Established in scope
E6 root subsystems admit no invariant native quarter clock
In the question: Active mathematical program: marked seam monodromies and lattice lifts
The discriminant proof covers all E6 root subsystems. The finite census covers the specified regular A2 complements. No claim about arbitrary non-root Lie subalgebras or physical scales. This does not forbid transported real E6/E7 reductions on the parity double cover with remaining ±I holonomy.
Read the exact result, assumptions and evidence
Result
No E6 root subsystem is preserved by J: its induced action on K*/K=Z3 would square both to identity and, from J²=-I, to nontrivial inversion. The same argument applies to A2. All1120 regular A2 complements form560 J pairs; their E6 intersections have12 roots in640 and24 roots in480 subsystem cases. An explicitly marked D5<E6<E7<E8 chain with40/72/126/240 roots exists but is not J invariant.
Required assumptions
- Active purely mathematical marked-seam program
Within the stated mathematical scope, marked pairs, lattice transport systems, reflections, clocks and cohomology are independent mathematical objects. Earlier origin/completion tasks are historical, not active. Distinguish new definitions, derived theorems and optional markings.
- 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
- PROOF.txt lines 64–91
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-quarter-clock-20261023/PROOF.txt
ac3e95975adb14c82815731b3d8aa0f6e1caf72d25fb749250a5b1bbcd269884
- checker.py lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-quarter-clock-20261023/checker.py
31e9fcf230273955bbf69536c6594255e3c0c53034a87e13ca1d3c56815b0562
- PROOF.txt lines 189–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-quarter-clock-20261023/PROOF.txt
ac3e95975adb14c82815731b3d8aa0f6e1caf72d25fb749250a5b1bbcd269884
finding:e6-root-subsystem-quarter-clock-discriminant-obstruction