Established in scope
Full local current response and sharp erasure one-third bound
In the question: Historical: common source, state and event selection
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.
Read the exact result, assumptions and evidence
Result
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.
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 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.
Original evidence
- LOCAL-CURRENT-ERASURE-AND-ORDERING.txt lines 97–146
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/LOCAL-CURRENT-ERASURE-AND-ORDERING.txt
4c3397bb7c0bc75c790b0cca29f5a38abfdff9a564ca5179203ef5a801c554de
finding:all-real-local-cartan-profiles-erasure-third-bound