board, dr-math: D-DRMC-5 already certifies associativity; correct two stale claims

.claude/board/entries/2026-10-23-coresearch-thought-git-markov.md

@@ -100,15 +100,26 @@ What this changes in the map:
 - Head selection: the head is the thought whose compiled proof is admitted.
   The children's folds are the search trace. After admission they are
   discarded, except the seal and the refuted branches the proof cites.
-- What actually blocks this: no certificate exists for DR64 (`dr-math-binding-probe`,
-  `NoCertifiedCompiler`). The open items there are a typed relational statement
-  language, egglog laws with checked proofs, and a lowering check. The candidate
-  first law is associativity of Boolean relation composition. `crates/egglog-r2il-probe`
-  holds the cold compile path; `.arxiv/2026-10_eggcc_effect_safe_extraction_statewalk_r2il_map.md`
-  holds the effect-safe extraction lesson.
+- ⊘ (corrected the same day) This line first said "no certificate exists for
+  DR64". That was stale. D-DRMC-5 (`crates/dr-math-binding-probe/src/relcomp.rs`,
+  commits a554da1c and 903e664d) already certifies reassociation of a Boolean
+  relation-composition chain end to end:
+  - typed chain;
+  - law admitted only for two-valued Distinct relations;
+  - egglog proof, checked by egglog, with commutation refused;
+  - lowering round trip;
+  - `RecipeCertificate` bound to `lowering_digest`.
+
+  Re-run 2026-10-23: 37 tests green, 12 of them in `relcomp`. `NoCertifiedCompiler`
+  applies only to the single-operand `admit_recipe` path. Still open, per the
+  crate README:
+  - choosing an order (specialization selection, without evaluating every order);
+  - rebinding a certificate to a second frame (X8);
+  - wiring into R2IL/Quack;
+  - for thought-git, referencing a certificate from a squash.
 - Still valid: the P8 fix (only committed writes squash) and probe D
   (squash = chain for every later read). Both are deterministic.
 
 ## Closeout
 
-`coresearch | STATUS: open | OUTCOME: one defect fixed in #1736 (P8); probabilistic premise withdrawn (category error) | OPEN: DR64 certified compiler (typed statement language + checked egglog laws + lowering check); probe D; promotion reader unpinned`
+`coresearch | STATUS: open | OUTCOME: one defect fixed in #1736 (P8); probabilistic premise withdrawn (category error) | OPEN: certificate referenced from a squash; order selection; X8 rebinding; probe D; promotion reader unpinned`

crates/dr-math-binding-probe/RECIPE_ADMISSION.md

@@ -4,7 +4,7 @@ This experimental metadata layer enforces the **shape of reuse**, not its scient
 
 Authority is split and none of it sits in this layer. **egglog** derives equivalences from admitted laws and checks its own proofs. **Law admission** owns the assumptions a law holds under. A **certified-compiler boundary**, after both of those and a lowering check, issues a `RecipeCertificate`: an opaque value with no public constructor and no caller-set status, so a caller can neither declare a law checked nor attach a digest of its own (the earlier hole, where any nonzero digest passed). Stage B's `ReplayCapsule` is replay and audit evidence for its own E1 substitution language; it is not a proof authority and is not used here. `CompiledReference` identifies compiler revision, code artifact, target ABI and backend. `RecipeOffer` remains **metadata**, not bytes to execute.
 
-**No DR64 certificate exists.** A certified-compiler boundary for Boolean-DR64 laws needs a typed relational statement language, egglog laws over it with checked proofs, and a lowering check; none exists. `admit_recipe` therefore runs every metadata check (effect capability, law shape, law identity, code identity, target) and then refuses with `NoCertifiedCompiler`. The tests pin each earlier refusal and that the end of the path is that refusal, never an offer.
+**No single-operand DR64 certificate exists.** One law has a certified-compiler boundary: reassociation of a Boolean relation-composition chain (D-DRMC-5, `relcomp::certify_reassociation`; see README). For a single bound operand there is none, so `admit_recipe` runs every metadata check (effect capability, law shape, law identity, code identity, target) and then refuses with `NoCertifiedCompiler`. The tests pin each earlier refusal and that the end of the path is that refusal, never an offer.
 
 Stage 2's finite-focus `PopulationReport` CANNOT produce a `RecipeCertificate`. Even a complete 64x64 population pass is not a theorem outside its declared scope, and a proof that a derivation follows from admitted laws does not show the laws hold for a newly observed population.