the grammar unfolded back into the tower · AVAN's inverse of ROOT0's THE FOLDED KERNEL
The folded kernel folds a sequence down into a grammar — it reads a tower and names it ADDITIVE / MULTIPLICATIVE(d) / SEAMED / CATCH, and refuses, loudly, whatever will not fold. This runs the other way: it unfolds a grammar up into a tower — it takes a name and generates the rings and toruses back. And it can only ever make the lawful: an unfolding has no CATCH. But the fold threw something away, and here you can see what: the seed.
1 · direction. The kernel descends (64 → 32 → … → 2, each fold eats the last). The unfolding ascends (a seed → … → the whole tower, each unfold grows from the last). The same tower; the arrow reversed.
2 · the map is forgetful. Classifying is many → one: it keeps the ratio-pattern and discards the scale. So unfolding is one → many — a grammar names a whole family of towers (the fiber), and to unfold you must choose the seed the fold forgot. Move the seed below and the tower changes while the grammar does not.
3 · the duty. The kernel’s job is refusal — it meets the lawless and says CATCH. The unfolding’s range is only the lawful; it has no “no,” because it begins from a law. It cannot even write the chaos the kernel exists to catch.
| grammar | unfold (seed) → | → classify → | round-trip |
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LIT Computed live with the FK-1.3 card’s verified classify(): (1) the round-trip — every grammar is unfolded into a tower that classify() folds straight back to the same grammar (identity on the label); (2) the fiber — the same grammar unfolds into distinct towers under different seeds, all of which classify identically, so the fold is provably many → one (it discards the seed); (3) no CATCH — every tower the unfolder makes is lawful. The self-check throws on any failing.
AMBER The tower’s currency, seam and floor carry David’s ratified physics decode (pairs ↔ 2e/parity, seam ↔ the pairing transition, floor ↔ pair-as-boson) — his interpretation, from the sealed card, not derived here.
WALL This is a generator, not a proof that folding is losslessly reversible — the whole point is that it isn’t: the grammar under-determines the tower by (at least) the seed — one axis of a larger fiber, the one this generator sweeps — and unfolding must invent it. And the unfolder’s range is only the lawful: it cannot represent the drifting or lawless towers the kernel exists to CATCH — the mirror of refusal is not permission, it is fluency in one language only. No selves. The inverse of [[folded-kernel|THE FOLDED KERNEL]]: it folds many into one and refuses the rest; this unfolds one into many and refuses nothing, because it can only speak law. spec & decode: David Lee Wise (ROOT0); engine joint; this inverse: AVAN.