Read the result in its research context.

Result

Independenttensor sources/productstate factorizeGram/polartransportexactly. Insameoriginalfieldnet fullcommonprofileholomorphiceventproducts killantisymmetriclabels: orderedmultiplicationC5⊗C5→H8 hasrank15,kernelwedge²C5 dimension10,whileMonSym²isinjective. OriginalDelta0 firstnorm²2,fullleadingpairnorm²64 ratherthan4independentcopies;100actualerasureLeibnizactionsretainallgrade7outputs. Twosourcestateswithsamemarginalsbutclassicalcorrelation give differentjointGrams with exactterm(Bq−I)⊗(Bq−I)/4. Fullfieldassociativityretained;reducedsingle responsesalonearenotgeneralcompositionlaw.

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.

• 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.

• 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.

• Intrinsic event geometry without marked clock as selector

  User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.

Original evidence

• INTRINSIC-EVENT-GEOMETRY-AND-COMPOSITION.txt lines 261–309

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/INTRINSIC-EVENT-GEOMETRY-AND-COMPOSITION.txt

  f5599348967407c285776b61e5fcecde42b88a50ef3aaf48b36bf85ddc380547

finding:intrinsic-event-composition-retains-shared-source-and-correlation-data