Established in scope
Full original erasure20 and joint25 retain all eight source arcs
In the question: Historical: common source, state and event selection
Exactly the original neutral erasure20, original norms and given M/O/NS eightfold dictionary; not a charged E8 twenty or physical particle identification. Completeness only within the existing linear25-field space, not allE8 fields/nonlinear products/admissibleP1 operations. No separate E24/joint25 preparation theorem or physicalP1/q/3+2 selection; earlier preparation-lemma hypotheses remain separate.
Read the exact result, assumptions and evidence
Result
The actual20 fields g_(i,a)=partial_a P_i/sqrt(N_i) have original Fock GramI20. Their highest six-fermion CAR map is56x20,rank20,nullity0,raw Gram determinant1032386052096,normalized194481/1099511627776. Every original-sheet commutator has Gram3/8G andrank20 in both quarters; original b shifts retain the principal term. Quartic5 and erasure20 cannot cancel their distinct highest CAR degrees8/6 and commutator degrees7/5. Every nonzero combination of the complete existing joint25 field space therefore has detectable support on ALL8 preimage arcs.
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
- ERASURE-AND-JOINT-25-MULTILOCAL-SUPPORT.txt lines 1–93
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/ERASURE-AND-JOINT-25-MULTILOCAL-SUPPORT.txt
73214df57a8a29b9c8adf209fb81b026e4942107773afbea3c23118062d0df55
- check_erasure_multilocal_support.py lines 1–112
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/check_erasure_multilocal_support.py
7effbd2f160066f082efd71abdf2b5a6d5b24fdc73c0272bbc9031b58fc253f6
- erasure_multilocal_support_results.json lines 78–89
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/erasure_multilocal_support_results.json
3a575d4642ed8c7877f9f36a451d79ad9e56ed3d05d4c06b18b4080fc516b578
- erasure_multilocal_support_results.json lines 2220–2227
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/erasure_multilocal_support_results.json
3a575d4642ed8c7877f9f36a451d79ad9e56ed3d05d4c06b18b4080fc516b578
- erasure_multilocal_support_results.json lines 2670–2728
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/erasure_multilocal_support_results.json
3a575d4642ed8c7877f9f36a451d79ad9e56ed3d05d4c06b18b4080fc516b578
- erasure_multilocal_support_results.json lines 3168–3168
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/erasure_multilocal_support_results.json
3a575d4642ed8c7877f9f36a451d79ad9e56ed3d05d4c06b18b4080fc516b578
- erasure_multilocal_support_results.json lines 3223–3223
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/erasure_multilocal_support_results.json
3a575d4642ed8c7877f9f36a451d79ad9e56ed3d05d4c06b18b4080fc516b578
- erasure_multilocal_support_review.json lines 1–135
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/erasure_multilocal_support_review.json
81b83992072b45b1b1f29c7e7e2e80e2c5fd154a68d9ae22c714d5f19304a3fc
finding:full-original-erasure20-and-joint25-have-all-eight-source-supports