constraint-theory 0.2.0

Exact geometric computation on Pythagorean constraint manifolds — snap, holonomy, and adaptive tolerance

constraint-theory

Exact geometric computation on Pythagorean constraint manifolds.

What is Constraint Theory?

Constraint theory replaces floating-point arithmetic with operations on discrete mathematical manifolds. Values are "snapped" to exact points (like Pythagorean triples) rather than approximated as floats.

Benefits:

• Zero drift — snap operations are exact by construction
• Provable correctness — snapped values satisfy a²+b²=c² exactly
• Deterministic — same input, same output, any hardware

Install

pip install constraint-theory

Quick Start

from constraint_theory import PythagoreanManifold, snap

# Generate a manifold of Pythagorean triples
m = PythagoreanManifold(max_c=10000)
print(f"Loaded {m.size} triples")

# Snap a float to the nearest triple
triple = snap(5.1)
print(triple)  # (3, 4, 5)

Holonomy Measurement

from constraint_theory import holonomy_loop

result = holonomy_loop(steps=100, max_c=10000, seed=42)
print(f"Displacement: {result.final_displacement:.6f}")
print(f"Angle drift: {result.total_angle_drift:.6f} rad")

Adaptive Tolerance

from constraint_theory import AdaptiveTolerance, FixedTolerance

adaptive = AdaptiveTolerance(k=1.0)
print(adaptive.epsilon(10.0))   # 0.1
print(adaptive.epsilon(100.0))  # 0.01

fixed = FixedTolerance(epsilon=0.05)
print(fixed.epsilon(100.0))     # 0.05

License

MIT