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Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Conditional result

Bounded proper-local operation cannot exactly prepare positive eigenpacket from same sea

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

Conditional on the same full CAR source, support-preserving source time and local vacuum separation, not merely finite compression4I. Exact preparation from same sea by ONE bounded proper-local operator, including products fitting in a larger proper interval. No approximation/probability/cost bound, no ban on unbounded field insertions, other initial states, global protocols or all P1 physics. NS/quarter reference transport explicit; physical P1 net identification remains open. No classification of abstract AQFT-local CP maps without such local Kraus implementers.

Read the exact result, assumptions and evidence

Result

In the given full positive CAR vacuum net, local separation of Omega and A Omega=psi,Hpsi=Epsi,E>0 for bounded proper-local A imply alpha_t(A)=exp(itE)A. Then A*Omega would have energy-E; positivity and separation force A0. Actual original constructor confirms both quarters: five full source states neutral in every residue, only H_alpha32, Gram rank5, supports694/710/711/713/688. Thus the lemma covers all nonzero actual R_b4 target directions without a closed-code assumption. Positivity extends the exclusion to pure or mixed exact E32 outputs of normal instruments with finite/countable bounded Kraus operators in the same proper interval algebra: every Kraus vector would lie in that positive eigenspace and vanishes.

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.

  • Same full positive CAR source with locally separating sea

    Given negative-D quarter-CAR representation with full H_alpha=sum(n+alpha):a_n* a_n:>=0,H Omega=0 and support-preserving time covariance. Omega separates each larger proper-interval algebra. Test class: bounded proper-local A with A Omega an exact positive-energy eigenvector. NS/quarter chart retains support, reference and time; no physical P1 net identification follows.

Original evidence

  • NATIVE-QUARTIC-MULTILOCAL-SUPPORT.txt lines 107–206

    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 110–123

    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_review.json lines 1–200

    Source checked at this snapshot

    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

    Source checked at this snapshot

    Original location and fingerprint

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

    46ee10086da6d9227f9344e24f25dcfb20a629ed703756642374c974099f1e6a

  • local_energy_eigenpacket_review.json lines 1–170

    Source checked at this snapshot

    Original location and fingerprint

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

    f911f9d9237c8056bb4f8add917682d02f43c0bca40e1da520942bb6c84e150f

finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket