Doc2math

DOC2MATH™ — Document-to-Mathematics Problem Genesis Engine

Originator: W. Kyle Million (~K¹), IntuiTek¹

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When to Use

• "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)

These constraints govern every extraction:

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 that grounds it ("evidence" field)
3. No Silent Filling — unknown values use null; ambiguous types use "ambiguous"
4. Inference Tagging — structural inferences must be tagged "inferred": true with "inference_basis" explanation
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

Standalone Workflow

Step 1 — Receive Document

Accept the document text, research excerpt, problem description, or specification as input. Ask for it if not provided.

Step 2 — Classify

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

Step 3 — Extract MPS Components

Extract in this order:

Variables Each variable needs: id, name, symbol (if stated), type (real/integer/boolean/vector/matrix/function/set/ambiguous), domain, units, role (decision/parameter/state/output/latent), evidence, inferred (true/false), status (DEFINED/MISSING)

Operators Each operator needs: id, name, symbol, arity (unary/binary/n-ary), acts_on, produces, evidence, inferred

Constraints Each constraint needs: id, type (equality/inequality/bound/logical/domain/implicit), expression, variables_involved, evidence, hardness (hard/soft/unknown), inferred, status

Objectives Each objective needs: id, direction (minimize/maximize/satisfy/find/prove), expression, variables_involved, evidence, inferred

Uncertainty Each uncertainty needs: id, type (stochastic/epistemic/measurement/model/none_stated), affects, characterization, evidence, status (QUANTIFIED/ACKNOWLEDGED/MISSING)

Step 4 — Surface Missing Information

After extraction, re-read the source and identify what the document implies but doesn't state: missing_information[] with element, needed_for, and missing_reason.

Step 5 — Validate and Score

Fill 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
• formalizability_notes: brief explanation

Output Format

Produce the complete MPS as a JSON object. Include in attribution:

"Generated using DOC2MATH™ — Document-to-Mathematics Problem Genesis Engine / Originator: William Kyle Million (~K¹), IntuiTek¹"

Example output structure:

{
  "mps_version": "1.0",
  "source_title": "...",
  "problem_class": "optimization",
  "problem_statement": "...",
  "domain": "...",
  "variables": [...],
  "operators": [...],
  "constraints": [...],
  "objectives": [...],
  "uncertainty": [...],
  "missing_information": [...],
  "validation_flags": {
    "overall_formalizability": "HIGH",
    "formalizability_notes": "..."
  },
  "attribution": "Generated using DOC2MATH™..."
}