fractal_ternary · audit bench

verdict

⏳ conductor booting — verdict renders only after all live checks complete…

conductor RUNNING

sweep · k(L) rank × gcd law QUEUED

task-3 · fractalization reduction QUEUED

task-4 · string search + q-probe QUEUED

2D — k(L) fingerprint & the fractal itself

top: orange bars = k(L) by live F₃ matrix rank · gold rings = independent gcd-law prediction 2·deg gcd((1+x)ᴸ−1, xᴸ−1). they must coincide. bottom: mod-3 Pascal raster — the support every logical operator is condemned to. orange = trit 1, amber = trit 2.

3D — the logical tower (soft-GL)

each layer down = one CA step s → (1+x)s. the operator's footprint is this tower — fractal, never a string. drag to rotate.

toddler corner

ELI5: we have a coloring rule: each new row of blocks is made by adding neighbor blocks (colors count 0,1,2 and 3 wraps to 0). the rule draws a snowflake. question 1: is our snowflake game one from the big library? YES — the shelf-count rule from the library book predicts our shelves perfectly, every size we tried. question 2: can you cheat with a thin straight line of blocks? NO — we hunted for skinny lines and there are none; only snowflakes. question 3: is there a catch? YES — one wrong block on the quiet side is invisible to the checkers. good toy, sharp edge.

method & provenance

double verification. every number here was computed once in Python (numpy, F₃ Gaussian elimination + polynomial gcd, 17/17 cross-method agreement) and is recomputed live in this page by an independent JS implementation. baked ≠ live ⇒ this page fails loud.

family anchors. CA/fractal stabilizer construction: Yoshida, PRB 88 (2013), arXiv:1302.6248 · fractalization map & integer intrinsic dimension caveat · reflected-CA-pair codes in current biased-noise qLDPC work · qutrit cubic codes, arXiv:2606.19873 (June 2026). none of these are claims of equivalence beyond what the gcd law demonstrates.