# Research calculation proofs Snapshot: 25 October 2026. This package records the mathematical scope for every research article in this release. Of 41 currently listed articles, 31 have selected exact-rational calculations checked in Lean, 6 have conditional formulas only, and 4 rely on source evidence with no formal proof claimed. Another 22 scheduled or unlisted articles have content-hashed records limited to conditional identities; their text and data are not included here. There are 103 arithmetic propositions and 65 displayed-value domain propositions. A domain check says that a displayed percentage lies in its stated range; it does not prove the observation or the article’s conclusion. The common libraries also prove fee, Brier-score, cost, weighted-price and timing identities under explicit assumptions. Sources remain essential. No proof in this package establishes that a source is authentic, that a collection is complete, that a sample is unbiased, that an allegation is true, or that a price is executable. Legal and regulatory claims remain linked to their documents. Where downloads are withheld, this package does not contain their study rows. ## Read and reproduce Frozen article copies are contained in the ZIP. The individual scope records point back to the original public articles and exports. Open an article’s scope below, then follow its named theorem and input locations inside the archive. [catalogue.json](catalogue.json) is the dated public inventory; [checks.json](checks.json) gives the arithmetic-to-input map; [sources.json](sources.json) records the public snapshots and their hashes. [verification.json](verification.json) records the actual checker results. Download [proofs.zip](proofs.zip), extract it, and run: ```sh python3 scripts/bootstrap_verify.py ``` The bootstrap downloads the checksum-pinned official Linux x86_64 toolchain recorded in toolchain-release.json. With the pinned Lean toolchain already installed, run `python3 scripts/verify.py --lean-bin /absolute/path/to/lean/bin`. This invokes Lean 4.35.0, kernel replay, a transitive axiom audit and the bundled external Nanoda checker. Permitted foundational axioms are `propext`, `Classical.choice` and `Quot.sound`; custom assumptions and proof placeholders are rejected. The verifier exercises altered-data, false-axiom and unfinished-proof controls. Exact rational arithmetic is used; actual venue rounding and production implementations are outside the model. `scripts/guard_repository.py --root /path/to/vultax-marketing` rejects new or edited research whose content has no matching scope record. The existing research-publishing test suite calls this guard, and it ran against this release candidate. The script is included for subsequent releases; this publication does not claim a hosted CI job has run. ## Reconciliation notes A few displayed totals and rounded claims cannot be certified exactly from the printed inputs. These are retained in the article records: 43 alerts between the daily chart and headline; duration shares of 59.54% versus an asset/headline total of 59.6%; six sports volume shares totaling 100.2%; separately rounded sports components totaling 58.1% versus 58.0% in prose; and approximate calibration claims whose printed inputs imply 9.375% and 10.4 points rather than 9.6% and 10.3. No source values or article prose were rewritten to make a proof pass. ## Article scope records - [Ballon d’Or 2026 Odds: Two Pre-Ceremony Checkpoints and the 2024 Upset](articles/ballon-dor-2026-odds-polymarket.md) — selected arithmetic checked. - [Best Polymarket Tools and Whale Trackers in 2026: 22 Compared, 4 Publish Their Latency](articles/best-polymarket-tools-2026.md) — selected arithmetic checked. - [Best Polymarket Traders: 36 Wallets Took 44% of Gains; Winners Repeat 41–51% of the Time](articles/best-polymarket-traders-leaderboards.md) — selected arithmetic checked. - [Brazil Election 2026: Runoff Date, Polls, Odds and Results](articles/brazil-election-2026-polls-odds-results.md) — selected arithmetic checked. - [Brazil Election Polls vs Polymarket Odds: What the Numbers Mean](articles/brazil-election-2026-polls-vs-prediction-markets.md) — selected arithmetic checked. - [Brazil Election Results 2026: When Counting Starts and Where to Check](articles/brazil-election-2026-results-time-tse.md) — selected arithmetic checked. - [Crypto Exchange Feed Latency and Coverage: 16 Venues Measured](articles/crypto-exchange-feed-latency-september-2026.md) — selected arithmetic checked. - [Crypto Wash Trading and Real Liquidity: Fake-Volume Estimates Run From 51% to 95%](articles/crypto-wash-trading-what-the-research-shows.md) — source evidence only. - [115,006 Large-Trade Alerts: Where and When Crypto Whales Trade, by Venue and Hour](articles/crypto-whale-trades-115000-alerts-six-exchanges.md) — selected arithmetic checked. - [What the Market Expected: 153 Historical Economic-Event Auctions](articles/economic-derivatives-auction-archive.md) — selected arithmetic checked. - [Polymarket efficiency: two tests, updated monthly](articles/efficiency-series.md) — selected arithmetic checked. - [Did a market move before the election call? First measure the clock](articles/election-market-call-timing-clock.md) — conditional model only. - [Elon Musk Tweet Count on Polymarket: 101 Rounds Checked, the Favourite Wins 1 in 3](articles/elon-musk-tweet-count-polymarket.md) — selected arithmetic checked. - [What the Ocean Forecast Remembers: The ENSOFORECAST Archive](articles/ensoforecast-historical-archive.md) — source evidence only. - [September Fed Odds: 87.5% Hike Price, but an Incomplete Scorecard](articles/fed-september-decision-coin-flip-polymarket-kalshi.md) — selected arithmetic checked. - [Gate Polymarket Fees: The Extra $8 on a $1,000 Trade](articles/gate-polymarket-fees.md) — selected arithmetic checked. - [How Polymarket Makes Money: $46.6 Million in Taker Fees in Four Months](articles/how-does-polymarket-make-money.md) — selected arithmetic checked. - [How Polymarket Settles: 110,576 Markets, a Median of 2.2 Hours, and 89 Disputes](articles/how-long-polymarket-takes-to-settle-markets.md) — selected arithmetic checked. - [Is Polymarket Just Sports Betting? 84.5% of Its Money on an NFL Sunday](articles/is-polymarket-just-sports-betting.md) — selected arithmetic checked. - [Is Polymarket Legal in the US? Where Prediction Markets Stand in 2026](articles/is-polymarket-legal-in-the-us-2026.md) — source evidence only. - [Kalshi–Polymarket Arbitrage: 32,638 Price Checks, and Where a Gap Survived Fees](articles/kalshi-polymarket-arbitrage-gaps-after-fees.md) — conditional model only. - [Where the Money Waits: Polymarket's Open Interest Is 55% Politics, Kalshi's 44% Sports](articles/kalshi-polymarket-open-interest-by-category.md) — conditional model only. - [Polymarket 2026 midterm scorecard: 13,186 contracts frozen before the vote](articles/midterm-scorecard-2026.md) — selected arithmetic checked. - [Nobel Peace Prize odds: 2026 result, saved forecast and 2025 study](articles/nobel-peace-prize-odds-before-announcement.md) — selected arithmetic checked. - [Order-Book Spoofing: What It Looks Like in Live Data](articles/order-book-spoofing-what-it-looks-like.md) — selected arithmetic checked. - [Polymarket API in Python: 3 Requests, No API Key Needed](articles/polymarket-api-python-tutorial.md) — selected arithmetic checked. - [Polymarket's Up-or-Down Crypto Markets: 60% of Its Trades, Priced About Right, 1.6% Fee](articles/polymarket-bitcoin-up-or-down-5-minute-markets.md) — selected arithmetic checked. - [Polymarket Copy Trading: Following 30 Seconds Late Cost 1.43¢ a Share, Before Fees](articles/polymarket-copy-trading-costs-and-tools.md) — selected arithmetic checked. - [Polymarket 'By Date' Favourites at 84¢ a Month Out Came True 64% of the Time](articles/polymarket-deadline-markets-accuracy.md) — selected arithmetic checked. - [Where unusual Polymarket wins concentrate](articles/polymarket-excess-wins-domain-concentration.md) — selected arithmetic checked. - [Liquidity Rewards: Polymarket Offers $150,000 a Day; Kalshi Paid $2.95M in 30 Days](articles/polymarket-kalshi-liquidity-rewards.md) — conditional model only. - [Polymarket Insider Trading: The Charged Cases, and What a Screen Catches](articles/polymarket-longshot-insider-screen-base-rate.md) — selected arithmetic checked. - [Polymarket Sports and Esports: Esports Took 21.4% of the Money on the Thinnest Books](articles/polymarket-sports-and-esports-markets.md) — selected arithmetic checked. - [Polymarket vs Kalshi Midterm Odds: 65 Matched Contracts and What a $50,000 Bet Moves](articles/polymarket-vs-kalshi-midterms-odds-2026.md) — conditional model only. - [1.6% of Polymarket Wallets Never Sleep. They Made 58% of All Trades.](articles/polymarket-wallets-that-never-sleep-trading-cadence.md) — selected arithmetic checked. - [We Tested Polymarket Prices Against 6,776 Resolved Markets. Here's Where They Bend.](articles/prediction-market-fair-value-calibration.md) — selected arithmetic checked. - [Prediction Market Lawsuit Tracker: 49 Cases, Checked Against the Court Record](articles/prediction-market-lawsuit-tracker.md) — source evidence only. - [Polymarket and Kalshi Order Book Depth: 10,000 Contracts Fit 64% and 57% of Books](articles/prediction-market-order-size-depth-audit.md) — conditional model only. - [Prediction Markets in Europe: Sixteen Blocking Orders, and Only Three Are Measured](articles/prediction-markets-europe-regulation-tracker.md) — selected arithmetic checked. - [Why Bitcoin's Price Differs Between Exchanges: 18 Venues Checked Every Minute](articles/why-bitcoin-price-differs-between-exchanges.md) — selected arithmetic checked. - [World Series 2026 Odds: Brewers 62%, Rays 38%, After the Dodgers Led 264 of 271 Days](articles/world-series-2026-odds-polymarket.md) — selected arithmetic checked. All records are dated snapshots. Changed article content requires a new scope check; this package does not certify later revisions.