FOCS Supplementary

FOCS has no supplementary-material upload, no appendix size cap, and no separate supplement deadline: the submission is one PDF, the CFP encourages it to be the full version, and everything beyond the abstract, references, and first ten pages is read at the committee's discretion (2026 CFP, checked 2026-07-08). "Supplementary material" at this venue therefore means the rest of your own paper — pages eleven onward — and the design question is how to serve two readers at once: the committee member who stops at page ten, and the assigned expert who reads to the end.

The two-reader contract

The contract's first clause is the one authors break: introducing a new result, a stronger bound, or a hidden assumption after page ten. Discretionary pages can prove anything, but may announce nothing.

Organizing the discretionary body

A structure that has served full-version submissions well:

% pages 1-10: intro, overview, formal statements (focs-writing-style)
\section{Preliminaries}                 % p.11+: full notation, standard facts
\section{Proof of Theorem 1}            % one top-level section per result
  \subsection{The key lemma}            % mirrors the overview's decomposition
  \subsection{From Lemma 3.1 to Theorem 1}
\section{Proof of Theorem 2}
\appendix
\section{Deferred calculations}         % mechanical verifications only
\section{Certificate for Lemma 4.7}     % computed-step documentation
                                        % (focs-experiments)

Design rules embedded there:

• Mirror the overview. The depth reviewer arrives holding the proof sketch from pages 3–6; the body's section tree should be that sketch made formal, in the same order with the same lemma names. A body organized differently from its own overview doubles refereeing work.
• One theorem, one section. Interleaved proofs (Lemma 6 needed by both Theorem 1 and 2) go in the earliest section that needs them, with a forward pointer from the later one.
• Appendices are for the mechanical. Reserve \appendix for calculations a reader could reproduce but should not have to: routine concentration arguments, case tables, computed certificates. A conceptually essential proof placed in an appendix reads as an attempt to hide its weakness.

Pointer discipline

Every formal statement inside the window carries an explicit address for its proof ("proved in Section 5.2"), and every body section opens by naming which windowed statement it discharges. Concretely test the navigation: a reader who doubts only Theorem 2 should reach its complete proof in one jump and find it self-contained given the preliminaries — not dependent on notation invented mid-proof of Theorem 1.

The window boundary is a design object

Page ten's edge deserves deliberate placement. Ending the window mid-proof wastes it; ending with the organization note leaves the breadth reader with a map in hand. If the formal statements run long (many theorems, heavy definitions), compress preliminaries rather than pushing statements past the edge — a definition can be informal-plus-pointer inside the window ("(formal version: Definition 11.2)") but a theorem cannot. Check the boundary on the compiled PDF, not the source: LaTeX pagination shifts, and a statement that drifted to page eleven during deadline-week edits is invisible in the diff.

Length judgment

No cap does not mean no cost. Referees allocate finite hours per paper; a 70-page submission whose last 30 pages are routine variations taxes exactly the reader you most need. Calibration:

• Include every proof needed for correctness — completeness is the point of full-version culture and reviewers penalize "details omitted" at this venue.
• Cut or fold repetitive case analyses into representative cases plus a stated symmetry argument, with the full enumeration in an appendix or a cited certificate.
• Extensions that need no new ideas ("the weighted case follows similarly") earn a remark, not a section — expand them later in the journal version.

Mechanics that keep a long document navigable

• Load cleveref (or equivalent) so every reference states its own type — "Lemma 5.3" not a bare "5.3" — because the discretionary reader jumps in cold at arbitrary depth.
• Hyperlink everything (hyperref with visible-but-quiet link colors); a reviewer reading on screen navigates a 50-page PDF through your links or not at all.
• Repeat, do not paraphrase: when a body section restates its windowed theorem, generate the restatement with thm-restate (focs-writing-style) so the two are mechanically identical.
• Number everything that might be referenced, including remarks and displayed equations used later; "the displayed inequality above" fails a reader who arrived by hyperlink.

Final check before upload

1. Claim audit: nothing asserted after page 10 that is not stated within it.
2. Navigation audit: window → proof in one hop for every statement.
3. Self-containment audit: each proof section readable given only the preliminaries and its own lemmas.
4. Anonymity audit: pages 11+ leak identity as often as page 1 — grant numbers in appendix headers and dataset paths in certificate listings are recurring offenders (focs-submission).