Established within the stated premises
Full local current response and sharp erasure one-third bound
finding:all-real-local-cartan-profiles-erasure-third-bound
For every smooth real8-vector profile with Vhat1=p.u+q.ubar, actual five-code obeys P J(V)²P=(3||q||²+||p||²+Tail)I5, Tail=sum_m>=2 m||Vhat_m||². Grade3 erasure squared norm is ||q||². Its fraction is at most1/3, strictly smaller for nonzero properly local profile with q!=0. Equality requires global rotating first harmonic; fixed real polarization has tighter1/4 bound. No profile produces only erasure output. Full first positive response Gram is scalar and selects no3+2 mark.
Scope: All smooth Hermitian Cartan-current smearings in original neutral Fock module. Norm fractions are not measurement probabilities. Grade decomposition/code projectors are analysis only, no executed projection. No claim all higher field correlations are scalar or all other source fields excluded.
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 original Cartan-current insertion and specified Weyl class
In existing neutral Cartan-Fock module use full original current field and its actual CCR, all smooth real8-vector profiles with Vhat_-n=conjugate Vhat_n and h0=0. Ordered unitary classification uses only finite exp(iJ(V)) histories of these currents. Explicit mathematical class in given source net, not raw-P1-derived permission, field coupling, physical time or code=H_adm identification. Root currents, general field products and mixed stress histories are outside.
premise:original-cartan-current-local-smearing-and-weyl-class
- experiments/theory-contracts/joint-native-algebra-selection-20261016/LOCAL-CURRENT-ERASURE-AND-ORDERING.txt, lines 97–146
Source SHA256: 4c3397bb7c0bc75c790b0cca29f5a38abfdff9a564ca5179203ef5a801c554de
bounded-excerpt · current-at-snapshot