Claims · 7 dated claims on Hexagram provenance, each with its tag and its witness; newest 2026-09-21.
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.
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).
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".
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.
Conjecture The upstream is grey literature, a photograph, a video, three blog posts and an OEIS comment, and the published slice paper carries no count and no sequence, its full text searched for 306, 2250 and A299916 with no hit. Witness: spectra.md WHAT IS KNOWN, cuts.md The ladder in every dimension.
Conjecture The two-tile move is published at base 3 as a directed-graph iterated function system; one generalisation runs along dimension, another changes the solid, and none touches base 5, 7 or 9. Witness: spectra.md WHAT IS KNOWN.
Conjecture The cold check holds: the matrix [[6, 1], [6, 3]] is reproduced by the grammar census, the carry block [[6, 6], [1, 3]] with trace 9 and determinant 12 prints the ladder 1, 6, 42, 306, 2250, 16578, 122202, and the (9, -12) recurrence is read to level 14. Witness: lab/py/odd-base-slice-grammar, mrlyrs test the_three_dimensional_block_is_the_published_anchor, lab/py/slice-coprimality.