Hexagram provenance

• 2026-08-28 [Verified] The hexagon-triangle substitution matrix [[6,1],[6,3]] (an encoding of published prose, "replace each hexagon with 6 hexagons and 6 triangles, and replace each triangle with 1 hexagon and 3 triangles", not a published matrix) iterated from (1,0) gives 1, 6, 42, 306, 2250, 16578, the A299916 row term for term, by matrix iteration and by the (9,-12) recurrence alike; one side counts tiles and the other holes, so the shared row is not by itself an identity of objects. Witness: A299916; slice-recurrence-order.
• 2026-08-28 [Conjecture] No peer-reviewed source states the hexagram count: the upstream is a photograph, a video, three blog posts and one OEIS comment, and the one peer-reviewed item upstream, the Bridges proceedings paper on three-dimensional diagonal cross-sections of four-dimensional sponges, states the cut and the star-of-David holes but gives no count and no sequence (its full text searched for hexagram, A299916, 306, 2250 and 1.8184).
• 2026-08-28 [Conjecture] The hexagram slice is not scooped at any base but 3: the adjacent published work generalises the cut along dimension n and a type-k hole parameter M^n_k or draws it on a different solid, fixed to the base-three expansion throughout, and none of it treats base 5, 7 or 9; the sequel on pentagon, dodecahedron and 120-cell slices frames the Menger slice as a two-tile closed fractal family and names the directed-graph iterated function system, the same structural reading at base = 3, so the correct statement is "generalises along dimension and hole type rather than base".
• 2026-08-28 [Conjecture] The seed's anchor is self-confirming and cannot falsify anything: "regenerate the A299916 row from two independent generators" holds whether or not the slice's object is A299916's object, since two generators of the same tile census agree by construction (matrix iteration and the (9,-12) recurrence agree exactly so); the real cold check is reproducing the matrix [[6,1],[6,3]] from the published prose.