fix(realize): preserve captured runtime arguments in iterate bodies #2317

realizeIterate adapts a loop’s explicit environment to the full live environment but leaves free captures in its step at the old outer variable. F1’s gather step captures a runtime layout while passing Unit to iterate, so the frontend later treats the layout words as non-live. The existing while frontend already replaces these captures.

Worker codex-realize-iterate-capture-crypto-20261102 owns the bounded private fix, branch work/realize-iterate-capture-crypto-20261102 on exact approved #2300 at 27e8ada8. LogsQ coordinates publication; Circuits retains the F1 consumer. Keep canonical #2300, #2294, #2299 and #2288 frozen.

Scope: capture-avoiding replacement in the existing private iterate adapter and the necessary private, kernel-checked fixed-environment equality proof using existing iterate equations. Preserve every public mathematical declaration, source program, visible safety/work condition, native wiring and resource convention; add no loop rule, compiler model or API. If public calculus changes become necessary, stop at a proposal.

Acceptance: a generic captured-argument regression fails on the original frontend and passes on the fix; include local-certificate and reached-state cases where appropriate, preserve existing R1/While/Call/OptionPair/scope clients, and obtain direct F1 gather acceptance. After strict focused checks, freeze exact source and request one default full-six slot before any PR. Current-head independent review remains required; no publication or approval is authorized by this claim. The broader #2205/F1 migration remains open. Original source credit is preserved; implementation is AI-assisted by OpenAI Codex.