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
48 lines
1.8 KiB
Python
48 lines
1.8 KiB
Python
"""
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algebra/rotor.py — Rotor construction operators for Cl(4,1).
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Rotors are operators. They live here, in algebra/, not in vocab/.
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A rotor between two word-versors is a contextual, field-level concern:
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it describes a transformation being applied, not a property of the vocabulary.
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"""
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import numpy as np
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from .cl41 import geometric_product, reverse
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from .versor import unitize_versor
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def word_transition_rotor(A: np.ndarray, B: np.ndarray) -> np.ndarray:
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"""
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Compute the rotor R that rotates versor A toward versor B in Cl(4,1).
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R = unitize(1 + B * reverse(A))
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This is a pure construction operation — building a new algebraic object
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from two input versors. unitize_versor() is the correct primitive here,
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not normalize_to_versor() (which is reserved for the injection gate).
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This is a pure operator — it transforms a field state, it does not
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encode a position. Call this from algebra-aware field logic; never
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store the result on a vocabulary structure.
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Antipodal or near-antipodal inputs can make 1 + B * reverse(A) null or
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near-zero. That is an ill-conditioned transition construction, not a
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case for synthetic fallback. unitize_versor() must fail closed, and the
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caller must decide whether to skip, terminate, or choose another edge.
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Args:
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A: Source versor, shape (32,), grade-normed to ±1.
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B: Target versor, shape (32,), grade-normed to ±1.
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Returns:
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R: Unitized rotor in Cl(4,1), shape (32,).
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Raises:
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ValueError: if the transition rotor is null, near-zero, non-scalar
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after multiplication by its reverse, or otherwise cannot be
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scaled into a clean +1 operator.
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"""
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R = geometric_product(B, reverse(A))
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R = R.copy()
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R[0] += 1.0
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return unitize_versor(R)
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