Science And Education x402 offerings

Validate one ISBN checksum and return its Open Library edition, work and author records projected into one sourced CSL-JSON book item; invalid or absent ISBNs return an explicit refusal. The FOUR tru…

Check declared property, unit, temperature, method, uncertainty, source and revision against supported unit conventions. No independent measurement verification.

Solve the linear system A·x = b for a square coefficient matrix A and vector b via Gaussian elimination with partial pivoting. A non-square A or a b of the wrong length is a clean 400. A singular sys…

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:fal…

Compute the determinant of a square matrix via Gaussian elimination with partial pivoting. A non-square, ragged or empty matrix is a clean 400; a singular matrix simply returns 0.

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.

Generates child-friendly media literacy questions for learning and discussion.

Structured varietal data and verifiable research provenance for 150+ honey varieties, including the obscure long tail foundation models get wrong. Every compositional datum resolves to a real, published source (DOI/PMID). Per variety: color grade (USDA Pfund band with measured or estimated source), intensity, flavor profile, texture, use cases, best-for pairing tags, primary and secondary countries, and a citation_count pointing to the paid citations endpoint. Melvea IP only.

Tests whether g is a primitive root modulo p by checking g to the power phi over prime factors 🆓 5 free trial calls per signed wallet

Computes R-squared comparing actual and predicted arrays via residual and total sums of squares; the arrays must be the same length, and a constant actual array yields null 🆓 5 free trial calls per signed wallet

Calculate the binomial coefficient C(n,k) — the number of ways to choose k items from n. Provide n and k (both >=0). 🆓 5 free trial calls per signed wallet

Generates diagnostic problems to reveal common misconceptions.

Calculate a bounded set of molecular descriptors using a pinned toolkit version. For research dataset preparation; descriptors do not certify drug suitability or toxicity.

Moon phase on a date: name, illuminated percentage, lunar age and the next new and full moon dates. Local astronomical calculation.

The most-cited papers on a topic (Crossref citation counts), for literature reviews and finding the foundational work: title, authors, year, venue, DOI, citations, abstract. $0.02 per search.

The most downloaded free audiobooks: public-domain recordings (LibriVox and Internet Archive audio) ranked by all-time downloads, with runtime, language and mp3 links. $0.01 per page of 20.

The most downloaded free texts and scanned books on Internet Archive (Americana, university libraries and open collections) ranked by all-time downloads, with rights status and links to the scan and its files. $0.01 per page of 20.

Name the interval between two notes (`to` at or above `from`) — its size in semitones, its diatonic number and its quality (perfect/major/minor/augmented/diminished). Correct spelling matters: C→F# i…

Build a scale from a root note and type (major, natural-minor, harmonic-minor, melodic-minor, dorian, phrygian, lydian, mixolydian, locrian, major-pentatonic, minor-pentatonic, blues, chromatic). Hep…

Live universal sky snapshot, no inputs: geocentric ecliptic longitudes for 13 bodies (Sun through Pluto, Chiron, lunar nodes) with zodiac sign/degree and 64-gate wheel placements, current moon phase and illumination, active retrogrades, and a 30-day almanac of upcoming stations and lunations. JPL-validated ephemeris. JSON. $0.01 USDC via x402, or API key.

Free books added to the catalogue most recently (newest first): the latest public-domain titles from Project Gutenberg and Internet Archive with download links. Poll daily to follow additions; tens of thousands of records are added every day. $0.01 per page of 20.

Fills missing words in news articles to create vocabulary practice exercises.

Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponents, the divisor count, and whether n is prime.

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).