Price the bank-absorption ladder against the suppliers' own allocation rules: +2.17% needs a new residual type this word does not have (target, not built)

.github/workflows/composed-diagonal-bit-bootstrap.yml

@@ -0,0 +1,35 @@
+name: Verify the composed diagonal-bit bootstrap record
+
+on:
+  push:
+    paths:
+      - 'research/composed-diagonal-bit-bootstrap/**'
+      - '.github/workflows/composed-diagonal-bit-bootstrap.yml'
+  pull_request:
+    paths:
+      - 'research/composed-diagonal-bit-bootstrap/**'
+      - '.github/workflows/composed-diagonal-bit-bootstrap.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 20
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.13']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Reproduce the composed record and check every pinned byte
+        run: python3 -B research/composed-diagonal-bit-bootstrap/verify.py
+      - name: Require an unchanged tree
+        run: git diff --exit-code

SOURCES.json

@@ -533,5 +533,25 @@
       "175": "f1081fabbfadaaaaf7292a40d428dbbb865ce920"
     },
     "notices": "research/coordinated-frames-and-entrance-banks/UPSTREAM-NOTICE.md"
+  },
+  "composed_diagonal_bit_bootstrap": {
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/200",
+    "contributor": "Maxime Fleury",
+    "research_assistance": "Codebuff",
+    "kappa": "1693287/2500000000",
+    "gain_vs_pr197": "0.001826",
+    "gain_vs_pr200_announced": "0.000639",
+    "package": "research/composed-diagonal-bit-bootstrap",
+    "certificate": "research/composed-diagonal-bit-bootstrap/certificate.json",
+    "verify": "research/composed-diagonal-bit-bootstrap/verify.py",
+    "inputs": {
+      "bit": "PR200 certified fixed-coordinate and face-diagonal bit local circuit (chafreaky): m=72, W=20634, deficit 1936, 34 sinks, coarse saving 677773948354561/10^18",
+      "complex": "PR193 complex word as carried by PR194 (ikeboy): saving 219037/312500000",
+      "assembly": "PR194 unchanged 47-constraint balanced assembly, PR168 v4 paired_cube_assembly.py (eumemic)",
+      "leaf": "PR185 finite acyclic ordinary-leaf wrapper recurrence (rohanarun)",
+      "pricing": "PR184 assemble_profiles.py and FINITE_BRIDGE.txt (icekylinx, GPT-6 Astra), carried by PR194",
+      "pinned_source": "PR168 v4 modules, eumemic, commit fd25adb7fbaa12ee761d02c733c54d1d2a7687ee"
+    },
+    "scope": "Conditional composition of two supplied words through the record's unchanged assembly: PR200's bit supplier with PR193/PR194's complex, priced by PR185's finite leaf. The bit branch binds and the claim sits under one 10^-10 grid step below the word's own C/(1+C) ceiling. Physical words are inherited pinned inputs, vendored and priced, not rebuilt or replayed; the wrapper's realization is PR185's construction, not one built here. No new word, no new all-size hypothesis."
   }
 }

research/composed-diagonal-bit-bootstrap/.gitignore

@@ -0,0 +1,2 @@
+.work/
+__pycache__/

research/composed-diagonal-bit-bootstrap/NOTICE.md

@@ -0,0 +1,59 @@
+# Notice and attribution
+
+This package is a composition. It adds no word, no construction and no all-size
+hypothesis; it prices suppliers that other contributors certified, and it retains
+their notices and authorship.
+
+## Vendored inputs, byte-identical
+
+* `references/pr168-v4/scripts/paired_cube_assembly.py` — the exact balanced
+  assembly with the RaD (hipotures) balanced prefix and the gates adapted from
+  Zhihao Chen's PR23; prepared by **eumemic** with Anthropic Claude assistance,
+  PR168 v4 at `fd25adb7fbaa12ee761d02c733c54d1d2a7687ee`. Apache-2.0.
+* `references/pr184/assemble_profiles.py` and `references/pr184/FINITE_BRIDGE.txt`
+  — the exact rational pricing, the accepted profiles and the finite bridge;
+  **icekylinx** and **GPT-6 Astra**, carried by ikeboy's PR194. The rational
+  enclosures are retained from icekylinx's `three_stage_cover_network.py`.
+  Apache-2.0.
+* `references/pr194/certificate.json` — PR194's published complex profile,
+  complex saving, assembly record and kappa (`1668581/2500000000`); **ikeboy**
+  (evmckinney9), building on icekylinx's source-assisted line and PR168 v4.
+  Apache-2.0.
+* `inputs/pr200-bit-certificate.json` — the certified fixed-coordinate and
+  face-diagonal bit local circuit, its physical layer, 34 terminal sinks and paid
+  moment; **chafreaky** (Chafik Boukhalfa), PR200, with substantial Anthropic
+  Claude and OpenAI Codex assistance, and with James Chang's PR166 terminal-output
+  substitution, DaysSky's PR162 carrier rule, icekylinx's PR144 configurable
+  circuit and the PR189/#196 lineage. Apache-2.0.
+* `references/pr200/interval_moment.py` — the independent exact interval moments
+  used by PR200's `bit/prove.py`: positive atanh series with range reduction,
+  explicit geometric tails and outward rounding on a `10^-45` grid. Vendored
+  byte-identically because the lever model prices with the arithmetic of the
+  supplier it is reproducing; **chafreaky**, PR200, prepared with OpenAI Codex
+  assistance. Apache-2.0.
+* `references/pr187/certificate.json` — the paired-cube rank-60 word and its
+  coarse saving, used only as the control row the lever model reproduces;
+  **evmckinney9** with the PR168/PR184 lineage. Apache-2.0.
+
+## Methods credited
+
+* the finite acyclic ordinary-leaf wrapper and its recurrence
+  `a_{n+1} = (1-C)C + C a_n` — **rohanarun**, PR185;
+* the packing mechanism on a bit word — **evmckinney9**, PR197 (referenced here
+  only as a published figure for what lowering `W` was worth on a different word);
+* the paid-moment pricing inequality and the certification grid on it —
+  **chafreaky**, PR200, whose `bit/prove.py` and enclosure module define the
+  arithmetic the lever model re-runs rather than a re-implementation of its own;
+* the pricing recurrence applied to a composed supplier — **Maxime Fleury**, PR199,
+  from which this package takes the same operation and generalises it to an
+  arbitrary certified bit profile.
+
+## This package
+
+`compose.py`, `verify.py`, `levers.py`, `certificate.json`, `levers.json`, the
+workflow and this notice were prepared by Maxime Fleury with Codebuff assistance,
+2026-10-09. Apache-2.0.
+
+The result is conditional. A finite certificate checked here is not a formal
+verification of the full multiplication theorem, and no claim is made about the
+practical cost of the construction.