API Reference

Get started in 3 steps.

Sign up, get your API key, connect via MCP. Your AI agent gets 209 precision math methods and a curated knowledge base of 981 entries — exact arithmetic, exact radical trig, deterministic results, no hallucination. Works with Claude, ChatGPT, Cursor, Windsurf, and any MCP client.

Easiest connection: If you're using Claude or ChatGPT, go to Settings → Connectors (or Apps) → add https://arithym.xyz/mcp as a remote MCP server. You'll be prompted to authorize with your email — no API key needed, no config files. OAuth handles everything automatically.

1 Create your account

Pick a tier on the pricing page, enter your email, and accept the Terms of Service. You'll receive your API key — a string starting with mc_free_, mc_pro_, or mc_eng_.

Your API key is shown once. Save it immediately. We store only the hash — we cannot recover it for you.

2 Connect your MCP client

Claude Desktop — Edit claude_desktop_config.json:

{
  "mcpServers": {
    "arithym": {
      "url": "https://arithym.xyz/mcp",
      "headers": {
        "Authorization": "Bearer YOUR_API_KEY"
      }
    }
  }
}

Replace YOUR_API_KEY with the key from Step 1. Restart Claude Desktop.

Tip: When Claude first uses an Arithym tool, your client may ask for permission. In Claude Desktop, click the Arithym server name in the MCP panel and select "Allow always" so you aren't prompted on every calculation. Other clients like Cursor have similar settings under their MCP server configuration.

Claude.ai — Connect via Settings → Connectors:

https://arithym.xyz/mcp
  1. Go to claude.ai/settingsConnectors
  2. Click Add custom connector
  3. Paste the URL above and click Connect
  4. Complete the OAuth flow (sign in or create an account)
  5. Start a new conversation — Arithym’s math tools are now available
Note: No API key needed — Claude.ai uses OAuth. Tool schemas are cached per conversation, so always start a new chat after connecting.

ChatGPT — Go to Settings → Connectors (or Apps) → Add custom connector:

# Server URL
https://arithym.xyz/mcp

# Authentication
OAuth (automatic via authorize page)

Cursor / Windsurf / Other MCP clients — Add as a remote server:

# Server URL
https://arithym.xyz/mcp

# Transport
SSE

# Header
Authorization: Bearer YOUR_API_KEY
Arithym uses SSE (Server-Sent Events) transport. Most MCP clients support this natively. If your client supports Streamable HTTP, use https://arithym.xyz/mcp instead.

3 Start computing

Once connected, your agent has a complete precision math engine — 209 methods across 22 domains, backed by 981 curated reference entries from CODATA 2022, IUPAC 2021, and SI definitions. Try these to confirm your connection works:

Exact arithmetic
compute("12847", "93", "multiply")
→ 1,194,771 (exact)
Factorization
factorize("48620")
→ 2² × 5 × 11 × 13 × 17
Fractions
fraction_math("0.1", "0.2", "add")
→ 0.3 (not 0.30000000000000004)
Multi-step chain
scratch_math([["multiply","99.95","1.0825"], ["multiply","$prev","3"]])
→ 324.587625 (exact through chain)

Epithreads knowledge base — 981 curated entries with 2,454 searchable names and aliases. Look up constants, elements, materials, trig values, and conversion factors:

Physical constant
reference action=lookup query="speed of light"
→ 299,792,458 m/s (CODATA 2022, exact)
Element lookup
reference action=lookup query="Fe"
→ Iron — atomic mass 55.845, density 7874 kg/m³, melting point 1811 K (IUPAC 2021)
Unit conversion
unit_factor("psi", "kPa")
→ 1 psi = 6894757/1000 kPa (exact fraction)
Chemistry
guide_call("chemistry", "molar_mass", '["C6H12O6"]')
→ 180.156 g/mol (glucose, exact)

Key tools

Arithym v6.2 is a precision math engine that routes to 209 exact-math methods across 22 domain modules, backed by the Epithreads knowledge base (981 curated entries). Your agent can call help() for a system overview, discover("keyword") to search all 209 methods, or recommend("describe your problem") to get the optimal tool suggestion.

What's New in v6.2

Transcendental graph operations — sin, cos, tan, log, exp, and abs as graph node ops. Build physics simulations, signal processing, and optimization models. Autodiff through all 6 ops.

Transcendental graph operations — sin, cos, tan, log, exp, and abs as graph node ops. Build physics simulations, signal processing, and optimization models. Autodiff through all 6 ops. 5-second computation budget per request.

Exact radical trig — sin(45°) = √2/2, cos(30°) = √3/2, sin(15°) = (√6−√2)/4. Special angles resolved via Epithreads radical lookup — fully exact, zero floats.

Epithreads knowledge base — 981 curated entries: CODATA 2022, IUPAC 2021, SI definitions, engineering materials, exact trig. All queryable by name, symbol, or alias.

Hybrid precision model — Algebraic operations (arithmetic, fractions, GCD, power, etc.) are exact — zero floating-point error. Transcendental functions (sin, cos, tan, log, exp) in computational models use IEEE 754 double precision (15 significant digits), with results flagged as precision: "IEEE 754 double" and sig_figs: 15. Every result carries its precision status.

Navigationhelp, domain_check, discover, recommend, guide_call

Arithmeticcompute, factorize, fraction_math, exact_sqrt, rational_sqrt, exact_trig

Multi-stepscratch_math, scratch_math_units, slide

Workspacefield_create, field_add, field_read, field_derive, field_update, field_sensitivity_all, field_optimize

Compute graphsgraph_define, graph_forward, graph_sensitivity, graph_solve, graph_what_if, graph_learn. Graph ops: add, subtract, multiply, divide, power, gcd, lcm, product, sin, cos, tan, log, exp, abs

Calculusgraph_derivative, graph_gradient, graph_jacobian, graph_hessian, graph_taylor, graph_integral, graph_critical_points

Unitsunit_factor, unit_check, list_units

Reference (Epithreads)lookup, query_entries, list_entries, db_stats — 981 entries: CODATA 2022 constants, IUPAC 2021 elements, exact unit conversions, formulas, material properties, exact trig

22 domain modules via guide_call — arithmetic, fractions, roots, trig, matrix, statistics, calculus, chemistry, physics, finance, geometry, signals, complex, number theory, algebra, medical, materials, quantum, scientific, verification, units, sphere-spiral


Rate limits

Usage is tracked per API key. Both MCP and REST endpoints share the same daily counter.

Tier
Daily limit
Price
Explorer
50 computations / day
Free
Pro
250 computations / day
$5/mo
Engineer
1,000 computations / day
$20/mo
Enterprise
Custom

Limits reset at midnight UTC. If you hit your limit, the server returns a 429 status. Upgrade anytime on the pricing page.


Authentication

All requests require a Bearer token in the Authorization header. This is your API key from Step 1.

# HTTP header (set in your MCP client config)
Authorization: Bearer mc_free_aBcDeFgH...

Invalid or missing keys receive a 401 Unauthorized response. Deactivated keys receive 403. Rate-limited keys receive 429 with a Retry-After header.


Support

Questions, bugs, or feature requests — email jacob@arithym.xyz.

For detailed tool documentation once connected, call help("tool_name") from your agent. Every tool has a built-in usage guide with examples, parameter descriptions, and routing advice.