write-correspondence-guide

a skill to take one mathematical paper, and write a correspondence guide placing it in the literature around it.

provisional draft. this skill is new and still being worked on. expect it to change, and treat what it produces as a first pass.

a Claude Code skill. point it at one mathematical paper and it maps the paper into the literature around it: for each thing the paper asserts or constructs, what the corresponding object in the existing literature is, how close the correspondence runs, and where it stops.

it sits beside write-paper-guide and shares its shape. the difference is the vantage. a reading guide explains the paper from inside; this one places it from outside.

who it is for

the author of a complete draft, running a final check. a reader working through the paper. a reader curious about it from the arXiv, who wants context and may never read it closely. someone placing a paper published years ago.

a referee is a valid reader — a particular kind, with a particular job — but is not what this is designed for, and nothing it produces is written for someone to sign.

what it will not say

it states correspondences. it never says what the paper drew on, and never says what it should cite. the words should cite, fails to cite, uncredited and omits do not appear, and neither do derives from, taken from or influenced by. whether a bibliography is adequate is a judgement for the paper’s readers; this is material for that judgement.

it also does not adjudicate. three disjoint entry points into the same object is a better result than consensus on one — the object surfaces in three literatures and a reader takes whichever they can read.

the two gates

most of what it finds stays in the notes, and that is the design.

standing asks whether a record is a placement at all, or textbook background, or an internal cross-reference. only placements reach a page.

consequence is the harder one: does this change what a reader of the paper would do or know? a record can be correctly located, read in full, be exactly the right source, and change nothing — a flawless identification of a tool the authors invoked by name is worth nothing to the people who invoked it. roughly one record in ten that passes standing passes consequence.

every admitted record names what changes. one that cannot is out, however good the identification.

consequences are written as what is the case, not as an instruction — “the restriction to $\mathbb{Q}$ in §1 is not needed: B. Author gives the same rank computation over any field in which $n$ is invertible”, rather than “drop the restriction”. the declarative form serves the author who can still edit and the reader who cannot, and it is the same sentence.

what comes back

annotated copies of the paper’s own source, one per literature, with the notes set at the passages they concern. generated reference views — the entries, the unlocated, the leads. and optionally a written guide in two parts: the neighbourhoods the paper turns out to sit in, then a thread through the paper with the connections at each point.

everything generated comes from one ledger, correspondences.yaml, so the prose cannot drift from what was found.

it is slow, on purpose

write-critical-guide runs about two hours; this runs longer. it is meant to be invoked once, on a complete draft, after months or years of writing. the expensive part is not finding a candidate — it is establishing what the candidate actually says, on both ends of a connection, well enough to argue it.

it runs unattended. every decision has a default, and the only thing that halts a run is being unable to identify the paper.