Withdrawn: PR71 assembly-backoff note

Makefile

@@ -428,3 +428,10 @@ pair-assembly-verify: pair-assembly-producer pair-assembly-check
 .PHONY: verify-pair
 verify-pair: pair-assembly-verify
 	python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json
+
+.PHONY: split-pair-verify
+split-pair-verify:
+	python3 scripts/experiments/verify_split_pair.py
+	python3 -m unittest discover -s tests -p 'test_split_pair*.py' -v
+
+verify-joint: split-pair-verify

NOTICE

@@ -302,3 +302,23 @@ inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
 uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
 are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
 verify_skip_frame.py. Original notices are retained.
+
+Aligned split-pair composition (2026-10-08)
+------------------------------------------
+Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik
+Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending
+live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules
+and refined exact arithmetic, and PR67 all-rank profile-cost selection and
+its profile oracle. Rohan Garg / rohangar1
+with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic
+with substantial OpenAI Codex assistance: PR57 joint reversible compiler and
+independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex
+assistance: PR60 ranked reclamation and this selected [1,1,2] split vector,
+aligned common-point permutation, next-use profile score, composition and
+certification package.
+The complete PR65 baseline words, profiles and arithmetic, plus 43 original
+source/provenance files, are preserved under references/frame-compiler/pr65.
+The original PR59 split operation and notices are separately preserved.
+PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof,
+retain their original bytes, licenses and notices in their own archives.
+All previous notices and mathematical dependencies remain applicable.

README.md

@@ -21,6 +21,27 @@ speedup. The model and general reduction are inherited from OpenAI's
 [Selected parameter certificate](research/matrix-exponent-synthesis/candidate/arithmetic.json) ·
 [Independent arithmetic check](docs/research/community-pair-arithmetic.json)
 
+## Additional conditional construction: anchored split frames with live reclamation
+
+The [split-pair proof and reproduction guide](research/split-pair/README.md)
+gives **κ=51414646104039/10^18=5.1414646104039e-5**, approximately
+**0.7463402960%** above the complete pinned PR67 witness. It combines
+the PR62/63 interval pair graph, the PR59 split operation, PR65's schedules
+and exact arithmetic, PR67's profile-cost selection, and PR68's pending live
+controls on the PR60/57 reversible frame compiler.
+The new selection uses split vector `[1,1,2]` and aligns the first intact
+global pair across common-point permutations. A new integer score uses each
+live control's known next-use frame. Actual roles are R23=27455
+and R25=36015, with W=135075665.
+
+`make split-pair-verify` regenerates the words, checks arbitrary dirty scratch
+and actual fixed-I+J profiles, and certifies the complete recursive child
+list and strict assembly inequalities. This separately submitted finite
+conditional witness retains the inherited all-size hypotheses. Its namespace,
+sources and comparison remain distinct from the maintainer-reviewed statement
+above. Prepared by Chafik Boukhalfa with OpenAI Codex assistance; contributor
+credits and original notices are retained in the package.
+
 ## What changed
 
 **Avi Eisenberg's interval strips and core-aware pair assembly (#62)** arrange

certificates/joint-dual-kappa.json

@@ -842,7 +842,7 @@
     "scripts/experiments/pin_joint_dual_sources.py": "4d31cc0e38b7902709ca5f8f714cba109760d2592346dd7f8dc0b900a2d9fe00",
     "scripts/experiments/verify_joint_dual.py": "7a31bba1e9c0ded32ae285df2ca9bc91ef20c330f6789fdba361876f3c7a1985"
   },
-  "source_manifest_sha256": "fd1aab7d75753b4b55b2377f26119dae74f367b0b4fab66cba42d944b3042cc9",
+  "source_manifest_sha256": "5cd14064a00c82909f76f63fe7f06d23058b6157b00e6402e9a535324592b543",
   "sources": [
     {
       "files": {

certificates/joint-dual-validation.json

@@ -226,7 +226,7 @@
     }
   },
   "bit_saving": "2382370177/50000000000000",
-  "certificate_sha256": "2ed658f05365b28825e24a6e7bac9fc9cc015d5a5d63d9579f4ac6e0640ae559",
+  "certificate_sha256": "1f8dc14c3f2e2420c39e2d77ad307f100fd2d5ef60771c30f2a9ecf3f55cf3fd",
   "kappa": "4764513337/100000000000000",
   "margins": 7,
   "producer_words_regenerated_and_matched": true,