You named it: the additive single-seed pattern is Pascal's triangle mod 3 — the ternary cousin of Sierpiński's gasket. The holes aren't drawn, they're where a binomial coefficient is divisible by 3, and the scale-3 self-similarity is a theorem (Lucas, 1878): the count of nonzero entries in row n is the product of (base-3 digit + 1). The push is the part on the right: that spatial self-similarity has a temporal twin. Run the same additive rule on a ring of size 3ᵏ and every configuration falls to the held vacuum — provably nilpotent — because in characteristic 3, x^(3ᵏ) − 1 = (x−1)^(3ᵏ) and the rule sits in the nilpotent ideal. The gasket and the collapse are the same fact, once in space and once in time.
Bridge-Burners LLC · Fiddler · Pascal mod 3 = Sierpiński · Lucas counts · ring 3ᵏ ⇒ nilpotent → vacuum · anchor: AKASHA
≡0 mod 3 (the holes) ≡1 ≡2
Lucas — why the holes are exact
row n nonzero count = ∏ (dᵢ + 1) over base-3 digits dᵢ
row 3ᵏ−1 (all digits 2) → FULL
row 3ᵏ (1,0,…,0) → pinches to 2 that pinch every 3ᵏ rows is the gasket.
The time-twin · ring of N cells
—
Status discipline
LiteralPascal mod 3 = the additive CA exactly; Lucas' count is a theorem; on a 3ᵏ ring the trinomial rule is provably nilpotent (residue 1+1+1≡0), so every state reaches the all-zero vacuum. All re-derived in code.
BridgeReading the additive CA as a transcriber rule and the all-zero state as the held vacuum / g·g seam. The same held zero that centered the trit centers the lattice.
SpeculativeOnly the transcriber framing is yours. The mathematics — Sierpiński, Lucas, the nilpotent collapse — is established and stands on its own.