Established in scope
First mixed response of original R and root currents derived
In the question: Historical: common source, state and event selection
Actual first algebraic source variation in given E8_1 vacuum;194 complex root responses are not particle counts or selected events. Leakage existence is orthogonally covariant; numerical code matrices require actual source isometry. Second responses, joint return histories, physical history, P1 source and marking selection remain undetermined.
Read the exact result, assumptions and evidence
Result
Original vertex formula gives E_beta,0 T_AR=(v_beta.h(-1))e_beta with v_beta=-AR beta+(beta^T AR beta)beta/2 and beta.v_beta=0. All240 original Chevalley roots have exact norm distribution0:46,14:96,30:32,32:60,64:6, hence194 nonzero source responses without fitted coefficients. Their weight-two zero mode on quartic f has PBW component [f(b)v_beta(-3)-(D_c f)(b)beta(-3)/3]e_beta. Basepoint freedom and transversality prove leakage of each individual nonzero direction; compression vanishes by lattice charge. Four original family omissions have R-sum0, without deriving a physical averaging rule.
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 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.
Original evidence
- NEUTRAL-QUADRATIC-AND-MIXED-RESPONSE.md lines 117–202
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/NEUTRAL-QUADRATIC-AND-MIXED-RESPONSE.md
e6c6fa871adde32db55168103d19aed89b41844e9ef32eca90ed0e58b363b83d
finding:original-neutral-root-mixed-response-derived