66 lines
2 KiB
Python
66 lines
2 KiB
Python
import numpy as np
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from algebra.versor import unitize_versor, versor_condition
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from algebra.holonomy import holonomy_encode, holonomy_similarity
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def _positive_unit_reflector(seed: int) -> np.ndarray:
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"""Construct a true positive-norm grade-1 versor in Cl(4,1)."""
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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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def _random_versors(n: int, seed: int = 0) -> list:
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return [_positive_unit_reflector(seed + i) for i in range(n)]
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def test_holonomy_is_versor():
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words = _random_versors(5)
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H = holonomy_encode(words)
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assert versor_condition(H) < 1e-4
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def test_holonomy_bounded_short():
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words = _random_versors(1)
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H = holonomy_encode(words)
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norm = float(np.linalg.norm(H))
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assert np.isfinite(norm)
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assert norm > 0.1, f"Holonomy norm out of range: {norm}"
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def test_holonomy_bounded_long():
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words = _random_versors(100)
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H = holonomy_encode(words)
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norm = float(np.linalg.norm(H))
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assert np.isfinite(norm)
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assert norm > 0.1, f"Long holonomy norm out of range: {norm}"
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def test_holonomy_distinguishes_prompts():
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words_a = _random_versors(5, seed=0)
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words_b = _random_versors(5, seed=99)
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Ha = holonomy_encode(words_a)
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Hb = holonomy_encode(words_b)
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# CGA inner product is indefinite and not a cosine bounded to [-1, 1].
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# The invariant here is not a bounded similarity score; it is that two
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# distinct prompt paths do not collapse to identical holonomy.
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assert not np.allclose(Ha, Hb)
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assert np.isfinite(holonomy_similarity(Ha, Hb))
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def test_holonomy_single_word():
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words = _random_versors(1)
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H = holonomy_encode(words)
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assert versor_condition(H) < 1e-5
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