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Result

Actual current product obeys j_ubar_a(z)F_i(0)=G_ia(0)/z²+sum_k>=0 z^k/k! :partial^k j_ubar_a F_i:(0), without simple pole. Double pole is original erasure twenty; regular t_ia=ubar_a(-1)f_i contains exactly prior h5 primary r=t−7/85L_-2g+3/170L_-1²g, Gram78/85I20 and rho5 tensor conjugate4 action. [ubar_a(1),j_u_b(w)]=delta_ab also shows pure erasure is global Fourier mode, not an operator localized in a proper interval of given current net. OriginalP1 defines locality by support and A/A*-invariant restriction, not global compression.

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.

• All modes of original canonical source stress tensor

  In given E8_1 lattice vacuum use exactly T_E8=(1/2)sum:h_A h_A:,c=8, without improvement/background charge. Examine all Virasoro modes and well-defined pure stress histories in original neutral Cartan-Fock space. This is a mathematically specified geometric transport class, not P1-selected physical history or time. It differs from prior class of all neutral weight2 ZERO MODES; do not combine exclusions. First erasure Ward action uses existing a_a=bar u_a(1), no extra source, root or family choice.

Original evidence

• LOCAL-CURRENT-ERASURE-AND-ORDERING.txt lines 4–95

  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:original-local-current-ope-forces-erasure-and-carry