Established in scope
Unique D8 frame belongs to the full D5+A3 flag
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Actual full D5+A3 root flags, not uniqueness from the A3 root subsystem alone.
Read the exact result, assumptions and evidence
Result
All135 D8 frames,7560 A3 tetrahedra and their actual incidences were generated. Each full pair of A3 normal system and common D5 core lies in exactly one D8; each D8 contains56 such flags. Bare A3 containment instead gives616 A3 systems per D8, consisting of56 coordinate D3 and560 four-axis A3 chains, and11 D8 per bare A3. Unique tetrahedron-to-frame incidence is therefore a full compiler-flag statement.
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 28–55
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-incidence-algebra-20261024/THEOREMS.txt
e80821d422297cfdfce23e892c1b099cc23505ae22ae92f01dcf77d4062f0a5d
finding:compiler-d8-frame-requires-full-d5-a3-flag