Read the result in its research context.

Result

Actual native reflections at givenq produce five local quartic difference fieldsDelta_j=F_nj−F_nq; full vacuumGramG=I+J, arbitrary common smooth local smearc_fG. All Wick classes/Taylor terms retained. Original three/two clockorbits give response tensorsKC=DQC D*,KW=DQW D* andR=KC+KW. Without insertingP2/targetangle, mathematical positive RELATIVE tensorR^−1/2 KW R^−1/2=UQW U* is exactly existing originalP2, U=D(I+J)^−1/2. Polar prescription thus has concrete common field/event-response interpretation as relatively normalized quantity.

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.

• 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.

• 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.

Original evidence

• SEAM-STATE-EVENT-POLAR-SELECTION.txt lines 4–160

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/joint-native-algebra-selection-20261016/SEAM-STATE-EVENT-POLAR-SELECTION.txt

  c55c96c733a3ad7c314fe251bc8ff8da8940129fd6e99dfc08e449bf4475c1cf

• marker_selection.py lines 58–102

  Source checked at this snapshot

  Original location and fingerprint

  tfpt_explorer/marker_selection.py

  f6d9907f0e9fa242c4f50d67681c499d7bff046f0032abed37f66f332965842a

finding:original-full-field-event-gram-reconstructs-relative-polar-mark