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new file mode 100644
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diff --git a/research/shared-kernel-pair-concentration/EXACT-MOMENT.json b/research/shared-kernel-pair-concentration/EXACT-MOMENT.json
new file mode 100644
index 0000000000..af70dc7a53
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/EXACT-MOMENT.json
@@ -0,0 +1,28 @@
+{
+ "status": "PASS_INDEPENDENT_EXACT_PAIR_MOMENT",
+ "complex_lower": "86004870116989085803/50000000000000000000000",
+ "root_bracket_30": [
+ "1720097402339781716060441963/1000000000000000000000000000000",
+ "430024350584945429015110491/250000000000000000000000000000"
+ ],
+ "kappa_rational": "17200974023397817160599999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+ "kappa_decimal_90": "0.0017200974023397817160599999999999999999999998999999999999999999999999",
+ "baseline_rational": "17200966286848326009719999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+ "gain_rational": "48353434319693/62500000000000000000000",
+ "gain_decimal_90": "7.73654949115088E-10",
+ "controls": {
+ "old_doubled_profile_rejected_at_candidate_endpoint": true,
+ "next_endpoint_grid_point_rejected": true
+ },
+ "profile": {
+ "1": 1611720,
+ "2": 427573,
+ "3": 183550,
+ "4": 85248,
+ "5": 26196,
+ "8": 5328,
+ "16": 1,
+ "48": 26758
+ },
+ "scope": "Directed integer atanh and exp enclosures; no floating point. Complete hosting and outer release required separately."
+}
diff --git a/research/shared-kernel-pair-concentration/EXPERIMENTS.md b/research/shared-kernel-pair-concentration/EXPERIMENTS.md
new file mode 100644
index 0000000000..253a5242bb
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/EXPERIMENTS.md
@@ -0,0 +1,37 @@
+# Experiment log
+
+Session: 2026-10-16, approximately 03:37–04:30 UTC. Default repository budget:
+about 60 minutes, no paid external compute, at most two native audit shards per
+replay. Source snapshots and command records include exact argv, exit codes,
+environment, elapsed time and log SHA256. Search seed: 20261016.
+
+| Step | Hypothesis / action | Result and decision |
+| --- | --- | --- |
+| Baseline | Paginated live PR census; reproduce PR2853 d01045df after distinguishing multiplication kappa from local/Fourier caps | Complete release passed in 838.88 s with four fresh native chains. |
+| H1a | Remaining 12 helpers in the four dirty-A quartets might admit extra dirty entrance lines | All 12 failed the inherited exact D-in-span census with climb and raise enabled. |
+| H1b | A coupled invertible raw-dirt transform within each fixed quartet could make two compensation columns vanish | Independent exact rational propagation: rank 3 and nullity 1 in every quartet, both providers. At most one zero column under an invertible 4x4 change at the fixed boundary. This does not exclude interleaved gates, changed receiving helpers or new frames. Controls raise rank to four / erase it to zero. |
+| H2 | Same-call distinct-width exchanges in PR2853's changed inventory may lower the idle bill | 66,685,248 pairs across two passes; two legal swaps, exact delta H3-H4-H6+H7. Independent full owner and 3000-digit moment checks passed. Complete release passed in 520.38 s. Kappa 0.00171937773626898616…; gain 7.75713995049e-11 over PR2853. Superseded by new PR2856/2857. |
+| H3 | Re-derive T248 composition for PR2853 | Not pursued after the new frontier appeared. No compatibility or summed-gain claim. |
+| Refresh | PR2857 0b2e2537 appears with cheaper staged kernels and a T37 fill | Its full documented reproduction passed twice. The second used its exact pinned dependencies; 499.15 s. Two current native chains fresh, older parent/native evidence explicitly authenticated and reused. |
+| H4 | The same exact pair-exchange method might improve PR2857 | 16,671,312 distinct-width same-call pairs; zero improving moves. This does not prove global allocation optimality. |
+| H5 | Two interleaved T37 copies permit a cross-copy transfer unavailable to a same-call swap | One width-7 transfer replaces 2H9 by H2+H16. Independent event/owner checks, exact moments and complete strict release pass. Final gain 7.73654949115088e-10 over exact PR2857. |
+
+The complete command stream is in `evidence/run-logs/`. `generate.py` reproduces
+H5 without a solver. The previous search/checker programs and receipts are in
+the saved session handoff bundle; relevant negative scripts are in `experiments/`.
+
+Development failures are retained: the first high-precision endpoint command
+used a nonexistent profile filename; the first paired-owner checker used the
+uncompressed name of a compressed pinned plan; the first paired-moment binary
+search began outside its deliberately narrow exponential-domain guard. These
+were corrected by supplying the actual filename and a certified initial root
+bracket. No mathematical predicate, guard or expected result was weakened.
+The complete inherited candidate verifier passed on its first run.
+
+The earlier PR2853 candidate's frozen CLAIM metadata says admission was pending
+when frozen. Its later PASS_RELEASE receipt is the authority for the completed
+run; frozen source was not edited after verification. It remains superseded.
+
+No further large fixed-inventory search was started. PR2857's reported tight
+fractional cap leaves only about 4.18e-9 above its original witness; this result
+uses about 0.774e-9 of that. A remaining relaxation gap is not a feasible witness.
diff --git a/research/shared-kernel-pair-concentration/FILL.json.gz b/research/shared-kernel-pair-concentration/FILL.json.gz
new file mode 100644
index 0000000000..83e8425ee1
Binary files /dev/null and b/research/shared-kernel-pair-concentration/FILL.json.gz differ
diff --git a/research/shared-kernel-pair-concentration/FRONTIER.json b/research/shared-kernel-pair-concentration/FRONTIER.json
new file mode 100644
index 0000000000..b8c80d8d9e
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/FRONTIER.json
@@ -0,0 +1,84 @@
+{
+ "retrieved_at": "2026-10-16T04:19:17.014807+00:00",
+ "open_count": 541,
+ "page_counts": {
+ "open-1.json": 100,
+ "open-2.json": 100,
+ "open-3.json": 100,
+ "open-4.json": 100,
+ "open-5.json": 100,
+ "open-6.json": 41,
+ "open-7.json": 0
+ },
+ "initial_open_count": 551,
+ "initial_closed_pages": 21,
+ "initial_closed_records": 2003,
+ "initial_merged_records": 1553,
+ "final_closed_pages": 2,
+ "api": "Direct GitHub REST, per_page=100, explicit page iteration through empty open page; not an atomic snapshot",
+ "reviewed_main": {
+ "commit": "d311a18c6061af67d0aa35cbeced605b8b7472ed",
+ "selected_pr": 1094,
+ "kappa": "836330098538459/500000000000000000",
+ "decimal": "0.001672660197076918",
+ "review": "docs/research/community-batch1099-review.md",
+ "target": "make frontier1094-verify"
+ },
+ "strongest_comparable_identified": {
+ "pr": 2857,
+ "head": "0b2e2537b368a0cade07ce3f71452ea018ebe394",
+ "status": "open; no mathematical maintainer review; exact-head API returned zero check runs",
+ "kappa": "17200966286848326009719999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+ "reproduction": "PASS_SHARED_KERNEL_PORTABLE_COMPLETE_REPLAY with pinned requirements; receipt under evidence/baseline-pinned"
+ },
+ "other_leads": [
+ {
+ "pr": 2856,
+ "head": "7a43b24c4b6729d171f3a2a11ef3b7dc77aabaa4",
+ "status": "weaker than PR2857; vacancy relay; method overlap credited"
+ },
+ {
+ "pr": 2853,
+ "head": "d01045dfb67428679618027dff552f1d032fa999",
+ "status": "initial strongest identified, four-chain fresh release reproduced; superseded"
+ },
+ {
+ "pr": 2848,
+ "head": "c50d12e4720cd1fef2b5a65e337e37de9731879a",
+ "status": "T248 construction weaker than PR2853; not added to another gain"
+ },
+ {
+ "pr": 2855,
+ "head": "90c52db35dd2f8cdf0dd81976e698a6192a09126",
+ "status": "T372 construction weaker than PR2857"
+ },
+ {
+ "pr": 2858,
+ "head": "8bd3d2985cfaef59d800409a283b2fbca15a4b73",
+ "status": "new obstruction, explicitly no kappa"
+ }
+ ],
+ "detailed_review_and_check_coverage": [
+ 2857,
+ 2856,
+ 2853,
+ 2833,
+ 2852,
+ 2848,
+ 2843,
+ 2802,
+ 2687,
+ 2593,
+ 2666,
+ 2636,
+ 2635,
+ 2681,
+ 2707,
+ 2709
+ ],
+ "coverage_limit": "All listed open PR bodies/titles/exact heads fetched and screened, but reviews/checks were examined for leading candidates and recent merged work, not exhaustively for every open PR. This is the strongest comparable construction identified in a bounded live census, not a certified global priority claim.",
+ "targets_excluded": "Local word coverage caps, fractional fixed-inventory relaxations, bit-supplier savings, Fourier exponents, runtime timings, and constructions with unpriced interfaces were not treated as multiplication kappa records.",
+ "guidance_refresh": "Initial 130a7ce63, intermediate a5b3fc6d9, final d311a18c6; selected record and applicable scientific guidance unchanged. Final required suites were rerun.",
+ "publication_refresh": "PUBLICATION-REFRESH.json",
+ "publication_status": "Verified pinned-baseline gain; superseded in reported kappa by pending PR2863 at 34328b1d5e5bebac62d5cabec993dfbfd7b2123f; no current-record claim."
+}
diff --git a/research/shared-kernel-pair-concentration/HANDOFF.md b/research/shared-kernel-pair-concentration/HANDOFF.md
new file mode 100644
index 0000000000..32dec384e9
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/HANDOFF.md
@@ -0,0 +1,121 @@
+# Research handoff — 2026-10-16
+
+## Publication refresh
+
+At the 05:08 UTC publication refresh, pending PR2863 at
+`34328b1d5e5bebac62d5cabec993dfbfd7b2123f` reported the stronger T185 saving
+`0.001720100805416885927944 - 10^-46 - 10^-70` and a fixed-inventory packing
+optimum. Its body, pinned README, review list and exact-head check list were
+inspected; its complete certificate was not replayed here. This T74 package
+is a verified improvement over its pinned baseline, superseded in reported
+kappa, with no current-record claim. See `PUBLICATION-REFRESH.json`.
+
+## Best verified result
+
+Conditional multiplication exponent saving:
+`kappa = 0.001720097402339781716060 - 10^-46 - 10^-70`.
+Exact rational and 70-place terminating decimal: `CLAIM.json`.
+Exact improvement over the reproduced PR2857 headline:
+`48353434319693/62500000000000000000000 = 7.73654949115088e-10`.
+Complete strict release, independent source-event/owner audit and independent
+directed-integer moment checks pass. The construction is two interleaved T37
+copies plus one width-seven transfer; complete delta `H2+H16-2H9`.
+
+The last paginated census at 2026-10-16 04:19:17 UTC found 541 open PRs, with
+PR2857 still the strongest comparable construction identified. PR2858 has no
+kappa claim. Exact source: PR2857
+`0b2e2537b368a0cade07ce3f71452ea018ebe394`. Final main:
+`d311a18c6061af67d0aa35cbeced605b8b7472ed`. Reviewed main still selects PR1094,
+`836330098538459/500000000000000000`; do not replace that reviewed record.
+Detailed PR review/check coverage is bounded and disclosed in FRONTIER.json.
+
+## Executed validation
+
+The initial PR2853 baseline (`d01045dfb67428679618027dff552f1d032fa999`)
+passed its complete release with four fresh native chains (838.88 seconds).
+Its manifest SHA256 is
+`44ed6a457e1d1ba24726f35db86dc9e551072dd9331a8fed3ad3f0efa33ff0be`.
+The first improved candidate also passed but was superseded during the run.
+
+The PR2857 baseline passed its documented portable full replay twice. The second
+run used its exact pinned numpy/scipy/sympy/mpmath/gmpy2/psutil requirements
+in a separate Python 3.12 environment and took 499.15 seconds. It freshly
+ran two current native chains and authenticated two older chains and the
+retained parent proof by complete source hashes. The final candidate reuses
+those unchanged current chains and passes its complete admission/release in
+493.89 seconds. Its complete tree and final rational are checked by
+`verify_release_binding.py` against the reproduced baseline.
+
+Actual inherited rejecting controls: 119 admission, 12 bit, 25 controller,
+8 owner and 6 geometry; the outer has 63 strict rows and 17 rejecting controls.
+Independent new owner checker rejects four role corruptions; exact moment
+checker rejects the old doubled profile at the candidate endpoint and the next
+endpoint grid point. The portable package additionally rejects changed source
+bytes. Full original local/kernel/native checks remain required.
+
+Exact commands, exit codes, environment variables, elapsed times and log hashes
+are in `evidence/run-logs/`. Receipt/source hashes are in CLAIM and evidence.
+`README.md` supplies bounded and full reproduction commands. The top-level
+`reproduce.py` orchestrator was assembled from those successfully executed
+constituent commands; it was not rerun end-to-end a third time. Its constituent
+full baseline, full candidate and final binding were executed separately.
+
+Required `make verify` and `make frontier1094-verify` failed on unchanged main,
+including final d311a18c6. See REPOSITORY-CHECKS.md. The new registered package
+passes. No expected hash was changed to bypass the historical-source failure,
+and no verifier predicate was weakened. No fresh Lean build or hosted CI pass
+is claimed.
+
+## Workspace and artifacts
+
+Run root: `/workspace/scratch/bc9e58970b2a`.
+Focused branch: `research/two-swap-exponent-20261016` in `integer-mult-bounds/`.
+Only `research/shared-kernel-pair-concentration/` is committed as the new result.
+The review patch records its exact commit and parent.
+
+Important retained paths:
+
+- `newer-frontier/replay-pinned/`: pinned PR2857 full replay and fresh natives.
+- `pair-candidate/`: generated literal input and independent receipts.
+- `pair-admission/`: complete derived package, discovery, frozen strict release.
+- `replay-pr2853/`: initial complete cold baseline.
+- `candidate-complete-release/`: superseded two-swap strict release.
+- `superseded-two-swap-package/`: source-bound reproduction of that earlier result.
+- `frontier-snapshot/`, `frontier-final/`: direct paginated API responses.
+- `run-logs/`: all successes and failures, including development mistakes.
+- `.venv/`, `.venv2857/`: isolated environments; dependency pins are saved.
+
+The saved archive contains the focused patch, PR description, full derived
+supplier, pinned dependency packages, command records, frontier snapshots and
+superseded research. It excludes reconstructible large native intermediates.
+No pre-existing work or upstream sources were removed or edited.
+
+## Failed and bounded searches
+
+See EXPERIMENTS.md and experiments/. Fixed-boundary quartet maps have rank
+three/nullity one, so invertible raw-dirt mixing alone cannot supply a second
+zero compensation column there. This is not a global circuit obstruction.
+The PR2853 pair census found two improving swaps; that result was superseded.
+The PR2857 same-call census screened 16,671,312 pairs with zero moves. Multi-role
+paths, different orders, families and local words are outside that negative result.
+
+## Next work and publication
+
+No additional large packing search is justified by this session. Independently
+reproduce PR2863 and its claimed fixed-inventory optimum before reopening that
+gap, or address a named all-size obligation in PROOF.md. Refresh GitHub first.
+
+The initial packaging lacked an available fork. Browser authentication later
+succeeded, `digitalis-p/integer-mult-bounds` was created, and the user approved
+adding that public fork to the existing GitHub app's selected repositories.
+The scientific package was uploaded on `research/two-swap-exponent-20261016`.
+Remote commit `b39aa97a6f4e6f784ebbde0d5f7dd73a3d70952c` has exactly the frozen
+local scientific tree `2921cc364eabb7f9ed0d24830cbd6ca45f437103` and original
+parent `d311a18c6061af67d0aa35cbeced605b8b7472ed`. This documentation refresh
+labels the intervening stronger proposal before opening the review-ready PR.
+No result is merged or claimed maintainer-accepted.
+
+All inherited all-size compiler, common-label/mutable-source, hosting,
+precision/tape, exact-recovery, analytic-transfer, corrected recurrence and
+bit H1–H5 assumptions remain. Finite success is not the complete asymptotic
+multiplication theorem. This result is not a measured runtime speedup.
diff --git a/research/shared-kernel-pair-concentration/INDEPENDENT-OWNERS.json b/research/shared-kernel-pair-concentration/INDEPENDENT-OWNERS.json
new file mode 100644
index 0000000000..376c3924ba
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/INDEPENDENT-OWNERS.json
@@ -0,0 +1,60 @@
+{
+ "status": "PASS_INDEPENDENT_INTERLEAVED_TRANSFER",
+ "calls": 666,
+ "roles": 271728,
+ "replicas": 74,
+ "live": 66304,
+ "physical": 66794,
+ "profile": {
+ "1": 1611720,
+ "2": 427573,
+ "3": 183550,
+ "4": 85248,
+ "5": 26196,
+ "8": 5328,
+ "16": 1,
+ "48": 26758
+ },
+ "idle": {
+ "1": 17316,
+ "2": 1,
+ "3": 6394,
+ "5": 8880,
+ "16": 1,
+ "48": 26758
+ },
+ "profile_delta_from_double": {
+ "2": 1,
+ "9": -2,
+ "16": 1
+ },
+ "controls": [
+ {
+ "name": "overlap",
+ "rejection": "overlap or gap"
+ },
+ {
+ "name": "capacity",
+ "rejection": "capacity"
+ },
+ {
+ "name": "port",
+ "rejection": "role ranges"
+ },
+ {
+ "name": "time",
+ "rejection": "role ranges"
+ }
+ ],
+ "input_sha256": {
+ "newer-frontier/research/shared-kernel-repacking/FILL.json.gz": "82218aaaf08825bd4a3cca676815c7e9c00d06d0da123b1c5ad234c8c91cb501",
+ "newer-frontier/research/shared-kernel-repacking/ORDER.json": "84f030a59dde4fa4635988ef0931ebae66964b3a202df79d38247fbe8a5592dc",
+ "newer-frontier/research/shared-kernel-repacking/DISPATCH.json": "5513481a70c83767b5836b15fb7ff204d2a8f8fca83c6bcaee90a20b3d1ec6c4",
+ "newer-frontier/research/shared-kernel-repacking/PROVIDERS.json": "b1e31d1b3af2c8db9b8dd8f1337fee7fc2570ee58c1d541c43963c640efa1aa2",
+ "pair-candidate/FILL.json.gz": "1c79800e68c35c35aade277f54da8dda54c843e40376171c597e1ee675925840",
+ "pair-candidate/ORDER.json": "1dcbeb826512d864ba5b4bc740d6125980d4b2edec834206c07348485d159e96",
+ "pair-candidate/DISPATCH.json": "a2ade66687d1ad6b788a79dd8bb31a128bda9d02b4583e82d347e8892e9a148d",
+ "pair-candidate/PROVIDERS.json": "aebb3d2bb894161fd5f2bff11425326a9e27e4a4c43ab02eeee4d0e0745cceaf"
+ },
+ "scope": "Literal complete roles, source event chronology, windows, disjoint families, no-gap capacities, complete profile. Native operations, interfaces and analytic transfer are retained dependencies, not established here."
+}
diff --git a/research/shared-kernel-pair-concentration/LICENSE b/research/shared-kernel-pair-concentration/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/LICENSE
@@ -0,0 +1,201 @@
+ Apache License
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+ http://www.apache.org/licenses/
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diff --git a/research/shared-kernel-pair-concentration/NOTICE b/research/shared-kernel-pair-concentration/NOTICE
new file mode 100644
index 0000000000..b1a6935191
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/NOTICE
@@ -0,0 +1,19 @@
+Four staged compensation kernels and chronological owner repacking
+Prepared for Yiyang (@Lyy-iiis), with substantial OpenAI Codex assistance.
+New contributions are licensed under Apache-2.0.
+
+Jeremy Kothe (@jeremykothe2), PR2833: pinned source words, dirt-entry mechanism,
+local audit, cleanup and native reconstruction lineage.
+@philippeVV, concurrent PR2853: the same four A-phase helper quartets
+and entrance mechanism, with a different early-read schedule and paid profile.
+Marius-Paul Dumitrean (@mdumitrean), PR2843 and predecessors: integer owner-flow
+construction and edge-coloring realization, retained in allocation/construction.
+Dugongue, PR2839: tensor-block norm and replica/owner interfaces.
+Tekalign (@tekuuu), native and source-bound admission lineage.
+David Arias C and the other contributors credited in the retained sources.
+
+Original source-specific licenses and notices are retained in sources/, vendor/
+and allocation/. This notice supplements, and does not replace, their attribution.
+Independent checks here are separate AI-assisted implementations; no independent
+human or maintainer review, new selected frontier, or full theorem formalization
+is claimed.
diff --git a/research/shared-kernel-pair-concentration/ORDER.json b/research/shared-kernel-pair-concentration/ORDER.json
new file mode 100644
index 0000000000..83fe657280
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/ORDER.json
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diff --git a/research/shared-kernel-pair-concentration/PACKAGE-MANIFEST.json b/research/shared-kernel-pair-concentration/PACKAGE-MANIFEST.json
new file mode 100644
index 0000000000..df52691d04
--- /dev/null
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+ "evidence/run-logs/refreshed-make-verify.json": "5474ac1c846f1682371f1dfd085b9a52016c89b37de9fcce1c3af6ec048a34a3",
+ "evidence/run-logs/refreshed-make-verify.log": "0ffa3379a6cae9d5f99247dd21cc6e625742d966d823aecadb685807a0fd995c",
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+ "evidence/run-logs/refreshed-selected.log": "dcba4b52bed7024ee26a8915ca18944597071a1d5ad939e8b9461f17f6aa4c86",
+ "evidence/run-logs/registered-pair-check.json": "08087143a0decf2123375eb13ef0dba19dab8edd95309cc3821823978da724df",
+ "evidence/run-logs/registered-pair-check.log": "f07efe2237f669555f318a2a6b931a2d9e72b0691a82ac835d05340daf61b768",
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+ "evidence/run-logs/selected-cold.json": "b0b5a2be2e47b29e47cb4873c9ffd317e5998e0de85c3edab4aef4e2d1805aca",
+ "evidence/run-logs/selected-cold.log": "d1574294faf0be255ccf8803047a6aaab3978a8e4af216c647d2999960c89da7",
+ "evidence/selected-historical-source.log": "11fb13272ffe207070890721461420e4f4083cc6cd933b351d4fd746b852b3dc",
+ "evidence/superseded-two-swap-release.json": "2bc19ca0e71e6a9c5c79385f1cec3df4bfc3a04d65948b89191bf0f9cda36f17",
+ "exact_moment.py": "421995ebd736f7d55540061ac7a23796a43f26a31981556f223de2bf6e9e974f",
+ "experiments/EXACT-MOMENT.json": "d79895b2fb2c024a624f46b629e9098bdf4f52a24570d057d9e2ee71f59b0adb",
+ "experiments/INDEPENDENT-OWNERS.json": "2d834a869ca05c163114b300c6815453a3ed8dbab4cf57e8611ba9f84232bd1e",
+ "experiments/NEWEST-SAME-CALL-CENSUS.json": "0c79b1ab7676db7527dbe2ecb9ce65e5de6951dd1ef8c72c3ae2dc1762900d8f",
+ "experiments/QUARTET-BOUNDARY.json": "8a83076adcfca248598f509bf9af3d021f7e2bf9396211810ffd67552285b7d8",
+ "experiments/SWAP-SEARCH.json": "c1d8914a10008d1d2f99aed4abb7b930c0705b853c6fbb9d1b1f329ef86b83f7",
+ "experiments/TASK-local.json": "00b92dd90620ea3f0c5854204d561e2b79614f2d8d6ec475514945f846ba9c61",
+ "experiments/exact_swaps.py": "6c11bbb5362162976722a00dc751fa65e004546e4a063e5fb8bf3419c9001754",
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+ "experiments/quartet_boundary.py": "e72c520c3ef2594d7cfcd1681c4ba7abd50667200654f3c88bc9551088d556af",
+ "generate.py": "91be2201b4ba805ad42a32074bc61c794c81cf843fc4fe040474fc378274ef06",
+ "independent.py": "2ae855ab3192d4e72d5ad45aa53a795c352a500e9df07c9d95a95863372d63db",
+ "reproduce.py": "6c763d149c842d4f60af87c524849385feaab8e5da8c50d436332836735a8d21",
+ "requirements-reproduction.txt": "5e665fa5c409df8f7a561a4c0286173802aad59f3f90587f83b804efa146f7bd",
+ "source-inputs/CLAIM.json": "c2a04b639c86f462caef654a29817545c57b8e5ba809e37d4d476d3577f5cd6f",
+ "source-inputs/DISPATCH.json": "5513481a70c83767b5836b15fb7ff204d2a8f8fca83c6bcaee90a20b3d1ec6c4",
+ "source-inputs/FILL.json.gz": "82218aaaf08825bd4a3cca676815c7e9c00d06d0da123b1c5ad234c8c91cb501",
+ "source-inputs/ORDER.json": "84f030a59dde4fa4635988ef0931ebae66964b3a202df79d38247fbe8a5592dc",
+ "source-inputs/PROFILE.json": "f5d91190e5a062585a99c3959615b837271feca987eed04ae7d707d5714b17aa",
+ "source-inputs/PROVIDERS.json": "b1e31d1b3af2c8db9b8dd8f1337fee7fc2570ee58c1d541c43963c640efa1aa2",
+ "source-inputs/sources/PR2833-NOTICE": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b",
+ "source-inputs/sources/PR2833-PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+ "source-inputs/sources/PR2833-T37-TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+ "source-inputs/sources/PR2839-CREDITS.md": "d8eea66efb6796d3caeec985949724eab9df1eb214182b7db2ef84ba6e19b5e9",
+ "source-inputs/sources/PR2839-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+ "source-inputs/sources/PR2843-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+ "source-inputs/sources/PR2843-NOTICE": "b1a13e97bf3503b4a52033518dd528d010f57be7b591245bf48910c20320d186",
+ "verify.py": "aebfb88eaf513cf49278ee672975a6b0fe9ee04cad763e93a9e82171fdb2775f",
+ "verify_release_binding.py": "d83faf90d213a8c15fbec52013aff30f482e7a95f0a6850b39786688d533c20b"
+}
diff --git a/research/shared-kernel-pair-concentration/PROFILE.json b/research/shared-kernel-pair-concentration/PROFILE.json
new file mode 100644
index 0000000000..543fd23786
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/PROFILE.json
@@ -0,0 +1 @@
+{"1":1611720,"2":427573,"3":183550,"4":85248,"5":26196,"8":5328,"16":1,"48":26758}
diff --git a/research/shared-kernel-pair-concentration/PROOF.md b/research/shared-kernel-pair-concentration/PROOF.md
new file mode 100644
index 0000000000..1eaf592048
--- /dev/null
+++ b/research/shared-kernel-pair-concentration/PROOF.md
@@ -0,0 +1,113 @@
+# Interleaved pair concentration
+
+## Pinned construction and change
+
+The source is Yiyang (@Lyy-iiis), PR2857, commit
+`0b2e2537b368a0cade07ce3f71452ea018ebe394`, package
+`research/shared-kernel-repacking`. Its local words and all native operations,
+frames, helper widths, private buffers and cleanup are retained exactly. The
+source itself depends on Jeremy Kothe's PR2833 at
+`e9307b48d7d1b690939935ecef0f8e524e6d92f4`. `DEPENDENCIES.json` pins the
+entire PR2857 package, including its inherited proof/admission adapters.
+
+Take two copies of the source T37 chronological allocation. A call `(s,r)` at
+time `t` becomes `(s,r+37k)` at time `2t+k`, for `k=0,1`. An owner row
+`[t,h,r,ch,port,off]` becomes `[2t+k,h,r+37k,ch,port,off]`. Each replica's
+30 source events retain exactly their original order. The final two global
+cover/translation events retain their original role in the full reconstruction.
+This is an interleaving of disjoint original blocks, with shared private buffers
+used sequentially; it is not concurrent reuse of a dirty buffer.
+
+In each source copy, bin `(35,16,37)` has capacity 16 and contains exactly
+helper 297 of call 329, width 7, at offset 0. Its unused rank is 9. In the doubled
+allocation, move just the first copy's role:
+
+| Item | Before | After |
+| --- | --- | --- |
+| Call/helper | `(658,297)` | `(658,297)` |
+| Owner replica/child/port | `(35,16,37)` | `(72,16,37)` |
+| Offset | 0 | 7 |
+| Occupancies of the two bins | 7, 7 | 0, 14 |
+| Idle ranks | 9, 9 | 16, 2 |
+
+No other role changes. At the destination the second copy's original width-7
+role occupies offsets 0 through 6, so the new role occupies offsets 7 through
+13. The independent checker derives strict windows from the expanded original
+source events, checks the actual moved call lies inside the destination window,
+and checks per-call physical families, offsets, capacities and every helper.
+Thus it does not assume that an arbitrary interleaving or cross-copy move is
+legal. All 271,728 roles, 666 calls and 74 original stage projections are checked.
+
+## Recurrence price
+
+Let `H_r` be the complete paid profile, including every idle child, and let
+`W` be live families. The complex recurrence moment is
+
+`M_H(a) = (1/W) sum_r H_r (r/73)^(1-a)`.
+
+Doubling the source profile and W leaves this moment unchanged. The transfer
+changes the doubled profile by exactly `H2 + H16 - 2 H9`. For `00\nassert m==73 and W==896*T and W==BJ['live']"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+ "before_sha256": "08ca58abff11bdfba721dc56ab8acf06ec1b7c48a8699a0955cf35324680aca7",
+ "path": "code/witness.py",
+ "replacements": [
+ [
+ " with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))",
+ " import time as _wr_time\n _wr_path=Path(os.environ['WITNESS_RECORD'])\n _wr_lock=_wr_path.with_name(_wr_path.name+'.append.lock')\n _wr_deadline=_wr_time.monotonic()+60\n _wr_fd=None\n while _wr_fd is None:\n try:_wr_fd=os.open(_wr_lock,os.O_CREAT|os.O_EXCL|os.O_WRONLY)\n except FileExistsError:\n if _wr_time.monotonic()>=_wr_deadline:raise TimeoutError('discovery record lock timeout; existing lock preserved')\n _wr_time.sleep(.005)\n try:\n with _wr_path.open('a',encoding='utf-8',newline='\\n')as _wr_out:\n _wr_out.write(json.dumps([key,got],default=str)+chr(10))\n _wr_out.flush()\n finally:\n os.close(_wr_fd)\n _wr_lock.unlink()"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "114a80b70c8c4819f10adf88aefc1571b18337e5da92bcff2ca3aa001650b83c",
+ "before_sha256": "1591a3eed02d3532e46183543bd2ddc7129c079a5fd70f1e6b4d9bc897153e92",
+ "path": "verify.py",
+ "replacements": [
+ [
+ "run('lift-parent',P/'lift_parent.py','--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')",
+ "run('lift-parent',P/'lift_parent.py','--package',P,'--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "0d8cc021d2401d047aaec79060ec2ea28ba06f12eca8dbf4c60c78bb31975c4e",
+ "before_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+ "path": "code/witness.py",
+ "replacements": [
+ [
+ "PAYLOAD==1<<(192+(GEO['dimension']+1)//2+2*CALLS+4).bit_length()",
+ "PAYLOAD==1<<(128+(GEO['dimension']+1)//2+18+1330+1+4).bit_length()"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+ "before_sha256": "bb213d0af12218ff7c9c572717e522d8bbeeb2856b87a253f4a7f44e0fd71f15",
+ "path": "code/invoice_allcold.py",
+ "replacements": [
+ [
+ " required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4",
+ " from blocknorm_certificate import certify\n blocknorm=certify(template, {pid:base/'providers'/pid for pid in template['local_providers']})\n assert blocknorm['status'] == 'PASS_TENSOR_BLOCK_NORM_CERTIFICATE'\n assert localbits <= 128, 'actual native scalar/Horner prefix exceeds charged local reserve'\n required_prefix=localbits+input_l2_bits+blocknorm['max_active_depth']+blocknorm['stock_l2_bits']+1+4"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+ "before_sha256": "02502a217fe8c9e10229075b50745518beac512c48db20e64c3e06514a4da5b5",
+ "path": "independent_core.py",
+ "replacements": [
+ [
+ " payload = 1 << (192 + (M+1)//2 + 2*len(c['order']) + 4).bit_length()",
+ " require(localbits <= 128, 'measured native prefix exceeds local reserve')\n payload = 1 << (128 + (M+1)//2 + 18 + 1330 + 1 + 4).bit_length()"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "d598a2ac1e2e8eaee14a8c285e0277a7ae44ca6a15bd2b5cfc67fb40844fb387",
+ "before_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+ "path": "code/invoice_allcold.py",
+ "replacements": [
+ [
+ " complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,",
+ " complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,blocknorm=blocknorm,"
+ ],
+ [
+ " primitive_arithmetic_margin_bits=4,controller_audit_sha256=",
+ " tensor_block_norm=blocknorm,partial_cover_margin_bits=1,physical_stock_l2_bits=blocknorm['stock_l2_bits'],primitive_arithmetic_margin_bits=4,controller_audit_sha256="
+ ],
+ [
+ "Sum every actual invocation and bridge sweep and take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
+ "All invocations and bridge sweeps remain charged. Bound completed-boundary energy by at most eighteen active steps per owner replica, using exact tensor-isomorphic whole-family helper unitaries. Add the full group-indexed physical-stock sup-to-l2 factor and one partial-cover margin, then the maximum local scalar/Horner prefix."
+ ]
+ ]
+ },
+ {
+ "after_sha256": "e051aaa166e01263780d5ae03699690670b597fed6593af4c37a7e978825eb85",
+ "before_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+ "path": "independent_core.py",
+ "replacements": [
+ [
+ " prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4",
+ " bn=c['blocknorm']\n require(bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['max_active_depth']==18 and bn['stock_l2_bits']<=1330, 'independent tensor block certificate')\n prefix = localbits + (M + 1) // 2 + bn['max_active_depth'] + bn['stock_l2_bits'] + 1 + 4"
+ ],
+ [
+ "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4)",
+ "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], active_block_depth=18,stock_l2=bn['stock_l2_bits'],partial_cover=1,margin=4),blocknorm=bn"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "393323f150d0bb686419804d51cf43d0f58450d2a1e7929725acdd26fdbb3640",
+ "before_sha256": "2286f00e462ff28abbb3f396095463482a1e063213b9526a7225275980c77eaf",
+ "path": "audit_mixed.py",
+ "replacements": [
+ [
+ "pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)",
+ "import blocknorm_certificate as BN;ctx['blocknorm']=BN.certify_context(ctx,roles,dirs,source_parent=parent);pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)"
+ ]
+ ]
+ },
+ {
+ "after_sha256": "4e7b5ddd11b23c92ab26bc0c80884ed64a2d45e9247b5f52bc03f27fa83dbee0",
+ "before_sha256": "f25e1e870df5d5a16a1e367b3df8843cb01644ab4b75895d7939af81e4fcb833",
+ "path": "code/assemble.py",
+ "replacements": [
+ [
+ " assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+CALLS+CALLS+4",
+ " bn=invoice['blocknorm']\n assert bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['replicas']==REPLICAS\n assert bn['max_active_depth']==bn['boundary_depth_bits']==18 and bn['active_calls_per_block']==bn['bridges_per_block']==9\n assert bn['block_width_families']==896 and bn['physical_families']==invoice['physical'] and bn['live_families']==invoice['live']\n assert bn['partial_cover_bits']==1 and bn['input_l2_bits']==37 and bn['local_reserve_bits']==128 and bn['retained_payload_bits']==PAYLOAD\n localbits=max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())\n assert bn['local_actual_prefix_bits']==localbits and localbits<=128\n assert invoice['global_prefix_bits']==bn['actual_prefix_bits']==localbits+37+18+bn['stock_l2_bits']+1+4\n assert bn['required_reserve_bits']==128+37+18+bn['stock_l2_bits']+1+4
Thank you both.
\n@philippeVV, followers 670/671. Thank you, that settles the question. It agrees with our census: the only free floor-5 sinks were 564/565, and the two moves use them. Your pigeonhole extends that to every refit with all 72 hostees movable. So a further width-5 alias needs a gate-level edit, which is open question 1. The PR body now records the answer and credits your checker (0610f3de).
@thakrarsagar, #2847. Thank you for the independent check. The provenance correction is right. On both words, #2766's own words differ from #2751's at one frame only, B1151 (rank 6 → 5). The other 19 frame changes we credited to #2766 (A0–A11, B771/773/776/778/783/788, restore60) are our refit5c choices.
17b2ee6e and several downstream claims vendor its words. The package README and CLAIM.json keep the old wording until the next package revision.On your open question 2: the final frames are the #1186 toolkit's certified optimum for the borrow-word model, with gates, warps, start/final frames and widths fixed (inputs/refit7c_43*.json; only B1170/B1171 move, dim 6 → 5). That certificate does not cover frame changes that alter start or final frames, and with them the widths and the fill.
Your questions 1 and 3 are open on our side too. Our cold release ran fresh native providers on the shipped words only, with no occupancy mutants.
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The complete source-bound line-normalized decoder is independently agent-reviewed and submitted, not maintainer-admitted. It implements the same credited PR2681 logical word with 336 positive rank-one children, no rank-eight children, all 224 outputs in F17, no early retention and untouched borrowed fields. Physical hosting, maps/wrappers, movement, precision and output-consumer costs remain explicit open obligations. Native CPython 3.12.7 registered primary plus four export groups and independent CPython 3.14.5 optimized primary passed; separate no-candidate-import phase/frame/kernel audit passed.\n\nUpdated 2026-10-15T17:56:08.643726+00:00. Original advance claim is preserved below.\n\n---\n\nCLAIM — local native frame lowering for this exact zero-retention decoder\n\nStatus: LOCAL-ONLY; no final result submitted. Updated 2026-10-15T17:28:36.223865+00:00; expires 2026-10-15T19:28:36.223865+00:00. Account: ywz65, with substantial OpenAI Codex assistance.\n\nSource: PR2681 at `ea96706295631be10d92ae149b63c3e24acaeabc`; current canonical main `1884c509efc004524786e9b7cfcc4aca572316d5`, priority revision 5. This responds to the failed cost comparison with a different physical frame implementation, retaining the same logical word and endpoints.\n\nBounded question: can the future-chart sweep use the common frame on axes 9..24, with a charged signed rank-one normalization at each of its 112 source/output roles, instead of upgrading every output to F25 and back? The source-exact phase screen and full symbolic prototype pass: each stage 2 map sends F17 to the common 16-axis frame times C_q using an explicitly computed affine shift; C_q^-1 enters the common frame and C_q plus the inverse map restores F17. The proposed 3823-event word has 336 positive rank-one children, no rank-eight children, 464 cover maps, 25840 real scalar primitives, 224 owned outputs, 16 peak scratch arrays and no early retention. All 224 current fields remain borrowed and untouched. These are provisional local measurements pending the independent native/source controls.\n\nDecision gate: versus PR2540 the child-moment numerator is 112−16*8^(1−a), strictly negative for 0≤a≤1/16 (8^15>7^16). This changes the child-cost decision, while the larger scalar/map/wrapper costs, physical hosting, movement, precision and output consumer remain explicit obligations; none are zero. No full supplier, optimum or kappa claim. The existing source's logical inverse, source reconstruction and scalar word retain full credit.\n\nBounded deliverable: one source-pinned transformed word, exact dynamic frame/affine-map proof, all signed rank-one native kernels and occurrences, complete arbitrary-input/dirty-restoration replay, meaningful missing/wrong normalization/shift/return controls, and full local comparison. Stop before a new family search or supplier expansion; reopen only with a pinned favorable complete consumer allowance. The picker originally selected verifier engineering; TASK will record the evidence-driven pivot from saturated acceptance-boundary audits to this concrete newly published source handoff.\n\nOverlap: complete 817-PR/1279-Discussion snapshot through 16:28/16:32 UTC plus the freshest 100 PRs and this source's exact head/comments now. PR2651 coalesces early-output banks but retains early values; PR2662 concerns P104. Full-current invertibility and this predecessor decoder are not claimed as new. This is a narrowed local-module result, not an optimization campaign.\n", + "user": { + "login": "ywz65", + "name": "ywz65", + "email": null, + "avatar_url": "https://avatars.githubusercontent.com/u/154373401?v=4", + "id": 154373401 + }, + "id": 6198194973, + "pull_request_review_id": null, + "in_reply_to_id": null, + "created_at": "2026-10-15T17:28:59Z", + "updated_at": "2026-10-15T17:56:32Z", + "review": null, + "side": null, + "line": null, + "start_line": null, + "path": null, + "body_html": "DONE - published local result: #2707
\nFinal head: efa51a6. The complete source-bound line-normalized decoder is independently agent-reviewed and submitted, not maintainer-admitted. It implements the same credited PR2681 logical word with 336 positive rank-one children, no rank-eight children, all 224 outputs in F17, no early retention and untouched borrowed fields. Physical hosting, maps/wrappers, movement, precision and output-consumer costs remain explicit open obligations. Native CPython 3.12.7 registered primary plus four export groups and independent CPython 3.14.5 optimized primary passed; separate no-candidate-import phase/frame/kernel audit passed.
\nUpdated 2026-10-15T17:56:08.643726+00:00. Original advance claim is preserved below.
\nCLAIM — local native frame lowering for this exact zero-retention decoder
\nStatus: LOCAL-ONLY; no final result submitted. Updated 2026-10-15T17:28:36.223865+00:00; expires 2026-10-15T19:28:36.223865+00:00. Account: ywz65, with substantial OpenAI Codex assistance.
\nSource: PR2681 at ea96706295631be10d92ae149b63c3e24acaeabc; current canonical main 1884c509efc004524786e9b7cfcc4aca572316d5, priority revision 5. This responds to the failed cost comparison with a different physical frame implementation, retaining the same logical word and endpoints.
Bounded question: can the future-chart sweep use the common frame on axes 9..24, with a charged signed rank-one normalization at each of its 112 source/output roles, instead of upgrading every output to F25 and back? The source-exact phase screen and full symbolic prototype pass: each stage 2 map sends F17 to the common 16-axis frame times C_q using an explicitly computed affine shift; C_q^-1 enters the common frame and C_q plus the inverse map restores F17. The proposed 3823-event word has 336 positive rank-one children, no rank-eight children, 464 cover maps, 25840 real scalar primitives, 224 owned outputs, 16 peak scratch arrays and no early retention. All 224 current fields remain borrowed and untouched. These are provisional local measurements pending the independent native/source controls.
\nDecision gate: versus PR2540 the child-moment numerator is 112−16*8^(1−a), strictly negative for 0≤a≤1/16 (8^15>7^16). This changes the child-cost decision, while the larger scalar/map/wrapper costs, physical hosting, movement, precision and output consumer remain explicit obligations; none are zero. No full supplier, optimum or kappa claim. The existing source's logical inverse, source reconstruction and scalar word retain full credit.
\nBounded deliverable: one source-pinned transformed word, exact dynamic frame/affine-map proof, all signed rank-one native kernels and occurrences, complete arbitrary-input/dirty-restoration replay, meaningful missing/wrong normalization/shift/return controls, and full local comparison. Stop before a new family search or supplier expansion; reopen only with a pinned favorable complete consumer allowance. The picker originally selected verifier engineering; TASK will record the evidence-driven pivot from saturated acceptance-boundary audits to this concrete newly published source handoff.
\nOverlap: complete 817-PR/1279-Discussion snapshot through 16:28/16:32 UTC plus the freshest 100 PRs and this source's exact head/comments now. PR2651 coalesces early-output banks but retains early values; PR2662 concerns P104. Full-current invertibility and this predecessor decoder are not claimed as new. This is a narrowed local-module result, not an optimization campaign.
" + } + ], + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2681", + "title": "CrocSwap/integer-mult-bounds PR #2681 comments", + "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2681", + "display_title": "CrocSwap/integer-mult-bounds PR #2681 comments" + }, + "2687": { + "comments": [], + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2687", + "title": "CrocSwap/integer-mult-bounds PR #2687 comments", + "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2687", + "display_title": "CrocSwap/integer-mult-bounds PR #2687 comments" + }, + "2707": { + "comments": [], + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2707", + "title": "CrocSwap/integer-mult-bounds PR #2707 comments", + "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2707", + "display_title": "CrocSwap/integer-mult-bounds PR #2707 comments" + }, + "2709": { + "comments": [], + "url": 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b/research/shared-kernel-pair-concentration/evidence/run-logs/final-registered-check.json new file mode 100644 index 0000000000..1dc911c1d3 --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/final-registered-check.json @@ -0,0 +1,24 @@ +{ + "command": [ + "timeout", + "240", + "python3", + "-B", + "scripts/research_package.py", + "--package", + "research/shared-kernel-pair-concentration" + ], + "cwd": "/workspace/scratch/bc9e58970b2a/integer-mult-bounds", + "started_epoch": 1792124499.740852, + "environment": { + "PATH": 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b/research/shared-kernel-pair-concentration/evidence/run-logs/final-release-binding.json new file mode 100644 index 0000000000..71a64d144f --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/final-release-binding.json @@ -0,0 +1,28 @@ +{ + "command": [ + "timeout", + "60", + "python3", + "-B", + "integer-mult-bounds/research/shared-kernel-pair-concentration/verify_release_binding.py", + "--admission", + "pair-admission", + "--moment", + "pair-candidate/EXACT-MOMENT.json", + "--baseline", + "newer-frontier/replay-pinned/RESULT.json" + ], + "cwd": "/workspace/scratch/bc9e58970b2a", + "started_epoch": 1792124337.0531936, + "environment": { + "PATH": 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b/research/shared-kernel-pair-concentration/evidence/run-logs/pair-independent-owners.json new file mode 100644 index 0000000000..bd58ef85b1 --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/pair-independent-owners.json @@ -0,0 +1,26 @@ +{ + "command": [ + "timeout", + "180", + "python3", + "-B", + "integer-mult-bounds/research/shared-kernel-pair-concentration/independent.py", + "newer-frontier/research/shared-kernel-repacking", + "pair-candidate", + "--out", + "pair-candidate/INDEPENDENT-OWNERS.json" + ], + "cwd": "/workspace/scratch/bc9e58970b2a", + "started_epoch": 1792123785.4139676, + "environment": { + "PATH": 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b/research/shared-kernel-pair-concentration/evidence/run-logs/pair-portable-bounded.json new file mode 100644 index 0000000000..ab703c795f --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/pair-portable-bounded.json @@ -0,0 +1,22 @@ +{ + "command": [ + "timeout", + "180", + "python3", + "-B", + "integer-mult-bounds/research/shared-kernel-pair-concentration/verify.py" + ], + "cwd": "/workspace/scratch/bc9e58970b2a", + "started_epoch": 1792124162.9918125, + "environment": { + "PATH": 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b/research/shared-kernel-pair-concentration/evidence/run-logs/refreshed-make-verify.json new file mode 100644 index 0000000000..ef0159883c --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/refreshed-make-verify.json @@ -0,0 +1,21 @@ +{ + "command": [ + "timeout", + "600", + "make", + "verify" + ], + "cwd": "/workspace/scratch/bc9e58970b2a/integer-mult-bounds", + "started_epoch": 1792123575.6161532, + "environment": { + "PATH": "/workspace/scratch/bc9e58970b2a/.venv/bin:/root/.codex/tmp/arg0/codex-arg0XhGjPO:/opt/codex/codex-path:/opt/codex/runtimes/codex-primary-runtime/dependencies/bin/override:/opt/codex/runtimes/codex-primary-runtime/dependencies/python/bin:/opt/codex/runtimes/codex-primary-runtime/dependencies/node/bin:/opt/codex/runtimes/codex-primary-runtime/dependencies/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/codex/runtimes/codex-primary-runtime/dependencies/bin/fallback", + "PYTHONDONTWRITEBYTECODE": "1", + 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b/research/shared-kernel-pair-concentration/evidence/run-logs/registered-pair-check.json new file mode 100644 index 0000000000..33fae2966a --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/registered-pair-check.json @@ -0,0 +1,24 @@ +{ + "command": [ + "timeout", + "240", + "python3", + "-B", + "scripts/research_package.py", + "--package", + "research/shared-kernel-pair-concentration" + ], + "cwd": "/workspace/scratch/bc9e58970b2a/integer-mult-bounds", + "started_epoch": 1792124277.487651, + "environment": { + "PATH": "/workspace/scratch/bc9e58970b2a/.venv/bin:/root/.codex/tmp/arg0/codex-arg0XhGjPO:/opt/codex/codex-path:/opt/codex/runtimes/codex-primary-runtime/dependencies/bin/override:/opt/codex/runtimes/codex-primary-runtime/dependencies/python/bin:/opt/codex/runtimes/codex-primary-runtime/dependencies/node/bin:/opt/codex/runtimes/codex-primary-runtime/dependencies/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/opt/codex/runtimes/codex-primary-runtime/dependencies/bin/fallback", + "PYTHONDONTWRITEBYTECODE": "1", + "OMP_NUM_THREADS": "1", + "OPENBLAS_NUM_THREADS": "1", + "TMPDIR": "/workspace/scratch/bc9e58970b2a/run-tmp", + "PYTHONINTMAXSTRDIGITS": "0" + }, + "exit_code": 0, + "seconds": 8.506113767623901, + "log_sha256": "f07efe2237f669555f318a2a6b931a2d9e72b0691a82ac835d05340daf61b768" +} \ No newline at end of file diff --git a/research/shared-kernel-pair-concentration/evidence/run-logs/requirements-lock.txt b/research/shared-kernel-pair-concentration/evidence/run-logs/requirements-lock.txt new file mode 100644 index 0000000000..f5b9b48b9a --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/requirements-lock.txt @@ -0,0 +1,6 @@ +gmpy2==2.3.2 +mpmath==1.3.0 +numpy==2.5.4 +psutil==7.2.2 +scipy==1.18.1 +sympy==1.14.0 diff --git a/research/shared-kernel-pair-concentration/evidence/run-logs/selected-cold.json b/research/shared-kernel-pair-concentration/evidence/run-logs/selected-cold.json new file mode 100644 index 0000000000..1ac417cb14 --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/run-logs/selected-cold.json @@ -0,0 +1,21 @@ +{ + "command": [ + "timeout", + "2100", + "make", + "frontier1094-verify" + ], + "cwd": "/workspace/scratch/bc9e58970b2a/integer-mult-bounds", + "started_epoch": 1792122159.3860142, + "environment": { + "PATH": 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b/research/shared-kernel-pair-concentration/evidence/superseded-two-swap-release.json new file mode 100644 index 0000000000..a0adbfa1a9 --- /dev/null +++ b/research/shared-kernel-pair-concentration/evidence/superseded-two-swap-release.json @@ -0,0 +1,7 @@ +{ + "status": "PASS_RELEASE", + "kappa_decimal": "0.0017193777362689861639711982065946965063211420953693804967340644511403357575297019072700578732866789291942771307638756204164826916198824422924608013702867384189900640228289198115039943559313554881741340267686086924885286761444124232536593248096762760764828060903757833470793905600316445047524111613399692417092561534353652493002739638111595620139647857917049637950717869433443580781525904932832526073831565015190802444811912222723326676786745003184507711582355687559344252476857234957071599817756969261895081638494263143718189199205400436830596718195653433971562974434419597195060401334670630979182189674893206760063053605975088411267841973395949058370315375216442800213626726150132112654192656488735348354442417128496877397682409496835616527660111207265993346347450464746817757402866260079105289482121876404327664485391794812521592401436128849397710795705346363061044343797642514638730945729961920615378368407100467499364230260345933678350265673593440260768241629360327411589740393997288621386586010383012566519026011171838694665665911064873609788657565893292342549247333451144395573268280295537541011524173607842893650131527140577419426039920673144639105065346866521313555509488085388979857372363645773626652958182849317883481482484580816462152217876477189974562607779251481311916770294085233676367929867902312071315907518569758563346477887424789412464508502703658301367764873244393412865254204481958819853089814751503348874406752585244302728762877281899215399180809219235651005883967181616898372549915008780437144442211332947921387479134581569001908194767914571095169960515280902628783215029000500046539223131305646531281416482925109715441713720726674686076308770039494883646356760816323414509282775497108910264035236160788195276371090229755455887284732526536338874207389672767143143648298273745587978206139439355607754514144305686513502495056353824328782581667887621115478065499911392215164147820446016777531907123244953111184476222819165556443940724162813945461625087990990577716975438977958247177602440798844970764785548140108047747885449268931777079214348106068399795725332722583588873893931211916417557291841389499231626688288639114565724825942799537743923702884033817323146199180941534380209949563355733575360812659800368807657779535320506507002007856828343857927624335787477428730548466214800948813327092197519928627304963052409483706595013948085266282808089382648144286719867501186577516520261483615060680305380676115046682810966255346960471888291133422790919604073086010498289685950689954018034840361616202078712392247022759317541975100170268667183126748716487116014520394086450242464992533048308107692932247538957445294670500536478451269689031297932589289650384552022154880661804374560977403405818967285903556721076359586814400340390321281788991217420706621068611660033194259029762947958105934083026188056815321095857131721952014632803640181298131250097019417732518413743739921074269129602007208069594267628535371769751911522743629960647425860763316593741319821732422899804017605258399119999999999999999999998999999999999999999999999", + "manifest_sha256": "b54478cd4dd566235062f1ef7747c337d481153b7141595cc56f10a6d2788d2a", + "proof": "Supplier: the package's own unchanged `verify.py` (retained PR1297 provider and parent admission, owner reconstruction, parent lift, strict T74 admission, geometry controls): `PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION`, native reuse {'base': 'e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e', 'extra': '7b0e9fbda32749aabc7e156d9fe09bceb0624a178628fe69e5dfea783462f905'}; its complex endpoint 214922217033623270496399775824... brackets the ledger's b = 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Outer (PR1673 capped phase-cell fusion): regenerated exact ledger (63 strict inequalities: the 62 retained rows plus the explicit main-binding row gaussian_above_main, the fixed-grid maximum kappa = C - 1/F - B asserted, 17 rejecting controls incl. the old g-factor union row, the old linear and old-theta chirp guards, the old 2*beta tag test, epsilon at 1 or at the r0 slack and beta outside its window, larger endpoint rejected by the native moment), independent balance derivation, the exact union-schedule simulation, the (retained, not used for kappa) structured-boundary displacement-rank check, the gauge-free identity/symbol/circuit checks, PR1786's finite prime/underflow controls and 19 exact evidence replays all pass. Conditional kappa 0.0017193777362689861639711982065946965063211420953693804967340644511403357575297019072700578732866789291942771307638756204164826916198824422924608013702867384189900640228289198115039943559313554881741340267686086924885286761444124232536593248096762760764828060903757833470793905600316445047524111613399692417092561534353652493002739638111595620139647857917049637950717869433443580781525904932832526073831565015190802444811912222723326676786745003184507711582355687559344252476857234957071599817756969261895081638494263143718189199205400436830596718195653433971562974434419597195060401334670630979182189674893206760063053605975088411267841973395949058370315375216442800213626726150132112654192656488735348354442417128496877397682409496835616527660111207265993346347450464746817757402866260079105289482121876404327664485391794812521592401436128849397710795705346363061044343797642514638730945729961920615378368407100467499364230260345933678350265673593440260768241629360327411589740393997288621386586010383012566519026011171838694665665911064873609788657565893292342549247333451144395573268280295537541011524173607842893650131527140577419426039920673144639105065346866521313555509488085388979857372363645773626652958182849317883481482484580816462152217876477189974562607779251481311916770294085233676367929867902312071315907518569758563346477887424789412464508502703658301367764873244393412865254204481958819853089814751503348874406752585244302728762877281899215399180809219235651005883967181616898372549915008780437144442211332947921387479134581569001908194767914571095169960515280902628783215029000500046539223131305646531281416482925109715441713720726674686076308770039494883646356760816323414509282775497108910264035236160788195276371090229755455887284732526536338874207389672767143143648298273745587978206139439355607754514144305686513502495056353824328782581667887621115478065499911392215164147820446016777531907123244953111184476222819165556443940724162813945461625087990990577716975438977958247177602440798844970764785548140108047747885449268931777079214348106068399795725332722583588873893931211916417557291841389499231626688288639114565724825942799537743923702884033817323146199180941534380209949563355733575360812659800368807657779535320506507002007856828343857927624335787477428730548466214800948813327092197519928627304963052409483706595013948085266282808089382648144286719867501186577516520261483615060680305380676115046682810966255346960471888291133422790919604073086010498289685950689954018034840361616202078712392247022759317541975100170268667183126748716487116014520394086450242464992533048308107692932247538957445294670500536478451269689031297932589289650384552022154880661804374560977403405818967285903556721076359586814400340390321281788991217420706621068611660033194259029762947958105934083026188056815321095857131721952014632803640181298131250097019417732518413743739921074269129602007208069594267628535371769751911522743629960647425860763316593741319821732422899804017605258399119999999999999999999998999999999999999999999999 (union schedule outer/UNION-SCHEDULE.md; explicit Strassen boundary tau=45/16 (the structured boundary of outer/STRUCTURED-BOUNDARY.md is not used); gauge-free interiors outer/GAUGEFREE-INTERIORS.md; fine source-prime padding PR1786 at the free point epsilon=1-(1025/1024)e-3080, outer/FINE-PADDING-COMPOSITION.md; fixed-grid maximum of PR2180/PR2161 (dataisfire), outer/PROOF-GRID-MAX.md; exact-integer coarse exponential PR2168/PR2184 (dataisfire) at the one 3000-digit rejection call).", + "seconds": 520.34 +} diff --git a/research/shared-kernel-pair-concentration/exact_moment.py b/research/shared-kernel-pair-concentration/exact_moment.py new file mode 100644 index 0000000000..e20d8b82f9 --- /dev/null +++ b/research/shared-kernel-pair-concentration/exact_moment.py @@ -0,0 +1,86 @@ +#!/usr/bin/env python3 +"""Directed integer log/exp enclosure, independently implemented for this run. + +No imported supplier or moment code. The geometric atanh remainder and the +positive exponential remainder are bounded explicitly. Floats are not used. +OpenAI Codex-assisted work. Apache-2.0. +""" +import argparse, hashlib, json, sys +from decimal import Decimal, localcontext +from fractions import Fraction +from pathlib import Path +try: + from gmpy2 import mpz as Z +except ImportError: + Z=int +sys.set_int_max_str_digits(0) + +def ceildiv(a,b):return (a+b-1)//b + +class Bounds: + def __init__(self,digits): + self.S=Z(10)**(digits+60) + self.ln2=self.unitlog(Fraction(2)) + self.cache={} + def unitlog(self,x): + assert 1<=x<=2 + z=(x-1)/(x+1);p=Z(z.numerator);q=Z(z.denominator) + if not p:return (Z(0),Z(0)) + lo=self.S*p//q;hi=ceildiv(self.S*p,q) + sl=sh=Z(0);j=0 + while True: + sl+=lo//(2*j+1);sh+=ceildiv(hi,2*j+1) + lo=lo*p*p//(q*q);hi=ceildiv(hi*p*p,q*q);j+=1 + if hi<=2:break + # Next power is z^(2j+1); all following denominators >=2j+1. + tail=ceildiv(2*hi*q*q,(2*j+1)*(q*q-p*p)) + return 2*sl,2*sh+tail + def log(self,x): + if x in self.cache:return self.cache[x] + y=x;k=0 + while y>=2:y/=2;k+=1 + lo,hi=self.unitlog(y) + ans=(lo+k*self.ln2[0],hi+k*self.ln2[1]);self.cache[x]=ans + return ans + def exp(self,xlo,xhi): + assert 0<=xlo<=xhi and 100*xhi