Paid clones on skip-prefix strips: conditional κ = 4.529040672e-5

.github/workflows/verify.yml

@@ -16,7 +16,7 @@ jobs:
       fail-fast: false
       matrix:
         python-version: ['3.11', '3.13', '3.14']
-        group: [community, producers, certificates, ternary, research, tests]
+        group: [community, skip, producers, certificates, ternary, research, tests]
     steps:
       - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
         with:

Makefile

@@ -9,17 +9,22 @@ community-audit-check:
 community-followup-check:
 	python3 scripts/audit_followup_candidate.py --candidate-root . --check docs/research/community-followup-arithmetic.json
 
-.PHONY: verify-community verify-producers verify-certificates verify-ternary verify-tests
+.PHONY: verify-community verify-skip verify-producers verify-certificates verify-ternary verify-tests
 # CI runs these in separate checkouts. Keep local verification sequential:
 # different groups regenerate certificates that another group may read.
 verify:
 	$(MAKE) verify-community
+	$(MAKE) verify-skip
 	$(MAKE) verify-producers
 	$(MAKE) verify-certificates
 	$(MAKE) verify-ternary
 	$(MAKE) verify-research
 	$(MAKE) verify-tests
 
+verify-skip:
+	$(MAKE) skip-strips-verify
+	$(MAKE) skip-clones-verify
+
 verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check
 	$(MAKE) copied-fixed-verify
 	$(MAKE) climbed-48-verify
@@ -269,6 +274,26 @@ copied-fixed-check:
 
 copied-fixed-verify: copied-fixed-producer copied-fixed-check
 
+.PHONY: skip-strips-verify skip-strips-producer skip-strips-check
+skip-strips-producer:
+	python3 research/skip-strips/producer.py
+
+skip-strips-check:
+	python3 research/skip-strips/audit.py
+	python3 research/skip-strips/verify.py --output research/skip-strips/certificate.json
+	cd research/skip-strips && python3 -m unittest discover -s ../../tests -p 'test_skip_strips.py' -v
+
+skip-strips-verify: skip-strips-producer skip-strips-check
+
+.PHONY: skip-clones-verify skip-clones-producer skip-clones-check
+skip-clones-producer:
+	python3 research/skip-clones/producer.py
+
+skip-clones-check:
+	python3 research/skip-clones/witness.py --output research/skip-clones/certificate.json
+	python3 -m unittest discover -s tests -p 'test_skip_clones.py' -v
+
+skip-clones-verify: skip-clones-producer skip-clones-check
 .PHONY: climbed-48-verify climbed-48-producer climbed-48-check
 climbed-48-producer:
 	python3 research/climbed-48/producer.py

NOTICE

@@ -203,3 +203,24 @@ Ryan S / princezuda contributes historical Lean certificate arithmetic, algebrai
 frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
 source notices and historical snapshots are preserved. Neither formal package
 claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.

README.md

@@ -28,6 +28,33 @@ AI-assistance disclosures remain credited in the source notices.
 [Maintainer review](docs/research/community-followup-review.md) ·
 [Integration record](docs/research/community-followup-integration.md)
 
+## Additional conditional circuit result: PR #54
+
+The [paid-clone construction](research/skip-clones/PROOF.md) gives
+**κ = 141532521/3125000000000 = 4.529040672e-5 > 2^-15**, conditional on
+OpenAI's base theorem and the retained analytic and fixed-tape interfaces.
+This branch result is additional to the maintainer-reviewed PR #49 witness
+above; it does not extend that review's scope or claim global optimality.
+
+Starting from Avi Eisenberg's [PR #53 skip-prefix strips](research/skip-strips/PROOF.md),
+606 explicitly paid whole-chain clones preserve the original core/cover
+envelopes. The pinned weighted matchings give R23=32693, R25=43056 and
+W=159592676, with every added operation charged and both complete dirty-basis
+orientations replayed. The conditional saving is 0.686876% above PR #53.
+The source-partition/whole-chain operation is adapted from RaD / hipotures
+(PR #51); this original-envelope specialization is by Chafik Boukhalfa with
+OpenAI Codex assistance. All predecessor notices remain in force.
+
+PR #53 itself reassociates each leave-one-out strip as
+`s_j = A_(j-2) + (v_(j-1) + B_(j+1))`, preserving every scalar term while
+creating nested consumer envelopes. Its matched roles are R23=32946 and
+R25=43409, giving W=160799739 and conditional κ=4498144/10^11.
+
+Run `make verify-skip` for both complete producer replays and their exact
+arithmetic and adversarial checks, or `make skip-clones-verify` for PR #54.
+Local `make verify` and every Python-version CI matrix include these checks
+alongside all reviewed community and historical checks.
+
 ## What changed
 
 The community work combines recursive batching and partial-swap frames with

docs/ci-verification.md

@@ -12,17 +12,18 @@ The Python 3.13 log shows these major sequential costs:
 | Prime-field network certificate | 83 seconds |
 | Endpoint-gauge producer regeneration | 54 seconds |
 
-The workflow now distributes each Python version across six independent
+The workflow now distributes each Python version across seven independent
 checkouts:
 
 | Make target | Coverage |
 |---|---|
 | `verify-community` | PR #39 and follow-up arithmetic, reversed/fixed producers, PR #48 and #49 complete replays |
+| `verify-skip` | PR #53 skip-prefix and PR #54 paid-clone complete producers, exact arithmetic, and focused adversarial tests |
 | `verify-producers` | Copied-center, structured-bulk, endpoint-gauge and partial-swap producers and certificates |
 | `verify-certificates` | Remaining exact arithmetic, historical constructions and research audits |
 | `verify-ternary` | Complex-compression and ternary checkpoint audits and patches |
 | `verify-research` | 28 recovered historical audits and their regenerated certificates |
-| `verify-tests` | All 419 current and recovered tests and all 20 historical patch-application checks |
+| `verify-tests` | All current and recovered tests and all 20 historical patch-application checks |
 
 Every group runs on **all three** Python versions (3.11, 3.13 and 3.14).
 Both pinned Lean packages remain separate jobs. No producer replay, negative
@@ -32,13 +33,15 @@ regenerated artifact cannot silently diverge from its recorded certificate.
 
 At the original five-group split, `make -n verify` expands to the same multiset of
 **94 leaf commands**, including identical multiplicities for duplicate checks.
-That split changed scheduling rather than mathematics or certificate inputs.
-The subsequent research reconciliation adds 28 audit commands (122 total leaf
-commands) and additional tests; it does not remove any existing check.
+The original split changed scheduling rather than mathematics or certificate inputs.
+The additional `verify-skip` group preserves those commands and adds the
+PR #53/#54 producer, exact checker and focused adversarial tests. The research
+reconciliation adds all 28 recovered audit commands and additional tests.
+Both additions remain in the combined workflow; no existing check is removed.
 The complete old run remains useful as a comparison; the new workflow must
 pass independently in clean checkouts.
 
-Local `make verify` invokes the six groups sequentially. Do not launch them
+Local `make verify` invokes the seven groups sequentially. Do not launch them
 concurrently in the same worktree: one group can read certificates another
 group regenerates. CI avoids that race by using a separate runner and checkout
 for each group. Directly invoking a group works from a fresh checkout; the