Read the result in its research context.

Result

In unchanged M/O/NS dictionary the highest eight-fermion CAR coefficient map of all five original quartics has exact rank5:70x5 map, raw Gram determinant495/8, normalized165/131072. For EVERY original preimage and both quarters its degree7 CAR commutator has Gram G/2 and rank5. No nonzero quartic ray or polar-plane field cancels its contribution at any of the eight source locations. Both b shifts and lower-CAR-degree normal-order/derivative terms cannot remove this witness.

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.

• 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 single-circle density and geometric stress

  Same stipulated chiral CAR source, negative-D sea, actual quarter domains, eightfold F and existing M/O. Local density J_m=sum:a_r* a_(r+m): and its half-density geometric stress with alpha ground energy follow from this source. Original scalar phases fold to correlated generally offdiagonal channel profiles, not independently selected E8 root weights. NS/quartic reference remains conditional. Global Fourier modes control existing fields; no P1-selected local profile/detector/coupling. No isolated b->-b invariance for these new responses; transport positive QWZ occupation with charges/currents/V/b together.

Original evidence

• NATIVE-QUARTIC-MULTILOCAL-SUPPORT.txt lines 1–105

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/NATIVE-QUARTIC-MULTILOCAL-SUPPORT.txt

  7801643ed85df8be24659a66e9437db8f549aea1497900aeeb1bfbbafd0f17ea

• check_native_quartic_multilocal_support.py lines 1–154

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/check_native_quartic_multilocal_support.py

  c0b4cc1bedf7a396146199fbbb538a7494c4b974cbb46e13cb8c64c07ff9ed3b

• native_quartic_multilocal_support_results.json lines 1–40

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_results.json

  8a50438e1d7c8e80f1f734d678bea2c81bd59629ec4cde901bb4ad927fa2c2d4

• native_quartic_multilocal_support_results.json lines 54–110

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  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_results.json

  8a50438e1d7c8e80f1f734d678bea2c81bd59629ec4cde901bb4ad927fa2c2d4

• native_quartic_multilocal_support_results.json lines 216–310

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  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_results.json

  8a50438e1d7c8e80f1f734d678bea2c81bd59629ec4cde901bb4ad927fa2c2d4

• native_quartic_multilocal_support_results.json lines 802–842

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  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_results.json

  8a50438e1d7c8e80f1f734d678bea2c81bd59629ec4cde901bb4ad927fa2c2d4

• native_quartic_multilocal_support_results.json lines 975–981

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  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_results.json

  8a50438e1d7c8e80f1f734d678bea2c81bd59629ec4cde901bb4ad927fa2c2d4

• native_quartic_multilocal_support_review.json lines 1–200

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  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_review.json

  46ee10086da6d9227f9344e24f25dcfb20a629ed703756642374c974099f1e6a

• native_quartic_multilocal_support_review.json lines 201–216

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  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/native_quartic_multilocal_support_review.json

  46ee10086da6d9227f9344e24f25dcfb20a629ed703756642374c974099f1e6a

finding:every-native-quartic-has-all-eight-original-car-supports