Scoped exclusion
Full source simplex structure does not select original polar mark
In the question: Historical: common source, state and event selection
No all-E8/P1 no-go or exclusion of covariant density channels, open outcomes, noninvariant preparation or spontaneous branches. No identification of real reconstruction functional with physical potential. Existing polar-fibre/clock theorem remains comparison; new source gives unmarked geometry, not physical selection.
Read the exact result, assumptions and evidence
Result
Six OPE-reconstructed axes give15 equivalent rank2 pair planes. None equals actual originalP2; minimum squaredHS distance is(21−6sqrt6)/25>0. Full logical field-mode imageM5 is irreducible with centerC, no distinguished3+2 superselection. With all exterior data invariant, fully contracted LINEAR code return/memory kernels stay scalarI5 by native irreducibility even with every exterior path. Nontrivial uncontracted OPE tensors remain and are not excluded.
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.
- Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
- Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Original evidence
- FULL-SOURCE-HULL-AND-QUARTIC-OPE.txt lines 229–265
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-source-simplex-does-not-select-original-polar-mark