The Theoremic API is a deterministic reasoning engine for mathematical intelligence. Send algebraic work or entity data via HTTP POST and receive a structured decision, confidence score, and auditable proof trace.
The engine is AST-based and non-probabilistic. It parses algebraic work into a structural tree, runs misconception checks against that tree, and applies forward-chaining inference over a concept knowledge graph. It does not use a language model to produce its output. Every decision is fully inspectable via the proof trace.
https://theoremic.io/v1/
Authentication
All API requests require a Bearer token in the Authorization header. Requests without a valid key return 401 Unauthorized.
Demo API Key — use this to test the API
th_demo_4f8a2c1b9e6d3a7f
This key is public and intended for evaluation only. Do not use in production.
HTTP Header
Authorization: Bearer th_demo_4f8a2c1b9e6d3a7f
POST /v1/algebra_reason
Analyzes algebraic working for misconceptions. Returns a decision, confidence score, detected concepts, and a proof trace showing which misconception checks fired.
POSThttps://theoremic.io/v1/algebra_reason
Request body
Field
Type
Description
steps
string[]
Array of algebraic steps, one per element. Either steps or text is required.
text
string
Raw algebraic work as a single string with steps separated by newlines.
config.threshold
float
Optional. Minimum misconception score to trigger detection. Default: 0.30.
Resolves whether two entity records refer to the same real-world entity. Returns a decision, confidence score with a 95% confidence interval, and a field-by-field proof trace.
POSThttps://theoremic.io/v1/entity_resolve
Request body
Field
Type
Description
entity_type
string
"person" or "organization". Required.
entity_a
object
First entity record. Required.
entity_b
object
Second entity record. Required.
config.match_threshold
float
Confidence above which decision is MATCH. Default: 0.85.
config.uncertain_threshold
float
Confidence above which decision is UNCERTAIN. Default: 0.60.
Person fields
Field
Type
Notes
full_name
string
Supports initial expansion (J. Smith → John Smith)
date_of_birth
string
Accepts multiple date formats: YYYY-MM-DD, MM/DD/YYYY, DD/MM/YYYY, etc.
address
string
Normalises abbreviations: St → Street, Ave → Avenue, etc.
id_number
string
Near-exact match required. Partial similarity is heavily discounted.
|expr| = k solved with only one solution — missing the negative case.
Error codes
200Success. Response body contains the reasoning result.
400Bad request. Missing or malformed JSON body, or required fields absent.
401Unauthorized. Missing or invalid API key in the Authorization header.
405Method not allowed. Only POST requests are accepted.
Error response shape
JSON
{
"error": "Unauthorized. Provide a valid API key in the Authorization header.",
"hint": "Authorization: Bearer YOUR_API_KEY",
"docs": "https://theoremic.io/docs"
}