Established in scope
Common conformal primary/multiplicity structure of native core
In the question: Historical: common source, state and event selection
Given canonical E8_1 stress field and original neutral Cartan-Fock embedding. Conformal weights are not particle counts or physical time; no new irreducibility/gauge-group premise. Analytic all-word theorem; finite Fock checks only accompany it.
Read the exact result, assumptions and evidence
Result
Original J-positive mode1 polynomials are all Virasoro primary because u_a.u_b=0: L0=d,Lm>0=0. Actual4/5/20 carriers thus have(c,h,r)=(8,1,4),(8,4,5),(8,3,20). For all Virasoro descendant words Gram=G_(8,h)(lambda,mu)delta_ij. Generated source cycles factor as common unitary highest-weight representation modulo common nulls tensor actual multiplicity; native G31 acts on second factor. No R_neut branch, individual root or family omission is needed.
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.
- 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
- CONFORMAL-HISTORY-AND-ERASURE-CARRY.txt lines 28–101
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/CONFORMAL-HISTORY-AND-ERASURE-CARRY.txt
8a50ef4c3621005d39ecaa93f38fa1d06f6c32f46c57e138fadcebb49c0ab184
finding:native-conformal-primary-multiplicity-source-factorization