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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

Relative response is metric covariant; complete state response remains dependent

In the question: Historical: common source, state and event selection

No unprovedGNSHilbertspaceidentification. FormalcentralOPEidentity isnotuniformUVlimittheoremforall singularstates. Controlsneedfinitecommonmoments,notautomaticallyadmissibleP1seeds;RP,clustering,relativeaction,time/collar mustadditionallyfit.

Read the exact result, assumptions and evidence

Result

Field/labelbasis changes musttransportmetric/adjoint. R=T L^-1 T*,K=T Q L^-1 T* invariantunderT→TA,L→A*LA,Q→A^-1QA;sourcecongruence givesunitarilyequivalentHermitianrelativetensors. InjectiveT givesE(Q)=WQW* inheritingrank/spectrumofsuppliedQ ratherthanselecting3+2. Canonicalstate-relativeformH0^-1/2H_omegaH0^-1/2 dependsonstatepair: completeoriginalf0/f4controlsspectra(19,8³,5),(5,9³,16),markedq gives1+4. Changingresponses leavescentralOP E tensors ofsamealgebraunchanged.

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

finding:intrinsic-relative-response-covariance-and-state-boundary