odd-base-slice-grammar

• Computes the centroid diagonal slice of the odd-base parity solid, the solid whose cells have at most one odd coordinate, as a tile census with no raster.
• The plane x + y + z = 3*base^level/2 meets exactly three integer layers, so a cell is cut as a hexagon at layer offset 1 and as a triangle at offsets 0 and 2.
• Peeling the top digit sends a window to one of three windows only, and complementing digits pairs the outer two, so the census closes on two tile symbols.
• Prints the 2x2 substitution matrix on (hexagons, triangles), its two-term recurrence, the dominant root, log_base of that root, and log_base(fill) - 1.
• Cross-checks the tile recursion against a direct layer census, the full digit-sum distribution built by convolution with no tile reduction.
• Also runs the middle-digit solid, the cells with at most one coordinate equal to (base-1)/2, which is the other reading of the base-3 sponge.
• Domain: matrices and dimensions at base 3, 5, 7, 9; closed forms at odd base 3..21; the mod 4 side test at odd base 3..401 by exact rational comparison of the dominant root against fill/base; direct layer cross-check to level 6 at base 3, 5 at base 5, 4 at base 7, 9.

RUN

• uv run python research/lab/py/odd-base-slice-grammar/slice_grammar.py

WITNESSES

• spectra.md:26 the four rules x9 -12, x11 +62, x42 -288, x28 +693
• spectra.md:26 dimensions 1.8184 / 1.6869 / 1.8026 / 1.7204
• spectra.md:26 log_base(fill) - 1 = 1.7268 / 1.7304 / 1.7430 / 1.7544
• spectra.md:28 the base-3 target [[6,1],[6,3]] and hexagons 1, 6, 42, 306, 2250, 16578, 122202
• spectra.md:29 [[7,3],[30,4]], [[30,3],[24,12]], [[19,9],[96,9]]
• spectra.md:30 both closed forms reproduce every census matrix at base 3..21
• spectra.md:37 112 of 125, dim_slice = 1.960651 against 1.931768, excess +2.888e-02
• spectra.md:37 81 of 125, 1.6869 against 1.7304
• spectra.md:38 the mod 4 side holds at every odd base up to 401