THE FOLD / SPAWN / CHECKPOINT ZERO / THE CYCLIC TAG
THE CYCLIC TAG
a universal computer from three strings and one rule
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A cyclic tag system is one of the tiniest known universal computers. It has a fixed cyclic list of production strings and a growing data string. Each step: remove the first data symbol; if it was a 1, append the current production; if a 0, append nothing; then advance to the next production, cycling. From this almost-nothing, Rule 110’s universality was proven — cyclic tag systems can emulate any computation.
LIT verified live: running the productions (010, 000, 1111) on the seed “11” reproduces the exact documented state sequence 11 → 1010 → 010000 → 10000 → … matching an independent hand derivation (window.__cyclictag). FIG no framing; exact.
LIT verified live: running the productions (010, 000, 1111) on the seed “11” reproduces the exact documented state sequence 11 → 1010 → 010000 → 10000 → … matching an independent hand derivation (window.__cyclictag). FIG no framing; exact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at checkpoint-zero — the barest starting point from which, astonishingly, all computation can grow. The cyclic tag system is that seed of universality. AVAN (AI) built the instrument: the remove-first / append-production / cycle step, the state trace, and the match against a hand-computed reference.
Credit as content: Matthew Cook (cyclic tag systems in the Rule 110 universality proof, 2004). The weave: David names checkpoint-zero; I run the three-rule step and confirm the state sequence exactly matches an independently hand-derived trace.
Credit as content: Matthew Cook (cyclic tag systems in the Rule 110 universality proof, 2004). The weave: David names checkpoint-zero; I run the three-rule step and confirm the state sequence exactly matches an independently hand-derived trace.
3 ONE DIMENSION
Remove the first symbol of the data. If it was 1, append the current production string; if 0, append nothing. Advance the production pointer, wrapping around the list. Repeat.
4 TWO DIMENSIONS · INTERACTIVE
Step the cyclic tag system and watch the data string evolve; the trace is checked against the documented sequence.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: universal computation from a cycling list.
AVAN’s addition (the inverse-companion): get Turing-completeness from almost nothing — a cyclic list of strings and a single “append-if-1, skip-if-0, then cycle” rule. The inverse of ‘a computer needs registers, memory, an instruction set’ is ‘three strings and one cycling rule already compute anything.’ Magenta is the elaborate machinery you don’t need; green is the minimal cycling engine. Universality from a handful of bits.
LIT Genuine cyclic tag system (Cook, in the Rule 110 universality proof, 2004). Verified live: running the productions (010, 000, 1111) on seed '11', the remove-first / append-if-1 / cycle step reproduces the exact state sequence 11, 1010, 010000, 10000, 0000010, 000010 — matching an independent hand-derived reference (window.__cyclictag.matchesReference).
FIG No framing: the remove-first / append-production / cycle step, the state trace, and the match against a hand-computed reference run in-browser and agree exactly. The AVAN inverse is honest — a cyclic list of strings and one 'append-if-1, skip-if-0, then cycle' rule is Turing-complete; magenta is the elaborate machinery you don't need, green the minimal cycling engine. Universality from a handful of bits.
FIG No framing: the remove-first / append-production / cycle step, the state trace, and the match against a hand-computed reference run in-browser and agree exactly. The AVAN inverse is honest — a cyclic list of strings and one 'append-if-1, skip-if-0, then cycle' rule is Turing-complete; magenta is the elaborate machinery you don't need, green the minimal cycling engine. Universality from a handful of bits.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of CHECKPOINT ZERO · David Lee Wise (ROOT0), with AVAN