Established within the stated premises
Originalwindingfullstateresponseremovesvacuumranktwoshortcut
finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut
ActualpreviouslyderivedglobalchiralW4:p→Pp+a,a1^40^4,Pk↔k+4. LiteralexistingG=O^TMPM^TOgivesu0→iubar0,u1→−u1,u2→u2,u3→−iubar3,notunchangednativeU4clock. Homogeneousquarticframeoverlapdiag(1/2,0,0,1/2,0)rank2. FULLoriginalR_bwithinputcharge0underW4isΓG R_bonoutgoingMa;literaloutgoingfieldshaveb_out=U_+^TO^T(d+Ma). Crossmatrixrank5BOTHquarters,fullW4outputGram=inputGram. Sourceincrements7/9(fold7/8,9/8)matchoriginalWard,chargecarryandallpolarizations/modesretained. Apparent2+3vacuumchartdeficiencyisnotactualstateresponse3+2.
Scope: OriginalW4isglobalCARimplementerofgivensource/evenD8E8extension,notP1localinstrument. Oppositepolarizationnotcreation/annihilationmixing. CrossGramfullmatrixelementswithoutgoingcharge,noperformedprojection/required5closure. Noallwinding/historyno-goorphysical3+2selection.
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 - Original seam/state data on actual60 flags without fitted selection
User17Oct: test originalseam/statedata onactual60 flags P(q,S); no fittedclock,coupling,newselectionrule. Additional EXISTING data topreviousunmarkedobject: fullchargedinternalv=(0^5,1/2^3),deck square,originalE8vacuum; optionaloriginalR_neut/retained48familyomission explicitgivenpremise,all4cases. SEPARATEactualoriginalfoldphasesalpha1/4,3/4withfixedexistingM,d=M((j+alpha)/8−1/2);disshift/timediagnostic,notautomaticallyfullCARcovarianceorE8vacuumexpectation. Fullroot/fieldaction,nocompressiononly. NopostulatedphysicalTheta,field/state/normalorderingdictionaryorP1selection.
premise:original-seam-state-data-on-native-flags-without-fitted-selector - Fixed conformal current reference in original fold-state transport
Continuation17Oct: same givenchiralCARquarterfold,sea,F Cα F*,existingM/literalO; no newcopies/clock/coupling/selectionrule. NativehidentifiedherewithFIXEDconformalNSpointsplitcurrents;countertermagainstsea-normalorderedHfollowskerneldifference. ThisreferenceidentificationisCONDITIONALdictionarypremise,notphysicalP1originfromM/O. OriginalQWZpositivej≥1andnegativeDfoldorientationwithcharge/current/particleholetransportseparate;bothquartersretained. E8DeltatwistedextensionandoriginalglobalW4fromexistingevenCAR/E8cocyclefactorizationremaingivenextension,nooddCAR/E8localityproof. Noreselectedgroundstate;sourcechargesinitiallyZ8. Fullproducts/oppositepolarization/exteriormodes/charges,noperformedcodeprojection;originali0boundaryvalues,nofittedcontactterms.
premise:fixed-conformal-current-reference-for-original-fold-state-transport
- experiments/theory-contracts/joint-native-algebra-selection-20261016/FOLD-COVARIANCE-TO-NATIVE-FIELD-RESPONSE.txt, lines 230–282
Source SHA256: cd35ac0e65ebf780cc99d3dd8a318255d11251125298d88e88cb676c72b27507
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/seam-joint-ward-state-20261014/PROOF.txt, lines 742–850
Source SHA256: 7c0cd92dfc5eca88260baae0af9edad66f958a27ce0d15d7965414b3971f8da0
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/seam-joint-ward-state-20261014/PROOF.txt, lines 1003–1087
Source SHA256: 7c0cd92dfc5eca88260baae0af9edad66f958a27ce0d15d7965414b3971f8da0
bounded-excerpt · current-at-snapshot