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Demonstrates the efficacy of the M-operator for numerical verification in mathematical transformations, indicating improved safety.
The M-operator reframes alignment as a sign-inversion / transformation (−a)(−b)=ab rather than masking. This revision adds a Reference Implementation & Verification note to Data Availability: the paper's falsifiable claims are now numerically verified in the open-source harmonic-engine package (tests/test_new_math.py, passing on CPU). Theorems 1–3 — refusal as the g≡0 special case, polarity restoration, and energy conservation (g=x) — are verified to unit tolerance in harmonic_engine/sign_inversion.py.
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Weslyn Cory Whitehead (2026) studied this question.
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