Established within the stated premises
Relative response is metric covariant; complete state response remains dependent
finding:intrinsic-relative-response-covariance-and-state-boundary
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.
Scope: No unprovedGNSHilbertspaceidentification. FormalcentralOPEidentity isnotuniformUVlimittheoremforall singularstates. Controlsneedfinitecommonmoments,notautomaticallyadmissibleP1seeds;RP,clustering,relativeaction,time/collar mustadditionallyfit.
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 - 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.
premise:native-g31-concrete-event-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.
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 - 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.
premise:intrinsic-native-event-geometry-without-marked-clock
- experiments/theory-contracts/joint-native-algebra-selection-20261016/INTRINSIC-EVENT-GEOMETRY-AND-COMPOSITION.txt, lines 177–260
Source SHA256: f5599348967407c285776b61e5fcecde42b88a50ef3aaf48b36bf85ddc380547
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex, lines 103–143
Source SHA256: 1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e
bounded-excerpt · current-at-snapshot