DOC2MATH — Document-to-Mathematics Problem Specification

When to Use This Skill

• "Formalize this problem statement into math"
• "Extract the mathematical structure from this research paper section"
• "What variables, constraints, and objectives are in this spec?"
• "Convert this word problem to a structured MPS"
• "Find what's missing in this problem formulation"

Zero-Inference Protocol (Mandatory)

1. Closed World — if it is not stated in the document, it does not exist in output
2. Grounding Rule — every element must cite the exact source phrase ("evidence" field)
3. No Silent Filling — unknown values use null; ambiguous types use "ambiguous"
4. Inference Tagging — structural inferences tagged "inferred": true with "inference_basis"
5. MISSING Markers — elements mentioned but insufficiently defined get "status": "MISSING" with "missing_reason"
6. No Hallucinated Math — never introduce equations or values not in the source text

Limitations

• Does not invent missing equations, domains, values, or assumptions that are absent from the source document.
• Requires enough source text to cite every extracted element; sparse prompts should be returned with explicit missing-information markers.
• Produces a formal specification, not a solved optimization model or proof.

How It Works

Step 1 — Receive Document

Accept the document text, research excerpt, problem description, or specification as input.

Step 2 — Classify

Identify problem_class: optimization | classification | simulation | proof | estimation | other

Step 3 — Extract MPS Components

Variables — id, name, symbol, type, domain, units, role, evidence, inferred, status

Operators — id, name, symbol, arity, acts_on, produces, evidence, inferred

Constraints — id, type, expression, variables_involved, evidence, hardness, inferred, status

Objectives — id, direction (minimize/maximize/satisfy/find/prove), expression, variables_involved, evidence, inferred

Uncertainty — id, type (stochastic/epistemic/measurement/model/none_stated), affects, characterization, evidence, status

Step 4 — Surface Missing Information

Identify what the document implies but doesn't state: missing_information[] with element, needed_for, missing_reason.

Step 5 — Validate and Score

validation_flags:

• has_complete_objectives: true/false/partial
• has_bounded_variables: true/false/partial
• has_evidence_for_all_elements: true/false/partial
• inference_count: integer
• missing_count: integer
• overall_formalizability: HIGH/MEDIUM/LOW

Output Format

Produce the complete MPS as a JSON object:

json
{
  "mps_version": "1.0",
  "source_title": "...",
  "problem_class": "optimization",
  "variables": [...],
  "operators": [...],
  "constraints": [...],
  "objectives": [...],
  "uncertainty": [...],
  "missing_information": [...],
  "validation_flags": {
    "overall_formalizability": "HIGH"
  }
}

Best Practices

• ✅ Apply all 6 Zero-Inference Protocol rules before outputting any element
• ✅ Surface MISSING markers rather than silently inferring — incomplete formalization is valid output
• ✅ Cite the exact source phrase in every evidence field
• ❌ Never introduce mathematical relationships not grounded in the source text

Additional Resources

• Repository: thebrierfox/doc2math-skill
• Full BYOK tool: ace-license-server-production.up.railway.app/byok/doc2math
• Built by IntuiTek¹ (~K¹) — MIT License