Determine the astronomical season for a date, based on the Sun's apparent ecliptic longitude (0°=March equinox, 90°=June solstice, …). Defaults to the northern hemisphere; pass `hemisphere` to flip.

Multiply two matrices A·B. The inner dimensions must agree (columns of A equal rows of B); a mismatch or a ragged/empty matrix is a clean 400.

Opens each URL in a cloud browser and returns one tab per URL, in input order, with the title, content type, extracted text, the accessibility tree and a link map. Results over the inline size limit return a preview per tab plus a download reference. Each call is one request.

Create an email validation job from a JSON list of addresses or CSV text (send exactly one). Poll its status, then fetch results as JSON or CSV. Billing counts only testable addresses, fixed at creation; unreachable, disposable and typo domains are free.

Invert a square matrix via Gauss-Jordan elimination. A non-square, ragged or empty matrix is a clean 400. A singular (non-invertible) matrix is NOT an error — it returns a successful { invertible:false, inverse:null }.

Opens each URL in a cloud browser and returns one tab per URL, in input order, with the title, content type, extracted text, the accessibility tree and a link map. Results over the inline size limit return a preview per tab plus a download reference. Each call is one request.

Validate a JSON value against a JSON Schema (draft-07, with the standard string formats enabled). An invalid schema is rejected as a clean 400 before payment; a valid schema that the data simply fails to satisfy is a successful result with valid=false and a list of errors (path, keyword, message).

Keyword suggestions API - find long-tail keywords that contain your seed phrase (full-text phrase match), each with Google monthly search volume, CPC, competition, keyword difficulty and search intent. Complements keyword-ideas (semantically related terms) with literal phrase-match variations. For long-tail content and PPC research. No matches returns empty results.

Binomial distribution with `trials` (n ≥ 0, ≤ 1e6) and success `probability` (0..1). `function` selects the mass (pmf), cumulative distribution (cdf) or quantile / inverse-CDF.

Area (Heron's formula), perimeter and interior angles of a triangle from its three side lengths. Sides that violate the triangle inequality are rejected as a clean 400.

Normal distribution with optional mean (default 0) and standard deviation sd (default 1). `function` selects the density (pdf), cumulative distribution (cdf) or quantile / inverse-CDF.

Fetch a public web page and return clean markdown (or structured JSON) — URL in, agent-ready content out, typically 80-85% fewer tokens than raw HTML. Handles redirects and compression.

Multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n = Σki items into labelled groups of the given sizes. The sum must be ≤ 20000.

Create an email validation job from a JSON list of addresses or CSV text (send exactly one). Poll its status, then fetch results as JSON or CSV. Billing counts only testable addresses, fixed at creation; unreachable, disposable and typo domains are free.

Area (shoelace formula), perimeter and centroid of a simple polygon given its vertices in order. Vertices are treated as a closed ring (last connects to first).

Exact factorial n! for 0 ≤ n ≤ 20000, returned as a decimal string with its digit count.

Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer. Returns { prime }.

Poisson distribution with rate `lambda` (> 0, ≤ 1e9). `function` selects the mass (pmf), cumulative distribution (cdf) or quantile / inverse-CDF.

Ground-up hotel development underwriting. Land + hard costs (S-curve draw) + soft costs + developer fee, funded by a construction loan (LTC) with capitalized interest, refinanced into a permanent loan sized on min(stabilized-value LTV, DSCR) at the CL term. Occupancy begins the month after construction; the hold is measured from construction end. Returns unlevered and levered project IRR and MOIC. Reconciled to a SHA-pinned Excel model — see /hotel-dev/reconciliation.

Industrial ground-up development underwriting — construction to hold to exit. S-curve hard cost draws, blended LTC construction loan, capitalized interest, per-tenant NNN lease stabilization, perm loan sizing, TI/LC reserves on rollover. Returns yield on cost, spread to cap, profit on cost, IRR and MOIC.