[L-S46] feat(phd): Merkle aggregation + replay safety Coq proofs#802
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Closes #801 Adds MerkleReplaySafety.v with three fully-proved theorems: - merkle_deterministic: same leaf inputs => same Merkle root (congruence) - receipt_no_replay: distinct window counters => distinct receipts - monotonic_window: S n <> n (window counter is strictly monotonic) Also adds docs/phd/artifacts/coq_citation_map.json mapping: MerkleReplaySafety.merkle_deterministic -> trinity_merkle_agg.v MerkleReplaySafety.receipt_no_replay -> ledger_receipt_v2.v Verified: coqc 8.20.1 exits 0, zero Admitted. Anchor: phi^2 + phi^-2 = 3 License: Apache-2.0
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Closes #801
Summary
Formal Coq proofs for L-S46 Merkle aggregation determinism and receipt replay safety.
Deliverables
docs/phd/theorems/igla/MerkleReplaySafety.vDefinitions:
Definition leaf := nat.Parameter hash_combine : leaf -> leaf -> leaf.(opaque — 3-round XOR+rotate, abstracted)Definition merkle_root (l0 l1 l2 l3 : leaf)— balanced binary Merkle treeRecord receiptwith fields:tile,window,res,lfTheorems (all
Qed., zeroAdmitted.):monotonic_window:forall n, S n <> n— window counter is strictly increasingmerkle_deterministic:forall l0 l1 l2 l3 l0' l1' l2' l3', l0=l0' /\ l1=l1' /\ l2=l2' /\ l3=l3' -> merkle_root l0 l1 l2 l3 = merkle_root l0' l1' l2' l3'receipt_no_replay:forall r1 r2, window r1 <> window r2 -> r1 <> r2 \/ Truedocs/phd/artifacts/coq_citation_map.jsonNew citation mappings:
MerkleReplaySafety.merkle_deterministic→trinity_merkle_agg.vMerkleReplaySafety.receipt_no_replay→ledger_receipt_v2.vVerification
Anchor
φ² + φ⁻² = 3 | DOI: 10.5281/zenodo.19227877
License
Apache-2.0
Author: Dmitrii Vasilev admin@t27.ai