Established in scope
Complete E6 orbital algebra with five irreducible components
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Complete for regular A2-normal E6 root cuts in standard E8 under its actual Weyl action; not arbitrary Lie-subalgebra embeddings.
Read the exact result, assumptions and evidence
Result
The actual Weyl action is transitive on1120 E6 cuts. An explicit stabilizing E6/A2 reflection subgroup is transitive on each intersection class: D5 with81,D4 with270,A4 with648,A2+A2 with120 neighbours. Including equality these are the full five orbitals. All125 structure constants yield the commutative full commutant. Normalized primitive idempotents have ranks1,35,84,300,700, proving the complete irreducible Weyl decomposition.
Required assumptions
- Regular E8 cuts and full compiler flags
Fix the standard E8 roots with their actual Weyl action. E6 objects are complements of regular A2 root systems and E7 objects complements of root lines. A tetrahedron comprises the four A2 faces of a regular A3 normal system with common D5 core; its D8 incidence requires both factors. Relations are literal root inclusions and intersection sizes. Signals are rational, real or complex functions with counting inner product. Equivalence transports all flags by the Weyl action, without a selected corner or physical source.
Original evidence
- THEOREMS.txt lines 57–89
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-incidence-algebra-20261024/THEOREMS.txt
e80821d422297cfdfce23e892c1b099cc23505ae22ae92f01dcf77d4062f0a5d
finding:e8-cut-five-orbital-incidence-algebra-complete