Multiagent with verifier

Multiagent with verifier: two architectures

A verifier checks another agent's mathematics and never writes any. It sits either after a round or beside each solver.

Architecture

Two panels. (a) Check rounds: in each round m, solvers A1 to AN return to checkers C1 to CN, one each; the reports go to R's review, which briefs the next round or, after round M, writes the verdict. (b) Paired verifiers: in each round, solver Si sends each step to its verifier Vi and gets issues back; R reviews citable steps and open issues, then the next round or the verdict. — (a) checks whole returns between rounds; (b) checks each step before it can be cited.

Where the check sits.
	(a) check rounds	(b) paired verifiers
checks	a whole return, after the round	each step, as it is written
checker	$C_i$, assigned by $R$ to a return	$V_i$, fixed beside $S_i$
an error lives until	the round ends	$V_i$ reports on its step
citing an unchecked step	allowed inside the round	blocked
agents per round	$N$ solvers + $N$ checkers	$N$ pairs
option	`verifier=check`	`verifier=paired`
design	Skill changes	Paired verifiers

Both: an independent check

(independent check)

A verifier $X$ of a proof or step $P$ ($X=C_i$ or $V_i$) satisfies

$$X\ne\lane(P),\qquad \text{brief}(X)=\big(P\ \text{verbatim},\ \text{checklist}\big);$$

it sees neither $R$'s opinion of $P$ nor another check of $P$.

$$\st(P)=\begin{cases}\text{proved} & P \text{ checked, nothing open}\\[2pt] \text{proved (unchecked)} & \texttt{verifier=off}\\[2pt] \text{partial} & \text{an issue or a gap is open.}\end{cases}$$

(a) is cheaper and reads a proof whole; (b) catches an error before later steps cite it: in the worked example 10 of 15 errors were found only after the run (latency). What one verifier should check: Verifying agent.