THE FOLD / RESPAWN / THE PHOENIX / THE FREDKIN
THE FREDKIN
a gate that conserves its ones
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Fredkin gate (controlled-SWAP) is a reversible and conservative logic gate. It takes three bits (a, b, c) and, if the control a is 1, swaps b and c; otherwise it leaves them alone. Being a bijection of the eight input states, it runs backwards — it is its own inverse. Its special virtue is that it conserves the number of 1s (a swap never changes the total), so it models physics that preserves particle count — and it is still universal for classical logic: with a constant input, controlled-SWAP computes AND, and with others NOT and OR.
LIT verified live: the gate is a permutation of the 8 states, applying it twice is the identity, it preserves the Hamming weight of every input, and it computes AND (c = 0 → a ∧ b appears) (window.__fredkin). FIG no framing; the truth table, self-inverse, weight-conservation and AND gadget run in-browser.
LIT verified live: the gate is a permutation of the 8 states, applying it twice is the identity, it preserves the Hamming weight of every input, and it computes AND (c = 0 → a ∧ b appears) (window.__fredkin). FIG no framing; the truth table, self-inverse, weight-conservation and AND gadget run in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-phoenix — a gate that conserves its ones and rises back to its start when run twice, losing nothing to ash. AVAN (AI) built the instrument: the controlled-SWAP truth table, the self-inverse and weight-conservation checks, and the AND gadget.
Credit as content: Edward Fredkin & Tommaso Toffoli (1982), conservative logic. The weave: David names the phoenix; I confirm the gate is reversible, conserves the number of 1s, and is universal for classical computation.
Credit as content: Edward Fredkin & Tommaso Toffoli (1982), conservative logic. The weave: David names the phoenix; I confirm the gate is reversible, conserves the number of 1s, and is universal for classical computation.
3 ONE DIMENSION
The 8-row table: rows with control a = 1 swap b and c; every row keeps the same number of 1s — a conservative permutation.
4 TWO DIMENSIONS · INTERACTIVE
Toggle a, b, c and watch the controlled swap; set c = 0 to read an AND gate — universal logic with the number of 1s preserved.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the gate as a weight-preserving permutation of the cube.
AVAN’s addition (the inverse-companion): don’t create or destroy bits — only move them. The inverse of ‘compute and discard’ is ‘swap conditionally, conserving the count of 1s and staying reversible.’ Magenta are the states that swap; green are the fixed ones. Conserve the ones.
LIT Genuine Fredkin gate / CSWAP (Edward Fredkin & Tommaso Toffoli, 1982), conservative logic. Verified live: permutation of the 8 states (window.__fredkin.permutation), own inverse (.selfInverse), conserves Hamming weight (.conservesWeight), and computes AND (c=0→a∧b) hence universal (.universalAND).
FIG No framing: the controlled-SWAP truth table, self-inverse, weight-conservation and AND-gadget checks all run in-browser. The AVAN inverse is honest — only moving bits (never creating or destroying them), conserving the count of 1s while staying reversible, is the defining property of a conservative gate; magenta are the states that swap, green the fixed ones. Conserve the ones.
FIG No framing: the controlled-SWAP truth table, self-inverse, weight-conservation and AND-gadget checks all run in-browser. The AVAN inverse is honest — only moving bits (never creating or destroying them), conserving the count of 1s while staying reversible, is the defining property of a conservative gate; magenta are the states that swap, green the fixed ones. Conserve the ones.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE PHOENIX · David Lee Wise (ROOT0), with AVAN