Bit leaf bootstrap: queue standing + the deferred #200 composition at conditional κ = 6.773148e-4

.github/workflows/bit-leaf-bootstrap-189.yml

@@ -0,0 +1,36 @@
+name: Verify bit-leaf bootstrap 189 record composition
+on:
+  push:
+    paths:
+      - 'research/bit-leaf-bootstrap-189/**'
+      - 'research/source-assisted-v4/certificate.json'
+      - 'research/paired-cube-twin-local-168/certificate.json'
+      - 'research/source-assisted/global/**'
+      - 'research/source-assisted/public/pr168_fd25adb7.tar.gz'
+      - '.github/workflows/bit-leaf-bootstrap-189.yml'
+  pull_request:
+    paths:
+      - 'research/bit-leaf-bootstrap-189/**'
+      - 'research/source-assisted-v4/certificate.json'
+      - 'research/paired-cube-twin-local-168/certificate.json'
+      - 'research/source-assisted/global/**'
+      - 'research/source-assisted/public/pr168_fd25adb7.tar.gz'
+      - '.github/workflows/bit-leaf-bootstrap-189.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: '3.13'
+      - name: Re-price the assembly with the bootstrapped bit leaf
+        run: python -B research/bit-leaf-bootstrap-189/verify.py
+      - name: Require an unchanged tree
+        run: git diff --exit-code

SOURCES.json

@@ -533,5 +533,23 @@
       "175": "f1081fabbfadaaaaf7292a40d428dbbb865ce920"
     },
     "notices": "research/coordinated-frames-and-entrance-banks/UPSTREAM-NOTICE.md"
+  },
+  "bit_leaf_bootstrap_189": {
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/194",
+    "contributor": "Maxime Fleury",
+    "research_assistance": "Codebuff",
+    "kappa": "267141/400000000",
+    "gain_vs_pr194": "0.000629",
+    "package": "research/bit-leaf-bootstrap-189",
+    "certificate": "research/bit-leaf-bootstrap-189/certificate.json",
+    "verify": "research/bit-leaf-bootstrap-189/verify.py",
+    "inputs": {
+      "complex": "PR193 complex word as carried by PR194",
+      "bit": "PR189 face-diagonal bit word certificate (chafreaky)",
+      "leaf": "PR185 finite leaf bootstrap recurrence (rohanarun)",
+      "assembly": "PR194 unchanged 47-constraint balanced assembly (ikeboy)",
+      "pinned_source": "PR168 v4 modules, eumemic, commit fd25adb7fbaa12ee761d02c733c54d1d2a7687ee"
+    },
+    "scope": "Conditional assembly composition: PR194's complex and bit suppliers with the binding bit leaf re-priced by PR185's verified finite acyclic bootstrap. Physical words are inherited pinned inputs and are not replayed. Terminal-sink and reuse-pair maximality on the bit word are recorded separately. No new word, no new all-size hypothesis."
   }
 }

research/bit-leaf-bootstrap-189/.gitignore

@@ -0,0 +1,3 @@
+.work/
+bootstrap-result.json
+__pycache__/

research/bit-leaf-bootstrap-189/NOTICE.md

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+# Notice and attribution
+
+`research/bit-leaf-bootstrap-189/` composes pinned, independently contributed
+suppliers. No upstream producer is executed here; the physical words are
+inherited inputs and only the assembly is re-priced and re-checked.
+
+## This package
+
+Exact assembly composition, reproduction harness and maximality searches:
+prepared by Maxime Fleury with Codebuff assistance, Apache-2.0.
+
+## Inherited inputs, with their contributors
+
+* **PR194 — source-assisted v4 complex word with PR189's bit supplier**
+  (ikeboy / Avi Eisenberg, head `research/source-assisted-v4-twin`).
+  This package reads its `certificate.json` (`complex_profile`, `kappa`) and
+  reuses its assembly route unchanged.
+* **PR193 — pair donors on the source-assisted v4 complex word** (ikeboy).
+  The complex supplier carried by PR194.
+* **PR189 — shared-edge complex and face-diagonal bit local circuits on
+  PR168 v4** (chafreaky / Chafik Boukhalfa). The bit word whose certified
+  `bit.profile` and `bit.coarse` this package prices.
+* **PR185 — finite leaf bootstrap above PR182** (rohanarun / Rohan Arun).
+  The three-level finite acyclic leaf recurrence applied here, itself verified
+  in `research/bit-leaf-bootstrap182` with 11 rejecting controls per depth.
+* **PR184 / PR182 — source-assisted and paired-cube local bit suppliers**
+  (icekylinx; chafreaky), whose `select()` pricing, legacy ordinary leaf
+  `384599/10^10`, finite bridge and 47-constraint balanced assembly this
+  package inherits through `research/source-assisted/global/assemble_profiles.py`
+  (GPT-6 Astra for icekylinx).
+* **PR168 v4 — paired-cube modules** (eumemic, commit `fd25adb7`), pinned as
+  `research/source-assisted/public/pr168_fd25adb7.tar.gz`.
+* **PR183 — closed-form assembly ceiling** (romainhedouin), the acceptance
+  arithmetic the assembly keeps.
+* **PR192 — frame-layout ceiling for #168's word** (DaysSky), the bound cited
+  for the remaining lever.
+
+Upstream author notices and Claude/OpenAI disclosures remain in `NOTICE`,
+`upstream/` and the retained package notices of the inputs listed above.

research/bit-leaf-bootstrap-189/README.md

@@ -0,0 +1,172 @@
+# Bit leaf bootstrap: PR194 pricing, and the higher bit supplier
+
+## Status (2026-10-09) — where this stands
+
+The queue moved after this package was opened. Exact standing claims, taken from
+the open pull requests (not from this package):
+
+| PR | author | kappa | lever | notes |
+| --- | --- | --- | --- | --- |
+| #200 | chafreaky | 6.65046903615388e-4 (`166261725903847/25e16`) | new bit **and** complex supplier | With its own complex word *the complex branch binds*, so its headline equals #196 and is *below* #197. It also states that composed with #193/#194's complex word its bit supplier "would give about 6.769e-4, which I am preparing as a separate stacked composition" — the composition computed below. |
+| #197 | evmckinney9 | **6.76080316519385e-4** (`135216063303877/2e17`) | packs #187 rank-4/rank-24 residuals; #193 complex | Its own body: +0.8398% packing gain over `0.000670450176035363`, 1.2957% above #194. **The highest standing kappa claim.** |
+| #198 | sennemmi | **6.679123e-4** (`6679123/10^10`) | 102 lowered PR189 endpoint frames + the finite leaf wrapper | Draft. Explicitly "not claimed as the current public record" and "do not claim to beat #197". Credited here: "the finite depth-2 ordinary-leaf wrapper uses the PR185 recurrence **first applied to PR189 by PR199**". |
+| #199 | this package | 6.678525e-4 (`267141/400000000`) | finite leaf bootstrap on PR194's inputs | Reproduces PR194's kappa exactly from PR194's own profiles; the wrapper is the only change. |
+
+So on the record's own inputs this package's headline is **superseded**:
+
+* by **#198**, which applies the same recurrence to a *descended* PR189 bit word
+  (lower W ⇒ higher coarse saving), and states plainly that the recurrence and
+  wrapper are "credited, not claimed as new work" to PR185 and this PR. This
+  package is therefore the first published application of the PR185 bootstrap to
+  PR189's bit word, not the current best;
+* by **#197**, which raised the bit supplier itself (residual packing) rather
+  than its pricing.
+
+What this package still provides uniquely:
+
+* an **exact reproduction harness** for a published record: it rebuilds PR194's
+  kappa `1668581/2500000000` from PR194's own profiles through PR194's own
+  `select()` and `assemble()` (depth 0 below *is* that reproduction), so any
+  re-pricing delta is isolated to the leaf;
+* the **maximality proofs** for the two W-lowering levers on PR189's bit word
+  (terminal sinks 34 of 34; donor reuse 1760 of 3960 gauges) — see
+  [bit-maximality.md](bit-maximality.md);
+* a **supplier-agnostic pricing path**: [next_bit_composition.py](next_bit_composition.py)
+  prices *any* certified bit profile with the same bootstrap against PR193's
+  complex through PR194's unchanged assembly. Applying it today gives the
+  highest kappa computed anywhere in this queue (next section).
+
+## Beating the standing best: the composition #200 deferred, plus the bootstrap
+
+#200 supplies a strictly stronger bit word — coarse saving
+`677773948354561/10^18 = 6.77773948355e-4` against PR189's
+`668298937775631/10^18 = 6.68298937775631e-4` — but publishes it with its own
+complex word, where the complex branch binds, and explicitly leaves the stacked
+composition "to be prepared separately". Pricing #200's certificate through
+PR194's unchanged assembly against PR193's complex (`219037/312500000 =
+7.009184e-4`) is exactly that deferred composition; the bootstrap then removes
+the same slack below the coarse saving that it removed for PR189:
+
+| depth | bit leaf | kappa | vs #197 | vs this package |
+| --- | --- | --- | --- | --- |
+| 0 (legacy atom wrapper, = #200's own "about 6.769e-4") | 6.77340866500955e-4 | 6768823/10000000000 = 6.768823e-4 | +0.1186% | +1.3521% |
+| 1 | 6.77773606501196e-4 | 1354629/2000000000 = 6.773145e-4 | +0.1825% | +1.4168% |
+| 2, 3 | 6.77773899999865e-4 | **1693287/2500000000 = 6.773148e-4** | **+0.1826%** | +1.4168% |
+
+**This is the highest computed kappa in the queue**: +0.1826% over the standing
+claim #197, and +0.0639% over the depth-0 row that #200 has announced but not yet
+published. The depth-0 row is an independent cross-check of the harness: #200's
+own announcement says the stacked composition "would give about 6.769e-4", and
+this harness returns 6.768823e-4 from that supplier's certificate. The bit side
+still binds at every depth (6.7777e-4 < 7.0092e-4).
+
+**Pricing headroom is now exhausted.** For a fixed bit word the assembly caps
+`kappa` at `C/(1+C)`; for #200's certificate `C = 6777739/10^10` gives
+`C/(1+C) = 6.7731483368e-4`, and the depth-2/3 rows sit 3.4e-11 below it. So no
+further pricing change can move this number: the only remaining levers reduce
+`W` on #200's word. Both known ways to do that are new work on that graph, not
+a recomposition:
+
+* **endpoint-frame descent** — #198 did this on PR189's word and gained
+  `+0.0090%` of coarse saving (`6.68298937775631e-4 -> 6.6835882709e-4`);
+* **residual packing** — #197's mechanism is bound to PR187's word and was worth
+  `+0.8403%` of coarse saving there (`6.70899981048852e-4 -> 6.76537710350481e-4`),
+  the largest single bit-side gain in the queue (`+0.8398%` on kappa).
+
+Because the bit branch binds, improving the complex side is worthless until the
+bit coarse saving exceeds the complex's `7.009184e-4`.
+
+Reproduce:
+
+```bash
+python3 -B research/bit-leaf-bootstrap-189/verify.py
+```
+
+which re-prices the vendored PR200 certificate, requires the result to beat #197,
+and requires the depth-0 row to equal `6768823/10^10`.
+
+Caveat, stated plainly: #200's bit word is that author's certified artifact,
+vendored here and priced — not rebuilt or replayed. The wrapper is a *pricing*
+change whose physical realization is PR185's construction, not one built here.
+
+## Result claimed here: PR194's inputs
+
+**kappa = 267141/400000000 = 6.6785250e-4**, against PR194's
+1668581/2500000000 = 6.674324e-4 (+0.0629%). One thing changes in the record: the
+ordinary leaf that prices the binding bit supplier. The complex supplier (PR193
+as carried by PR194), the bit word (PR189), its terminal sinks, its reuse pairs,
+the finite bridge and the 47-constraint balanced assembly are PR194's, unchanged.
+
+| quantity | PR194 (record) | this composition |
+| --- | --- | --- |
+| complex saving | 7.009184e-4 | 7.009184e-4 (unchanged, PR193) |
+| bit coarse saving `C` | 6.68298937775631e-4 | 6.68298937775631e-4 (unchanged, PR189) |
+| bit ordinary leaf | 384599/10^10 = 3.84599e-5 (legacy) | 6.68298899999874e-4 (bootstrapped) |
+| bit effective saving | 6.67878244234e-4 | 6.68298899999874e-4 |
+| **kappa** | 1668581/2500000000 = 6.674324e-4 | **267141/400000000 = 6.6785250e-4** |
+
+### Why it moves kappa
+
+PR194's assembly sets `a = min(bit_effective, (1-1e-9)*complex_saving - 1e-10)`
+and `kappa = a/(1+a)`; the bit side binds. PR184's `select()` prices that side as
+`effective = (1-atom)*C + atom*OLD` with `OLD = 384599/10^10`, which holds the
+effective value 4.207e-7 below `C`. PR185's finite acyclic wrapper
+
+    a_{n+1} = (1-C)*C + C*a_n = C - C^n (C - a_0)
+
+recovers it; three levels give `C` to within 1.3e-15. Details and per-depth rows:
+[certificate.json](certificate.json).
+
+### Searched and rejected
+
+Both W-lowering levers on PR189's bit word are maximal
+([bit-maximality.md](bit-maximality.md)): `word.py::row()` gives
+`W = 2*v + (R - pairs)` at fixed rank deficit, and
+
+* **terminal sinks: 34 of 34.** 474 per-root-admissible roots enumerated; the
+  shipped 34 reproduce the frozen profile bit-for-bit and each of the 440 rank-23
+  extras is rejected by the exact target chronology of `terminal.py::prove`;
+* **donor reuse: 1760 of 3960 gauges.** All 2200 unpaired gauges carry rank-20
+  entrance birth frames and no donor end frame among all 8628 is contained in
+  any of them (`word.py::exact_frames` eligibility).
+
+A frame-layout search on the same word was started and abandoned: re-choosing
+operation frames only moves kappa when chain gaps are re-nested, and #198
+published a deterministic endpoint-frame descent that does this properly (it
+lowers W to `1670897/2500000000` coarse). The remaining big lever is the one
+#197 used — residual packing, bound to PR187's word (`packing.py` +
+`--bit-root`); carrying it onto #200's new bit graph is new work, not a
+recomposition. Note that #198's own descent route and #200's stronger supplier
+are *independent*: a descent on #200's word would start from the higher coarse
+saving.
+
+## Reproduce
+
+```bash
+python3 -B research/bit-leaf-bootstrap-189/verify.py
+```
+
+pins every input and package file by SHA-256 ([SOURCE.json](SOURCE.json)),
+reproduces PR194's kappa exactly, re-checks 47 strict constraints and 7 margins
+at every depth, re-prices the vendored PR200 supplier, and requires the result to
+beat #197.
+
+## Verification boundary
+
+* Reproduced here: PR194's kappa from PR194's own profiles through its own
+  `select()`/`assemble()`; the wrapper recurrence, its closed form and the strict
+  tolls `a_0 < a_n < C < 1 - a_n`; 47 strict constraints and 7 margins per depth;
+  the PR200 composition.
+* Inherited pinned inputs, not replayed: PR168 v4 `fd25adb7`, and the
+  #182/#184/#189/#193/#194/#200 packages. The wrapper's physical realization is
+  PR185's claimed construction, not one built here; #200's bit word is its
+  author's certified artifact, vendored and priced, not rebuilt.
+* Conditional on #183's closed-form acceptance ceiling, #184's finite bridge, and
+  the retained contracts of those inputs. Gains are small and live on the
+  10^-10 selection grid.
+
+## Stacking
+
+Inputs are vendored byte-identical from the open PRs named above, so this package
+runs on its own branch; the PRs' own changes are not claimed here. See
+[NOTICE.md](NOTICE.md).

research/bit-leaf-bootstrap-189/SOURCE.json

@@ -0,0 +1,36 @@
+{
+  "package": "bit-leaf-bootstrap-189",
+  "date_utc": "2026-10-09",
+  "claim": {
+    "kappa": "267141/400000000",
+    "kappa_decimal": 0.0006678525,
+    "record_kappa": "1668581/2500000000",
+    "gain_vs_record": 0.0006294270401017391,
+    "scope": "Conditional assembly composition; the physical words are inherited pinned inputs."
+  },
+  "composition": {
+    "complex": "PR193 complex word as carried by PR194 (research/source-assisted-v4/certificate.json complex_profile)",
+    "bit": "PR189 face-diagonal bit word certificate bit.profile and bit.coarse (research/paired-cube-twin-local-168/certificate.json)",
+    "bootstrap": "PR185 bit-leaf-bootstrap182 three-level finite acyclic leaf recurrence",
+    "assembly": "PR194's unchanged 47-constraint balanced assembly, PR184 finite bridge, PR183 closed-form acceptance arithmetic",
+    "pinned_source": "research/source-assisted/public/pr168_fd25adb7.tar.gz (PR168 v4, eumemic, commit fd25adb7fbaa12ee761d02c733c54d1d2a7687ee)"
+  },
+  "files": {
+    "research/bit-leaf-bootstrap-189/assemble_bootstrap.py": "362f70dc83771388a5e6442bfc8b8f816d7c2dd8d8fd69401ed29c754eaddad7",
+    "research/bit-leaf-bootstrap-189/bit_sink_pack.py": "1bf96be1aa9926c47c7137c2fd0dd24722db9f1ed8eed5d44c2d260be5982c18",
+    "research/bit-leaf-bootstrap-189/bit_reuse_pack.py": "00541ab88f42ce71dbd3fc71dc55a7717ca80d4bb1f51fcf510323522cfee737",
+    "research/bit-leaf-bootstrap-189/bit_reuse_maximal.py": "91792e33ff057080c91369b788c88b9cc01e1df6ce2bcd173e67d68132cd4a61",
+    "research/bit-leaf-bootstrap-189/bit-reuse-maximal.json": "30418cac689093de5b4d3cb7d6eeae450f8a74de5be7d66cc9be6087ed3ea61c",
+    "research/bit-leaf-bootstrap-189/verify.py": "4e1572042285e492a2bd0a52351b07f29ff7c16a1c2c2577f5167b9d62439ec4",
+    "research/bit-leaf-bootstrap-189/certificate.json": "a9a03b92b6c49c38a949fdb258d99f08b75d83782dc20376634d287c0d69cfcb",
+    "research/bit-leaf-bootstrap-189/README.md": "b8d76bb1c7dee713a4a1654cd7449d2793daaa302e01d98529b59b929c0ee1e3",
+    "research/bit-leaf-bootstrap-189/NOTICE.md": "5b0a2f4b6dc0a4c7020487246bb0d49ca89570fdd94cc40b73d83410fb1ce45e",
+    "research/bit-leaf-bootstrap-189/bit-maximality.md": "f0bd33993327c53ae81fe49d292f722352bdb3b0cb61bc9828de0243cf733f42",
+    "research/source-assisted/global/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de",
+    "research/source-assisted/global/FINITE_BRIDGE.txt": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46",
+    "research/source-assisted/global/COMMON_FRAME_LIFT_AND_GLOBAL_CONTRACT.txt": "102a012e8938d60d0d7e5360b7088f317c51e42a148288882612b8635a463d16",
+    "research/source-assisted/public/pr168_fd25adb7.tar.gz": "44211bb3c927b152f3e3027ec8c5852a612f93d9e5d137a42955775fa9c93044",
+    "research/source-assisted-v4/certificate.json": "1600b77cb1f41c0f87967f20133eccda5e6c5f215b70361dfd0c49c861248e59",
+    "research/paired-cube-twin-local-168/certificate.json": "a781a738228609937165cfbc50d2eb9bfb0ecca2a28084d4deef6fb4f3bc9139"
+  }
+}