Read the result in its research context.

Result

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.

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 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.

• 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.

Original evidence

• FOLD-COVARIANCE-TO-NATIVE-FIELD-RESPONSE.txt lines 230–282

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/FOLD-COVARIANCE-TO-NATIVE-FIELD-RESPONSE.txt

  cd35ac0e65ebf780cc99d3dd8a318255d11251125298d88e88cb676c72b27507

• PROOF.txt lines 742–850

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/seam-joint-ward-state-20261014/PROOF.txt

  7c0cd92dfc5eca88260baae0af9edad66f958a27ce0d15d7965414b3971f8da0

• PROOF.txt lines 1003–1087

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/seam-joint-ward-state-20261014/PROOF.txt

  7c0cd92dfc5eca88260baae0af9edad66f958a27ce0d15d7965414b3971f8da0

finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut