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).

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.

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 }.

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).

Area, perimeter and diagonal of a rectangle from its width and height.

Poisson distribution with rate `lambda` (> 0, ≤ 1e9). `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.

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

Transpose a matrix, swapping rows and columns. A ragged/empty matrix is a clean 400.

Validate an IBAN (mod-97 checksum, length, country format) and decompose it into country, bank, branch and account parts.

AI Web Extractor — turn ANY url into clean, LLM-ready markdown. POST {url}; get the main content as markdown (boilerplate/nav/ads stripped) with title, description, and links. The scrape / read / url-to-markdown primitive for RAG and research agents. Fast, cheap, x402-native.

Number of ordered arrangements of r items from n, nPr = n!/(n-r)!. Requires r ≤ n and r ≤ 10000.

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.

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.

Multifamily acquisition underwriting — mixed unit mix through a monthly proforma to unlevered AND levered project returns (IRR via XIRR + equity multiple). Stub acquisition month, trailing-NOI exit. Deterministic, Excel-reconciled, SHA-pinned (pass attest=true).

Hotel acquisition underwriting — stabilized or bridge-to-perm value-add. Quarterly ADR x occupancy RevPAR build, other/ancillary revenue, PIP capital, construction loan with capitalized interest, permanent loan sized on min(stabilized-value LTV, purchase-price LTV, DSCR), and exit. Returns unlevered and levered project IRR and MOIC. Reconciled to a SHA-pinned Excel model — see /hotel-acq/reconciliation.

Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.

Single-Family Rental (SFR) underwriting — monthly buy-and-hold proforma to unlevered AND levered project returns (IRR via XIRR + equity multiple). Loan-to-cost financing, optional interest-only, appreciation-floored exit. Deterministic, Excel-reconciled, SHA-pinned (pass attest=true).

Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed from the prime factorization).

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.