Established within the stated premises
Original unmarked W6 simplex from full local quartic OPE
finding:unmarked-native-w6-simplex-from-full-quartic-ope
Actual2+2 flatteningsH_i of normalized original quartics give ten intrinsic logical rank1 raysv_t in localr2 product, sumP_t=2I5, Tr(P_tP_s)=1/9. Configuration fixes projective real structure through antiunitary fixing all rays unique up to common phase. On intrinsic real projective locus, sum_t(v_t.w)^4>=2/5 has exactly12 oriented equality points, hence six axes with regular simplex Gram6/5I6−1/5J6. All1024 sign cases exhausted. OriginalN introduced ONLY AFTERWARDS matches literally w_jw_j^T=(6/5)N_pi(j)N_pi(j)^T without fitrotation. Previously separately used UNMARKED W6 simplex thus gains concrete common local field-operator origin.
Scope: Geometric data reconstruction in given source, no physical minimization/real-state rule. Full complex state space has additional continuous minimacosθw1+i sinθw2; explicitly checked, never discarded. Overallantipode/permutation remain. No positivepolar transport or physical3+2 mark. Quartic code remains input; no new independent empirical confirmation or priority claim.
Required premises and original source excerpts
- Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
premise:local-e8-current-response-realization - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Actual positive Cartan quartic Fock embedding
Use original Construction-A roots with physical metric dot/2 and u_j=(h_2j-i h_2j+1)/sqrt2 as J=+i basis. Canonically embed the actual five Sym^4 code support sums as neutral grade4 Heisenberg polynomials in the given E8_1 lattice vacuum. No physical preparation follows.
premise:literal-native-positive-cartan-quartic-fock-embedding - Original displayed J-equivariant root isometry
Use existing S=_SIMPLE and T=_TARGET_SIMPLE from cartan_source._glue_deck_character_certificate: O=T S^-1/sqrt2 maps actual Construction-A roots r/sqrt2 to original Chevalley roots r/2, preserving metric and J. This is the existing concrete map, not a newly fitted embedding; physical P1 selection stays separate.
premise:original-displayed-j-equivariant-cartan-root-isometry - Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
premise:full-existing-local-e8-field-hull-observer-code
- experiments/theory-contracts/joint-native-algebra-selection-20261016/FULL-SOURCE-HULL-AND-QUARTIC-OPE.txt, lines 158–227
Source SHA256: 1d949c2a77e996e63446255d13f41856a00cde4b4d57c78b4b7766204870b2a0
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