Established in scope
Coxeter seventh-power action has exactly thirty E8 lattice lifts
In the question: Common clock sectors, quartic geometry and operational reconstruction
Common actual E8 root carrier and complete lift classification; no canonical lift selection or field dictionary between clock subalgebras. Scalar-square theta alpha remains distinct. v634 J sign is +i and traces compare the same real dimension8.
Read the exact result, assumptions and evidence
Result
Actual Bourbaki Coxeter W has unimodular Krylov basis (r,Wr,...,W7r), so every lattice lift GWG^-1=W7 is determined by one of240 root images of r. Complete census gives30 lifts:10 order8 with G4=W15=-I,10 order24 with G4=W5 and10 with G4=W25. They square C5=W6 and fix cyclotomic C3=W10. None normalizes native J or sigma to itself or its inverse. Native sigma real trace2 differs from W10 trace-4.
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.
- Original Pauli and v419 F20 source words
Use frozen v783 two-qubit Clifford generators, existing Pauli16 and central mu8, and actual cyclotomic v419 C5,G matrices. A constructed source-word F20 subgroup is available; its physical seam selection is not assumed.
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
Original evidence
- COMMON-CLOCK-BUNDLE-AND-E8-CARRIER.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/COMMON-CLOCK-BUNDLE-AND-E8-CARRIER.txt
106374c87838e492186dd4eca0145d1592a6d4eaa59a09e02511c377737ec671
- COMMON-CLOCK-BUNDLE-AND-E8-CARRIER.txt lines 201–292
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/COMMON-CLOCK-BUNDLE-AND-E8-CARRIER.txt
106374c87838e492186dd4eca0145d1592a6d4eaa59a09e02511c377737ec671
- check_e8_common_clock_carrier.py lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/check_e8_common_clock_carrier.py
703143bdd86e65a298a2fdd8c636a6117b6dec9001dc2615fc2c3dfc13fae499
- check_e8_common_clock_carrier.py lines 201–279
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/check_e8_common_clock_carrier.py
703143bdd86e65a298a2fdd8c636a6117b6dec9001dc2615fc2c3dfc13fae499
- e8-common-clock-results.json lines 1–178
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/e8-common-clock-results.json
d7973aaffe0be66455e1aa6f267b76d1f1ade6b6207d09f50c929cc693679c3a
finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts