Established in scope
Octic field already lies in the original even CAR current algebra
In the question: Common clock sectors, quartic geometry and operational reconstruction
Given reference dictionary; local eight original arcs, no c1/c8 point-net identity or P1 selection. No naive fermionic degree16 normal order.
Read the exact result, assumptions and evidence
Result
A=U+^T O^T M obeys AA*=I4, AA^T=0 and b=Aδ. F8^d=:I8(A(j_sea+δ/z))/(96sqrt140): is a neutral even CAR current composite of the same source with original point splitting and finite derivative counterterms. Full correlations and i0 are retained; no E8 root/spinor vertices are needed. Fold energy8 equals source energy64.
Required assumptions
- Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
- 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.
Original evidence
- CAR-OCTIC-DICTIONARY.txt lines 1–109
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-octic-seam-origin-20261025/CAR-OCTIC-DICTIONARY.txt
c82fce3ad57904fb7628a1abaf2c6eacd94d230d73f2ac69d8da0fe9d49f22c2
- ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt lines 108–160
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt
62a9eeb4519b59d4514445f9d4dd5d2059e29179956a4c97ec94b7bae9ae3094
finding:native-octic-is-an-original-even-car-current-composite