[WIP/experiment] formal proofs with aeneas/hax#692
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Extract the STARK Merkle-tree verifier path to Lean via charon+aeneas and prove, with no `sorry` (axioms only propext/Classical.choice/Quot.sound): - panic-freedom of `Proof::verify` (conditional on total backend hash/eq) - panic-freedom + closed forms of the index utils (sibling/parent/power-of-two) - completeness of the verifier: `verify_path_complete` (an honest path is accepted) and the end-to-end `honest_proof_verifies` (a `get_proof_by_pos` proof from a tree satisfying the binary-heap invariant verifies). Pipeline: zero-maintenance carve script (`carve_merkle_verify.py`) slices the buildable verify+path subset out of the un-compilable monolithic extraction; behavior-preserving loop rewrites in the Rust source make it extractable; hax output also emitted (upstream-blocked on assoc-type equality, #1921). Wired into `make proofs`/`proofs-check` as a green CI gate.
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