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Bayes' theorem: posterior probability from a prior, sensitivity and false-positive rate, with natural frequencies and odds form.

UMA resolution dispute and flip base rates by category and criterion clarity; descriptive historical compatibility, not a market-specific forecast. BEFORE YOU PAY: free substitute https://dash.polym.uk/uma-base-rates.json and https://dash.polym.uk/uma-flip-rate.json. THIS ADDS: The two artifacts joined into one response, dispute axis and flip axis already aligned by category. The underlying number

UUID inspector — parses any UUID (canonical, braces, URN or 32-hex form) and returns its version, variant, embedded timestamp for v1/v6/v7, nil/max flags, hex and URN forms. Use to validate identifiers or recover the creation time of UUIDv7 keys.

Fare Pulse — cheapest live fares from a major US hub, cached snapshot.

Sample autocorrelation (ACF) and partial autocorrelation (PACF, Durbin-Levinson) of a series up to lag k, with 95% bounds.

Format a numeric amount as currency for a given locale using Intl, honouring the currency's own minor-unit convention (USD→2, JPY→0). display selects the symbol, narrow symbol, ISO code or full name. An unknown currency or locale is a clean 400.

Call before installing or updating an npm or PyPI dependency. Returns a verdict (ok, caution, avoid, unknown) plus evidence signals: install script added, maintainer or publisher change, very recent publish, build provenance dropped, known malware and vulnerability advisories. A clean result is not a guarantee of safety.

Node4All Fortune — deterministic fortune reading derived from the x402 payment authorization nonce. Flagship demo of the Node4All x402 v2 payment flow. Operator: Node4All (https://node4all.com). Currency: USDC on Base.

Pay once to receive a short-lived WebSocket ticket for the live Bitcoin mempool stream.

Address-to-zoning lookup for published municipalities. Coverage: 63 municipalities in 6 states. Resolves a street address to supported municipality and, where GIS is verified, zoning district_code with lookup method. Positioning: Records tell you what's on file; ZoningVerdict tells you what the ordinance actually says, independently verified, with the citation. Responses include source citations a

UK VAT number format + check-digit test: Checks a UK VAT number's format and HMRC check digits (mod 97 / 9755). Catches fake or mistyped VAT numbers instantly without an HMRC call. Use /v1/business/check to confirm live registration.

npm / PyPI package metadata (keyless). Ecosystem + name → latest version, license, homepage.

Parse CSV into JSON rows keyed by trimmed snake_case headers. Offline. Amp port.

Base64 encode/decode UTF-8 text (standard or URL-safe). Offline. Amp port.

Returns the full version history of a package from a single normalised schema that covers seven ecosystems. Versions are ordered by semantic version, not alphabetically and not in registry order, so 1.10.0 sorts after 1.9.0 — the mistake that quietly breaks naive comparisons. For each version you get the publication timestamp, whether it is the registry default, whether it is deprecated and the de

Calibrated 1X2 probabilities plus derived markets (totals, BTTS, correct score) for every upcoming fixture across the big-five European leagues. Backed by a public, Brier-scored track record.

Get a random interesting joke. Secured with x402 payment protocol on Base mainnet.

Get one piece of thoughtful life advice, paid per request over x402.

Which US federal income tax bracket a taxable income falls in: marginal rate, bracket edges and dollars to the next bracket.

Resolve a relative or absolute reference against a base URL, following RFC 3986 reference resolution (e.g. base 'https://a.com/x/y' + ref '../z' → 'https://a.com/z'). The base must itself be a valid absolute URL, else a clean 400.

Parse an A1 range like "A1:C10" into its start and end cells (normalized so start is the top-left) and its extent — row count, column count and total cell count.

Count syllables per word and in total across the text.

Sentence BLEU (1-4 gram, brevity penalty, optional smoothing) and ROUGE-1, ROUGE-2, ROUGE-L F1 for text against references.

Critical depth where Froude number is 1 (Q^2/g = A^3/T) for rectangular, trapezoidal, triangular or circular channels.

Floyd-Warshall all-pairs shortest distances for up to 100 nodes; negative weights ok; detects negative cycles.

Daily mean PM2.5, PM10, ozone, NO2 and US AQI over a date range, plus the count of days above an AQI threshold.

Battery bank layout (series and parallel counts) and runtime from load, voltage, Ah, depth of discharge and efficiency.

Check a US ABA routing number: 3-7-1 weighted checksum and the Federal Reserve district from the prefix.

Add a new memory. This method is called every time the user informs anything about themselves, their preferences, or anything that has any relevant information which can be useful in the future conversation. This can also be called when the user asks you to remember something.

Elo rating update after a game: win probability for each side, new ratings and the points exchanged.