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Argon2 on x86-64: prove the active segment loop - #506
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Fill every active cell from a segment's starting index to its segment length, with a public index loop. Prove termination, the exact reviewed filling fold, final position, retained matrix/scratch allocation and cache validity, register/permission/MXCSR preservation, and the derive memory frame.
Prove the complete loop's trace depends only on public parameters and its specified reference log. A log-suffix lemma recovers each dependent reference from the final log; independent addressing requires no secret reference equality. Prove public cache counters remain equal across source selection and cell updates so regeneration remains public in subsequent iterations.
Builds on #505. This is the nonempty active segment suffix; first-segment setup and empty suffix handling follow. Inline implementation and proofs only; no specification, TCB, public API or generated assembly changes.
Validation: targeted Lean correctness and trace builds, standard-axiom and compiler-override audits, specification-origin audit, Lean import/proof-speed checks, and
git diff --check. Full checks run in CI.