Release v1.12 — When the Lens Goes Blind

A fourth structural note: papers/phase_and_masking.md. The companion to li_lens_law.md — that note took the modulus of the Li–Sekatskii image and found an exact optimal lens width; this one takes the phase. At the matched lens the phase is exactly −π/2, independent of β and T, so a planted off-line quartet contributes on a strict n mod 4 cycle: detection at n ≡ 0, active masking at n ≡ 2, no exponential term at all for odd n. Measured, the first negative index was ≡ 0 (mod 4) in 24 of 24 runs. Following the rate to the far end recovers Sekatskii's Theorem 3, and the detection index grows linearly in the shift, N(d)·r(d) = log M + O(1) — so hiding a violation past order m costs a shift of order mR. Two natural refinements were tested and both fail. Its usable consequence: a numerical search that finds the first m coefficients positive has established nothing unless it states its shift.

Corrections to li_lens_law.md. Corollary 3's limit is T + 1/(4T), not T — the excess is the ¼ carried by the classical lens, and the note's own gain column was already measuring it. A guess attributing a 3% residue to the background is withdrawn: a 24-run sweep shows scatter, not a systematic effect.

Contributed. §3.1 now carries a second derivation of the same optimum by S. K. Sekatskii, included with his permission and machine-checked alongside the original.

Three new scripts, all exiting nonzero on failure; PDFs and landing pages for both notes added to docs/.