Established in scope
Full local quartic Wick ladder gives code/erasure action
In the question: Historical: common source, state and event selection
Mode components are not entire local zero modes or selected physical instruments. Matrixunit law only weight4, not all grades. Leadingr2 is not whole fourth-pole coefficient; retainr3 Taylor term. Wick contraction is field algebra, not executed measurement. ChosenM5 coefficients available, not physically selected. Endpoint map A→PAP is not multiplicative for full field algebra; M5 is realized by stated code-preserving weight4 family, not a representation of all source operations onC5.
Read the exact result, assumptions and evidence
Result
Actual local F_i(z)F_j#(w) has exactly five Wick contraction classesr0..4 with all Taylor terms. Leading weight8/6/4/2/0 Grams areI25,4I25,(18^1,8^9,0^15),4|I><I|,|I><I|. r1=sum_a g_ia conjugate(g_ja) contains actual erasure20; isolated3creation/3annihilation mode component actsEij tensorI4 on that grade3 carrier.4/4 componentsEij=P_i(u_-1)conjugate(P_j)(ubar_1)/sqrt(NiNj) on ENTIRE weight4 are exactly|f_i><f_j| plus0 on rest, without intermediate projection. Full local products permit nonscalar logical action and entireM5; old pureCartan-Weyl exclusions are not all-field exclusions.
Required assumptions
- 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.
- 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.
- 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.
- 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.
- 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.
Original evidence
- FULL-SOURCE-HULL-AND-QUARTIC-OPE.txt lines 102–188
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/FULL-SOURCE-HULL-AND-QUARTIC-OPE.txt
1d949c2a77e996e63446255d13f41856a00cde4b4d57c78b4b7766204870b2a0
finding:full-local-quartic-wick-ladder-and-unprojected-native-actions