Deterministic reasoning for mathematical intelligence.

Built for systems where mathematical correctness is non-negotiable.

Early access — read before continuing

Theoremic is an AST-based structural reasoning engine in active development. The Reasoning API detects algebraic misconceptions and resolves entity records using deterministic structural analysis — not a language model. The Concept Reinforcement Platform is available to early access members.

Expect gaps: The knowledge base and rule set are expanding. Edge cases and unsupported expression types may return INSUFFICIENT_DATA rather than a definitive result.

Not for production use: This is a pre-release system. Do not use it in operational, critical, or regulated workflows.

No PII: Do not input Personally Identifiable Information — names, email addresses, phone numbers, ID numbers, or financial data.

Reasoning API

Structural comparison, uncertainty quantification, and auditable proof traces — exposed as an API endpoint.

Field-level structural comparison

Each field is compared using the appropriate algorithm — Jaro-Winkler with soundex for names, normalised date parsing for dates, near-exact matching for identifiers. The method applied is returned alongside every result.

Confidence with uncertainty bounds

Similarities are aggregated by field weight, variance is computed across all comparisons, and a 95% confidence interval is returned. Missing fields widen the interval — the engine does not pretend to certainty it does not have.

Auditable proof trace

Every decision includes a complete field-by-field breakdown: values compared, algorithm used, similarity score, weight, and contribution to the final confidence. The reasoning is inspectable at every step.

What the API returns

Two person records with different name formatting, date formats, and email prefixes. The engine resolves them structurally — field by field.

Input
{
  "entity_type": "person",
  "entity_a": {
    "full_name": "J. Smith",
    "date_of_birth": "1985-03-12",
    "address": "14 Oak St, Boston MA",
    "email": "john.smith@acme.com"
  },
  "entity_b": {
    "full_name": "John Smith",
    "date_of_birth": "12/03/1985",
    "address": "14 Oak Street, Boston MA",
    "email": "j.smith@acme.com"
  }
}
Engine output
{
  "decision": "MATCH",
  "confidence": 0.8742,
  "confidence_interval": [0.7918, 0.9566],
  "proof_trace": [
    {
      "field": "full_name",
      "similarity": 0.95,
      "method": "initial_expansion",
      "weight": 0.30,
      "contribution": 0.285
    },
    {
      "field": "date_of_birth",
      "similarity": 1.0,
      "method": "exact_match",
      "weight": 0.25,
      "contribution": 0.25
    },
    {
      "field": "address",
      "similarity": 0.9312,
      "method": "jaro_winkler",
      "weight": 0.20,
      "contribution": 0.1862
    },
    {
      "field": "email",
      "similarity": 0.5625,
      "method": "same_domain",
      "weight": 0.05,
      "contribution": 0.0281
    }
  ]
}

Built for the student. Not the syllabus.

Theoremic doesn't just mark answers wrong — it finds exactly where your reasoning broke down and shows you how to fix it.

Finds the exact mistake

Most tools tell you an answer is wrong. Theoremic tells you which step broke and why — whether you distributed an exponent incorrectly, applied the wrong inverse operation, or skipped a case in an absolute value problem.

Shows you a worked example

Every correction comes with a different problem of the same type, solved step by step. You see the correct reasoning in action — not just a mark and a grade.

Ask about the example

Still unclear? Ask in plain language directly on the worked example. The response is scoped to that specific concept and your specific mistake — not a generic explanation pulled from a textbook.

What it looks like in practice

A student submits their working. Theoremic analyses the structure of their reasoning, not just the final answer.

Student's working

Expand: (x + 3)²

= x² + 9

∴ x² + 9

Theoremic identifies

Exponent distribution error

You applied the exponent to each term individually. Exponents do not distribute over addition — you must expand using FOIL:

(x + 3)² = (x + 3)(x + 3) = x² + 6x + 9

Under the Hood

The engine behind Theoremic is not a language model. It is a structural reasoning system that enforces mathematical logic before any output is produced.

Empowering STEM Education
The engine powers granular, step-by-step misconception detection for students. A hierarchical task network plans corrective feedback based on each student's specific reasoning failures — not a one-size-fits-all explanation. When a student needs more, they can ask questions in plain language and receive contextual answers scoped to exactly what they are working on.
Reasoning API for Critical Systems
The same structural approach that catches student misconceptions can validate any system where reasoning must be correct. By treating reasoning as structure rather than surface text, the engine identifies logical errors and inconsistencies without relying on another language model to do the checking. This applies across AI output validation, formal verification of logical arguments, scientific reasoning audits, financial model integrity checks, and educational domains beyond mathematics — anywhere a chain of reasoning can be formalized, the engine can audit it.