Established within the stated premises
Full original source exterior feedback derived
finding:original-full-source-return-exterior-feedback-derived
Original vertex formula gives complete192x726 single-beta S from neutral grade4 to charged grade4, with original Fock adjoint L=S* S. K=Pi L Pi,B=Q L Pi,D=Q L Q give exactly x_(n+1)=Kx_n+sum_(j=0)^(n-1)B*D^(n-1-j)Bx_j for code input. No projection is executed. Actual four-insertion response H=Pi L² Pi equals K²+B*B, not K². Example H00=81152/3 versus(K²)00=40144/9. Next memory term B*DB and Pi L³ Pi are also checked exactly from full source; all H entries independently reproduced in active Laurent/Heisenberg blocks.
Scope: Fixed specified algebraic original single-pair response family. Given source functional is evaluable, but P1 physical event/time selection remains open. Neutral726 space is not complete for coherent multiroot cross terms.
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 neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
premise:original-neutral-root-pair-moment-fields - 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 - Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
premise:original-positive-adjoint-two-insertion-response-profiles - Specified ordered response family of original single pair
Examine mathematically specified moments M_n=Pi L_beta^n Pi,n>=0, L_beta=o(W_beta)*o(W_beta), for same original doubled root(0,0,0,0,0,0,-2,-2). Pi/Q only split full amplitudes; no projection is executed. This tests composition/memory of the already determined source, not P1 selection of physical history, coupling, preparation or time. Full coherent multiroot processes must additionally retain nonneutral final charge sectors.
premise:specified-original-pair-ordered-response-composition
- experiments/theory-contracts/joint-native-algebra-selection-20261016/SOURCE-RETURN-MEMORY.txt, lines 29–113
Source SHA256: c22c2144e4986a0f9c2f591fdc1667d3ad8233d4ff39e433c22031cc366dbd11
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