Documentation

Getting started

• Installation and licensing
• Basic usage
• Input expectations

ULM-PD Engine requires an internet connection and an active openai API key to run.

Input and execution model

• Natural language as input
• Translation to invariant-governed execution
• Deterministic execution
• Constrained semantics

Why intent inference is excluded

Invariants are relationships or constraints that remain true regardless of perspective, interpretation, or context, provided the governing conditions are satisfied.

ULM-PD Engine is not a predictive problem-solver. It is an auditor of invariant-governed reality: evaluating systems constrained by such invariant relationships.

For example, gravitational interaction obeys invariant relationships that hold regardless of opinion, interpretation, or intent. Validity arises from invariant structure, not belief.

Systems that infer intent must act on predicted future states rather than realized ones. This introduces ambiguity, responsibility shifts, and non-auditable execution paths.

By refusing planning and stepwise execution, ULM-PD Engine preserves causal ordering: nothing is acted upon unless it is explicitly instantiated.

This is the foundational principle behind this reality engine. It prevents probability from being treated as causality and avoids enforcement based on inferred future behaviour.

Single-step execution constraint

ULM-PD Engine executes exactly one invariant per query. The engine does not perform stepwise calculations, multi-stage reasoning, or implicit execution planning.

Any input that requires multiple operations, intermediate results, or execution order resolution will be refused. This includes natural-language requests that imply “step by step”, “combine”, or sequential evaluation.

This is a structural constraint, not a limitation. ULM-PD Engine enforces invariant isolation by design.

Refusal and boundary behaviour

• Invariant violations
• Undefined invariants
• Boundary states returned as data

Refusal has a single meaning. See Invariants. The Large Language Model does not "do math", it is a natural language interface only.

Invariant packs, domains and capabilities

Mathematics Core (included)

• arithmetic
• calculus
• algebra
• discrete_math
• number_theory
• linear_algebra
• probability
• geometry
• vector_calculus
• special_functions
• elliptic_curves
• symbolic_analysis
• set_theory
• graph_theory
• logic
• information_theory
• optimization
• symbolic_state
• systems
• dynamical_systems
• control_theory

Other invariant packs (coming soon)

Each domain exposes only explicitly declared capabilities.

Examples

Invalid (composite execution)

❓ Compute the result of combining addition, subtraction, and multiplication:
   10 + 5 × 3 − 8
  

✖ Refused
This request requires multiple invariants.
ULM-PD Engine executes single-step invariants only.
  

Valid (single lawful equation)

❓ Evaluate the equation: 10 + (5 × 3) − 8
✔ Result
17
  

Valid (split into invariant-safe steps)

❓ Multiply 5 by 3
✔ Result
15
  

❓ Add 10 to 15
✔ Result
25
  

❓ Subtract 8 from 25
✔ Result
17
  

When multiple operations are required, users must either: (a) submit a single lawful equation, or (b) decompose the task into separate queries.

Documentation is expanded incrementally as execution surfaces are declared. Behaviour not documented here should not be assumed.