Established within the stated premises
Tetrahedron sums reconstruct all E6 data without loss
finding:tetrahedron-incidence-lossless-e6-reconstruction
For E6/E7 incidence N and E6/tetrahedron incidence M, every entry satisfies NNt=A_D5+3I and MMt=A_D5+27I. Hence MMt=NNt+24I and for every signal f, norm(Mt f)^2=norm(Nt f)^2+24norm(f)^2. N has rank120 and loses1000 directions300+700; M has rank1120. All tetrahedron sums recover f exactly as (NNt+24I)^(-1)M(Mt f), also through an explicit rational degree3 polynomial. The information theorem does not require irreducible decomposition.
Scope: Linear data reconstruction on the same finite E6 set with counting inner product. Preserves supplied data; does not generate a distinguished corner, source or physical state law.
Required premises and original source excerpts
- 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.
premise:standard-e8-root-cut-full-flag-incidence-category
- experiments/theory-contracts/e-series-incidence-algebra-20261024/THEOREMS.txt, lines 92–163
Source SHA256: e80821d422297cfdfce23e892c1b099cc23505ae22ae92f01dcf77d4062f0a5d
bounded-excerpt · current-at-snapshot