9723941a38
Make versor construction fail closed instead of synthesizing hash-derived fallback rotors. - remove pseudo-random construction fallback from unitize_versor - add signed residual helper for +1 field states vs ±1 manifold entries - validate vocab manifold entries with full residuals - document antipodal transition rotor failure contract - add focused invariant tests for versor closure and manifold validation
111 lines
3.2 KiB
Python
111 lines
3.2 KiB
Python
"""
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CRITICAL: This test must pass before any other file is extended.
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It verifies the core algebraic invariant of the entire system.
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"""
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import numpy as np
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import pytest
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from hypothesis import given, settings
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from hypothesis import strategies as st
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from algebra.rotor import word_transition_rotor
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from algebra.versor import (
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unitize_versor,
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versor_apply,
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versor_condition,
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versor_unit_residual,
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)
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def _positive_unit_reflector(seed=None) -> np.ndarray:
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"""
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Construct a true positive-norm Cl(4,1) grade-1 versor.
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The current field action uses V * F * reverse(V), so the operator fixture
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must satisfy V * reverse(V) = +1, not -1. We therefore keep the fifth
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basis component bounded below the positive four-space norm.
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"""
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rng = np.random.default_rng(seed)
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vec4 = rng.standard_normal(4).astype(np.float32)
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norm4 = float(np.linalg.norm(vec4))
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if norm4 < 1e-6:
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vec4[0] = 1.0
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norm4 = 1.0
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vec = np.zeros(5, dtype=np.float32)
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vec[:4] = vec4
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vec[4] = 0.25 * norm4 * np.tanh(float(rng.standard_normal()))
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mv = np.zeros(32, dtype=np.float32)
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mv[1:6] = vec
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return unitize_versor(mv)
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@given(st.integers(min_value=0, max_value=99))
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@settings(max_examples=100)
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def test_versor_apply_preserves_manifold(seed):
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V = _positive_unit_reflector(seed)
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F = _positive_unit_reflector(seed + 1000)
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result = versor_apply(V, F)
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cond = versor_condition(result)
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assert cond < 1e-4, f"versor_apply broke the manifold: condition={cond:.2e}"
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def test_unitize_clean_scalar_constructs_positive_unit_versor():
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raw = np.zeros(32, dtype=np.float32)
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raw[0] = 2.0
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V = unitize_versor(raw)
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assert np.allclose(V[0], 1.0, atol=1e-7)
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assert versor_condition(V) < 1e-7
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def test_unitize_rejects_non_scalar_residue_instead_of_hash_fallback():
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dirty = np.zeros(32, dtype=np.float32)
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dirty[0] = np.sqrt(0.5)
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dirty[1] = np.sqrt(0.5)
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with pytest.raises(ValueError, match="bad_residue"):
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unitize_versor(dirty)
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def test_unitize_rejects_non_positive_scalar_norm():
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negative_norm = np.zeros(32, dtype=np.float32)
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negative_norm[5] = 1.0
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with pytest.raises(ValueError, match="bad_scalar"):
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unitize_versor(negative_norm)
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def test_versor_unit_residual_can_accept_signed_manifold_versors():
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negative_norm = np.zeros(32, dtype=np.float32)
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negative_norm[5] = 1.0
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assert versor_condition(negative_norm) > 1.0
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assert versor_unit_residual(negative_norm, allow_negative=True) < 1e-7
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def test_word_transition_rotor_fails_closed_for_antipodal_inputs():
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A = np.zeros(32, dtype=np.float32)
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A[0] = 1.0
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B = np.zeros(32, dtype=np.float32)
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B[0] = -1.0
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with pytest.raises(ValueError, match="near_zero"):
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word_transition_rotor(A, B)
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def test_composition_closed():
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V1 = _positive_unit_reflector(0)
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V2 = _positive_unit_reflector(1)
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F = _positive_unit_reflector(2)
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F2 = versor_apply(V1, F)
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F3 = versor_apply(V2, F2)
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assert versor_condition(F3) < 1e-4
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def test_identity_versor():
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identity = np.zeros(32, dtype=np.float32)
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identity[0] = 1.0
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F = _positive_unit_reflector(42)
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result = versor_apply(identity, F)
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assert np.allclose(result, F, atol=1e-5)
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