Established in scope
Single chiral vacuum line under cycle exchange selects E8 in the complete four-extension class
In the question: Common clock sectors, quartic geometry and operational reconstruction
Conditional exact selection test, not a P1-derived chiral block map or new general CFT classification. Reviewed originals do not define this torus functor there. Actual H=8(L0+delta.p) time and Jacobi background must be transported. M=I is a logical control, not a full P1 countermodel or generic OS output. No forced local-versus-global dichotomy. Not an additional requirement for other possible origin proofs.
Read the exact result, assumptions and evidence
Result
For all four isotropic supports, exactly S v_H=(|H|/4)v_Hperp. An S-stable chiral vacuum line forces |H|=4 and H=Hperp, hence E8plus or E8minus; fixed source h=(1,1) marking selects plus. S vacuum coefficients are1/4,1/2,1,1. Scalar paired control M=I16 is modular invariant with vacuum multiplicity1 but rank16. CAR purity, unique ordinary vacuum eigenspace or tau=i equality do not imply a single torus-block line. Within this class the test is equivalent to holomorphy and explicitly connects the earlier mu16->4->1 completion to the four-extension classification.
Required assumptions
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
- Local conformal compiler extension without preselected sector support
U=V_D5 tensor V_A3 carries its fixed unitary conformal structure and marked discriminant chart C4² with q(a,b)=(5a²+3b²)/8. W is a connected local unitary VOA extension with the same conformal vector and finite-dimensional weight spaces. No M_(1,1), exact support or holomorphy is assumed. Existing classification yields U,D8,E8plus,E8minus. Modular S is the finite discriminant Fourier after the common Jacobi factor and correct background transport. This is a mathematical class, not asserted membership of original P1.
Original evidence
- CHIRAL-SEWING-SELECTION.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/CHIRAL-SEWING-SELECTION.txt
f46ba6a9c8ccf9a55aa130be9220c272109b00415f5709512118be228afe65c4
- MODULAR-SEWING-INDEPENDENT-REVIEW.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/MODULAR-SEWING-INDEPENDENT-REVIEW.txt
71e46a6b7a60fc1a837bee0225912afd086dbf0bbdd5b98001499e37662cac20
- MODULAR-SEWING-INDEPENDENT-REVIEW.txt lines 201–215
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/MODULAR-SEWING-INDEPENDENT-REVIEW.txt
71e46a6b7a60fc1a837bee0225912afd086dbf0bbdd5b98001499e37662cac20
- check_modular_sewing.py lines 1–66
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/check_modular_sewing.py
9fec3ac832649d79b13fe5d84f198f15e8b1a8a570aab1be6aa3185f59049d87
- modular-sewing.json lines 1–92
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/modular-sewing.json
7c6b99699f1eed64a966a93eca7c4ed4adb988f59baf030cd64f6652a34c7769
- CLAUDE-CORRECTED-FINAL-REVIEW.txt lines 1–77
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/CLAUDE-CORRECTED-FINAL-REVIEW.txt
414ea356e714135c14a2c67e25bb944b23b8831c0a50a8c7781e0850ebc2eb29
finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class