# Arithym

Exact arithmetic engine for AI agents. 62 tools across 22 domains —

## Quick Start

```bash
# Connect this server (installs CLI if needed)
npx -y @smithery/cli@latest mcp add Arithym/Arithym

# Browse available tools
npx -y @smithery/cli@latest tool list Arithym/Arithym

# Get full schema for a tool
npx -y @smithery/cli@latest tool get Arithym/Arithym help

# Call a tool
npx -y @smithery/cli@latest tool call Arithym/Arithym help '{}'
```

## Direct MCP Connection

Endpoint: `https://arithym--arithym.run.tools`

**Required config:**
- `apiKey` (header) — Your Arithym API key from arithym.xyz

## Tools (62)

- `help` — Arithym — precision math engine for AI agents. Eliminates math hallucination.
- `domain_check` — ★ CALL THIS FIRST — your computation steering wheel. Exact routing, zero guesswork.
- `discover` — Search all 202 exact-math methods by keyword. Returns matching methods with ready-to-use call syntax.
- `list_refs` — List all 22 reference modules with domain-specific rules, formulas, and pitfalls.
- `read_ref` — Load a reference module's rules, tables, and guidance on demand. Example: read_ref('calculus')
- `guide_call` — Universal dispatcher — call any of 202 exact-math methods across 22 domain modules.
- `guide_list` — List available modules and their methods. No args = all 22 modules. With name = methods in that module.
- `factorize` — Exact prime factorization of any integer. Handles arbitrarily large numbers.
- `compute` — Exact integer arithmetic: add, subtract, multiply, divide, gcd, lcm, power. No floating point.
- `exact_sqrt` — Exact symbolic square root via the computation layer. No decimal approximation.
- `rational_sqrt` — Exact symbolic square root of any rational number (integers, fractions, decimals).
- `exact_trig` — Exact trig for special angles, IEEE 754 for others (clearly flagged).
- `compare` — Compare two integers: exact GCD, LCM, shared factors, and similarity.
- `verify` — Cross-verify an integer's properties: factorization roundtrip, divisor count, consistency checks.
- `project` — Classify a value's mathematical domain and structural properties.
- `route` — Show domain path between two values.
- `landmarks` — List reference values in a domain: integer, rational, radical, trig, complex, or all.
- `recommend` — Describe a problem in natural language, get the optimal tool call. Use when unsure which of the 202 methods to use.
- `field_create` — Create or reset the computation workspace. Only needed when building a persistent model with multiple related values.
- `field_add` — Store a single raw value (urchin) in the workspace. Use for constants, rates, and single inputs.
- `field_read` — Read workspace state or compare two stored urchins (GCD, LCM, ratio, divisibility).
- `field_gcd` — Exact GCD of 3+ values in one call. Takes raw numbers — no workspace needed.
- `field_lcm` — Exact LCM of 3+ values in one call. Takes raw numbers — no workspace needed.
- `field_lattice` — Full divisibility lattice from a set of values. All pairwise GCDs and LCMs.
- `field_ratios` — All pairwise exact ratios for a set of values. For comparing proportions across a dataset.
- `field_derive` — Compute from workspace urchins with tracked dependencies and auto-cascade.
- `field_update` — Update an urchin's value — all dependents auto-recompute through the full dependency graph.
- `field_sensitivity_all` — Compute sensitivity gradients for ALL tunable inputs against all outputs.
- `field_optimize` — Iterative gradient-based optimization on the urchin field.
- `field_links` — View dependency graph between workspace urchins. Shows what derives from what.
- `field_query` — Search workspace by structural properties: dimension, similarity, domain, tag, or all.
- `field_cluster` — Auto-group workspace urchins by similarity. Only useful with 5+ stored urchins.
- `field_snapshot` — Save, restore, list, or delete named workspace states. For branching scenarios and what-if analysis.
- `field_export` — Export workspace + snapshots to JSON. For persisting a model across sessions.
- `field_import` — Import workspace state from a previous JSON export. For resuming work on a saved model.
- `field_diff` — Compare two workspace snapshots. Shows added, removed, and modified urchins.
- `field_note` — Annotate workspace urchins, pairs, or the field itself.
- `field_notes` — Read annotations from the workspace log. Optional filter by target.
- `field_clear_notes` — Clear annotations. No args = all. With target = matching only.
- `scratch_math` — ★ SCRATCH PAD — Multi-step exact calculations in one call.
- `scratch_math_units` — scratch_math with dimensional analysis — tracks units through every step.
- `slide` — Exact addition and subtraction for raw values. Use for leaf inputs, not for combining urchins.
- `fraction_math` — Exact fraction arithmetic — add, subtract, multiply, divide.
- `graph_define` — Define a complete computational graph in one call.
- `graph_observe` — Read full computational graph state — all inputs, intermediates, and outputs with values and lineage.
- `graph_forward` — Forward pass: update inputs, cascade through graph, return all outputs.
- `graph_sensitivity` — Compute exact gradients: how much each output changes per unit change in an input.
- `graph_solve` — Inverse solve: find the input value that produces a target output via bisection search.
- `graph_what_if` — Run multiple scenarios against the graph and compare outcomes.
- `graph_learn` — Iterative gradient-based adjustment toward target outputs using exact-fraction gradients.
- `graph_derivative` — Compute exact d(output)/d(input) using reverse-mode automatic differentiation.
- `graph_gradient` — Compute all partial derivatives of an output w.r.t. all tunable inputs in one pass.
- `graph_jacobian` — Full Jacobian matrix: d(output_i)/d(input_j) for all output-input pairs. All entries exact fractions.
- `graph_hessian` — Second derivative d²(output)/d(input)² plus curvature classification (concave up/down/flat).
- `graph_taylor` — Compute exact Taylor series coefficients around current evaluation point.
- `graph_integral` — Exact definite integral using Simpson's rule with exact fraction arithmetic.
- `graph_critical_points` — Find critical points where f'(x) = 0. Classifies each as local min, max, or inflection.
- `graph_tangent_line` — Compute exact tangent line at current evaluation point. Returns slope, intercept, and equation.
- `graph_curve_analysis` — Full calculus analysis at current point: f(a), f'(a), f''(a), tangent line, curvature, and point type.
- `unit_check` — Check dimensional compatibility before computing. Catches mismatches like adding dollars to square feet.
- `unit_factor` — Return the exact conversion factor between two compatible units as a Fraction.
- `list_units` — List available units, optionally filtered by dimension. 35 dimensions supported.

```bash
# Get full input/output schema for a tool
npx -y @smithery/cli@latest tool get Arithym/Arithym <tool-name>
```

## Prompts (3)

- `solve_exact` (problem) — Solve a math problem using exact arithmetic — no floating point, no hallucination. Walks through domain classification,…
- `convert_units` (value, from_unit, to_unit) — Convert a value between units with exact fractional results. No rounding, no approximation.
- `analyze_function` (function, at_point) — Full calculus analysis of a mathematical function: derivatives, critical points, tangent lines, integrals, and Taylor s…