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When the Lens Goes Blind

The phase cycle of the Li–Sekatskii detector, and the price of a shift taken too far

Mohamed Osman · ORCID 0009-0004-5912-999X · independent researcher · 2026-08-03

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Abstract. A companion note that takes the phase of the Li-Sekatskii detector rather than its modulus. At the matched lens width the phase is exactly -pi/2 independent of the zero's displacement and height, so a planted off-line quartet contributes on a strict cycle of period four: detection at n = 0 mod 4, active masking at n = 2, and no exponential term at all for odd n. Following the rate to the far end recovers Sekatskii's Theorem 3 as the other zero of a single curve, and the detection index is measured to grow linearly in the shift. Two natural refinements are tested and both fail.

Every number printed in this note is regenerated by a script in code/ of the repository. Licence: CC BY 4.0 (text), MIT (code).