines 1–93

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/check_roles.py

    47cd63f5a4668dfb0ce5d4d4e665106c2d24371c9fd32ea97593e9f04e9daa96

  • role-check-results.json lines 1–135

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/role-check-results.json

    a280573489b8e43aebba2959800f42134fc4ed3247ebd074bc744b3929950750

  • ROLE-CHECK-REVIEW.txt lines 1–97

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/ROLE-CHECK-REVIEW.txt

    5451b0ccdb7965db4cac9bd82d7b7f69c6ee75eebfb604aa9bfb12f11ab0700e

  • A7-E7-CLOCK-DECOMPOSITION.txt lines 1–175

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/A7-E7-CLOCK-DECOMPOSITION.txt

    62c251a47e1b0b67f034027fec66a5d0ffaab35abf61dcb2e709395c3bc82581

finding:e-series-operational-role-review-and-source-time-centralizer