[AdaWorldAPI]

This PR closes L1 (#1740) with the smallest change. It touches only the lab crate and the board. Nothing in it is production.

Code (crates/dr-math-binding-probe)

• RecipeCertificate used to store the proof as egglog's pretty-printed string. It now stores relcomp::EggProof { store: egglog::proof::ProofStore, root: ProofId }, which is egglog's own proof arena.
• EggProof exposes render() for display only, and node_count(), which counts distinct nodes reachable through the justifications. It is never reduced to a string or a hash.
• RecipeCertificate no longer derives PartialEq or Eq, because ProofStore has no equality.
• prove_equation and prove_reassociation now return EggProof.
• The comments now say what they mean:
  • egglog checks every proof with its own crate-private check_proof, which is not an independent check.
  • _law gates the call, but the rewrites are fixed in HEADER.
• The same egglog-check wording was clarified in egglog-r2il-probe/src/lib.rs, a comment-only change.
• New test the_proof_object_grows_with_the_reassociation. A full left-deep to right-deep proof must have more nodes than the trivial equation, and its root must relate two different terms.
  • Disable check: with node_count changed to return 1, the test went red. After restoring the code it is green.

Measured (report_costs, --release; reported, not gated)

• Certificate without the proof: 272 B, 9 steps.
• Proof: 8 nodes. The 1 012 B rendering is display only.
• The earlier 1 284 B figure counted the rendering as the proof. A correction has been appended to the L1 result entry.
• The arena's heap size is not measured.

Board

• PR_ARC_INVENTORY entries for dr-math-binding-probe: L1, reuse a D-DRMC-5 certificate on a fresh frame (X8) #1740 and board: coresearch map — Julia e-graphs vs egglog/datafrog/Ascent; Lisp vs Prolog for MeTTa #1741.
• New D-DRMC section in STATUS_BOARD with the rows EXP-DRMC-L1 (MEASURED) and EXP-DRMC-L2 (held behind the ProofRef agreement on EXO-50).
• A LATEST_STATE line.
• The entries index was regenerated. The supersession index is unchanged.

Gates run

• cargo fmt
• cargo clippy --release --all-targets -- -D warnings
• cargo test --release: all suites green, including the new test.

Not done

• ProofRef / Option B with CC1 is still open.
• probe(P-S2): a Palette256 compose table does not survive two hops #1726–thought-git-probe: Probe D (D-TGA-5D), protected readers of a squash #1739 still have no PR_ARC records.

---

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Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-23T19:46:06.706536Z	c0802ce	Draft marked ready

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