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deduction.md

Last edited by David Bloomin · 2d ago ·

Deduction, and who leaks what

A fact

Every fact is a hard constraint on the chemistry. There are three kinds:

fact	meaning	who holds it
`mixFull(a, b, potion)`	mixing `a` and `b` gives exactly this potion	private to the tester; public for `sell` and `debunk` results
`mixSign(a, b, class)`	mixing `a` and `b` gives a potion of this class (`positive` / `negative` / `mud`)	public, from every `test_self`
`notSig(x, v)`	ingredient `x` is not signature `v`	public, minted when a seal burns

Seat s knows every public fact, plus its own private mixFull facts, plus the standing rule that the chemistry is a bijection.

The grid

A seat's grid is computed by exact enumeration of all 40,320 bijections, keeping those consistent with every fact it knows:

grid[x] is the set of signatures v such that some consistent bijection maps x -> v;
chemistries is how many bijections survive.

There is no heuristic propagation, so the grid never over- or under-claims. An ingredient whose set is a singleton is SOLVED - that is when a seat may publish without gambling. The grid is recomputed once per seat per phase open, and the wasm replay viewer runs the same code, which is why spectators can watch all four grids narrow like a hole-cam instead of taking anybody's word for it.

The prompt receives the grid as a table, not as prose:

YOUR DEDUCTION GRID (12 chemistries still possible)
Nightcap      SOLVED  R+G-B+
Emberroot     2       R-G+B+ | R-G+B-
Fen Lily      3       R+G+B+ | R+G+B- | R-G-B+

The information economics

forage leaks the two cards you drew, and nothing else.
test_student leaks the two ingredients you burned. The potion is yours alone. It costs a coin precisely because the silence is worth paying for.
test_self leaks the two ingredients and the sign class - everybody sees you glow or retch - but the colour stays yours. It is free because you are the one who suffers.
sell leaks the whole potion. Selling is how you make coin and how you hand the table a fact.
debunk leaks the whole potion of x with y to everyone, whether the attack works or not, so every demonstration is a free public experiment paid for by the attacker.
publish leaks what you claim, which need not be what you know.
A burn mints notSig(x, claim) for everyone: a false seal, once exposed, narrows every seat's grid.

Because a coloured potion is produced by only 2 of the 28 signature pairs, a coloured result cuts the hypothesis space by roughly fourteen; MUD, produced by 16 of 28, barely moves it. Choosing which pair to burn a phase on is the whole science: prefer the pair whose worst-case outcome would leave the fewest chemistries standing.

Attacking well

A false seal burns only when the attacker brings a reagent that exposes it. p == q happens often against a wrong claim whose error this particular pairing cannot see - the attack fails, the attacker pays 2 reputation, and the fraud is strengthened by a recorded vindication. A safe attack is one where every chemistry still consistent with the attacker's own grid predicts a different potion from the seal's claim. Attacking well therefore requires knowing more than the author.