What question did this study set out to answer?

This research aims to establish the M-operator as a generative safety operator through sign-inversion transformations.

June 18, 2026Open Access

Sign-Inversion as a Generative Safety Operator: The M-Operator and Reflect-Not-Mask Repair

Key Points

This research aims to establish the M-operator as a generative safety operator through sign-inversion transformations.
Introduced the M-operator for reframing alignment through sign-inversion transformations.
Provided a numerical verification in the open-source harmonic-engine package.
Verified key theorems related to energy conservation and polarity restoration to unit tolerance.
Theorems verified include refusal as special case g≡0, polarity restoration, and energy conservation with g=x.
Falsifiable claims numerically verified using tests in the harmonic-engine package, confirming the effectiveness of the proposed transformations.

Abstract

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/testₙewₘath. 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 harmonicₑngine/signᵢnversion. py.

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