Arithym

Arithym — precision math engine for AI agents. Eliminates math hallucination.

★ CALL THIS FIRST — your computation steering wheel. Exact routing, zero guesswork.

Search all 202 exact-math methods by keyword. Returns matching methods with ready-to-use call syntax.

List all 22 reference modules with domain-specific rules, formulas, and pitfalls.

Load a reference module's rules, tables, and guidance on demand. Example: read_ref('calculus')

Universal dispatcher — call any of 202 exact-math methods across 22 domain modules.

List available modules and their methods. No args = all 22 modules. With name = methods in that module.

Exact prime factorization of any integer. Handles arbitrarily large numbers.

Exact integer arithmetic: add, subtract, multiply, divide, gcd, lcm, power. No floating point.

Exact symbolic square root via the computation layer. No decimal approximation.

Exact symbolic square root of any rational number (integers, fractions, decimals).

Exact trig for special angles, IEEE 754 for others (clearly flagged).

Compare two integers: exact GCD, LCM, shared factors, and similarity.

Cross-verify an integer's properties: factorization roundtrip, divisor count, consistency checks.

Classify a value's mathematical domain and structural properties.

Show domain path between two values.

List reference values in a domain: integer, rational, radical, trig, complex, or all.

Describe a problem in natural language, get the optimal tool call. Use when unsure which of the 202 methods to use.

Create or reset the computation workspace. Only needed when building a persistent model with multiple related values.

Store a single raw value (urchin) in the workspace. Use for constants, rates, and single inputs.

Read workspace state or compare two stored urchins (GCD, LCM, ratio, divisibility).

Exact GCD of 3+ values in one call. Takes raw numbers — no workspace needed.

Exact LCM of 3+ values in one call. Takes raw numbers — no workspace needed.

Full divisibility lattice from a set of values. All pairwise GCDs and LCMs.

All pairwise exact ratios for a set of values. For comparing proportions across a dataset.

Compute from workspace urchins with tracked dependencies and auto-cascade.

Update an urchin's value — all dependents auto-recompute through the full dependency graph.

Compute sensitivity gradients for ALL tunable inputs against all outputs.

Iterative gradient-based optimization on the urchin field.

View dependency graph between workspace urchins. Shows what derives from what.

Search workspace by structural properties: dimension, similarity, domain, tag, or all.

Auto-group workspace urchins by similarity. Only useful with 5+ stored urchins.

Save, restore, list, or delete named workspace states. For branching scenarios and what-if analysis.

Export workspace + snapshots to JSON. For persisting a model across sessions.

Import workspace state from a previous JSON export. For resuming work on a saved model.

Compare two workspace snapshots. Shows added, removed, and modified urchins.

Annotate workspace urchins, pairs, or the field itself.

Read annotations from the workspace log. Optional filter by target.

Clear annotations. No args = all. With target = matching only.

★ SCRATCH PAD — Multi-step exact calculations in one call.

scratch_math with dimensional analysis — tracks units through every step.

Exact addition and subtraction for raw values. Use for leaf inputs, not for combining urchins.

Exact fraction arithmetic — add, subtract, multiply, divide.

Define a complete computational graph in one call.

Read full computational graph state — all inputs, intermediates, and outputs with values and lineage.

Forward pass: update inputs, cascade through graph, return all outputs.

Compute exact gradients: how much each output changes per unit change in an input.

Inverse solve: find the input value that produces a target output via bisection search.

Run multiple scenarios against the graph and compare outcomes.

Iterative gradient-based adjustment toward target outputs using exact-fraction gradients.

Compute exact d(output)/d(input) using reverse-mode automatic differentiation.

Compute all partial derivatives of an output w.r.t. all tunable inputs in one pass.

Full Jacobian matrix: d(output_i)/d(input_j) for all output-input pairs. All entries exact fractions.

Second derivative d²(output)/d(input)² plus curvature classification (concave up/down/flat).

Compute exact Taylor series coefficients around current evaluation point.

Exact definite integral using Simpson's rule with exact fraction arithmetic.

Find critical points where f'(x) = 0. Classifies each as local min, max, or inflection.

Compute exact tangent line at current evaluation point. Returns slope, intercept, and equation.

Full calculus analysis at current point: f(a), f'(a), f''(a), tangent line, curvature, and point type.

Check dimensional compatibility before computing. Catches mismatches like adding dollars to square feet.

Return the exact conversion factor between two compatible units as a Fraction.

List available units, optionally filtered by dimension. 35 dimensions supported.