Excluded in the stated class
Raw event response and state positivity do not execute polar prescription
finding:raw-event-state-positivity-does-not-execute-polar-normalization
Actual raw orbit kernels have spectraKC=(4,1,1,0,0),KW=(3,1,0,0,0), coefficient-matrix commutatorHS²72 and do not preserve originalP2. GNS supplies metricG; originalslotcutQW is notG-selfadjoint ([G,QW]HS²12). Oblique transport has antihermiticitydefect²2, rawWeakSupport distance²(28−8sqrt6)/25 fromP2. Full weight8 regular quartic insertion on given marked source state hasGq=(43/5)I+(73/5)J; same vacuum-normalized fields retain eigenvalues68/5,43/5^4 instead ofI. NativeJ fixes quartics. Positive source metric alone therefore does not select physical positive normalization/readout law.
Scope: No all-E8/P1 no-go or claim physical instruments need orthogonal outcome states. Weight8 control disproves corresponding full formal normalization identity, not replacement of all local profiles. Given instrument or other originally grounded nonvacuum history not excluded. Full source,both20s,exterior/memory paths retained.
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 - Original clock/simplex without an imposed polar mark
Retain actual normalized W6 simplex, sigma=(234), tau=(01), q=5. Consider ALL Hermitian rank2 projectors P with RanP inside Fixsigma, [P,tau]=0 and one positive/one negative tau eigenvalue on RanP. The original polar rule is a comparison point, not an imposed condition of this compatibility class.
premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark - Actual native event fields and distinct state controls
In accepted full E8 field net test actual native reflection automorphisms on reconstructed quartic fields and coherent difference against identity. Original sigma=(234),tau=(01),markedq=5 remain given comparison data; preparation ofq not derived. Vacuum and normalized marked source state are distinct mathematical controls. Difference of automorphism and identity is NOT assumed physically allowed intervention/instrument. Retain all local Wick/Taylor products and complete source states. Positive Gram/relative normalization is examined as computable tensor, never imposed as physical selection rule.
premise:original-native-event-difference-fields-and-state-controls
- experiments/theory-contracts/joint-native-algebra-selection-20261016/SEAM-STATE-EVENT-POLAR-SELECTION.txt, lines 162–215
Source SHA256: c55c96c733a3ad7c314fe251bc8ff8da8940129fd6e99dfc08e449bf4475c1cf
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex, lines 302–343
Source SHA256: 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex, lines 103–143
Source SHA256: 1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e
bounded-excerpt · current-at-snapshot