Soda Reproducibility

SODA Reproducibility

At SODA, "reproducibility" is not seeds and GPUs — it is whether a competent reader can re-derive every claim from the submitted document. Because SODA takes full versions with no page limit (2027 CFP, checked 2026-07-08), there is no "details omitted" escape hatch: the community's expectation is that the PDF on HotCRP contains a complete, checkable argument. This skill is the audit for that standard.

The verifiability ledger

Build a table with one row per claim before the July deadline. It doubles as the rebuttal-preparation ledger in September (soda-author-response).

Every row must close before submission. The last column is the single most valuable ritual an algorithms group can institutionalize: author-blind proof checking catches the drift bugs that referees otherwise find in August.

Failure modes referees actually report

• Statement-proof drift. The theorem says O(m log n), the proof delivers O(m log^2 n) after a late edit. Mechanically re-derive the final bound from the final proof, not from memory.
• Imported-theorem hypothesis gaps. A cited result requires constant degree; your graph is merely sparse. Quote the hypothesis next to each use.
• Model slippage. The lower bound is proved against oblivious adversaries; the abstract claims it for adaptive ones. State the model in the theorem, not only in the preliminaries.
• Randomness accounting. "With high probability" needs a stated exponent and a union-bound budget that survives all invocations.
• Case-analysis holes. For arguments with many cases, include the case inventory explicitly; referees count cases before reading any.

Worked micro-example: a probability budget

The randomness-accounting failure deserves its own drill because it compounds silently. Keep a single budget table in the source comments and make every "w.h.p." claim draw from it:

% Failure-probability budget for Theorem 2 (target: n^{-2} overall)
%   E1: sampling lemma (Lemma 3.1), invoked <= n times ... n * n^{-4}
%   E2: hash collision (Lemma 3.4), invoked once      ... n^{-3}
%   E3: concentration (Lemma 4.2), invoked <= log n   ... log n * n^{-4}
%   Union bound: n^{-3} + o(n^{-3}) <= n^{-2} for n >= n_0 (state n_0!)

Audit questions the table forces: does each lemma's stated exponent survive its actual invocation count in the final proof (invocation counts drift when algorithms get restructured)? Is the constant n_0 stated anywhere? Does the theorem statement promise the same exponent the budget delivers? A referee who finds one unbudgeted invocation will re-check every probabilistic step in the paper — the budget table is cheap insurance against that spiral.

Machine-checked steps

When part of the argument is computational (exhaustive search over configurations, extremal-object certificates, verified constants), the reproducibility bar is a rerunnable check, not a claim of one:

# The paper should let a referee do exactly this:
git clone <anonymous-archive-url> && cd verification
python3 check.py            # deterministic; prints per-case status
echo $?                     # 0 iff every case verified

State in the paper the case count, total runtime on commodity hardware, and the reduction proving that check.py succeeding implies the lemma. See soda-artifact-evaluation for packaging and anonymity.

Full version as the reproducibility instrument

The arXiv full version is the community's long-term verification record — SODA proceedings versions are often condensations (soda-camera-ready). Discipline:

• The submitted HotCRP version, the arXiv version, and the proceedings version must agree on every theorem statement; keep a single source with build flags rather than three diverging files.
• When a bug is found post-publication, fix the arXiv version with a dated erratum note; silent replacement erodes exactly the trust this skill protects.
• Version the bibliography: a "personal communication" load-bearing citation is a reproducibility hole; get the statement into a citable preprint or prove it yourself in an appendix.

Pre-submission audit sequence

1. Ledger complete: every claim has a proof location and a blind checker.
2. Bound re-derivation pass: recompute each headline bound from its final proof.
3. Import pass: every external theorem quoted with hypotheses verified in-text.
4. Probability pass: failure probabilities summed and stated once, correctly.
5. Computation pass: certificates rerun from a clean clone on a second machine.
6. Cross-version pass: submission, arXiv, and any slides state identical bounds.

Output format

[Verifiability verdict] Checkable / Gaps found / Not checkable
[Ledger gaps] <claims lacking proof location, blind check, or model statement>
[Drift findings] <statement-proof or cross-version mismatches>
[Import findings] <external results with unverified hypotheses>
[Computation findings] <uncertified machine-checked steps>
[Fix order] <ranked repairs before the July deadline>

Source: brycewang-stanford/Awesome-Journal-Skills → SODA-Skills/skills/soda-reproducibility/SKILL.md