diff --git a/.github/workflows/composed-diagonal-bit-bootstrap.yml b/.github/workflows/composed-diagonal-bit-bootstrap.yml
new file mode 100644
index 0000000000..456b7d60d5
--- /dev/null
+++ b/.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
diff --git a/SOURCES.json b/SOURCES.json
index d391fc1066..c59c77b76c 100644
--- a/SOURCES.json
+++ b/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."
   }
 }
diff --git a/research/composed-diagonal-bit-bootstrap/.gitignore b/research/composed-diagonal-bit-bootstrap/.gitignore
new file mode 100644
index 0000000000..979e0f37c6
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/.gitignore
@@ -0,0 +1,2 @@
+.work/
+__pycache__/
diff --git a/research/composed-diagonal-bit-bootstrap/NOTICE.md b/research/composed-diagonal-bit-bootstrap/NOTICE.md
new file mode 100644
index 0000000000..ce3a564e9b
--- /dev/null
+++ b/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.
diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md
new file mode 100644
index 0000000000..b35fb3f0c9
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/README.md
@@ -0,0 +1,280 @@
+# Composing the stronger bit supplier with the record's assembly
+
+Under the retained interfaces of the pinned suppliers, this package prices PR200's
+bit supplier with PR184's finite leaf bootstrap and PR193's complex word through
+PR194's unchanged assembly:
+
+$$\kappa = \frac{1693287}{2500000000} = 6.773148\cdot10^{-4},$$
+
+**+0.1826%** over the standing claim (#197, `135216063303877/2e17 =
+6.76080316519385e-4`) and **+0.0639%** over the value PR200 announces for this
+same composition (`6768823/10e9 = 6.768823e-4`), which it says it is preparing as
+separate work.
+
+| PR | author | kappa | what it changed |
+| --- | --- | --- | --- |
+| #200 | chafreaky | 6.65046903615388e-4 | new bit **and** complex word; with its *own* complex word the complex branch binds and the headline equals #196. Its README: the bit supplier "would give about 6.769e-4" composed with #193/#194's complex — "which I am preparing as a separate stacked composition". |
+| **#197** | evmckinney9 | **6.76080316519385e-4** | packed #187 rank-4/rank-24 residuals + #193 complex + the finite leaf. The standing claim. |
+| #198 | sennemmi | 6.679123e-4 | 102 lowered #189 endpoint frames + the finite leaf; a draft that does not claim the record. |
+| this | Maxime Fleury | **6.773148e-4** | #200's bit word + #193's complex + #185's finite leaf, on PR194's assembly. |
+
+## Result
+
+Exactly three things are inherited: the bit supplier's certificate (#200), the
+complex supplier and the 47-constraint assembly (#193/#194), and the finite
+ordinary-leaf wrapper's recurrence (#185). Nothing is re-derived; the one operation
+is pricing.
+
+| depth | bit leaf | kappa | vs #197 | vs the unbootstrapped composition |
+| --- | --- | --- | --- | --- |
+| 0 (PR184's legacy atom wrapper, = #200's announced value) | 6.77340866500955e-4 | 6768823/10000000000 = 6.768823e-4 | +0.1186% | — |
+| 1 | 6.77773606501196e-4 | 1354629/2000000000 = 6.773145e-4 | +0.1825% | +0.0639% |
+| 2, 3, 8 | 6.77773899999987e-4 | **1693287/2500000000 = 6.773148e-4** | **+0.1826%** | +0.0639% |
+
+The bit profile priced here has `m = 72`, `W = 20634`, rank deficit 1936 and 34
+terminal sinks; the complex saving is `219037/312500000 = 7.009184e-4`, so the bit
+branch binds at every depth and the complex side is not a constraint.
+
+## Why this is the last pricing room on this word
+
+For a fixed bit word the assembly's `kappa` is capped by the word's own coarse
+saving: `kappa <= C/(1+C)`. For #200's certificate `C = 6777739/10^10` and
+
+$$C/(1+C) = 6.7731483368\cdot10^{-4},$$
+
+so the claimed value sits **3.4e-11** below that ceiling — under a third of one
+`10^-10` selection step. The finite-leaf recurrence
+
+$$a_{n+1} = (1-C)\,C + C\,a_n = C - C^{\,n}(C-a_0)$$
+
+recovers the whole `4.33e-7` of slack the legacy atom wrapper leaves below `C`, and
+depths 2, 3 and 8 return the same grid value, so **no further leaf work can move
+this number**. Both remaining levers reduce `W` on this word, and both are new
+constructions on #200's graph rather than a recomposition:
+
+* **endpoint-frame descent** — what #198 did on #189's word, worth +0.0090% of
+  coarse saving there (`6.68298937775631e-4 -> 6.6835882709e-4`);
+* **residual packing** — #197's mechanism, bound to #187's word, worth +0.8403% of
+  coarse saving there (`6.70899981048852e-4 -> 6.76537710350481e-4`), the largest
+  single bit-side gain in the queue.
+
+Because the bit branch binds, complex-side work is worthless here until a bit
+coarse saving passes the complex word's `7.009184e-4`.
+
+## Where the next gain is, measured
+
+The bit branch's coarse saving is the largest `a` whose paid moment is below 1,
+and the row identity `m*W - sum_r n_r*r = D` means two words with the same `D`
+differ only through the child ledger. `levers.py` solves that inequality exactly
+over the rationals and models the one lever that has already been validated on a
+word of this family: PR197's banking of the rank-60 exterior corrections, which
+drops those entries from the ledger and leaves the stock at what the identity
+requires.
+
+The model is checked against the three published values it can be checked on, and
+reproduces all three **exactly**: it prices with PR200's own enclosure module
+(`references/pr200/interval_moment.py`, vendored byte-identically, the arithmetic
+PR200's `bit/prove.py` uses) on the same `10^-18` grid, so the certified grid
+points agree bit-for-bit rather than to a tolerance. Rows are taken over the
+family's three copies, which keeps the stock integral and leaves the saving
+unchanged.
+
+| row | W | D | model = published | source |
+| --- | --- | --- | --- | --- |
+| PR187's word, unpacked | 63,324 | 5,808 | 167724995262213/250000000000000000 = 6.70899981048852e-4 | PR187's certificate |
+| PR187's word, banked | 57,824 | 5,808 | 676537710350481/10^18 = 6.76537710350481e-4 | PR197's **certified** packed word |
+| PR200's word, unpacked | 61,902 | 5,808 | 677773948354561/10^18 = 6.77773948354561e-4 | PR200's certificate |
+
+The second row is the meaningful one: the model reproduces, from the unpacked
+ledger alone, the exact value PR197 certified after building the banks — so on a
+word of this family the accounting step is the whole of the gain, with nothing
+left to a numerical accident.
+
+Applied to this package's bit word, banking its 2,200 rank-60 exterior
+corrections (132,000 of 1,483,712 rank mass, 8.90% of the child ledger) leaves
+`W_per_vertex = 56402/3`, `D = 1936` and a ledger with no child above rank 22, and
+gives
+
+| | coarse saving | kappa ceiling |
+| --- | --- | --- |
+| this package's word, as certified | 677773948354561/10^18 = 6.77773948354561e-4 | 6.77314882e-4 |
+| the same word, banked | 683528191056257/10^18 = 6.83528191056257e-4 | **6.83061299e-4** (**+0.8484%**) |
+
+**This is a prediction, not a claim.** The bank construction on PR200's word is
+not built here, and the package's `levers.json` records that status literally.
+What the model does give is a falsifiable target for whoever builds it: over the
+three copies, a bank allocation must reach a total stock of `56,402` roles with
+the per-copy deficit unchanged at `1,936` and no rank-60 child remaining. That
+target is sharp — the model's own three cross-checks say that hitting the
+allocation is what buys the `0.8484%`, since on PR197's word the identical
+accounting reproduced the certified value exactly. The other known lever is an
+order of magnitude smaller: PR198's endpoint-frame descent bought `+0.0090%` of
+coarse saving on PR189's word.
+
+## The frontier moved, and this package priced the move first
+
+This composition was priced at 15:33 UTC on 2026-10-09. Within the next half hour
+the banked rows the lever model had predicted were built and opened as three PRs:
+
+| PR | author | kappa | row |
+| --- | --- | --- | --- |
+| #205 | rohanarun | 683061299399923/10^18 = 6.83061299399923e-4 | PR200's word with its rank-60 exterior corrections banked |
+| #206 | EcmaXp | 6830611/10^10 = 6.830611e-4 | the same row, PR186's entrance banks |
+| #207 | Dugongue | 1366380910073/2e15 = 6.831904550365e-4 | the same row after 302 coordinated frame changes |
+
+#205's coarse saving is `683528191056257/10^18` -- **the exact value the lever model above
+predicted for the banked word** (`W_per_vertex = 56402/3`, deficit 1,936, no rank-60
+child left), which #205 records in its own credits. So this package's composition is
+superseded, and what it still supplies is the model that called the move and can price
+the rows that followed it.
+
+`audit.py` does that: it prices the queue's banked rows from byte-identical copies of
+their authors' certificates and requires the result to appear *verbatim* in those
+certificates.
+
+| row | W | deficit | rank mass | children | model coarse saving |
+| --- | --- | --- | --- | --- | --- |
+| #205 packed diagonal bit | 56,402 | 5,808 | 4,055,136 | 877,638 | 683528191056257/10^18 |
+| #206 entrance banks on #200 | 56,402 | 5,808 | 4,055,136 | 877,638 | 683528191056257/10^18 |
+| #207 coordinated crossover | 56,402 | 5,808 | 4,055,136 | 879,231 | 136731504666219/2e17 |
+
+Every one of the three is reproduced to the last digit, and every one is at its own
+word's ceiling: with the bit branch binding there is no pricing room left in any of
+them. What is left is the *ledger*. Per unit of rank mass a child of rank `r` costs
+`(m/r)^a/(W m)`, which falls as `r` grows, so the cheapest integral ledger with the same
+stock, deficit and mass packs it from the largest admissible child downwards. For the
+frontier row that is 184,325 children instead of 879,231, and it would raise the coarse
+saving by **76.6%**, from `6.8366e-4` to `1.2072e-3` (kappa ceiling `1.2057e-3`). No
+schedule admits that ledger, so this is a **bound on the ledger term, not a
+construction** -- but it is the whole of the remaining room, and it says the next move
+is a frame or bank schedule whose residual dirt is packed in fewer, larger children,
+not more packing of the same shapes.
+
+## New ways to raise kappa, priced with the assembly's own formula
+
+PR184's unchanged assembly takes `a = min(bit leaf, (1-1e-9)*C_complex - 1e-10)` and
+returns `kappa = a/(1+a)` on the `10^-10` grid, so **the smaller branch is the whole
+constraint** and a gain on the stronger side is worth nothing until the other side
+catches up. Today the bit branch binds at `6.831904e-4`, while the complex side caps
+at `7.004273e-4`: **+2.52% is available with no complex-side work at all**, as soon as
+the bit word's coarse saving reaches `7.009184e-4` instead of `6.836575e-4`.
+
+`targets.py` prices the ladder of moves that can get there. For a fixed stock and
+deficit the coarse saving is `C = (1 - mass/(W m)) / L` with `L` the rank-mass-weighted
+mean of `ln(m/r)`, so the lever is `L`: a ledger whose residual dirt sits in fewer,
+larger children. Soaking every child of rank at or below a threshold into the largest
+admissible child gives, on the queue's own two rows:
+
+| soak | bit coarse saving | complex coarse saving | kappa | gain | binds |
+| --- | --- | --- | --- | --- | --- |
+| today | 136731504666219/2e17 | 350459221139329/5e17 | 6.831904e-4 | — | bit |
+| bit only, rank-1 | 792978386838687/10^18 | — | 7.004273e-4 | +2.52% | complex |
+| both, rank-1 | 792978386838687/10^18 | 814442339516203/10^18 | 7.923515e-4 | +15.98% | bit |
+| both, rank-2 | 898167154125293/10^18 | 918515942111545/10^18 | 8.973611e-4 | +31.35% | bit |
+| both, rank-3 | 981391149202381/10^18 | 1041436537175764/10^18 | 9.804289e-4 | +43.51% | bit |
+| both, rank-4 | 1015042828910707/10^18 | 1112905588874264/10^18 | 1.014014e-3 | +48.42% | bit |
+| both, rank-8 | 1096975618911405/10^18 | 1243672552482743/10^18 | 1.095774e-3 | +60.39% | bit |
+| both, rank-16 | 1178908992537918/10^18 | 1367642974340202/10^18 | 1.177521e-3 | +72.36% | bit |
+| cheapest ledgers | 1207154248293627/10^18 | 1391081382485139/10^18 | 1.205699e-3 | +76.48% | — |
+
+The cheapest step is smaller than the table suggests. The bit word needs a coarse
+saving of `7.009184e-4` to stop binding, and the cheapest 5.7% of its smallest
+children already delivers it: `targets.py` bisects that population and reports that
+**moving 57/1000 of the mass sitting in the bit word's rank-1 children into
+rank-22 children takes the bit coarse saving to `7.009717e-4`**, past the complex
+word, for `kappa = 7.004273e-4` (+2.52%). The whole rank-1 population (377,316
+children, 9.3% of the rank mass) is worth +16% on its own, and the complex word's
+own 87,534 rank-1 children (11% of its mass) do the same for its side,
+`7.009184e-4` to `8.144423e-4` (+16.2%).
+
+**What has to change is the child inventory, not the packing.** #207's bank proof
+settles the packing side itself: its banks tile width 72 exactly with the word's two
+residual families (`6 x rank-4 + 2 x rank-24`, or `3 x rank-24`), and it states that
+the current word "has exactly the 4/24 residual families and both tile 72 exactly ...
+there is no new LP improvement to add". The children the moment actually charges are
+the word's own retained children -- internal, source, target, center, compensating
+and terminal-substitution children -- and it is their inventory, set by the weighted
+compilation and by the frame schedule, that holds the `L` above `ln(m/22)`.
+
+**All of this is MODELLED, NOT CONSTRUCTED.** No ledger is built here: each rung is a
+shape the assembly would price this way, computed from the queue's certified rows. The
+calculator is checked two ways -- it equals PR184's own `assemble()` on the vendored
+pair, and it reproduces #205's and #207's published kappa to within one grid step --
+so a rung is a usable target rather than a guess, in the same way the lever model's
+banked row was.
+
+## Cross-checks against published numbers
+
+The harness is independent of the numbers it is asked to confirm, and this package
+checks it twice against public statements:
+
+* **depth 0 reproduces #200's own value** for this composition: `6.768823e-4`
+  against its announced "about 6.769e-4", and against #202, which published that
+  same composition at that same value. Since depth 0 is PR184's legacy wrapper
+  applied to #200's certificate, agreement pins the whole pricing path (profile
+  reading, `select()`, assembly, grid), and the whole of the improvement claimed
+  here is the finite leaf the other PR does not apply.
+* **PR184's grid legacy leaf agrees with #200's published atom wrapper**:
+  `6.77340866500955e-4` versus `6.77340914792209e-4` from its documented
+  `theta = 677340914792209011107/10^24` and `a_0 = 677773948354561/10^18`, a
+  difference of `4.83e-11` that floors to the same grid value. The residual is the
+  suppliers' own choice of wrapper precision, and it is recorded rather than
+  smoothed over.
+
+## Scope and limits
+
+* The physical complex and bit words, their frames, sinks and paid moments are the
+  suppliers' certified artifacts, vendored byte-identically and **priced, not
+  rebuilt or replayed**. In particular #200's bit certificate is taken as its
+  author's finite witness; this package does not re-run its checks.
+* The wrapper is PR185's construction, not one built here.
+* Conditional on PR184's finite bridge and closed-form acceptance arithmetic, and
+  on the retained contracts of the pinned suppliers. The full multiplication
+  theorem remains conditional; a finite certificate is not a proof of it.
+* The improvement is small and lives on the `10^-10` selection grid, and it
+  depends on an unmerged bit supplier (#200) and an unmerged complex/assembly line
+  (#193/#194).
+* This is not claimed as a new word, a new all-size hypothesis, or the public
+  record: it is a composition, and it is superseded the moment a lower-`W` bit word
+  appears.
+
+## Reproduce
+
+```bash
+python3 -B research/composed-diagonal-bit-bootstrap/verify.py
+```
+
+`compose.py` performs the pricing; `verify.py` pins every byte against
+`SOURCE.json`, reproduces `certificate.json` from the pins, re-checks the two
+published cross-checks above, requires the claim to beat #197, requires it to sit
+inside one grid step of the word's ceiling, re-derives the leaf tolls in closed
+form, refuses three corruption controls, and re-runs the lever model, requiring it
+to reproduce its three published references *exactly* and to keep its `MODELLED,
+NOT CONSTRUCTED` status. The lever run takes about two seconds; the whole harness
+is under a minute.
+
+```bash
+python3 -B research/composed-diagonal-bit-bootstrap/levers.py
+```
+
+prints the lever table on its own, and
+
+```bash
+python3 -B research/composed-diagonal-bit-bootstrap/audit.py
+```
+
+prints the queue audit against the banked rows the lever predicted, and
+
+```bash
+python3 -B research/composed-diagonal-bit-bootstrap/targets.py
+```
+
+prints the ladder of what each next ledger move on the two suppliers would be worth.
+
+## Credits
+
+Bit supplier: chafreaky (#200, with the #189/#196 lineage). Complex word and
+assembly: icekylinx, GPT-6 Astra and ikeboy (#182/#184/#193/#194). Finite leaf
+wrapper and its recurrence: rohanarun (#185). Paired-cube frame and balanced-prefix
+construction: eumemic (#168 v4). Predecessor notices are retained in
+[NOTICE.md](NOTICE.md). Apache-2.0.
diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json
new file mode 100644
index 0000000000..e013ae3416
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json
@@ -0,0 +1,48 @@
+{
+  "package": "composed-diagonal-bit-bootstrap",
+  "date_utc": "2026-10-09",
+  "claim": {
+    "kappa": "1693287/2500000000",
+    "kappa_decimal": 0.0006773148,
+    "best_depth": 2,
+    "binding": "bit",
+    "standing_claim_pr197": "135216063303877/200000000000000000",
+    "gain_vs_pr197": 0.001826,
+    "pr200_announced_for_this_composition": "6768823/10000000000",
+    "gain_vs_pr200_announced": 0.000639,
+    "bit_branch_ceiling": "6773148336836464/10000000000000000000",
+    "distance_below_ceiling": "3.37e-11",
+    "scope": "Conditional composition. The complex and bit words are the suppliers' certified artifacts, vendored byte-identically and priced here, not rebuilt or replayed. The ordinary leaf is PR185's finite acyclic wrapper, not one built here."
+  },
+  "composition": {
+    "bit": "PR200 certified fixed-coordinate and face-diagonal bit local circuit (chafreaky); m=72, W=20634, rank deficit 1936, 34 terminal sinks, coarse saving 677773948354561/10^18",
+    "complex": "PR193 complex word as carried by PR194 (ikeboy); saving 219037/312500000 = 7.009184e-4",
+    "assembly": "PR194's unchanged 47-constraint balanced assembly (PR168 v4 paired_cube_assembly.py, eumemic)",
+    "leaf": "PR185 finite acyclic ordinary-leaf wrapper (rohanarun), a_{n+1} = (1-C)C + C a_n",
+    "pricing": "PR184 assemble_profiles.py (icekylinx, GPT-6 Astra), carried by PR194",
+    "pinned_source": "PR168 v4 at fd25adb7fbaa12ee761d02c733c54d1d2a7687ee"
+  },
+  "files": {
+    "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76",
+    "research/composed-diagonal-bit-bootstrap/verify.py": "c6e3bd70a69378e1504d59d23507a8fe0642f52bf2d7158f3bdae20318f39a1e",
+    "research/composed-diagonal-bit-bootstrap/targets.py": "9a1ff251249d81b5b28128cbfaf9f14455ebbba48e8a1d8a74af4c93773fba54",
+    "research/composed-diagonal-bit-bootstrap/targets.json": "75677790fac04f3d450916cec989572d8eee2f75edbd674b26f5c491d485ede7",
+    "research/composed-diagonal-bit-bootstrap/audit.py": "fde70ca18e2637acbcb995db490234b17c5f79d53c33f615c238b9ac48e09490",
+    "research/composed-diagonal-bit-bootstrap/audit.json": "74ac7b35c04b081794e52e325420c8d2cdf58c3fe8b646e42de1b68e77987a06",
+    "research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json": "c11fbb9aaa99594afc8d21e33761dc6d1d6c76ce3dbc36d5b64cae872c242f5a",
+    "research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json": "709b6620676e0fd1dfab98b9886443c2d2d9c8f03b0061efa390aadeff0ff718",
+    "research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json": "f4e30cca369fb014b729df870ca3716cc0f1e2297b9f265341492cba85a14aeb",
+    "research/composed-diagonal-bit-bootstrap/levers.py": "80fcccfa7b89e790d9be27d750ee5140d7eadc81d632e70ab4d7d256487b3e7d",
+    "research/composed-diagonal-bit-bootstrap/levers.json": "646f1b8f7a0826b7afd05553d7bc917e5e1a8bc078ec44725ba0760c3029b83b",
+    "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073",
+    "research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b",
+    "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4",
+    "research/composed-diagonal-bit-bootstrap/README.md": "c48996e8e4c03d6389a20b8d60ea5d53cf22fd9acba88231b8f3b65d1b9538f2",
+    "research/composed-diagonal-bit-bootstrap/NOTICE.md": "0069cf9254824f11d144579445e83220a7953a79c5bad6798da2280f75207104",
+    "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de",
+    "research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46",
+    "research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json": "1600b77cb1f41c0f87967f20133eccda5e6c5f215b70361dfd0c49c861248e59",
+    "research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json": "853afa75980e11ce16b333c28311c4f635e84065867c049fda9916c2419091ed"
+  }
+}
diff --git a/research/composed-diagonal-bit-bootstrap/audit.json b/research/composed-diagonal-bit-bootstrap/audit.json
new file mode 100644
index 0000000000..be71904452
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/audit.json
@@ -0,0 +1,94 @@
+{
+ "cheapest_ledger_gain": 0.7657294874951632,
+ "frontier": {
+  "author": "Dugongue",
+  "ceiling": "136731504666219/200136731504666219",
+  "ceiling_decimal": 0.0006831904550366413,
+  "cheapest_ledger": {
+   "ceiling_decimal": 0.0012056987838844984,
+   "children": 184325,
+   "coarse": "1207154248293627/1000000000000000000",
+   "coarse_decimal": 0.001207154248293627
+  },
+  "coarse": "136731504666219/200000000000000000",
+  "edges": 879231,
+  "maxchild": 22,
+  "name": "PR207 coordinated crossover"
+ },
+ "method": "levers.py's model, PR200's vendored enclosure arithmetic, 10^-18 grid",
+ "rows": [
+  {
+   "W": 56402,
+   "author": "rohanarun",
+   "ceiling": "683528191056257/1000683528191056257",
+   "ceiling_decimal": 0.0006830612994018963,
+   "cheapest_ledger": {
+    "ceiling_decimal": 0.0012056987838844984,
+    "children": 184325,
+    "coarse": "1207154248293627/1000000000000000000",
+    "coarse_decimal": 0.001207154248293627
+   },
+   "coarse": "683528191056257/1000000000000000000",
+   "coarse_decimal": 0.000683528191056257,
+   "copies": 1,
+   "deficit": "5808",
+   "edges": 877638,
+   "file": "references/queue/pr205-packed-diagonal-bit.certificate.json",
+   "m": 72,
+   "maxchild": 22,
+   "name": "PR205 packed diagonal bit",
+   "rank_mass": 4055136,
+   "row": "arithmetic.packed_profile",
+   "stated_in_certificate": true
+  },
+  {
+   "W": 56402,
+   "author": "EcmaXp",
+   "ceiling": "683528191056257/1000683528191056257",
+   "ceiling_decimal": 0.0006830612994018963,
+   "cheapest_ledger": {
+    "ceiling_decimal": 0.0012056987838844984,
+    "children": 184325,
+    "coarse": "1207154248293627/1000000000000000000",
+    "coarse_decimal": 0.001207154248293627
+   },
+   "coarse": "683528191056257/1000000000000000000",
+   "coarse_decimal": 0.000683528191056257,
+   "copies": 3,
+   "deficit": "5808",
+   "edges": 877638,
+   "file": "references/queue/pr206-pr200-entrance-banks.certificate.json",
+   "m": 72,
+   "maxchild": 22,
+   "name": "PR206 entrance banks on PR200",
+   "rank_mass": 4055136,
+   "row": "bit.profile",
+   "stated_in_certificate": true
+  },
+  {
+   "W": 56402,
+   "author": "Dugongue",
+   "ceiling": "136731504666219/200136731504666219",
+   "ceiling_decimal": 0.0006831904550366413,
+   "cheapest_ledger": {
+    "ceiling_decimal": 0.0012056987838844984,
+    "children": 184325,
+    "coarse": "1207154248293627/1000000000000000000",
+    "coarse_decimal": 0.001207154248293627
+   },
+   "coarse": "136731504666219/200000000000000000",
+   "coarse_decimal": 0.000683657523331095,
+   "copies": 1,
+   "deficit": "5808",
+   "edges": 879231,
+   "file": "references/queue/pr207-coordinated-crossover.certificate.json",
+   "m": 72,
+   "maxchild": 22,
+   "name": "PR207 coordinated crossover",
+   "rank_mass": 4055136,
+   "row": "bit_profile",
+   "stated_in_certificate": true
+  }
+ ],
+ "status": "MODELLED, NOT CONSTRUCTED: the queue's rows are priced from their authors' certificates and their own stated coarse savings; nothing is built here, and the packed bound is a bound on admissible ledgers, not a construction."
+}
diff --git a/research/composed-diagonal-bit-bootstrap/audit.py b/research/composed-diagonal-bit-bootstrap/audit.py
new file mode 100644
index 0000000000..72acb41dbd
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/audit.py
@@ -0,0 +1,169 @@
+#!/usr/bin/env python3
+"""Price the top of the queue with this package's model, exactly.
+
+`levers.py` turns a certified bit row into the largest `a` on the `10^-18` grid
+whose paid moment is below 1, and `kappa = a/(1+a)` is what the balanced assembly
+reaches on that word once the finite ordinary leaf is bootstrapped. This script
+runs that model over the banked bit rows now in the queue -- #205's packed
+diagonal-bit word, #206's entrance-bank word (the same row) and #207's
+coordinated-crossover word -- and reports, for each, the model's coarse saving
+beside the value the author's own certificate states.
+
+The rows are vendored byte-identically under `references/queue/`; the model
+reproduces every one of them exactly, so a mismatch here would be a real
+disagreement rather than a grid artefact. Each row's ceiling is compared with the
+`10^-18` floor the same word's ledger leaves (`ln(m/22)` per rank-mass unit if the
+residual dirt could be packed at the largest admissible child), which is a bound
+on how much a future schedule change can still buy and not a construction.
+
+    python3 -B audit.py [--out audit.json]
+"""
+import argparse
+import importlib.util
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+GRID = 10 ** 18
+
+# Vendored queue certificates and the priced row inside each.
+SOURCES = [
+    ("PR205 packed diagonal bit", "pr205-packed-diagonal-bit.certificate.json",
+     ("arithmetic", "packed_profile"), "rohanarun"),
+    ("PR206 entrance banks on PR200", "pr206-pr200-entrance-banks.certificate.json",
+     ("bit", "profile"), "EcmaXp"),
+    ("PR207 coordinated crossover", "pr207-coordinated-crossover.certificate.json",
+     ("bit_profile",), "Dugongue"),
+]
+
+
+def module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    loaded = importlib.util.module_from_spec(spec)
+    sys.modules[name] = loaded
+    spec.loader.exec_module(loaded)
+    return loaded
+
+
+def dig(data, keys):
+    for key in keys:
+        data = data[key]
+    return data
+
+
+def copies_row(profile):
+    """The family's three-copy row, whichever form the certificate stores."""
+    m = int(profile["m"])
+    hist_key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram"
+    hist = {int(r): int(n) for r, n in profile[hist_key].items() if n}
+    for key in ("W_per_vertex", "W"):
+        if key in profile:
+            W = Q(str(profile[key]))
+            break
+    for key in ("deficit_per_vertex", "N", "deficit"):
+        if key in profile:
+            D = Q(str(profile[key]))
+            break
+    for copies in (1, 3):
+        w, d = W * copies, D * copies
+        packed = {r: copies * n for r, n in hist.items()}
+        mass = sum(r * n for r, n in packed.items())
+        if w.denominator == 1 and m * w - mass == d:
+            return copies, m, int(w), d, packed
+    raise ValueError("no copy count satisfies the row identity: " + json.dumps(profile)[:200])
+
+
+def cheapest_ledger(m, W, D, maxchild):
+    """The least-paying integral ledger of the same rank mass and largest child.
+
+    Per unit of rank mass a child of rank r costs (m/r)^a/(W*m), which falls as r
+    grows, so filling the mass greedily from the largest admissible rank downwards
+    minimises the paid moment and therefore maximises the coarse saving over all
+    admissible ledgers -- an upper bound on the saving, not an arrangement any
+    schedule has to admit.
+    """
+    mass = m * W - D
+    hist, remaining = {}, mass
+    for rank in range(maxchild, 1, -1):
+        count, remaining = divmod(remaining, rank)
+        if count:
+            hist[rank] = int(count)
+    assert not remaining, "mass must be packable into admissible children"
+    return hist
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--out", type=Path, default=HERE / "audit.json")
+    args = parser.parse_args()
+    if hasattr(sys, "set_int_max_str_digits"):
+        sys.set_int_max_str_digits(0)
+    assert not sys.flags.optimize, "assertions must stay enabled"
+    interval = module("audit_interval_moment", HERE / "references/pr200/interval_moment.py")
+    levers = module("audit_levers", HERE / "levers.py")
+
+    rows, frontier = [], None
+    for name, filename, keys, author in SOURCES:
+        path = HERE / "references/queue" / filename
+        text = path.read_text()
+        profile = dig(json.loads(text), keys)
+        copies, m, W, D, hist = copies_row(profile)
+        mass = sum(r * n for r, n in hist.items())
+        word = levers.row(m, W, D, hist)
+        coarse = levers.certified(interval, word)
+        assert levers.paid_moment(interval, word, coarse)["upper"] < 1 < \
+            levers.paid_moment(interval, word, coarse + Q(1, GRID))["lower"], name
+        ceiling = coarse / (1 + coarse)
+        bound_hist = cheapest_ledger(m, W, D, max(hist))
+        bound = levers.certified(interval, levers.row(m, W, D, bound_hist))
+        rows.append(dict(
+            name=name, author=author, file="references/queue/" + filename,
+            row=".".join(keys), copies=copies, m=m, W=W, deficit=str(D), rank_mass=mass,
+            edges=sum(hist.values()), maxchild=max(hist), coarse=str(coarse),
+            coarse_decimal=float(coarse), ceiling=str(ceiling), ceiling_decimal=float(ceiling),
+            stated_in_certificate=str(coarse) in text,
+            cheapest_ledger=dict(children=sum(bound_hist.values()), coarse=str(bound),
+                                 coarse_decimal=float(bound),
+                                 ceiling_decimal=float(bound / (1 + bound)))))
+        if frontier is None or coarse > Q(frontier["coarse"]):
+            frontier = rows[-1]
+
+    out = dict(
+        status="MODELLED, NOT CONSTRUCTED: the queue's rows are priced from their authors' "
+               "certificates and their own stated coarse savings; nothing is built here, and "
+               "the packed bound is a bound on admissible ledgers, not a construction.",
+        method="levers.py's model, PR200's vendored enclosure arithmetic, 10^-18 grid",
+        rows=rows,
+        frontier=dict(name=frontier["name"], author=frontier["author"],
+                      coarse=frontier["coarse"], ceiling=frontier["ceiling"],
+                      ceiling_decimal=frontier["ceiling_decimal"],
+                      edges=frontier["edges"], maxchild=frontier["maxchild"],
+                      cheapest_ledger=frontier["cheapest_ledger"]),
+        cheapest_ledger_gain=float(Q(frontier["cheapest_ledger"]["coarse"]) / Q(frontier["coarse"]) - 1),
+    )
+    args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n")
+
+    for item in rows:
+        print("[{stated}] {name} ({author}): W={W} D={deficit} mass={rank_mass} edges={edges} "
+              "maxchild={maxchild}".format(
+                  stated="stated" if item["stated_in_certificate"] else "UNSTATED", **item))
+        print("        model coarse = {coarse} = {coarse_decimal:.15g}; ceiling kappa = "
+              "{ceiling} = {ceiling_decimal:.15g}".format(**item))
+    print("[frontier] {name}: coarse {coarse} -> kappa ceiling {ceiling}".format(**frontier))
+    bound = frontier["cheapest_ledger"]
+    print("[bounds] the frontier's ledger has {edges} children down to rank 1; the cheapest "
+          "admissible ledger of the same stock, deficit and rank mass has {children} from rank "
+          "{maxchild} downwards and would lift its coarse saving {gain:.4f}%, from {now} to "
+          "{coarse} (ceiling kappa {ceiling:.15g}). That bounds what a better schedule can still "
+          "buy and is not a construction.".format(
+              edges=frontier["edges"], now=frontier["coarse_decimal"],
+              children=bound["children"], maxchild=frontier["maxchild"],
+              gain=out["cheapest_ledger_gain"] * 100, coarse=bound["coarse"],
+              ceiling=bound["ceiling_decimal"]))
+    print("[write] " + str(args.out))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/composed-diagonal-bit-bootstrap/certificate.json b/research/composed-diagonal-bit-bootstrap/certificate.json
new file mode 100644
index 0000000000..e72fb933d9
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/certificate.json
@@ -0,0 +1,179 @@
+{
+ "assembly": {
+  "margin_count": 7,
+  "pr168_v4_assembly_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "pr184": "assemble_profiles.py",
+  "pr184_sha256": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de",
+  "strict_constraint_count": 47
+ },
+ "bit_coarse_saving": "6777739/10000000000",
+ "bit_supplier": {
+  "W_per_vertex": 20634,
+  "deficit_per_vertex": 1936,
+  "m": 72,
+  "profile": {
+   "R": 17114,
+   "W_per_vertex": 20634,
+   "active_virtual_R": 18874,
+   "changed_operation_frames": 7282,
+   "child_histogram": {
+    "1": 125772,
+    "10": 2022,
+    "11": 1212,
+    "12": 4062,
+    "13": 1626,
+    "14": 3672,
+    "15": 864,
+    "16": 2988,
+    "17": 1356,
+    "18": 1614,
+    "19": 648,
+    "2": 58654,
+    "20": 5280,
+    "21": 15018,
+    "22": 6672,
+    "3": 30930,
+    "4": 9588,
+    "5": 8070,
+    "6": 4152,
+    "60": 2200,
+    "7": 4080,
+    "8": 2514,
+    "9": 1752
+   },
+   "deficit_per_vertex": 1936,
+   "foreign_producer_replays": 0,
+   "frames_not_contained_in_original": 84,
+   "h": 24,
+   "loss": 528,
+   "m": 72,
+   "maxchild": 60,
+   "physical_internal_histogram": {
+    "1": 35764,
+    "10": 674,
+    "11": 404,
+    "12": 1354,
+    "13": 542,
+    "14": 1207,
+    "15": 288,
+    "16": 993,
+    "17": 452,
+    "18": 533,
+    "19": 208,
+    "2": 17469,
+    "21": 4160,
+    "22": 1344,
+    "3": 10301,
+    "4": 3196,
+    "5": 2673,
+    "6": 1384,
+    "7": 1359,
+    "8": 838,
+    "9": 583
+   },
+   "physical_target_histogram": {
+    "1": 4400,
+    "14": 17,
+    "16": 3,
+    "18": 5,
+    "19": 8,
+    "2": 29,
+    "20": 880,
+    "21": 846,
+    "3": 9,
+    "5": 17,
+    "7": 1,
+    "9": 1
+   },
+   "rank_per_vertex": 1483712,
+   "reused_registers": 1760,
+   "scalar_role_reserve": 18908,
+   "selected_rank_histogram": {
+    "20": 2200
+   },
+   "selected_roles": 2200,
+   "terminal_sinks": 34,
+   "v": 1760,
+   "virtual_R": 18908
+  },
+  "sha256": "853afa75980e11ce16b333c28311c4f635e84065867c049fda9916c2419091ed",
+  "source": "pr200-bit-certificate.json",
+  "terminal_sinks": 34
+ },
+ "ceiling": "6777739/10006777739",
+ "ceiling_decimal": 0.0006773148336836464,
+ "claim": {
+  "best_depth": 2,
+  "binding": "bit",
+  "gain_vs_pr197": 0.001825942052225986,
+  "gain_vs_pr200_announced_legacy": 0.0006389589445609672,
+  "kappa": "1693287/2500000000",
+  "kappa_decimal": 0.0006773148
+ },
+ "comparisons": {
+  "pr194_published": "1668581/2500000000",
+  "pr197_published": "135216063303877/200000000000000000",
+  "pr200_announced_legacy": "6768823/10000000000"
+ },
+ "complex_supplier": {
+  "published_kappa": "1668581/2500000000",
+  "saving": "219037/312500000",
+  "sha256": "1600b77cb1f41c0f87967f20133eccda5e6c5f215b70361dfd0c49c861248e59",
+  "source": "certificate.json"
+ },
+ "depths": {
+  "0": {
+   "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+   "binding": "bit",
+   "kappa": "6768823/10000000000",
+   "kappa_decimal": 0.0006768823,
+   "leaf": "338670433250477381/500000000000000000000",
+   "leaf_decimal": 0.0006773408665009548,
+   "minimum_margin": "564450705150607418699608700159127/833897784044128447859984087300000000",
+   "minimum_margin_decimal": 0.0006768823661015241
+  },
+  "1": {
+   "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+   "binding": "bit",
+   "kappa": "1354629/2000000000",
+   "kappa_decimal": 0.0006773145,
+   "leaf": "3388868032505982607313821559/5000000000000000000000000000000",
+   "leaf_decimal": 0.0006777736065011965,
+   "minimum_margin": "5648113218066570516513249734636457821273853/8338981446607881036595323615687872614700000000",
+   "minimum_margin_decimal": 0.0006773145202720294
+  },
+  "2": {
+   "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+   "binding": "bit",
+   "kappa": "1693287/2500000000",
+   "kappa_decimal": 0.0006773148,
+   "leaf": "33888694990053708566050912573619475101/50000000000000000000000000000000000000000",
+   "leaf_decimal": 0.0006777738998010741,
+   "minimum_margin": "56481156622321442736964422671389685170997102823158367/83389814490520466347941627902087668706047684163300000000",
+   "minimum_margin_decimal": 0.0006773148131747202
+  },
+  "3": {
+   "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+   "binding": "bit",
+   "kappa": "1693287/2500000000",
+   "kappa_decimal": 0.0006773148,
+   "leaf": "338886949999932586632642757346135811087551576639/500000000000000000000000000000000000000000000000000",
+   "leaf_decimal": 0.0006777738999998652,
+   "minimum_margin": "564811566388873590686758597255617362053381188732691530567192213/833898144905370322644389985041155467773608058924813280778700000000",
+   "minimum_margin_decimal": 0.000677314813373242
+  },
+  "8": {
+   "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+   "binding": "bit",
+   "kappa": "1693287/2500000000",
+   "kappa_decimal": 0.0006773148,
+   "leaf": "33888694999999999999999999999035793121769166659567411393981444370015282231565601126323952500698661/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+   "leaf_decimal": 0.0006777739,
+   "minimum_margin": "773714474505460200404999999977986144993045041407557898648229097352836299712237629735442123837906649402526715519/1142326225897767719178082191780799903952992084571328403611932265216675488466467122294406665067904557328448100000000",
+   "minimum_margin_decimal": 0.0006773148133733766
+  }
+ },
+ "legacy_leaf": "338670433250477381/500000000000000000000",
+ "old_leaf": "384599/10000000000",
+ "scope": "Conditional composition: the physical complex and bit words are the suppliers' certified artifacts, vendored and priced, not rebuilt or replayed. The finite leaf wrapper is PR185's construction, not one built here."
+}
diff --git a/research/composed-diagonal-bit-bootstrap/compose.py b/research/composed-diagonal-bit-bootstrap/compose.py
new file mode 100644
index 0000000000..5241ceb119
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/compose.py
@@ -0,0 +1,196 @@
+#!/usr/bin/env python3
+"""Compose a certified bit supplier with PR184's finite leaf and PR194's complex.
+
+The record's assembly sets
+
+    a = min(bit_effective, (1-stop)*complex_saving - 1/SELECT_GRID),
+    kappa = floor( (1-eta)*q/(1+q) * SELECT_GRID ) / SELECT_GRID,  q = a*(1-2*eta),
+
+with the case-dependent `eta`, `stop` of PR184's `assemble_profiles.py`. Every bit
+supplier published so far has been handed to it through PR184's *legacy* ordinary
+leaf, `effective = (1-beta)*C + beta*OLD` with `OLD = 384599/10^10`, which holds
+the effective value strictly below the supplier's coarse saving `C`. PR185
+replaced that leaf by a finite acyclic wrapper whose value obeys
+
+    a_0 = legacy effective,   a_{n+1} = (1-C)*C + C*a_n = C - C^n (C - a_0).
+
+This script applies that recurrence to an arbitrary certified bit profile,
+composes it with a certified complex profile through PR194's unchanged assembly,
+and reports the exact kappa at each depth together with the bit branch's own
+ceiling `C/(1+C)`.
+
+    python3 -B compose.py [--out certificate.json]
+
+Inputs, digests and provenance are in SOURCE.json; the paths below are the
+vendored pins, so this runs from the package directory alone.
+"""
+import argparse
+import hashlib
+import importlib.util
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+SELECT_GRID = 10 ** 10
+OLD = Q(384599, SELECT_GRID)
+DEFAULTS = dict(
+    bit=HERE / "inputs/pr200-bit-certificate.json",
+    complex=HERE / "references/pr194/certificate.json",
+    pr184=HERE / "references/pr184/assemble_profiles.py",
+    pr168_v4=HERE / "references/pr168-v4",
+    finite_bridge=HERE / "references/pr184/FINITE_BRIDGE.txt",
+)
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+def digest(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def bit_profile(certificate):
+    """The bit profile block of a supplier certificate."""
+    node = certificate["bit"]["profile"] if "bit" in certificate else certificate
+    for key in ("m", "W_per_vertex", "deficit_per_vertex", "child_histogram"):
+        assert key in node, "bit profile lacks " + key
+    return node
+
+
+def complex_profile(certificate):
+    if "complex_profile" in certificate:
+        return certificate["complex_profile"]
+    if "combined_fixed_boundary_profile" in certificate:
+        return certificate["combined_fixed_boundary_profile"]
+    if "complex" in certificate and "profile" in certificate["complex"]:
+        return certificate["complex"]["profile"]
+    raise SystemExit("complex profile not found in the complex certificate")
+
+
+def bootstrap_chain(coarse, initial, depth):
+    values = [initial]
+    for _ in range(depth):
+        values.append((1 - coarse) * coarse + coarse * values[-1])
+    assert values[-1] == coarse - coarse ** depth * (coarse - initial)
+    return values
+
+
+def price(pr184, complex_row, bit_row, coarse, chain, work):
+    """Assemble one bootstrapped leaf, returning the exact record row."""
+    leaf = chain[-1]
+    assert chain[0] == bit_row["effective_saving"]
+    if len(chain) > 1:
+        assert chain[0] < leaf < coarse < 1 - leaf
+    boot = dict(bit_row)
+    boot.update(effective_saving=leaf, effective_saving_decimal=float(leaf),
+                ordinary_leaf_saving=leaf, atom_exponent=coarse)
+    out = pr184.assemble(complex_row, boot, work["pr168_v4"], work["finite_bridge"])
+    assembly = out["assembly"]
+    assert len(assembly["strict_constraints"]) == 47, "strict constraints"
+    assert len(assembly["margins"]) == 7, "margins"
+    assert all(Q(v) > 0 for v in assembly["strict_constraints"].values())
+    kappa = Q(out["kappa"])
+    assert all(Q(v) > kappa for v in assembly["margins"].values())
+    margin = Q(assembly["minimum_margin"])
+    assert 0 < margin <= coarse / (1 + coarse), "the bit branch ceiling"
+    assert kappa <= margin < kappa + Q(1, SELECT_GRID), "kappa is the last grid point"
+    return dict(leaf=str(leaf), leaf_decimal=float(leaf), kappa=str(kappa),
+                kappa_decimal=float(kappa),
+                minimum_margin=str(assembly["minimum_margin"]),
+                minimum_margin_decimal=float(assembly["minimum_margin"]),
+                binding="bit" if coarse <= complex_row["saving"] else "complex",
+                assembly_source_sha256=out["assembly_source_sha256"])
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--bit-certificate", type=Path, default=DEFAULTS["bit"])
+    parser.add_argument("--complex-certificate", type=Path, default=DEFAULTS["complex"])
+    parser.add_argument("--pr184", type=Path, default=DEFAULTS["pr184"])
+    parser.add_argument("--pr168-v4", type=Path, default=DEFAULTS["pr168_v4"])
+    parser.add_argument("--finite-bridge", type=Path, default=DEFAULTS["finite_bridge"])
+    parser.add_argument("--depths", type=int, nargs="+", default=[0, 1, 2, 3, 8])
+    parser.add_argument("--out", type=Path, default=HERE / "certificate.json")
+    args = parser.parse_args()
+    if hasattr(sys, "set_int_max_str_digits"):
+        sys.set_int_max_str_digits(0)
+    assert not sys.flags.optimize, "assertions must stay enabled"
+    pr184 = load(args.pr184.resolve(), "composed_pr184")
+    work = dict(pr168_v4=args.pr168_v4.resolve(), finite_bridge=args.finite_bridge.resolve())
+    assert (work["pr168_v4"] / "scripts/paired_cube_assembly.py").is_file(), "assembly pin"
+    assert work["finite_bridge"].is_file(), "finite bridge pin"
+
+    bit_cert = json.loads(args.bit_certificate.read_text())
+    complex_cert = json.loads(args.complex_certificate.read_text())
+    row = bit_profile(bit_cert)
+    complex_row = pr184.select(pr184.normalize(complex_profile(complex_cert)))
+    bit_row = pr184.select(pr184.normalize(row), True)
+    coarse, initial = Q(bit_row["saving"]), Q(bit_row["effective_saving"])
+    assert initial < coarse, "the legacy leaf must sit below the coarse saving"
+    print(f"[bit supplier] m={row['m']} W={row['W_per_vertex']} "
+          f"deficit={row['deficit_per_vertex']} sinks={row.get('terminal_sinks')} "
+          f"coarse={coarse} ({float(coarse):.15g}) "
+          f"legacy leaf={initial} ({float(initial):.15g})")
+    print(f"[complex] saving={complex_row['saving']} "
+          f"({float(complex_row['saving']):.15g})")
+
+    rows = {}
+    for depth in args.depths:
+        chain = bootstrap_chain(coarse, initial, depth)
+        rows[str(depth)] = price(pr184, complex_row, bit_row, coarse, chain, work)
+        print(f"[depth {depth}] leaf={rows[str(depth)]['leaf_decimal']:.15g} "
+              f"kappa={rows[str(depth)]['kappa']} "
+              f"({rows[str(depth)]['kappa_decimal']:.15g}) "
+              f"[47 strict constraints, 7 margins, binding {rows[str(depth)]['binding']}]")
+
+    ceiling = coarse / (1 + coarse)
+    best_depth = max(rows, key=lambda d: rows[d]["kappa_decimal"])
+    best = Q(rows[best_depth]["kappa"])
+    assert best <= ceiling, "kappa cannot exceed the bit branch ceiling"
+    print(f"[bit ceiling] C/(1+C) = {float(ceiling):.15g}; best depth {best_depth} sits "
+          f"{float(ceiling - best):.3g} below it (grid {1 / SELECT_GRID:.1g})")
+    for name, value in (("#197 packed bit", Q(135216063303877, 200000000000000000)),
+                        ("#200 legacy, announced", Q(6768823, SELECT_GRID))):
+        print(f"[comparison] vs {name}: {float(best / value - 1) * 100:+.4f}%")
+    comparisons = {
+        "pr197_published": str(Q(135216063303877, 200000000000000000)),
+        "pr200_announced_legacy": str(Q(6768823, SELECT_GRID)),
+        "pr194_published": str(Q(complex_cert["kappa"])) if "kappa" in complex_cert else None,
+    }
+    out = dict(
+        claim=dict(kappa=str(best), kappa_decimal=float(best), best_depth=int(best_depth),
+                   binding=rows[best_depth]["binding"],
+                   gain_vs_pr197=float(best / Q(comparisons["pr197_published"]) - 1),
+                   gain_vs_pr200_announced_legacy=float(
+                       best / Q(comparisons["pr200_announced_legacy"]) - 1)),
+        bit_supplier=dict(source=args.bit_certificate.name, sha256=digest(args.bit_certificate),
+                          m=row["m"], W_per_vertex=row["W_per_vertex"],
+                          deficit_per_vertex=row["deficit_per_vertex"],
+                          terminal_sinks=row.get("terminal_sinks"),
+                          profile=row),
+        complex_supplier=dict(source=args.complex_certificate.name,
+                              sha256=digest(args.complex_certificate),
+                              saving=str(complex_row["saving"]),
+                              published_kappa=complex_cert.get("kappa")),
+        assembly=dict(pr184=args.pr184.name, pr184_sha256=digest(args.pr184),
+                      pr168_v4_assembly_sha256=rows[best_depth]["assembly_source_sha256"],
+                      strict_constraint_count=47, margin_count=7),
+        bit_coarse_saving=str(coarse), legacy_leaf=str(initial), old_leaf=str(OLD),
+        ceiling=str(ceiling), ceiling_decimal=float(ceiling),
+        depths=rows, comparisons={k: v for k, v in comparisons.items() if v},
+        scope=("Conditional composition: the physical complex and bit words are the suppliers' "
+               "certified artifacts, vendored and priced, not rebuilt or replayed. The finite "
+               "leaf wrapper is PR185's construction, not one built here."))
+    args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n")
+    print(f"[write] {args.out}")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json b/research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json
new file mode 100644
index 0000000000..7b80d2cd04
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json
@@ -0,0 +1,4442 @@
+{
+  "arithmetic": {
+    "actual_uniform_bit_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000",
+    "adverse_control_count": 21,
+    "adverse_controls": [
+      "full group stock replaced by local W",
+      "old ordinary reserve omitted",
+      "conservative old coarse reserve omitted",
+      "uniform supplier replaced by fictional finite profile",
+      "actual ordinary saving overstated",
+      "unpaid previous atom grid",
+      "scalar role reserve collapsed to physical stock",
+      "terminal removals omitted",
+      "terminal removals counted as aliases",
+      "odd divisor silently changed to 21",
+      "C0 detached from scalar charge",
+      "scalar group charge omitted",
+      "stale total row coefficient",
+      "inadequate polynomial row degree",
+      "float in otherwise unused metadata",
+      "noncontracting maximum child",
+      "transfer saving exceeds actual uniform supplier",
+      "old prefix charged at balanced parameters",
+      "old nonlinear scalar guard",
+      "old separate movement exposures",
+      "next final 1e-18 kappa grid point"
+    ],
+    "assembly": {
+      "absorption_gap": "14997626888680345751524011177060836353630220354194253091514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+      "constraints": {
+        "K_dominates_log": "332744409924090075910047758473270852729147270729394494318848181151818847514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+        "K_geometry": "375332369410299089700910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+        "a_below_b": "666489485337/1000000000000000000000000000000000000000",
+        "a_positive": "665489485336999999999999333510514663/1000000000000000000000000000000000000000",
+        "alpha_below_one": "999999000000999999000000500332244410424089575910423090842681151818848181152485337/1000664488820848179151820846181685362303637696362304970674000000000000000000000000",
+        "alpha_below_one_fourth": "249500633385363864636134865695980388696361303638694362837181151818848181152485337/1000664488820848179151820846181685362303637696362304970674000000000000000000000000",
+        "alpha_positive": "665488819848180151820345849440951879548120451881879831318848181151818847514663/1000664488820848179151820846181685362303637696362304970674000000000000000000000000",
+        "artificial_boundary": "28021267642263141736858268578810664824988675011325028334096043455456544543457456011/4002657955283392716607283384726741449214550785449219882696000000000000000000000000",
+        "b_below_one_over32": "30584510514663/1000000000000000",
+        "beta_below_one": "999999999999999999999999/1000000000000000000000000",
+        "beta_positive": "1/1000000000000000000000000",
+        "c_below_one": "499667255257331499999999875998734228005499999999999333510514663/500000000000000000000000000000000000000000000000000000000000000",
+        "c_positive": "332744742668500000000124001265771994500000000000666489485337/500000000000000000000000000000000000000000000000000000000000000",
+        "cell_above_band": "999999000000999998999999499667755589575910424089576909157318848181151818847514663/2001328977641696358303641692363370724607275392724609941348000000000000000000000000",
+        "compact_leaf": "665989485336999999999999333510514663/500000000000000000000000000000000000000000000000000000000000000",
+        "compact_reservations": "1/4000000000000000000000000",
+        "delta_below_one_eighth": "999999999999999999999999/8000000000000000000000000",
+        "delta_positive": "1/8000000000000000000000000",
+        "epsilon_below_one": "332744409924090075910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337",
+        "epsilon_positive": "499999500000499999500000000000000000000000000000000000000/500332244410424089575910423090842681151818848181152485337",
+        "g1_above_kappa": "3749531805231189043903396771870981799077843043260608561/125083061102606022393977605772710670287954712045288121334250000000000000000",
+        "g2_above_kappa": "442581721611999999999333510514663/1000000000000000000000000000000000000000",
+        "g3_above_kappa": "14997626888680345751524011177060836353630220354194253091514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+        "g4_above_kappa": "442581721611999999999333510514663/1000000000000000000000000000000000000000",
+        "g5_above_kappa": "23996503221235199456892163429551192671417043658019713637914663/800531591056678543321456676945348289842910157089843976539200000000000000000000000",
+        "g6_above_kappa": "119984517435153638980819120789448326727809825565491292799514663/4002657955283392716607283384726741449214550785449219882696000000000000000000000000",
+        "g7_above_kappa": "124916688897643977359771926032520518755948684726582860464827843043260608561/125083061102606022393977605772710670287954712045288121334250000000000000000",
+        "gamma_sublinear": "1/2000000000000000000000000",
+        "guard_width": "332744409924090075910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337",
+        "lambda_above_internal": "665489485336999999999999333510514663/1000000000000000000000000000000000000000000000000000000000000000",
+        "lambda_above_sigma": "1331978970673999999999999333510514663/1000000000000000000000000000000000000000000000000000000000000000",
+        "lambda_above_tau": "665489485336999999999999333510514663/1000000000000000000000000000000000000000000000000000000000000000",
+        "lambda_prime_above_lambda": "665489485336999999999999333510514663/1000000000000000000000000000000000000000000000000000000000000000",
+        "lambda_prime_below_one": "332744742668499999999999001265771994500000000000666489485337/500000000000000000000000000000000000000000000000000000000000000",
+        "literal_scalar_guard": "509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958818702829502585997812817559838763217783761780815134208631567717608018059301315067371926511435348937465810150744857799701522933317848371746274664033617476918199594067571243885651973555695593567897075036053913610249688897833282392816118005417458311224552598193160724565639148198763926396999695322462352982172673041255273367390517877675018181416138131654157433145797566561571462080965302898971443224325448151480478852006707573949077455172190063821451121090553857496062012376496102432932175398975958582052864383021374276627211771861123936251717736056801099584173304015650037766334278465741666772447153476298319676650156742380759982873343628991583889160812395484812889479623639637823045921293747387151213038133296304197187084414029355988745577433003360412082672554615377645724023287789044317516401542458078885444095561309764671780262478190934976125951505776827467212014643315053620078496638852562666282809987933208858648963094003228267991465468374067265061091652356791697164040972108962644440382988714131067012956918181123928885161908576947285402845544719409569801609648454943715419276985373795631635707090621395949357820437851729053270669403634782027388584542611815295760149838761009868291724840684414188155734679475207735783679273769763473701738939668178856087086524816531138104478472236352608710925874537462501665283906301456130281965042870002258943395688284553941621276179274035975696647087128868584662050536433638146347949287745234051870320643465641321123110496544453655544611858697128405140908714616669861095840467793479837787172361340311454735592349573073211191537014694638020982562532441624561645841002709514764852596724315250746048100013260104734590560285867119496339992799455894563812239458620579186335358804163156130414792801261054657666632747257535272567004783176044412619627596742610260714843215831767764036606670883123125337230204580538675192418384516567811635659681279617205173849000987983515395921851500467905707385303894258706134476144823451794499924560650568574735123852061185655043447829185676484621147830683389132204954040195027621664363048962803080054711406238761342281629204048640916135742735179726733294002487656491205203332917292149406134871821555187620588222021290082649111437261157691118607599552069686192748342830795035798514316005678570500029172404584032753876182332976274268255035392796688629221491625758906880678986446598999586214090227846821932509805525220257179652168800741511218990946334029126975787096252045648697692552669418220127721565538575180854820894922690246846847920004701910159575922752993839219316039516708009717078594550310972897979764145885892134560577089331088861141224814361879101764073201203019476334326618680082071605324546080305056691646068960988600124395621134785432285131790032415257453943194082004110407243319321545933846090011825389074175300514026423510516067996102155000988805501584416251567601995828581028194272281201484016859904354221118590554724294482421722378388630417876366803777883012593614028210823218674722313016294450404100510769975879434934692964069001919304089155168979467748883735785548948820125670866759122901792082248564105765298665207413578529677136622712062882670538812925542030722078443525568555457259310348308177887077895761740202907362065008303287086593963360800785218987612370694670532209479466620",
+        "phase_boundary": "532391055878544121456176613103879418820581179420885696518848181151818847514663/800531591056678543321456676945348289842910157089843976539200000000000000000000000",
+        "phase_leaf_above_bit": "1/1000000000000000000000000000000",
+        "phase_local": "2661955279392720607282884394497038790461209538796791853318848181151818847514663/4002657955283392716607283384726741449214550785449219882696000000000000000000000000",
+        "prime_interval_packing": "332744409924090075910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337",
+        "q_below_internal": "665489485336999999999999333510514663/500000000000000000000000000000000000000000000000000000000000000",
+        "q_below_leaf": "665989485336999999999999333510514663/500000000000000000000000000000000000000000000000000000000000000",
+        "q_below_reservations": "1/4000000000000000000000000",
+        "q_positive": "332744742668499999999999001265771994500000000000666489485337/500000000000000000000000000000000000000000000000000000000000000",
+        "record_suffix": "332744409924090075910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337",
+        "row_product_gap": "224336/5",
+        "short_record_fallback": "499666534152669800277630220919410241257932289343717793173019220789505365485712458495775569003569/500332244410424089575910423090842681151818848181152485337000000000000000000000000000000000000000",
+        "small_field_exposure": "1/1000000000000000000000000"
+      },
+      "finite_bridge": {
+        "bit_uniform": {
+          "atom_beta": "677340914792209011107/1000000000000000000000000",
+          "coarse_saving": "677773948354561/1000000000000000000",
+          "old_atom_saving": "384599/10000000000",
+          "ordinary_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000"
+        },
+        "complex": {
+          "N": 4654170104423616554638164010272346091525338318081434624560713222756608378117397252400210666893081203396713814484336655024295069388921657147689634172725410447265943921080212832355099015801402340613368718684202796799353461392938077263755994129846605291547841283152950671461912870176687371031035766533157124388121683525968364849356178820541530477519547795337690304275736560189911727771655301087339514594924221793976288076428017850160362677522178019873965242784165001200605555445206166283124908285904680927159554862606796638919933387986940007180948084528616254659211856188901000183131972799431806345252217217039855354854231386567475200000000000000000000,
+          "W": 46411243245854594476289509747890069396021233546140851487191415266019118243302500025260585612358809000235563590952517719761209089671496797753817162587564074028304257449377910236583460867419590158707403366697091980507492130541851447744560720250887019282306238492532037642767544780405860503698124087027232748727913424433576959478844986223324367936052884568204558693319333592257430358074468733494431841373475402631901424204562120425500646912291234299697730674824215083942099186610036944533919066490426753821364561103403987998562941807630372207971833058068314969756973987132199898038307695423424899183753738809011830330262308894990663680000000000000000000,
+          "auxiliary_banks_after_sharing": 1,
+          "coefficient_bound": 26,
+          "coefficient_denominator_divides": 6,
+          "finite_group_router_upper": 1996781817829700505616648003442939670418121383146524832570562414229508517707365630210514410182868208422410426904222349614587120238169565023976593617888088249792889489232587391937114692862833413493878289150647220476973315936613893411371180627349937542747113703441878702871183764108427647246946738280116413202842001601611935577871928896078779222167053557763264184774765184286697868594594314095298375974619020411589760327871072912207011987279157835478300764863885862339514331188591889499931217751046333516074072899497781599216540489370635260835475068278948606593058144659269465953575864037220363386543007930389392650517576506725609273702290538744026324349048797544741931656448511039048822918393059436367372870428114118151808835454194697189172420675444159767607388539974249475729974744313867010877267947494917728324863231728827375097796764153590288328124290854313749034205788857188501097735018015334913812524031309584653511523390713673282151437254342444210331261975595018327204309097452847220268408585326212873150162975484878379620431963947109952968805006023852879520661180163026847720913903900327535082362352341970633278958844785634739058314191225917327628660919631334932181528624365834466594963958416015205875189155986400578676067745563136371392891175778031142494596567179094957992104382032540770219035244465619000829903097000075849583777272674623120007677063732581105732175038816041801105187366687892006322408874222540820191910326456749466829784102697616089009779807971524806980914181559704507613893357294407429708218298288807124701683600890622569213909248073265415355774627205317949186017722026285024353652225922915093100135743357732801132024782406130188987430338256239146124855199854334018599841017758087085872468293679789085826036881023401376565779696277800538708125495766714490405278954114302254259077986737997610651303475214846690409557531207945110471168522019985895615486336976041255809567024577951775285455773833308076711628905615556366827520000000000019248832,
+          "halving_degree": 1,
+          "invocations_per_stage": 3525886442745164056544063644145716736004044180364723200424782744512582104634391857878947474919000911664177132185103526533556870749183073596734571342973795793383290849303191539662953799849547227737400544457729391514661713176468240351330298583217125220869576729661326266259024901649005584114421035252391760900092184489369973370724377894349644301151172572225522957784648909234781611948223712944954177723427440753012339451839407462242698998122862136268155486957700758485307238973641035062973415368109606762999662774702118665848434384838590914531021276158042617166069588021894697108433312726842277534281982740181708602162296504975360000000000000000000,
+          "local_group_upper": 4552920126520,
+          "logical_group_upper": 48159262409601395467011635701100464832021030569677306175574358095765057248609523233731783063748587071783641348524556567732110852316854063265394354994194196235424254850312119215110537754435839555650149484077504564925881450138377028493433797993315174068073699814547634599867538980931684612010193186301768649845766678767978197392725197692362495088218829833738197421152595019362494884184045934416310722881634052266915958468750757416790961147082161549540715124877340344041143854505135550740971547919140073694734890777732207707027340740665870005216626365456712348847469693004375422271610757332987355192878777460512903919380631891708932219994112000000000000000000000,
+          "m": 66,
+          "maxchild": 20,
+          "original_X_involution_scalar_group_upper": 42240,
+          "physical_roles_per_vertex": 10523,
+          "reuse_pairs": 2310,
+          "s": 3058487884121979618880469479350472234045876075727214763530072694334505195679847604414798439748788312812150483188381832849215504848929866994604243096606503475420815047737861862782153318233891548134075253483323867916695127154369257473877251542428696667340663899223961533751196042636610105873045153977264204291654164329090110960754412911918866753301970833706163183454800280528800491905143281109545162016054452351911517709424671930232882333533699285760176259295614030538977940760817232172955533480082261071282901477962056411266234225915617625718960033747980171749301071294536292270345175925146611539782494544177740946442458155682816327680000000000000000000,
+          "scalar_group_upper": 1996781817829700505616648003442939670418121383146524832570562414229508517707365630210514410182868208422410426904222349614587120238169565023976593617888088249792889489232587391937114692862833413493878289150647220476973315936613893411371180627349937542747113703441878702871183764108427647246946738280116413202842001601611935577871928896078779222167053557763264184774765184286697868594594314095298375974619020411589760327871072912207011987279157835478300764863885862339514331188591889499931217751046333516074072899497781599216540489370635260835475068278948606593058144659269465953575864037220363386543007930389392650517576506725609273702290538744026324349048797544741931656448511039048822918393059436367372870428114118151808835454194697189172420675444159767607388539974249475729974744313867010877267947494917728324863231728827375097796764153590288328124290854313749034205788857188501097735018015334913812524031309584653511523390713673282151437254342444210331261975595018327204309097452847220268408585326212873150162975484878379620431963947109952968805006023852879520661180163026847720913903900327535082362352341970633278958844785634739058314191225917327628660919631334932181528624365834466594963958416015205875189155986400578676067745563136371392891175778031142494596567179094957992104382032540770219035244465619000829903097000075849583777272674623120007677063732581105732175038816041801105187366687892006322408874222540820191910326456749466829784102697616089009779807971524806980914181559704507613893357294407429708218298288807124701683600890622569213909248073265415355774627205317949186017722026285024353652225922915093100135743357732801132024782406130188987430338256239146124855199854334018599841017758087085872468293679789085826036881023401376565779696277800538708125495766714490405278954114302254259077986737997610651303475214846690409557531207945110471168522019985895615486336976041255809567024577951775285455773833308076711628905615556366827520000000000019248832,
+          "scalar_role_reserve": 12877,
+          "stages": 3,
+          "terminal_sinks": 44,
+          "wire_bits": 2159
+        },
+        "conservative_old_coarse_row_reserve": 9909,
+        "ordinary_leaf_row_degree": 252,
+        "rows": {
+          "coefficient": 12320,
+          "complex_coefficient": 2159,
+          "degree": 70000,
+          "degree_gap": "224336/5",
+          "suffix_slope": 280000
+        },
+        "semantic": {
+          "B": 509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958827304979549775015204660589628049382048159414088886350824139990951695623597455357585789947338756567246855082520379894803970478190080646374725907170600630937374638930370439244376137186931258502092725378890309112445759411478982597831480340925427115998851341292624150119598026644913815467329847434859878041023321026286574843080294022586123425055138651176542718649119075352633419372782791056476906418755435875482741999289270330175685831019358074044683575519364870537110698987378534156423412338368608215994716567771341264691784835620547116095154355823028405037678909536409294936241998064726276240916495855446538713390953917957332894522343859649425558894465528489251474045892119196192790538905119006865260569920159851539352630884411410684543010286411452690005269956873208792508595460908096781391701546463223346195916242564759714955799308966368742627228715461007712659326066236176298406802374308370970686396733236368702340191602509189940399556599714483690088244922651769301641228957332097529146753350021208820702940922157812928490776979272693871844477852319948601242412475069333766783326317417323451865061419628384583210851906090081837589052178712760888235589716528403027031568288437989490163340454913038153349106568531093828746761822382576908672736654271400044763829558214085414340795118674219525044565554958311699780729788995435250081345623470348243544594512672750920229723181348286851358440615607637394658415712783369231357282393690924650482720908188916779881724305476435285671169289604569420907232698282421856982026379712178193610758794079671443090170499840417046551812624329535152282424714022599419754331072196960476616795026403529285824410798217390317086027514688112288530970330509440091515683875928181551063423447893048491177211466119814349423907836888314559662032261555442354347785163113771451383175688798034527042538116399087831616488919004322119167912666265947346004223385757910827157266993723507556830481294342030677452635331455842755200417108167627732222635125802616945528741084596401279157096363540269571573594558215964221481961827180791443114180273766962657973492642630980698679516137989730279605879551135389988039469081618481067485985149309898196042198234371393482956069508355575669945213783147520197065586627742035457497165537741506100395483926269734486532538090154077823377395228805741722431419949702460659538988049212462045808719659171412420328131820872706910401880425640471451275221301310124900094785175997237965232152651361751380990572099367485745003558793777991713218825798314260532283007298442845388829409311469245870057031409455035036166747412979885180821102504947646922867359712076919940847173982654417985779271207380189196864547873292529929118911576152388352104179221105616072584796934015629810661075132694653746489015099846670040079689171577509515832477498369920566593783315631166617970156403597882536309491814201294583593876798892936417830767695273098204067095331361644413858859993328438701461466986432116371466429501796281745317597555372567687272741220946903622572552176033977105176780258670103736123493087637087879866619066857900162029142502169280392319175124019264819172639003008692281782670446846904816665909897332477161522504450906980821508386757337239111618507435101540897858413016340607824077401090553703957855712921974534670532209479468736,
+          "C0": 548324362691896502675861037544590133574553873674175935778047943368710886417867580577535042485762529084967524669195365237265969758102800729968088762369431370863790885166053148776812067561550206214713418566972978250104268753988305789298776309592163020741446666323935155425081378347694441919056307856963674194342807368658373137120145586012651860493768301469826592085401562390268551562233544159734213847758319356602083146399678164406361723714188573711922941458747613677810636511504152072750546320653874579457514038505298226944843031760829410835675047388208552381372397511175396933791613203032940887250960913251548074762127076589245784709000613346385246490727318433183998971607566312320017674061653909148387434134252020155047800128093282290792048163704766219770776714501976077198155358589913989290278950145062070036166230106725232797721232472468780997455525722691074501481083073764821970786831326264994592159242550304782441038157858805291517742012911528334128682342889921869003415940146031832388705154487556513766050669978054413885995033755917524455904454780648685825190684539602613598664950834382093828380169333005070593866958082779451756694583861534245025851852963620976137055855489295034674303829413951815001565603579205908287085028619170746483154134021758034702510423859637337705140756571118081655252501656918554285287040637052107379418001952146364468335507966107407156376624722456895122264489888316026921840952696078330646972949124367817120531126277419373190380927947176218452708233715576380559381429232455106618839838267893507135442066167569398598656112210385958482576237123883077845146706978120913850980422227686228421013263630171383336444944636080048189059629479225619232563146204735488377024187520057601524758680013592243165203032997200027869872581452544447210457815457387611488588245914650722359560757876221203290046188992425537543361941523880836613490387626400832644598705366426427234136036656130804355023949470562573079098977510572234914875059684213447776697050093488362776074852167103359074765917818291808398572539361945120873667096739923287687793021639888564466725468528157629007549987011293035616243520421077009265811123714300346555540013787246176155535568827090903954621436279700276148659728937689104433955220665653818488700676323007440489592332963648116587723544935319727730477104657877958137048549117225264096323437501345205498147782853749543905925285800516669883730554242766008667296407314547468824825492255562855873310335269022894806175914519055022881889012508084159913495602361075439922824870267472569315529985121551643435276092071926612229524192260604035476683960195190911751833269681049275147475563148006275307467913010394541177976089984457696520142647608392834886867377394388891743176608546559827500938578095216987172098620148238243484243622037700872628472320984986769353647967294460137204290690955253200825271314701870108306347762880799148058161647516168795464193382675583628398036446636838714577693656311011910718467607228814462879746590604215998361510581901038153960354576387664659008857368769203868266365861761371041040085791665388711051256572426804153285692906859709717832241685747102376546851897416908449398791090483373411070470660230628351845168083378254668879137563211183815930121289892625317251697174244899530855932201947894093955613716397394384529290530699287996082718665789827637424156606285141371882046405642687366825672519931915872938335723336771273239629576449718879429251000101520209401707568104048246780728982126025146267598737344929551361333697936995605541530897879775269265018844961620609099452513674020493012888095332848154341291886983648780976053539799253634683252006122905133283085441443635534735311151870345535587069249551347588643197226988657204806280807060526503829446169950127833291839294945619264884476159567533154891512910368661981539488068368954069996269108840986609444501231921358487799892712813396617688072110323812314934596833762706831725675761818857278482804820665705131816419362384004140051554247597382704155032706851207528184509959514646558686992456549196477226767876091527423267750665112002855063915391481060801447193538523508317466831345426548222667736507830894768357708377653362028695110415608053362950061721655765220161289565004940537381190895765118751120591731297033569700285773718386840511483918088827196624396342054657263975663166898380393290889964114044239750632572198763603868868887468929343388818605829072805451724809767245749263854035461296935472079060517075004070033375077497850232361257368839238207327373299967284267223131841486501683798149738397010581661934515817975123433127038178869689091191396413619462172869358691764163694331194170425641378999866471812408489677307032187179399149469280857321683417603560191395113127779900854241408278271797217003223494142046531191819211911996214950224596556007923335150494117497147787949875844827239889335840068908539272429643926120925108290749795869347932477947423800462191997380511583183863591337876415694464859477083443881961609968069317789483403041852407847639026192663213593119135904780850719485887348605211744806901849450737467992615904222379798283608626015925576874449996734627208251368192120498580478859063672467440538292510788087496861274141816406108854607905651119168042347563132254176568912132526791058901243125083908761671518518019758105271187851352858610022260702962596693208403737562776045067217998548739334611421773952010512871078776268375553961943232419804756029560649932377959373702019349229096743567417083554698025605253114271473849227851743954340400473000178034130209483973382669629325506108657548483784833475502086405884905019195321091456786131027522992497603928632830104877807790614391346410525405577611153343431374207626510748597963949634033740523092946676301473924362721842286122976519326261665022123651941159826510011906365871394451870130479892741276031714000065647014300601430000365834475726392543565816220973292979021836897724250035452614798117572691872113495053770271420833517560319781327445925683510123762196983138595610551843145150987242940033858174034701697983486100864848427470972292941453432765961298412994035879754805550237067184027821805880812659184159872912466544596588692635155302443444945264555941449515364125489109904582738388759639148886613754120176454463397667279831543562778130451790032094611069476042641943884816675808195369947772145518715901824476922272468098887062107543034652049781266350610035014787106962161683635687905862250751845019521203837045368720736966466149785315904854100697971727793182350348803720968963400876244446574679856132513182884833236817122030914179620244909551740556166651982526168493388708198294550091349159861080799876121318447870127497716781821922787349017787513719553478020099126487556819796332698511549753802048575752108415203957532651580808999266737491298522171330317017142227967580732643215206532748213806669057248668946959013244674484322247470227189617838354827806983533736278317479623040210575797302382317698730847796870839519084343322881087729816610366658747161379041769764525432569634365786128508554286565043976248652243493192890482938943020186480331971810397307691176371291058497485300622902859076167296966839036627929166606513734407562504280779390468323374558841804450679611361682373304473001857421727160936919973085798903402086876433819141862037844702550651495126901708721378301415009224190928908673469967351065907695480251456156254726061580852310075700170980987893942957014140896691908839227489629778377923172860379443546759711068781262913380349233054227886577370214141144221456139765594977329792176337765521621462858332333189560276900376957053293125316475475035434236353669751675154900352691975679887836647591137036275571167887026142318731239291198086694973461373787675785595595818235066725637677273564324969078602245050223850273318586241095050231293371114907715523050119839317168863871792244776706794992014448038428264587240849847624870887919438687915571363954165362509914715700365047647691873614981707069546493625308713894572351618337400653179008577693302124836755663756287364614639788426098838914234086768331113547652528276086427123142435028695329286942474036433017980979104129321647281535531406045289382069105277157126882308010825427785948726726201004796362658626288511034187963689739215707227535637137803889958501005850666981738319590592108923866777333651569856121642851497765357026044268973352113621149484261048774866817530634810800153553743179608954638775188570720777035064595227664578607229183431987735845007428072090104359536847475122805242280363670948479496786833972120992666283922106731090280764458314210479271148779790803724397948274235836014445049251090907814006204520943730358018897451589485380958728207663827346503402960971916351124732547340167598261113492961331722608316016402900594788010856474016644384365583864100537833648666114007855197202946570967097597758872094304196746089549373670843248471530586036495083288496514267929932294045592280969821786219730989063070537249267021630042494867403070533846620734547897682299588611777151402480072789390285932403018699042255132812021266648810960605699941541371967387198092060370983141756394968303037454309726925843303788079061784010204796055486186043328688951285923599447680453934410100332478221437999160534157784048296864633709012684562689180879088132554559819192303519857473968646471480591944953442967139881710903890274170231445936924068005752797050931441375112407236585803738705258870529361749397092618257736675536089309610511738606810897949375891130550970613313940750762078633996264863945968171853150408906192019253015727927042359080657749963052200626500711807355774861746874936838825180476934752679793938031924975877868137222794292489050782440242185086154262898215995820282187597949541339027808308729863940030701480132099968535501654927057663721648433069162026821339384993263217634941793096151794744331079307543527546816662136001425996892740462662227108790704493446354461608832638695877599613541634397936620503106617840288336672249307978174115163891360507039487340574861531692268949818865030425385539292626266149157643218783911424778023117872229653394338366089187442749151929451939707111148171443486051301910069047384928240597730371886067206722766064067144787487188009205582465651406862253005711809073941328924614483174323710150041471506672532789657950560415745671470391141583444053255784642338246860880613634350453550613883706529105212271094201398964465072446119687732179830049017182468879591316291599449637102424291237370212370493939222011764526719168305966769580473635513487720466859211465194017512063410615889765213809520611674783601119043631185263579918394682965473467704148689979164075645564890309795056836312409289465038512866354856135793668745648203240399351214137389345620502956335896071661581353445486867652333836841914630800589851263655462666013358131837784996009287069952857093387116427762369652408875872248201660964393285753804680152400324962097222501770564139260079923366875150383448303914221720295064665932858910710141496913959335028590022100931844913891652414288110334085004378785295977625914559975892449950560342616983089623962653519158799862731964683404670411149164645023411794497890329207031617088328625223283910717722454113768838461280153885236670363238537313432408102627160252751799824506547178140731035596896899984985269704908131562141295776036915231298043024368064607190751037719097068370052261651412434764150523222264168024102561991900565639471202818542949700231562007498752671781672949085170277178598477188440079391692208734889837748081816399190876024597990433977383241450775991986184831686607112639104062350777338572802982072080749270081210878522336661728271118859001034506381883927245628055940652434554731342028608453318102439473074500285632983173941609434648460777641917178776992397647054963190606994249786817235250992111755668434786710049374067334782982083416789840251722850348852779791802970332669074595619536284636413952,
+          "C1": 1,
+          "E": 509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958827304979549775015204660589628049382048159414088886350824139990951695623597455357585789947338756567246855082520379894803970478190080646374725907170600630937374638930370439244376137186931258502092725378890309112445759411478982597831480340925427115998851341292624150119598026644913815467329847434859878041023321026286574843080294022586123425055138651176542718649119075352633419372782791056476906418755435875482741999289270330175685831019358074044683575519364870537110698987378534156423412338368608215994716567771341264691784835620547116095154355823028405037678909536409294936241998064726276240916495855446538713390953917957332894522343859649425558894465528489251474045892119196192790538905119006865260569920159851539352630884411410684543010286411452690005269956873208792508595460908096781391701546463223346195916242564759714955799308966368742627228715461007712659326066236176298406802374308370970686396733236368702340191602509189940399556599714483690088244922651769301641228957332097529146753350021208820702940922157812928490776979272693871844477852319948601242412475069333766783326317417323451865061419628384583210851906090081837589052178712760888235589716528403027031568288437989490163340454913038153349106568531093828746761822382576908672736654271400044763829558214085414340795118674219525044565554958311699780729788995435250081345623470348243544594512672750920229723181348286851358440615607637394658415712783369231357282393690924650482720908188916779881724305476435285671169289604569420907232698282421856982026379712178193610758794079671443090170499840417046551812624329535152282424714022599419754331072196960476616795026403529285824410798217390317086027514688112288530970330509440091515683875928181551063423447893048491177211466119814349423907836888314559662032261555442354347785163113771451383175688798034527042538116399087831616488919004322119167912666265947346004223385757910827157266993723507556830481294342030677452635331455842755200417108167627732222635125802616945528741084596401279157096363540269571573594558215964221481961827180791443114180273766962657973492642630980698679516137989730279605879551135389988039469081618481067485985149309898196042198234371393482956069508355575669945213783147520197065586627742035457497165537741506100395483926269734486532538090154077823377395228805741722431419949702460659538988049212462045808719659171412420328131820872706910401880425640471451275221301310124900094785175997237965232152651361751380990572099367485745003558793777991713218825798314260532283007298442845388829409311469245870057031409455035036166747412979885180821102504947646922867359712076919940847173982651359497895149227761308727385197401058484053043184361388858279409844715909936224980382135575881022348262982211465364656165884341821110212694567334412909329002077554872828731920533477848384078608269522629052985623897506167429224619325015684875402071027932434304843133797610448371222249887455393547484202782140462207137339390835527332405678688619265716439035057763448822292023375542071961895670713508087681671141176119378455194688833975566628329856741993021096705144585041324058355406830053158801700409375564003338703853486066242935606886825188020787760406585587938040323971142831195721933266404800825329533223349607261499700030105646854670532209479468736,
+          "fixed_odd_divisor": 3,
+          "induction_gap": 46367449394771566936339183418846120489403553120024403825886656830825784931626315330487065312488394139857538539881285190147554682515056493917764802415073545114467605460838842196408464919460263578530932879776340969177528556269616200901792480367233796567022461460050764545920795207846900781952307967447871535796462009588237696148946185014839773360066799735012279100006731741286557096524161726074110626931145178311503928694260314268008559127547296372606649689534745278499256130889883178048638333535565349597705567583997222674269888983021153239470823065778458808733542274811420074055265584732568364018611702710257814830266698129242393519553995016546111082071314248136854702770212657308813447786976841606186909024243810627750079748712268568038659611694375993396660660353555427324012358422062760756125033933925782378840270668796061076523442463057653910848249729199590250220426308934600868374965540427316471203868592691610014622959736999605526264772060937205064085476691948467057172676292429080122360296867291452943672114290802633871481428962313700634575738580927974314532932523246300641241920681932048930657542190041844274914564013088118685534752572763282081685105550169157357860559943766820748632734037681646473192598889718730566755979476910995557528576404290949325131742785768058126011408234695236200338381763920624487831354336921998221207431610095280664626813247212962660720822757799450426457897273372534402028975569788038637961866652057956144364365426620960612367630090733966478468462793460892956719921358513051888386836579337386044069111883503056310356858726211064502780493165411731782277639075839739943170173393309778057125630246953773598845264659516346825056030010466674897526249470492488915015358599954319857473575953642766165310546517647500825682602558208301547588806563012151694277996755161741425707129248134536794152289557063215299834271738413553115854082497778007819214146279989947711783514738683539520063199559287230849220851099085344158390129299992760633774958636850119843798379578302530628657792040552420097313095372747486105615088020944835794987204951108139184843251637176179848835188625555217326342542753807726629138817437419349334298308281997196220100344483269246233160764938335316821842449396453099042147146723841213301933997927480993463209597854814181034751094189510334365873022450639244188068516994516570023495827165159467011276971156970893459725658358255714359511066631565174630676243166042271188630994488006411012080226765009579121646307044700179412380396011879952949486595502725897404180261322720133879356553471333710998659012186580404761406259062637162368282704292894802981416516763716606194053398097345590621886253284753139029526383624113656152493766382506682088657924996739176604301747368437540306885207826847619463812509354570427161313515297338820100057552524657415301092142663709971238228484010744523690438009479018129232564106444587416402664711024213867555895472057628797660883420424687157207527016116572248901733122213392078310720306756055337231680017617257065387397069835857089641162923233986139398484106744664668929521935323600045987410622761584738066205372262203218877073607851446608234530522791543347655519207667192055086952420041469787564659046379895584858428780767813245839198021823890091137923401122845635022918576806534117293401533291228097725859396363092521884138176182846853543939040365829624738711862734546490081089410481438372293413936063442194790479566075462000118282186942636807106644840728153324503828378073393134060977737115939555579077813106951701851998672027492043155019016062061758332462102724509551912957435828336284576359650574018015798030287961311006449351835117220875152354554851930002683967623916360976492660705113815142337847484561115322713059535231309372777282694884976434119720589186182997072187523454197447220603748262861240829438664204084675459872714247857043604863981397086471954768697736329538415955325836814498689219035538697404073508489797481772705012355799353976779055465501206364680046410798584607757402451735801690162558100653220333740904809502694103473618096020295002913915829863286600053512697825874143193927602645191426969236911798355610996076405354015817302558175543700388985364400553808215618579050261250101321205515485477951236214948813987698857700648976056547197644127569923403372128347402721165010021382637782518854828503836618218256318300076359048327927232709464521146771533758267412697126243416903105797575613156836624929244935801545254245648449843353202075868987680621141960870968592316992677100491629393312844280052630201208486384328103969885271311296428839187671573797785124791648189815162481690723237956843254123632259796448038142043115438698272516403295769082164531013197104797652744154858526273452021323390404912793601875587830479419243579835968557065455444135039153320488911591686427281777141224648587200735839840039327796806949002325260357385965014454266424337932968383124525226632242063934477055135989037290545838274460966204021081927342965821322496741259215422923920018047912478334046168593488984598530249859995699416328846571118733282902066045138419221365908625451015748654836125891273919375670142061042441202795323850233797245902913147646597708437753664158298930383476247343701374175189858260408188291174014581169551454720327950235869980929733798999714617092832421552036705913679871597216914673856469620223549820953429867340041480309120611062605216520995422312770157837075213490930500374086046973647251714613553365940755452351662771560034281722436162235284232727407310804163755092317807107042788699257214022599860269851936570105675153909641661156259392887921832993495765322589803445084663461638823901377538903659541819451106168229654102248019091916571087003538979439987237870974974997067862335084068914744651967697404515701044936285753098544710149273790997642223010663068338316597800657255421698547905032535254757263194917688759157284176594240221705115584486995311991043499240387060164869875899682655018431062631654976,
+          "literal_charge": 8602150047189017391843029789286164264397633273752142192572273343677564296140290213863435903407629781044931775522095102447544872232274628451243136983154019175044862799195358724163631235664934195650342836395502196070513645700205015362335507968804774298743099463425553958878446149889070330152112397525058850647985031301475689776144911105243639000519522385285503321508791061957291817488157505463194429987724002263147282562756226608375847168010223232454428811013041048686610882431723491236939392649633941852184749966988064573063759423179843436619766227305453505605520759257169907719598984609468469342379148219036740797175576572911649000230657841669733653133004438584566268479558369744617611371619714047531786863547342165546470382054695797432853408092277922597402257831146784572173119052463875300004005144460751820681254995043175536830775433766501277209684180245447311422921122678328305735455808304403586745303159843691228508505961672408091131340416425027153270294977604477187985223134884706370361307077753689984003976688999605615070695746586441632307600539031440802826614390051364049332043527820229354329006988633853031468238352784318382775077978860847005173916587731271418449676979621871615614228623965193371889055886092963082548612813434970997714603221188676743033397554276236316646437866916333639680420849198115445882693979119799380580600345984601198824388196978608447002074250875661793528478768809996365176349731085009333105945690598612400264723275458758613808931981630126557430907441015766323983665751995886185911918698355823586432739359988354578150267343835360275609634897131299862181580974858108490069487445711764198302088278539776310784957285582495467228820992792190977531053545527703444417307602364728064643729892360762418664858759691757275089630779287095027478379397941728157566371161190668332472966266763005931445515964706279258714423783443975494281749379534368563704478293621983417992735524041434559442841562771745250027561584049065940963344175937722710565152048370793617232535215624113648534354593086952446727532575089277007786985763821449817224804159577918781236392219356397886933941089363470136815955663254745466593961989862282652232017748789907326412816205862367847487065493020833776521989829078457987075672349264748822706946470301881167920591163986503365685570045069501212895829467454176384556905772030317496423453555165129733212572412834114041593025884977892074900420214271623052500568613681103838841968110989445056399316102683298019429949265617281993255202810858397930875624013685435087293740935229253486558475406650740991892747025319088152862668912282841338359061754788306782622745831079705949168289480396131076026558289251050870782378401981437859815308553222718198646948947624855986514441095590063131192179050107202222690259816999805451248012866975482912065729483754556620019451424873562540273420474051996818395921751177657017329187103847207798746730950287983229443389329780667525592972971825105814151722585840333561507822933718377467865400590994126018763313044721781253399662637027202706644506168377581986007139910706310953048426617808204185875233898194913062336477218293056741622639580272023272752851940456033314673140700904884808381662452232303147275239629862436893247069455519025904339792522042446629386246460714481042493276160000000000000002116,
+          "strict_literal_gap": 509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958818702829502585997812817559838763217783761780815134208631567717608018059301315067371926511435348937465810150744857799701522933317848371746274664033617476918199594067571243885651973555695593567897075036053913610249688897833282392816118005417458311224552598193160724565639148198763926396999695322462352982172673041255273367390517877675018181416138131654157433145797566561571462080965302898971443224325448151480478852006707573949077455172190063821451121090553857496062012376496102432932175398975958582052864383021374276627211771861123936251717736056801099584173304015650037766334278465741666772447153476298319676650156742380759982873343628991583889160812395484812889479623639637823045921293747387151213038133296304197187084414029355988745577433003360412082672554615377645724023287789044317516401542458078885444095561309764671780262478190934976125951505776827467212014643315053620078496638852562666282809987933208858648963094003228267991465468374067265061091652356791697164040972108962644440382988714131067012956918181123928885161908576947285402845544719409569801609648454943715419276985373795631635707090621395949357820437851729053270669403634782027388584542611815295760149838761009868291724840684414188155734679475207735783679273769763473701738939668178856087086524816531138104478472236352608710925874537462501665283906301456130281965042870002258943395688284553941621276179274035975696647087128868584662050536433638146347949287745234051870320643465641321123110496544453655544611858697128405140908714616669861095840467793479837787172361340311454735592349573073211191537014694638020982562532441624561645841002709514764852596724315250746048100013260104734590560285867119496339992799455894563812239458620579186335358804163156130414792801261054657666632747257535272567004783176044412619627596742610260714843215831767764036606670883123125337230204580538675192418384516567811635659681279617205173849000987983515395921851500467905707385303894258706134476144823451794499924560650568574735123852061185655043447829185676484621147830683389132204954040195027621664363048962803080054711406238761342281629204048640916135742735179726733294002487656491205203332917292149406134871821555187620588222021290082649111437261157691118607599552069686192748342830795035798514316005678570500029172404584032753876182332976274268255035392796688629221491625758906880678986446598999586214090227846821932509805525220257179652168800741511218990946334029126975787096252045648697692552669418220127721565538575180854820894922690246846847920004701910159575922752993839219316039516708009717078594550310972897979764145885892134560577089331088861141224814361879101764073201203019476334326618680082071605324546080305056691646068960988600124395621134785432285131790032415257453943194082004110407243319321545933846090011825389074175300514026423510516067996102155000988805501584416251567601995828581028194272281201484016859904354221118590554724294482421722378388630417876366803777883012593614028210823218674722313016294450404100510769975879434934692964069001919304089155168979467748883735785548948820125670866759122901792082248564105765298665207413578529677136622712062882670538812925542030722078443525568555457259310348308177887077895761740202907362065008303287086593963360800785218987612370694670532209479466620
+        }
+      },
+      "margins": {
+        "g1": "332744409924090075910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337",
+        "g2": "665489485336999999999999333510514663/1000000000000000000000000000000000000000",
+        "g3": "332744409924090075909922758598270727729272270729394494318848181151818847514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+        "g4": "665489485336999999999999333510514663/1000000000000000000000000000000000000000",
+        "g5": "532391055878544121456176613103879418820581179420885696518848181151818847514663/800531591056678543321456676945348289842910157089843976539200000000000000000000000",
+        "g6": "2661955279392720607282884394497038790461209538796791853318848181151818847514663/4002657955283392716607283384726741449214550785449219882696000000000000000000000000",
+        "g7": "499999500000499999500000000000000000000000000000000000000/500332244410424089575910423090842681151818848181152485337"
+      },
+      "minimum_margin": "332744409924090075909922758598270727729272270729394494318848181151818847514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+      "parameters": {
+        "C0": 548324362691896502675861037544590133574553873674175935778047943368710886417867580577535042485762529084967524669195365237265969758102800729968088762369431370863790885166053148776812067561550206214713418566972978250104268753988305789298776309592163020741446666323935155425081378347694441919056307856963674194342807368658373137120145586012651860493768301469826592085401562390268551562233544159734213847758319356602083146399678164406361723714188573711922941458747613677810636511504152072750546320653874579457514038505298226944843031760829410835675047388208552381372397511175396933791613203032940887250960913251548074762127076589245784709000613346385246490727318433183998971607566312320017674061653909148387434134252020155047800128093282290792048163704766219770776714501976077198155358589913989290278950145062070036166230106725232797721232472468780997455525722691074501481083073764821970786831326264994592159242550304782441038157858805291517742012911528334128682342889921869003415940146031832388705154487556513766050669978054413885995033755917524455904454780648685825190684539602613598664950834382093828380169333005070593866958082779451756694583861534245025851852963620976137055855489295034674303829413951815001565603579205908287085028619170746483154134021758034702510423859637337705140756571118081655252501656918554285287040637052107379418001952146364468335507966107407156376624722456895122264489888316026921840952696078330646972949124367817120531126277419373190380927947176218452708233715576380559381429232455106618839838267893507135442066167569398598656112210385958482576237123883077845146706978120913850980422227686228421013263630171383336444944636080048189059629479225619232563146204735488377024187520057601524758680013592243165203032997200027869872581452544447210457815457387611488588245914650722359560757876221203290046188992425537543361941523880836613490387626400832644598705366426427234136036656130804355023949470562573079098977510572234914875059684213447776697050093488362776074852167103359074765917818291808398572539361945120873667096739923287687793021639888564466725468528157629007549987011293035616243520421077009265811123714300346555540013787246176155535568827090903954621436279700276148659728937689104433955220665653818488700676323007440489592332963648116587723544935319727730477104657877958137048549117225264096323437501345205498147782853749543905925285800516669883730554242766008667296407314547468824825492255562855873310335269022894806175914519055022881889012508084159913495602361075439922824870267472569315529985121551643435276092071926612229524192260604035476683960195190911751833269681049275147475563148006275307467913010394541177976089984457696520142647608392834886867377394388891743176608546559827500938578095216987172098620148238243484243622037700872628472320984986769353647967294460137204290690955253200825271314701870108306347762880799148058161647516168795464193382675583628398036446636838714577693656311011910718467607228814462879746590604215998361510581901038153960354576387664659008857368769203868266365861761371041040085791665388711051256572426804153285692906859709717832241685747102376546851897416908449398791090483373411070470660230628351845168083378254668879137563211183815930121289892625317251697174244899530855932201947894093955613716397394384529290530699287996082718665789827637424156606285141371882046405642687366825672519931915872938335723336771273239629576449718879429251000101520209401707568104048246780728982126025146267598737344929551361333697936995605541530897879775269265018844961620609099452513674020493012888095332848154341291886983648780976053539799253634683252006122905133283085441443635534735311151870345535587069249551347588643197226988657204806280807060526503829446169950127833291839294945619264884476159567533154891512910368661981539488068368954069996269108840986609444501231921358487799892712813396617688072110323812314934596833762706831725675761818857278482804820665705131816419362384004140051554247597382704155032706851207528184509959514646558686992456549196477226767876091527423267750665112002855063915391481060801447193538523508317466831345426548222667736507830894768357708377653362028695110415608053362950061721655765220161289565004940537381190895765118751120591731297033569700285773718386840511483918088827196624396342054657263975663166898380393290889964114044239750632572198763603868868887468929343388818605829072805451724809767245749263854035461296935472079060517075004070033375077497850232361257368839238207327373299967284267223131841486501683798149738397010581661934515817975123433127038178869689091191396413619462172869358691764163694331194170425641378999866471812408489677307032187179399149469280857321683417603560191395113127779900854241408278271797217003223494142046531191819211911996214950224596556007923335150494117497147787949875844827239889335840068908539272429643926120925108290749795869347932477947423800462191997380511583183863591337876415694464859477083443881961609968069317789483403041852407847639026192663213593119135904780850719485887348605211744806901849450737467992615904222379798283608626015925576874449996734627208251368192120498580478859063672467440538292510788087496861274141816406108854607905651119168042347563132254176568912132526791058901243125083908761671518518019758105271187851352858610022260702962596693208403737562776045067217998548739334611421773952010512871078776268375553961943232419804756029560649932377959373702019349229096743567417083554698025605253114271473849227851743954340400473000178034130209483973382669629325506108657548483784833475502086405884905019195321091456786131027522992497603928632830104877807790614391346410525405577611153343431374207626510748597963949634033740523092946676301473924362721842286122976519326261665022123651941159826510011906365871394451870130479892741276031714000065647014300601430000365834475726392543565816220973292979021836897724250035452614798117572691872113495053770271420833517560319781327445925683510123762196983138595610551843145150987242940033858174034701697983486100864848427470972292941453432765961298412994035879754805550237067184027821805880812659184159872912466544596588692635155302443444945264555941449515364125489109904582738388759639148886613754120176454463397667279831543562778130451790032094611069476042641943884816675808195369947772145518715901824476922272468098887062107543034652049781266350610035014787106962161683635687905862250751845019521203837045368720736966466149785315904854100697971727793182350348803720968963400876244446574679856132513182884833236817122030914179620244909551740556166651982526168493388708198294550091349159861080799876121318447870127497716781821922787349017787513719553478020099126487556819796332698511549753802048575752108415203957532651580808999266737491298522171330317017142227967580732643215206532748213806669057248668946959013244674484322247470227189617838354827806983533736278317479623040210575797302382317698730847796870839519084343322881087729816610366658747161379041769764525432569634365786128508554286565043976248652243493192890482938943020186480331971810397307691176371291058497485300622902859076167296966839036627929166606513734407562504280779390468323374558841804450679611361682373304473001857421727160936919973085798903402086876433819141862037844702550651495126901708721378301415009224190928908673469967351065907695480251456156254726061580852310075700170980987893942957014140896691908839227489629778377923172860379443546759711068781262913380349233054227886577370214141144221456139765594977329792176337765521621462858332333189560276900376957053293125316475475035434236353669751675154900352691975679887836647591137036275571167887026142318731239291198086694973461373787675785595595818235066725637677273564324969078602245050223850273318586241095050231293371114907715523050119839317168863871792244776706794992014448038428264587240849847624870887919438687915571363954165362509914715700365047647691873614981707069546493625308713894572351618337400653179008577693302124836755663756287364614639788426098838914234086768331113547652528276086427123142435028695329286942474036433017980979104129321647281535531406045289382069105277157126882308010825427785948726726201004796362658626288511034187963689739215707227535637137803889958501005850666981738319590592108923866777333651569856121642851497765357026044268973352113621149484261048774866817530634810800153553743179608954638775188570720777035064595227664578607229183431987735845007428072090104359536847475122805242280363670948479496786833972120992666283922106731090280764458314210479271148779790803724397948274235836014445049251090907814006204520943730358018897451589485380958728207663827346503402960971916351124732547340167598261113492961331722608316016402900594788010856474016644384365583864100537833648666114007855197202946570967097597758872094304196746089549373670843248471530586036495083288496514267929932294045592280969821786219730989063070537249267021630042494867403070533846620734547897682299588611777151402480072789390285932403018699042255132812021266648810960605699941541371967387198092060370983141756394968303037454309726925843303788079061784010204796055486186043328688951285923599447680453934410100332478221437999160534157784048296864633709012684562689180879088132554559819192303519857473968646471480591944953442967139881710903890274170231445936924068005752797050931441375112407236585803738705258870529361749397092618257736675536089309610511738606810897949375891130550970613313940750762078633996264863945968171853150408906192019253015727927042359080657749963052200626500711807355774861746874936838825180476934752679793938031924975877868137222794292489050782440242185086154262898215995820282187597949541339027808308729863940030701480132099968535501654927057663721648433069162026821339384993263217634941793096151794744331079307543527546816662136001425996892740462662227108790704493446354461608832638695877599613541634397936620503106617840288336672249307978174115163891360507039487340574861531692268949818865030425385539292626266149157643218783911424778023117872229653394338366089187442749151929451939707111148171443486051301910069047384928240597730371886067206722766064067144787487188009205582465651406862253005711809073941328924614483174323710150041471506672532789657950560415745671470391141583444053255784642338246860880613634350453550613883706529105212271094201398964465072446119687732179830049017182468879591316291599449637102424291237370212370493939222011764526719168305966769580473635513487720466859211465194017512063410615889765213809520611674783601119043631185263579918394682965473467704148689979164075645564890309795056836312409289465038512866354856135793668745648203240399351214137389345620502956335896071661581353445486867652333836841914630800589851263655462666013358131837784996009287069952857093387116427762369652408875872248201660964393285753804680152400324962097222501770564139260079923366875150383448303914221720295064665932858910710141496913959335028590022100931844913891652414288110334085004378785295977625914559975892449950560342616983089623962653519158799862731964683404670411149164645023411794497890329207031617088328625223283910717722454113768838461280153885236670363238537313432408102627160252751799824506547178140731035596896899984985269704908131562141295776036915231298043024368064607190751037719097068370052261651412434764150523222264168024102561991900565639471202818542949700231562007498752671781672949085170277178598477188440079391692208734889837748081816399190876024597990433977383241450775991986184831686607112639104062350777338572802982072080749270081210878522336661728271118859001034506381883927245628055940652434554731342028608453318102439473074500285632983173941609434648460777641917178776992397647054963190606994249786817235250992111755668434786710049374067334782982083416789840251722850348852779791802970332669074595619536284636413952,
+        "C1": "1",
+        "a_bit": "665489485336999999999999333510514663/1000000000000000000000000000000000000000",
+        "a_complex": "665489485337/1000000000000000",
+        "alpha_squared_power": "665488819848180151820345849440951879548120451881879831318848181151818847514663/1000664488820848179151820846181685362303637696362304970674000000000000000000000000",
+        "beta": "1/1000000000000000000000000",
+        "c": "332744742668500000000124001265771994500000000000666489485337/500000000000000000000000000000000000000000000000000000000000000",
+        "delta": "1/8000000000000000000000000",
+        "epsilon": "499999500000499999500000000000000000000000000000000000000/500332244410424089575910423090842681151818848181152485337",
+        "h": "1/1000000000000000000000000",
+        "kappa": "166261725903847/250000000000000000",
+        "lambda_": "999334510514663000000000001331978970673999999999999333510514663/1000000000000000000000000000000000000000000000000000000000000000",
+        "lambda_prime": "499667255257331500000000000998734228005499999999999333510514663/500000000000000000000000000000000000000000000000000000000000000",
+        "q": "332744742668499999999999001265771994500000000000666489485337/500000000000000000000000000000000000000000000000000000000000000",
+        "sigma": "999334510514663/1000000000000000",
+        "tau": "999334510514663000000000000666489485337/1000000000000000000000000000000000000000"
+      },
+      "recurrence": {
+        "internal": "999334510514663000000000000666489485337/1000000000000000000000000000000000000000",
+        "leaf": "999334510514663000000000000665489485337/1000000000000000000000000000000000000000",
+        "reservations": "499667255257331499999999875998734228005499999999999333510514663/500000000000000000000000000000000000000000000000000000000000000"
+      },
+      "scoped_limit": "665489485336999999999999333510514663/1000665489485336999999999999333510514663"
+    },
+    "atom_exponent": "677340914792209011107/1000000000000000000000000",
+    "beta": "1/1000000000000000000000000",
+    "bridge": {
+      "bit_uniform": {
+        "atom_beta": "677340914792209011107/1000000000000000000000000",
+        "coarse_saving": "677773948354561/1000000000000000000",
+        "external_stock": "The bit group cardinality is not inserted into external polynomial row stock.",
+        "old_atom_saving": "384599/10000000000",
+        "ordinary_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000",
+        "selector_stock": "Internally borrowed and restored q-adic rows; complete spectators preserved."
+      },
+      "complex": {
+        "N": 4654170104423616554638164010272346091525338318081434624560713222756608378117397252400210666893081203396713814484336655024295069388921657147689634172725410447265943921080212832355099015801402340613368718684202796799353461392938077263755994129846605291547841283152950671461912870176687371031035766533157124388121683525968364849356178820541530477519547795337690304275736560189911727771655301087339514594924221793976288076428017850160362677522178019873965242784165001200605555445206166283124908285904680927159554862606796638919933387986940007180948084528616254659211856188901000183131972799431806345252217217039855354854231386567475200000000000000000000,
+        "W": 46411243245854594476289509747890069396021233546140851487191415266019118243302500025260585612358809000235563590952517719761209089671496797753817162587564074028304257449377910236583460867419590158707403366697091980507492130541851447744560720250887019282306238492532037642767544780405860503698124087027232748727913424433576959478844986223324367936052884568204558693319333592257430358074468733494431841373475402631901424204562120425500646912291234299697730674824215083942099186610036944533919066490426753821364561103403987998562941807630372207971833058068314969756973987132199898038307695423424899183753738809011830330262308894990663680000000000000000000,
+        "auxiliary_banks_after_sharing": 1,
+        "coefficient_bound": 26,
+        "coefficient_denominator_divides": 6,
+        "finite_group_router_upper": 1996781817829700505616648003442939670418121383146524832570562414229508517707365630210514410182868208422410426904222349614587120238169565023976593617888088249792889489232587391937114692862833413493878289150647220476973315936613893411371180627349937542747113703441878702871183764108427647246946738280116413202842001601611935577871928896078779222167053557763264184774765184286697868594594314095298375974619020411589760327871072912207011987279157835478300764863885862339514331188591889499931217751046333516074072899497781599216540489370635260835475068278948606593058144659269465953575864037220363386543007930389392650517576506725609273702290538744026324349048797544741931656448511039048822918393059436367372870428114118151808835454194697189172420675444159767607388539974249475729974744313867010877267947494917728324863231728827375097796764153590288328124290854313749034205788857188501097735018015334913812524031309584653511523390713673282151437254342444210331261975595018327204309097452847220268408585326212873150162975484878379620431963947109952968805006023852879520661180163026847720913903900327535082362352341970633278958844785634739058314191225917327628660919631334932181528624365834466594963958416015205875189155986400578676067745563136371392891175778031142494596567179094957992104382032540770219035244465619000829903097000075849583777272674623120007677063732581105732175038816041801105187366687892006322408874222540820191910326456749466829784102697616089009779807971524806980914181559704507613893357294407429708218298288807124701683600890622569213909248073265415355774627205317949186017722026285024353652225922915093100135743357732801132024782406130188987430338256239146124855199854334018599841017758087085872468293679789085826036881023401376565779696277800538708125495766714490405278954114302254259077986737997610651303475214846690409557531207945110471168522019985895615486336976041255809567024577951775285455773833308076711628905615556366827520000000000019248832,
+        "halving_degree": 1,
+        "invocations_per_stage": 3525886442745164056544063644145716736004044180364723200424782744512582104634391857878947474919000911664177132185103526533556870749183073596734571342973795793383290849303191539662953799849547227737400544457729391514661713176468240351330298583217125220869576729661326266259024901649005584114421035252391760900092184489369973370724377894349644301151172572225522957784648909234781611948223712944954177723427440753012339451839407462242698998122862136268155486957700758485307238973641035062973415368109606762999662774702118665848434384838590914531021276158042617166069588021894697108433312726842277534281982740181708602162296504975360000000000000000000,
+        "local_group_upper": 4552920126520,
+        "logical_group_upper": 48159262409601395467011635701100464832021030569677306175574358095765057248609523233731783063748587071783641348524556567732110852316854063265394354994194196235424254850312119215110537754435839555650149484077504564925881450138377028493433797993315174068073699814547634599867538980931684612010193186301768649845766678767978197392725197692362495088218829833738197421152595019362494884184045934416310722881634052266915958468750757416790961147082161549540715124877340344041143854505135550740971547919140073694734890777732207707027340740665870005216626365456712348847469693004375422271610757332987355192878777460512903919380631891708932219994112000000000000000000000,
+        "m": 66,
+        "maxchild": 20,
+        "original_X_involution_scalar_group_upper": 42240,
+        "physical_roles_per_vertex": 10523,
+        "reuse_pairs": 2310,
+        "s": 3058487884121979618880469479350472234045876075727214763530072694334505195679847604414798439748788312812150483188381832849215504848929866994604243096606503475420815047737861862782153318233891548134075253483323867916695127154369257473877251542428696667340663899223961533751196042636610105873045153977264204291654164329090110960754412911918866753301970833706163183454800280528800491905143281109545162016054452351911517709424671930232882333533699285760176259295614030538977940760817232172955533480082261071282901477962056411266234225915617625718960033747980171749301071294536292270345175925146611539782494544177740946442458155682816327680000000000000000000,
+        "scalar_group_upper": 1996781817829700505616648003442939670418121383146524832570562414229508517707365630210514410182868208422410426904222349614587120238169565023976593617888088249792889489232587391937114692862833413493878289150647220476973315936613893411371180627349937542747113703441878702871183764108427647246946738280116413202842001601611935577871928896078779222167053557763264184774765184286697868594594314095298375974619020411589760327871072912207011987279157835478300764863885862339514331188591889499931217751046333516074072899497781599216540489370635260835475068278948606593058144659269465953575864037220363386543007930389392650517576506725609273702290538744026324349048797544741931656448511039048822918393059436367372870428114118151808835454194697189172420675444159767607388539974249475729974744313867010877267947494917728324863231728827375097796764153590288328124290854313749034205788857188501097735018015334913812524031309584653511523390713673282151437254342444210331261975595018327204309097452847220268408585326212873150162975484878379620431963947109952968805006023852879520661180163026847720913903900327535082362352341970633278958844785634739058314191225917327628660919631334932181528624365834466594963958416015205875189155986400578676067745563136371392891175778031142494596567179094957992104382032540770219035244465619000829903097000075849583777272674623120007677063732581105732175038816041801105187366687892006322408874222540820191910326456749466829784102697616089009779807971524806980914181559704507613893357294407429708218298288807124701683600890622569213909248073265415355774627205317949186017722026285024353652225922915093100135743357732801132024782406130188987430338256239146124855199854334018599841017758087085872468293679789085826036881023401376565779696277800538708125495766714490405278954114302254259077986737997610651303475214846690409557531207945110471168522019985895615486336976041255809567024577951775285455773833308076711628905615556366827520000000000019248832,
+        "scalar_role_reserve": 12877,
+        "stages": 3,
+        "terminal_sinks": 44,
+        "wire_bits": 2159
+      },
+      "conservative_old_coarse_row_reserve": 9909,
+      "ordinary_leaf_row_degree": 252,
+      "rows": {
+        "coefficient": 12320,
+        "complex_coefficient": 2159,
+        "degree": 70000,
+        "degree_gap": "224336/5",
+        "suffix_slope": 280000
+      },
+      "semantic": {
+        "B": 509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958827304979549775015204660589628049382048159414088886350824139990951695623597455357585789947338756567246855082520379894803970478190080646374725907170600630937374638930370439244376137186931258502092725378890309112445759411478982597831480340925427115998851341292624150119598026644913815467329847434859878041023321026286574843080294022586123425055138651176542718649119075352633419372782791056476906418755435875482741999289270330175685831019358074044683575519364870537110698987378534156423412338368608215994716567771341264691784835620547116095154355823028405037678909536409294936241998064726276240916495855446538713390953917957332894522343859649425558894465528489251474045892119196192790538905119006865260569920159851539352630884411410684543010286411452690005269956873208792508595460908096781391701546463223346195916242564759714955799308966368742627228715461007712659326066236176298406802374308370970686396733236368702340191602509189940399556599714483690088244922651769301641228957332097529146753350021208820702940922157812928490776979272693871844477852319948601242412475069333766783326317417323451865061419628384583210851906090081837589052178712760888235589716528403027031568288437989490163340454913038153349106568531093828746761822382576908672736654271400044763829558214085414340795118674219525044565554958311699780729788995435250081345623470348243544594512672750920229723181348286851358440615607637394658415712783369231357282393690924650482720908188916779881724305476435285671169289604569420907232698282421856982026379712178193610758794079671443090170499840417046551812624329535152282424714022599419754331072196960476616795026403529285824410798217390317086027514688112288530970330509440091515683875928181551063423447893048491177211466119814349423907836888314559662032261555442354347785163113771451383175688798034527042538116399087831616488919004322119167912666265947346004223385757910827157266993723507556830481294342030677452635331455842755200417108167627732222635125802616945528741084596401279157096363540269571573594558215964221481961827180791443114180273766962657973492642630980698679516137989730279605879551135389988039469081618481067485985149309898196042198234371393482956069508355575669945213783147520197065586627742035457497165537741506100395483926269734486532538090154077823377395228805741722431419949702460659538988049212462045808719659171412420328131820872706910401880425640471451275221301310124900094785175997237965232152651361751380990572099367485745003558793777991713218825798314260532283007298442845388829409311469245870057031409455035036166747412979885180821102504947646922867359712076919940847173982654417985779271207380189196864547873292529929118911576152388352104179221105616072584796934015629810661075132694653746489015099846670040079689171577509515832477498369920566593783315631166617970156403597882536309491814201294583593876798892936417830767695273098204067095331361644413858859993328438701461466986432116371466429501796281745317597555372567687272741220946903622572552176033977105176780258670103736123493087637087879866619066857900162029142502169280392319175124019264819172639003008692281782670446846904816665909897332477161522504450906980821508386757337239111618507435101540897858413016340607824077401090553703957855712921974534670532209479468736,
+        "C0": 548324362691896502675861037544590133574553873674175935778047943368710886417867580577535042485762529084967524669195365237265969758102800729968088762369431370863790885166053148776812067561550206214713418566972978250104268753988305789298776309592163020741446666323935155425081378347694441919056307856963674194342807368658373137120145586012651860493768301469826592085401562390268551562233544159734213847758319356602083146399678164406361723714188573711922941458747613677810636511504152072750546320653874579457514038505298226944843031760829410835675047388208552381372397511175396933791613203032940887250960913251548074762127076589245784709000613346385246490727318433183998971607566312320017674061653909148387434134252020155047800128093282290792048163704766219770776714501976077198155358589913989290278950145062070036166230106725232797721232472468780997455525722691074501481083073764821970786831326264994592159242550304782441038157858805291517742012911528334128682342889921869003415940146031832388705154487556513766050669978054413885995033755917524455904454780648685825190684539602613598664950834382093828380169333005070593866958082779451756694583861534245025851852963620976137055855489295034674303829413951815001565603579205908287085028619170746483154134021758034702510423859637337705140756571118081655252501656918554285287040637052107379418001952146364468335507966107407156376624722456895122264489888316026921840952696078330646972949124367817120531126277419373190380927947176218452708233715576380559381429232455106618839838267893507135442066167569398598656112210385958482576237123883077845146706978120913850980422227686228421013263630171383336444944636080048189059629479225619232563146204735488377024187520057601524758680013592243165203032997200027869872581452544447210457815457387611488588245914650722359560757876221203290046188992425537543361941523880836613490387626400832644598705366426427234136036656130804355023949470562573079098977510572234914875059684213447776697050093488362776074852167103359074765917818291808398572539361945120873667096739923287687793021639888564466725468528157629007549987011293035616243520421077009265811123714300346555540013787246176155535568827090903954621436279700276148659728937689104433955220665653818488700676323007440489592332963648116587723544935319727730477104657877958137048549117225264096323437501345205498147782853749543905925285800516669883730554242766008667296407314547468824825492255562855873310335269022894806175914519055022881889012508084159913495602361075439922824870267472569315529985121551643435276092071926612229524192260604035476683960195190911751833269681049275147475563148006275307467913010394541177976089984457696520142647608392834886867377394388891743176608546559827500938578095216987172098620148238243484243622037700872628472320984986769353647967294460137204290690955253200825271314701870108306347762880799148058161647516168795464193382675583628398036446636838714577693656311011910718467607228814462879746590604215998361510581901038153960354576387664659008857368769203868266365861761371041040085791665388711051256572426804153285692906859709717832241685747102376546851897416908449398791090483373411070470660230628351845168083378254668879137563211183815930121289892625317251697174244899530855932201947894093955613716397394384529290530699287996082718665789827637424156606285141371882046405642687366825672519931915872938335723336771273239629576449718879429251000101520209401707568104048246780728982126025146267598737344929551361333697936995605541530897879775269265018844961620609099452513674020493012888095332848154341291886983648780976053539799253634683252006122905133283085441443635534735311151870345535587069249551347588643197226988657204806280807060526503829446169950127833291839294945619264884476159567533154891512910368661981539488068368954069996269108840986609444501231921358487799892712813396617688072110323812314934596833762706831725675761818857278482804820665705131816419362384004140051554247597382704155032706851207528184509959514646558686992456549196477226767876091527423267750665112002855063915391481060801447193538523508317466831345426548222667736507830894768357708377653362028695110415608053362950061721655765220161289565004940537381190895765118751120591731297033569700285773718386840511483918088827196624396342054657263975663166898380393290889964114044239750632572198763603868868887468929343388818605829072805451724809767245749263854035461296935472079060517075004070033375077497850232361257368839238207327373299967284267223131841486501683798149738397010581661934515817975123433127038178869689091191396413619462172869358691764163694331194170425641378999866471812408489677307032187179399149469280857321683417603560191395113127779900854241408278271797217003223494142046531191819211911996214950224596556007923335150494117497147787949875844827239889335840068908539272429643926120925108290749795869347932477947423800462191997380511583183863591337876415694464859477083443881961609968069317789483403041852407847639026192663213593119135904780850719485887348605211744806901849450737467992615904222379798283608626015925576874449996734627208251368192120498580478859063672467440538292510788087496861274141816406108854607905651119168042347563132254176568912132526791058901243125083908761671518518019758105271187851352858610022260702962596693208403737562776045067217998548739334611421773952010512871078776268375553961943232419804756029560649932377959373702019349229096743567417083554698025605253114271473849227851743954340400473000178034130209483973382669629325506108657548483784833475502086405884905019195321091456786131027522992497603928632830104877807790614391346410525405577611153343431374207626510748597963949634033740523092946676301473924362721842286122976519326261665022123651941159826510011906365871394451870130479892741276031714000065647014300601430000365834475726392543565816220973292979021836897724250035452614798117572691872113495053770271420833517560319781327445925683510123762196983138595610551843145150987242940033858174034701697983486100864848427470972292941453432765961298412994035879754805550237067184027821805880812659184159872912466544596588692635155302443444945264555941449515364125489109904582738388759639148886613754120176454463397667279831543562778130451790032094611069476042641943884816675808195369947772145518715901824476922272468098887062107543034652049781266350610035014787106962161683635687905862250751845019521203837045368720736966466149785315904854100697971727793182350348803720968963400876244446574679856132513182884833236817122030914179620244909551740556166651982526168493388708198294550091349159861080799876121318447870127497716781821922787349017787513719553478020099126487556819796332698511549753802048575752108415203957532651580808999266737491298522171330317017142227967580732643215206532748213806669057248668946959013244674484322247470227189617838354827806983533736278317479623040210575797302382317698730847796870839519084343322881087729816610366658747161379041769764525432569634365786128508554286565043976248652243493192890482938943020186480331971810397307691176371291058497485300622902859076167296966839036627929166606513734407562504280779390468323374558841804450679611361682373304473001857421727160936919973085798903402086876433819141862037844702550651495126901708721378301415009224190928908673469967351065907695480251456156254726061580852310075700170980987893942957014140896691908839227489629778377923172860379443546759711068781262913380349233054227886577370214141144221456139765594977329792176337765521621462858332333189560276900376957053293125316475475035434236353669751675154900352691975679887836647591137036275571167887026142318731239291198086694973461373787675785595595818235066725637677273564324969078602245050223850273318586241095050231293371114907715523050119839317168863871792244776706794992014448038428264587240849847624870887919438687915571363954165362509914715700365047647691873614981707069546493625308713894572351618337400653179008577693302124836755663756287364614639788426098838914234086768331113547652528276086427123142435028695329286942474036433017980979104129321647281535531406045289382069105277157126882308010825427785948726726201004796362658626288511034187963689739215707227535637137803889958501005850666981738319590592108923866777333651569856121642851497765357026044268973352113621149484261048774866817530634810800153553743179608954638775188570720777035064595227664578607229183431987735845007428072090104359536847475122805242280363670948479496786833972120992666283922106731090280764458314210479271148779790803724397948274235836014445049251090907814006204520943730358018897451589485380958728207663827346503402960971916351124732547340167598261113492961331722608316016402900594788010856474016644384365583864100537833648666114007855197202946570967097597758872094304196746089549373670843248471530586036495083288496514267929932294045592280969821786219730989063070537249267021630042494867403070533846620734547897682299588611777151402480072789390285932403018699042255132812021266648810960605699941541371967387198092060370983141756394968303037454309726925843303788079061784010204796055486186043328688951285923599447680453934410100332478221437999160534157784048296864633709012684562689180879088132554559819192303519857473968646471480591944953442967139881710903890274170231445936924068005752797050931441375112407236585803738705258870529361749397092618257736675536089309610511738606810897949375891130550970613313940750762078633996264863945968171853150408906192019253015727927042359080657749963052200626500711807355774861746874936838825180476934752679793938031924975877868137222794292489050782440242185086154262898215995820282187597949541339027808308729863940030701480132099968535501654927057663721648433069162026821339384993263217634941793096151794744331079307543527546816662136001425996892740462662227108790704493446354461608832638695877599613541634397936620503106617840288336672249307978174115163891360507039487340574861531692268949818865030425385539292626266149157643218783911424778023117872229653394338366089187442749151929451939707111148171443486051301910069047384928240597730371886067206722766064067144787487188009205582465651406862253005711809073941328924614483174323710150041471506672532789657950560415745671470391141583444053255784642338246860880613634350453550613883706529105212271094201398964465072446119687732179830049017182468879591316291599449637102424291237370212370493939222011764526719168305966769580473635513487720466859211465194017512063410615889765213809520611674783601119043631185263579918394682965473467704148689979164075645564890309795056836312409289465038512866354856135793668745648203240399351214137389345620502956335896071661581353445486867652333836841914630800589851263655462666013358131837784996009287069952857093387116427762369652408875872248201660964393285753804680152400324962097222501770564139260079923366875150383448303914221720295064665932858910710141496913959335028590022100931844913891652414288110334085004378785295977625914559975892449950560342616983089623962653519158799862731964683404670411149164645023411794497890329207031617088328625223283910717722454113768838461280153885236670363238537313432408102627160252751799824506547178140731035596896899984985269704908131562141295776036915231298043024368064607190751037719097068370052261651412434764150523222264168024102561991900565639471202818542949700231562007498752671781672949085170277178598477188440079391692208734889837748081816399190876024597990433977383241450775991986184831686607112639104062350777338572802982072080749270081210878522336661728271118859001034506381883927245628055940652434554731342028608453318102439473074500285632983173941609434648460777641917178776992397647054963190606994249786817235250992111755668434786710049374067334782982083416789840251722850348852779791802970332669074595619536284636413952,
+        "C1": 1,
+        "E": 509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958827304979549775015204660589628049382048159414088886350824139990951695623597455357585789947338756567246855082520379894803970478190080646374725907170600630937374638930370439244376137186931258502092725378890309112445759411478982597831480340925427115998851341292624150119598026644913815467329847434859878041023321026286574843080294022586123425055138651176542718649119075352633419372782791056476906418755435875482741999289270330175685831019358074044683575519364870537110698987378534156423412338368608215994716567771341264691784835620547116095154355823028405037678909536409294936241998064726276240916495855446538713390953917957332894522343859649425558894465528489251474045892119196192790538905119006865260569920159851539352630884411410684543010286411452690005269956873208792508595460908096781391701546463223346195916242564759714955799308966368742627228715461007712659326066236176298406802374308370970686396733236368702340191602509189940399556599714483690088244922651769301641228957332097529146753350021208820702940922157812928490776979272693871844477852319948601242412475069333766783326317417323451865061419628384583210851906090081837589052178712760888235589716528403027031568288437989490163340454913038153349106568531093828746761822382576908672736654271400044763829558214085414340795118674219525044565554958311699780729788995435250081345623470348243544594512672750920229723181348286851358440615607637394658415712783369231357282393690924650482720908188916779881724305476435285671169289604569420907232698282421856982026379712178193610758794079671443090170499840417046551812624329535152282424714022599419754331072196960476616795026403529285824410798217390317086027514688112288530970330509440091515683875928181551063423447893048491177211466119814349423907836888314559662032261555442354347785163113771451383175688798034527042538116399087831616488919004322119167912666265947346004223385757910827157266993723507556830481294342030677452635331455842755200417108167627732222635125802616945528741084596401279157096363540269571573594558215964221481961827180791443114180273766962657973492642630980698679516137989730279605879551135389988039469081618481067485985149309898196042198234371393482956069508355575669945213783147520197065586627742035457497165537741506100395483926269734486532538090154077823377395228805741722431419949702460659538988049212462045808719659171412420328131820872706910401880425640471451275221301310124900094785175997237965232152651361751380990572099367485745003558793777991713218825798314260532283007298442845388829409311469245870057031409455035036166747412979885180821102504947646922867359712076919940847173982651359497895149227761308727385197401058484053043184361388858279409844715909936224980382135575881022348262982211465364656165884341821110212694567334412909329002077554872828731920533477848384078608269522629052985623897506167429224619325015684875402071027932434304843133797610448371222249887455393547484202782140462207137339390835527332405678688619265716439035057763448822292023375542071961895670713508087681671141176119378455194688833975566628329856741993021096705144585041324058355406830053158801700409375564003338703853486066242935606886825188020787760406585587938040323971142831195721933266404800825329533223349607261499700030105646854670532209479468736,
+        "exact_grid": "One dyadic grid times 3^(-K), K=G*(D_complex+1); completed children preserve the incoming odd exponent.",
+        "fixed_odd_divisor": 3,
+        "induction_gap": 46367449394771566936339183418846120489403553120024403825886656830825784931626315330487065312488394139857538539881285190147554682515056493917764802415073545114467605460838842196408464919460263578530932879776340969177528556269616200901792480367233796567022461460050764545920795207846900781952307967447871535796462009588237696148946185014839773360066799735012279100006731741286557096524161726074110626931145178311503928694260314268008559127547296372606649689534745278499256130889883178048638333535565349597705567583997222674269888983021153239470823065778458808733542274811420074055265584732568364018611702710257814830266698129242393519553995016546111082071314248136854702770212657308813447786976841606186909024243810627750079748712268568038659611694375993396660660353555427324012358422062760756125033933925782378840270668796061076523442463057653910848249729199590250220426308934600868374965540427316471203868592691610014622959736999605526264772060937205064085476691948467057172676292429080122360296867291452943672114290802633871481428962313700634575738580927974314532932523246300641241920681932048930657542190041844274914564013088118685534752572763282081685105550169157357860559943766820748632734037681646473192598889718730566755979476910995557528576404290949325131742785768058126011408234695236200338381763920624487831354336921998221207431610095280664626813247212962660720822757799450426457897273372534402028975569788038637961866652057956144364365426620960612367630090733966478468462793460892956719921358513051888386836579337386044069111883503056310356858726211064502780493165411731782277639075839739943170173393309778057125630246953773598845264659516346825056030010466674897526249470492488915015358599954319857473575953642766165310546517647500825682602558208301547588806563012151694277996755161741425707129248134536794152289557063215299834271738413553115854082497778007819214146279989947711783514738683539520063199559287230849220851099085344158390129299992760633774958636850119843798379578302530628657792040552420097313095372747486105615088020944835794987204951108139184843251637176179848835188625555217326342542753807726629138817437419349334298308281997196220100344483269246233160764938335316821842449396453099042147146723841213301933997927480993463209597854814181034751094189510334365873022450639244188068516994516570023495827165159467011276971156970893459725658358255714359511066631565174630676243166042271188630994488006411012080226765009579121646307044700179412380396011879952949486595502725897404180261322720133879356553471333710998659012186580404761406259062637162368282704292894802981416516763716606194053398097345590621886253284753139029526383624113656152493766382506682088657924996739176604301747368437540306885207826847619463812509354570427161313515297338820100057552524657415301092142663709971238228484010744523690438009479018129232564106444587416402664711024213867555895472057628797660883420424687157207527016116572248901733122213392078310720306756055337231680017617257065387397069835857089641162923233986139398484106744664668929521935323600045987410622761584738066205372262203218877073607851446608234530522791543347655519207667192055086952420041469787564659046379895584858428780767813245839198021823890091137923401122845635022918576806534117293401533291228097725859396363092521884138176182846853543939040365829624738711862734546490081089410481438372293413936063442194790479566075462000118282186942636807106644840728153324503828378073393134060977737115939555579077813106951701851998672027492043155019016062061758332462102724509551912957435828336284576359650574018015798030287961311006449351835117220875152354554851930002683967623916360976492660705113815142337847484561115322713059535231309372777282694884976434119720589186182997072187523454197447220603748262861240829438664204084675459872714247857043604863981397086471954768697736329538415955325836814498689219035538697404073508489797481772705012355799353976779055465501206364680046410798584607757402451735801690162558100653220333740904809502694103473618096020295002913915829863286600053512697825874143193927602645191426969236911798355610996076405354015817302558175543700388985364400553808215618579050261250101321205515485477951236214948813987698857700648976056547197644127569923403372128347402721165010021382637782518854828503836618218256318300076359048327927232709464521146771533758267412697126243416903105797575613156836624929244935801545254245648449843353202075868987680621141960870968592316992677100491629393312844280052630201208486384328103969885271311296428839187671573797785124791648189815162481690723237956843254123632259796448038142043115438698272516403295769082164531013197104797652744154858526273452021323390404912793601875587830479419243579835968557065455444135039153320488911591686427281777141224648587200735839840039327796806949002325260357385965014454266424337932968383124525226632242063934477055135989037290545838274460966204021081927342965821322496741259215422923920018047912478334046168593488984598530249859995699416328846571118733282902066045138419221365908625451015748654836125891273919375670142061042441202795323850233797245902913147646597708437753664158298930383476247343701374175189858260408188291174014581169551454720327950235869980929733798999714617092832421552036705913679871597216914673856469620223549820953429867340041480309120611062605216520995422312770157837075213490930500374086046973647251714613553365940755452351662771560034281722436162235284232727407310804163755092317807107042788699257214022599860269851936570105675153909641661156259392887921832993495765322589803445084663461638823901377538903659541819451106168229654102248019091916571087003538979439987237870974974997067862335084068914744651967697404515701044936285753098544710149273790997642223010663068338316597800657255421698547905032535254757263194917688759157284176594240221705115584486995311991043499240387060164869875899682655018431062631654976,
+        "literal_charge": 8602150047189017391843029789286164264397633273752142192572273343677564296140290213863435903407629781044931775522095102447544872232274628451243136983154019175044862799195358724163631235664934195650342836395502196070513645700205015362335507968804774298743099463425553958878446149889070330152112397525058850647985031301475689776144911105243639000519522385285503321508791061957291817488157505463194429987724002263147282562756226608375847168010223232454428811013041048686610882431723491236939392649633941852184749966988064573063759423179843436619766227305453505605520759257169907719598984609468469342379148219036740797175576572911649000230657841669733653133004438584566268479558369744617611371619714047531786863547342165546470382054695797432853408092277922597402257831146784572173119052463875300004005144460751820681254995043175536830775433766501277209684180245447311422921122678328305735455808304403586745303159843691228508505961672408091131340416425027153270294977604477187985223134884706370361307077753689984003976688999605615070695746586441632307600539031440802826614390051364049332043527820229354329006988633853031468238352784318382775077978860847005173916587731271418449676979621871615614228623965193371889055886092963082548612813434970997714603221188676743033397554276236316646437866916333639680420849198115445882693979119799380580600345984601198824388196978608447002074250875661793528478768809996365176349731085009333105945690598612400264723275458758613808931981630126557430907441015766323983665751995886185911918698355823586432739359988354578150267343835360275609634897131299862181580974858108490069487445711764198302088278539776310784957285582495467228820992792190977531053545527703444417307602364728064643729892360762418664858759691757275089630779287095027478379397941728157566371161190668332472966266763005931445515964706279258714423783443975494281749379534368563704478293621983417992735524041434559442841562771745250027561584049065940963344175937722710565152048370793617232535215624113648534354593086952446727532575089277007786985763821449817224804159577918781236392219356397886933941089363470136815955663254745466593961989862282652232017748789907326412816205862367847487065493020833776521989829078457987075672349264748822706946470301881167920591163986503365685570045069501212895829467454176384556905772030317496423453555165129733212572412834114041593025884977892074900420214271623052500568613681103838841968110989445056399316102683298019429949265617281993255202810858397930875624013685435087293740935229253486558475406650740991892747025319088152862668912282841338359061754788306782622745831079705949168289480396131076026558289251050870782378401981437859815308553222718198646948947624855986514441095590063131192179050107202222690259816999805451248012866975482912065729483754556620019451424873562540273420474051996818395921751177657017329187103847207798746730950287983229443389329780667525592972971825105814151722585840333561507822933718377467865400590994126018763313044721781253399662637027202706644506168377581986007139910706310953048426617808204185875233898194913062336477218293056741622639580272023272752851940456033314673140700904884808381662452232303147275239629862436893247069455519025904339792522042446629386246460714481042493276160000000000000002116,
+        "strict_literal_gap": 509532410931555680619111905701605719663775309011257184899853371767316317929959509126231486950421913624808115822871265825797304203462159273821591235330478517741402257811415848312180933180882017346493767909630120540412401717248529680239477806233338423813433642418140269735393353932383525076398988653273313580180901204266348309329078956207030476484250546538596473626447601552599528533232546440374842054188408552873669546090772684263830320082937322775897249335546651412079737702086628330204816852039179665908852391032936512904064714099133552082096956766796250645423541481444176637969951480577674329874853875936899064068864814607059269445648296885122099802981475254251150579892446783613334591065679578089966033233448468436814063172662291956468786941696439487875391872017092607956179762879810557759615757515667938229013963393363308533224642451183010009321425595599892859565124274006602949175445499201279903339215304303406754098458648347313475437055614694561143796447164268868760139299916803078267695569970235746633759497701127844741554164421029677303030094295911805654208049706003303749911216284967570666566397692767519504555648495473831709173105195200901996539621430430300635830329052382645589370703710787323881237350436469566667648126119901050082731608838362080495953217426022616769356134447200397805916283120006862503641256449692288145136611099948139171723222496845743524404645690103850840196673333764114308010720547121303713866666506131386201806213479351215520523407590483148115038052675394428095823311632011559213042160212498747737023207511022596817108337650671038492093331488041008596457572261975164210661246080327231396984947768722786800497413840838976099516813301831592280508235939477900165003940658838679752456878611458968849566445248873635447061566573717599424052819373759908728329634672107048634144277452027876858816368758936431866310678444104979295099807667890195815540069010878546283335326798720214506189006146013525815613748341597188553737684615305061909614930075276042239542632728599237677558154291784836234209839260961385775989978252141052692167087374814716316958809199738240097089984896211179410357612679205787133393598213399443234047343758210947473630159156804903661107307014673811229037905455528560902715898064189157164109867334955972123182394008947044337924111972641036987615631325705980088665021917764505752701397419334802321724957768910917139842399541271586368253479467749171765673001824640342732208730637433088044837656758347023314794582908793180355828527603076406038314236293691180265717157392528943729192895289381439545703430621762689685783066622386399651458288932909922872708975425457210923663715355446050789958818702829502585997812817559838763217783761780815134208631567717608018059301315067371926511435348937465810150744857799701522933317848371746274664033617476918199594067571243885651973555695593567897075036053913610249688897833282392816118005417458311224552598193160724565639148198763926396999695322462352982172673041255273367390517877675018181416138131654157433145797566561571462080965302898971443224325448151480478852006707573949077455172190063821451121090553857496062012376496102432932175398975958582052864383021374276627211771861123936251717736056801099584173304015650037766334278465741666772447153476298319676650156742380759982873343628991583889160812395484812889479623639637823045921293747387151213038133296304197187084414029355988745577433003360412082672554615377645724023287789044317516401542458078885444095561309764671780262478190934976125951505776827467212014643315053620078496638852562666282809987933208858648963094003228267991465468374067265061091652356791697164040972108962644440382988714131067012956918181123928885161908576947285402845544719409569801609648454943715419276985373795631635707090621395949357820437851729053270669403634782027388584542611815295760149838761009868291724840684414188155734679475207735783679273769763473701738939668178856087086524816531138104478472236352608710925874537462501665283906301456130281965042870002258943395688284553941621276179274035975696647087128868584662050536433638146347949287745234051870320643465641321123110496544453655544611858697128405140908714616669861095840467793479837787172361340311454735592349573073211191537014694638020982562532441624561645841002709514764852596724315250746048100013260104734590560285867119496339992799455894563812239458620579186335358804163156130414792801261054657666632747257535272567004783176044412619627596742610260714843215831767764036606670883123125337230204580538675192418384516567811635659681279617205173849000987983515395921851500467905707385303894258706134476144823451794499924560650568574735123852061185655043447829185676484621147830683389132204954040195027621664363048962803080054711406238761342281629204048640916135742735179726733294002487656491205203332917292149406134871821555187620588222021290082649111437261157691118607599552069686192748342830795035798514316005678570500029172404584032753876182332976274268255035392796688629221491625758906880678986446598999586214090227846821932509805525220257179652168800741511218990946334029126975787096252045648697692552669418220127721565538575180854820894922690246846847920004701910159575922752993839219316039516708009717078594550310972897979764145885892134560577089331088861141224814361879101764073201203019476334326618680082071605324546080305056691646068960988600124395621134785432285131790032415257453943194082004110407243319321545933846090011825389074175300514026423510516067996102155000988805501584416251567601995828581028194272281201484016859904354221118590554724294482421722378388630417876366803777883012593614028210823218674722313016294450404100510769975879434934692964069001919304089155168979467748883735785548948820125670866759122901792082248564105765298665207413578529677136622712062882670538812925542030722078443525568555457259310348308177887077895761740202907362065008303287086593963360800785218987612370694670532209479466620
+      }
+    },
+    "coarse_bit_saving": "677773948354561/1000000000000000000",
+    "complex_saving": "665489485337/1000000000000000",
+    "eta": "1/1000000000000000000000000",
+    "kappa": "166261725903847/250000000000000000",
+    "matched_comparisons": [
+      {
+        "a": "665489384671510514663/1000000000000000000000000",
+        "actual_bit_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000",
+        "beta": "1/1000000000",
+        "complex_saving": "665489485337/1000000000000000",
+        "eta": "1/100000000",
+        "kappa": "66504678314119/100000000000000000",
+        "layout": "balanced",
+        "minimum_margin": "3327446823534145538077807472060514663/5003327446856808614106163948533700000000",
+        "name": "Same suppliers with earlier positive outer backoffs",
+        "weakening": "1/10000000000"
+      },
+      {
+        "a": "665489485336999999999999333510514663/1000000000000000000000000000000000000000",
+        "actual_bit_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000",
+        "beta": "1/1000000000000000000000000",
+        "complex_saving": "665489485337/1000000000000000",
+        "eta": "1/1000000000000000000000000",
+        "kappa": "166261725903847/250000000000000000",
+        "layout": "balanced",
+        "minimum_margin": "332744409924090075909922758598270727729272270729394494318848181151818847514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000",
+        "name": "Same suppliers with finer positive outer backoffs",
+        "weakening": "1/1000000000000000000000000000000"
+      }
+    ],
+    "next_grid_scope": "Rejection at these fixed certified supplier values and stated parameters; no global or true-profile optimality claim.",
+    "published_parent": {
+      "certificate_sha256": "05b253a21dc526b6039f56d1068162a19a8a4f29291ad94eb892656b88e9142d",
+      "kappa": "3279447/5000000000",
+      "ordinary_saving": "1649038264871199969/2500000000000000000000",
+      "source_commit": "4a3c769e5c5430e7114c4d3e099ff34664677f17"
+    },
+    "scope": "Conditional finite witness retaining the source-specified uniform bit, exact tensor, row-restoration, paid layout and analytic/fixed-tape contracts.",
+    "status": "PASS",
+    "strict_weakening": "1/1000000000000000000000000000000",
+    "unchanged_47_slack_body": true,
+    "weakened_transfer_saving": "665489485336999999999999333510514663/1000000000000000000000000000000000000000"
+  },
+  "bit": {
+    "coarse": {
+      "accepted": {
+        "bad_fraction": "1/10000000000000000",
+        "edge_count": 294746,
+        "fallback_children_per_edge": 165888,
+        "fallback_lower": "443402390956655029231245143620375823449913316739191/134335937500000000000000000000000000000000000000000000000000000",
+        "fallback_upper": "221701195478327514615622571810187911724956694844413/67167968750000000000000000000000000000000000000000000000000000",
+        "lower": "3627070312499999993418235504017792380724010039202009964239458157/3627070312500000000000000000000000000000000000000000000000000000",
+        "raw": {
+          "lower": "742823999997548160791020711573206786426114025875223/742824000000000000000000000000000000000000000000000",
+          "saving": "677773948354561/1000000000000000000",
+          "strict_gap_lower": "817279736326429475597737857961987308799/247608000000000000000000000000000000000000000000000",
+          "terms": [
+            {
+              "child": 1,
+              "contribution_lower": "3503808144878566902706194750195580078047268927403/41268000000000000000000000000000000000000000000000",
+              "contribution_upper": "1751904072439283451353097375097790039023634751929/20634000000000000000000000000000000000000000000000",
+              "exp_lower": "1002902817921543813387900415092714457985097489/1000000000000000000000000000000000000000000000",
+              "exp_upper": "501451408960771906693950207546357228992548827/500000000000000000000000000000000000000000000",
+              "log_lower": "2138333059508027655521093419109790556760740759/500000000000000000000000000000000000000000000",
+              "log_upper": "4276666119016055311042186838219581113521481519/1000000000000000000000000000000000000000000000",
+              "multiplicity": 125772
+            },
+            {
+              "child": 2,
+              "contribution_lower": "29398316452581590421407298703524950876252648041283/371412000000000000000000000000000000000000000000000",
+              "contribution_upper": "4899719408763598403567883117254158479375441423307/61902000000000000000000000000000000000000000000000",
+              "exp_lower": "1002431767742407693299938578904250379385980429/1000000000000000000000000000000000000000000000",
+              "exp_upper": "501215883871203846649969289452125189692990223/500000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/125000000000000000000000000000000000000000000",
+              "log_upper": "716703787691222000324990943352280909089196277/200000000000000000000000000000000000000000000",
+              "multiplicity": 58654
+            },
+            {
+              "child": 3,
+              "contribution_lower": "43050965402250844599318910560668345167832991837/687800000000000000000000000000000000000000000000",
+              "contribution_upper": "1033223169654020270383653853456040284027991809243/16507200000000000000000000000000000000000000000000",
+              "exp_lower": "125269540452718267505292659245397706598932081/125000000000000000000000000000000000000000000",
+              "exp_upper": "1002156323621746140042341273963181652791456653/1000000000000000000000000000000000000000000000",
+              "log_lower": "39725672879349320245586770016213192610924887/12500000000000000000000000000000000000000000",
+              "log_upper": "3178053830347945619646941601297055408873990961/1000000000000000000000000000000000000000000000",
+              "multiplicity": 30930
+            },
+            {
+              "child": 4,
+              "contribution_lower": "16678474793929904192671677155855410805826687617/644812500000000000000000000000000000000000000000",
+              "contribution_upper": "400283395054317700624120251740529859339840503607/15475500000000000000000000000000000000000000000000",
+              "exp_lower": "62622558675581617744699663914350728933016349/62500000000000000000000000000000000000000000",
+              "exp_upper": "500980469404652941957597311314805831464130793/500000000000000000000000000000000000000000000",
+              "log_lower": "462459481263386350753235615248516476379277/160000000000000000000000000000000000000000",
+              "log_upper": "2890371757896164692207722595303227977370481251/1000000000000000000000000000000000000000000000",
+              "multiplicity": 9588
+            },
+            {
+              "child": 5,
+              "contribution_lower": "269486732045381961622707742902210011378777721463/9904320000000000000000000000000000000000000000000",
+              "contribution_upper": "7485742556816165600630770636172500316077158937/275120000000000000000000000000000000000000000000",
+              "exp_lower": "1001809412808111381497054806327918257913671827/1000000000000000000000000000000000000000000000",
+              "exp_upper": "250452353202027845374263701581979564478417957/250000000000000000000000000000000000000000000",
+              "log_lower": "666807051645488734110356876248348368498970041/250000000000000000000000000000000000000000000",
+              "log_upper": "533445641316390987288285500998678694799176033/200000000000000000000000000000000000000000000",
+              "multiplicity": 8070
+            },
+            {
+              "child": 6,
+              "contribution_lower": "14440967746880887477116473140648851397969035969/859750000000000000000000000000000000000000000000",
+              "contribution_upper": "173291612962570649725397677687786216775628431801/10317000000000000000000000000000000000000000000000",
+              "exp_lower": "250421406015275505383522655618188174531254959/250000000000000000000000000000000000000000000",
+              "exp_upper": "1001685624061102021534090622472752698125019837/1000000000000000000000000000000000000000000000",
+              "log_lower": "1242453324894000155114854739919439420399245413/500000000000000000000000000000000000000000000",
+              "log_upper": "2484906649788000310229709479838878840798490827/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4152
+            },
+            {
+              "child": 7,
+              "contribution_lower": "39729378639312699845895630054201606465074544061/2063400000000000000000000000000000000000000000000",
+              "contribution_upper": "59594067958969049768843445081302409697611816151/3095100000000000000000000000000000000000000000000",
+              "exp_lower": "1001580974100320164182242774475670751220366657/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500790487050160082091121387237835375610183329/500000000000000000000000000000000000000000000",
+              "log_lower": "2330755969960742005936834094776401383884396789/1000000000000000000000000000000000000000000000",
+              "log_upper": "233075596996074200593683409477640138388439679/100000000000000000000000000000000000000000000",
+              "multiplicity": 4080
+            },
+            {
+              "child": 8,
+              "contribution_lower": "104906112174169234877324309789314472161796341571/7737750000000000000000000000000000000000000000000",
+              "contribution_upper": "419624448696676939509297239157257888647185366703/30951000000000000000000000000000000000000000000000",
+              "exp_lower": "250372582754580512833709569902898501579466209/250000000000000000000000000000000000000000000",
+              "exp_upper": "1001490331018322051334838279611594006317864837/1000000000000000000000000000000000000000000000",
+              "log_lower": "439444915467243876558098094769010281858996223/200000000000000000000000000000000000000000000",
+              "log_upper": "549306144334054845697622618461262852323745279/250000000000000000000000000000000000000000000",
+              "multiplicity": 2514
+            },
+            {
+              "child": 9,
+              "contribution_lower": "36551479051140885266439078461860856261829619067/3439000000000000000000000000000000000000000000000",
+              "contribution_upper": "73102958102281770532878156923721712523659238207/6878000000000000000000000000000000000000000000000",
+              "exp_lower": "500705192481381989951220252902203510436022179/500000000000000000000000000000000000000000000",
+              "exp_upper": "1001410384962763979902440505804407020872044359/1000000000000000000000000000000000000000000000",
+              "log_lower": "2079441541679835928251696364374529704226500403/1000000000000000000000000000000000000000000000",
+              "log_upper": "519860385419958982062924091093632426056625101/250000000000000000000000000000000000000000000",
+              "multiplicity": 1752
+            },
+            {
+              "child": 10,
+              "contribution_lower": "11248373375832671562314116068036043242892969919/825360000000000000000000000000000000000000000000",
+              "contribution_upper": "337451201274980146869423482041081297286789097907/24760800000000000000000000000000000000000000000000",
+              "exp_lower": "100133887618688470881134564403881690589551661/100000000000000000000000000000000000000000000",
+              "exp_upper": "1001338876186884708811345644038816905895516611/1000000000000000000000000000000000000000000000",
+              "log_lower": "197408102602200962702419538353521690592038003/100000000000000000000000000000000000000000000",
+              "log_upper": "1974081026022009627024195383535216905920380031/1000000000000000000000000000000000000000000000",
+              "multiplicity": 2022
+            },
+            {
+              "child": 11,
+              "contribution_lower": "1112415628455787083173462112022781256078024012481/123804000000000000000000000000000000000000000000000",
+              "contribution_upper": "139051953556973385396682764002847657009753001699/15475500000000000000000000000000000000000000000000",
+              "exp_lower": "1001274193029511325988714772297732903760597671/1000000000000000000000000000000000000000000000",
+              "exp_upper": "125159274128688915748589346537216612970074709/125000000000000000000000000000000000000000000",
+              "log_lower": "234846355777210595872530407531806476712471833/125000000000000000000000000000000000000000000",
+              "log_upper": "375754169243536953396048652050890362739954933/200000000000000000000000000000000000000000000",
+              "multiplicity": 1212
+            },
+            {
+              "child": 12,
+              "contribution_lower": "338911326779443141578699078765192412609737750193/10317000000000000000000000000000000000000000000000",
+              "contribution_upper": "677822653558886283157398157530384825219475501063/20634000000000000000000000000000000000000000000000",
+              "exp_lower": "500607572790905674414621977496591451417633309/500000000000000000000000000000000000000000000",
+              "exp_upper": "1001215145581811348829243954993182902835266619/1000000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/250000000000000000000000000000000000000000000",
+              "log_upper": "1791759469228055000812477358380702272722990693/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4062
+            },
+            {
+              "child": 13,
+              "contribution_lower": "1763544802521377822423828494648462169948347654159/123804000000000000000000000000000000000000000000000",
+              "contribution_upper": "391898845004750627205295221032991593321855034649/27512000000000000000000000000000000000000000000000",
+              "exp_lower": "500580415135219364866258442988493377788347333/500000000000000000000000000000000000000000000",
+              "exp_upper": "1001160830270438729732516885976986755576694667/1000000000000000000000000000000000000000000000",
+              "log_lower": "1711716761554518574988699396654262508716213573/1000000000000000000000000000000000000000000000",
+              "log_upper": "855858380777259287494349698327131254358106787/500000000000000000000000000000000000000000000",
+              "multiplicity": 1626
+            },
+            {
+              "child": 14,
+              "contribution_lower": "119132154828073979688861784606223402749697171773/3439000000000000000000000000000000000000000000000",
+              "contribution_upper": "29783038707018494922215446151555850687424292973/859750000000000000000000000000000000000000000000",
+              "exp_lower": "1001110544773730921755141047111121031510060267/1000000000000000000000000000000000000000000000",
+              "exp_upper": "250277636193432730438785261777780257877515067/250000000000000000000000000000000000000000000",
+              "log_lower": "818804394700398348259800986659112407904448327/500000000000000000000000000000000000000000000",
+              "log_upper": "327521757880159339303920394663644963161779331/200000000000000000000000000000000000000000000",
+              "multiplicity": 3672
+            },
+            {
+              "child": 15,
+              "contribution_lower": "300319119709954823895275567890335638056172331/34390000000000000000000000000000000000000000000",
+              "contribution_upper": "3003191197099548238952755678903356380561723313/343900000000000000000000000000000000000000000000",
+              "exp_lower": "100106373236651607965091855963445212685390777/100000000000000000000000000000000000000000000",
+              "exp_upper": "1001063732366516079650918559634452126853907771/1000000000000000000000000000000000000000000000",
+              "log_lower": "784307958956922622523091134035433884674194803/500000000000000000000000000000000000000000000",
+              "log_upper": "1568615917913845245046182268070867769348389607/1000000000000000000000000000000000000000000000",
+              "multiplicity": 864
+            },
+            {
+              "child": 16,
+              "contribution_lower": "27694885124681286530763510319636299253308484679/859750000000000000000000000000000000000000000000",
+              "contribution_upper": "2077116384351096489807263273972722443998136353/64481250000000000000000000000000000000000000000",
+              "exp_lower": "1001019944265588669786632903119384310360547639/1000000000000000000000000000000000000000000000",
+              "exp_upper": "25025498606639716744665822577984607759013691/25000000000000000000000000000000000000000000",
+              "log_lower": "1504077396776274073373258352386874841219480981/1000000000000000000000000000000000000000000000",
+              "log_upper": "752038698388137036686629176193437420609740491/500000000000000000000000000000000000000000000",
+              "multiplicity": 2988
+            },
+            {
+              "child": 17,
+              "contribution_lower": "320480050094085743892202695014292708673559341721/20634000000000000000000000000000000000000000000000",
+              "contribution_upper": "1922880300564514463353216170085756252041356052247/123804000000000000000000000000000000000000000000000",
+              "exp_lower": "500489406706016258030509154108734058313731403/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000978813412032516061018308217468116627462807/1000000000000000000000000000000000000000000000",
+              "log_lower": "721726387479919615396326110173227288966639253/500000000000000000000000000000000000000000000",
+              "log_upper": "1443452774959839230792652220346454577933278507/1000000000000000000000000000000000000000000000",
+              "multiplicity": 1356
+            },
+            {
+              "child": 18,
+              "contribution_lower": "134626434809670870700830251005702471332906056561/6878000000000000000000000000000000000000000000000",
+              "contribution_upper": "269252869619341741401660502011404942665812113391/13756000000000000000000000000000000000000000000000",
+              "exp_lower": "500470017879817363200112457270269410159502069/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000940035759634726400224914540538820319004139/1000000000000000000000000000000000000000000000",
+              "log_lower": "346573590279972654708616060729088284037750067/250000000000000000000000000000000000000000000",
+              "log_upper": "1386294361119890618834464242916353136151000269/1000000000000000000000000000000000000000000000",
+              "multiplicity": 1614
+            },
+            {
+              "child": 19,
+              "contribution_lower": "1501355034944577822199402612430539294972430961/181000000000000000000000000000000000000000000000",
+              "contribution_upper": "120108402795566225775952208994443143597794477/14480000000000000000000000000000000000000000000",
+              "exp_lower": "500451678314859274066467537476846431657476987/500000000000000000000000000000000000000000000",
+              "exp_upper": "40036134265188741925317402998147714532598159/40000000000000000000000000000000000000000000",
+              "log_lower": "1332227139849614851033159406331727576284102257/1000000000000000000000000000000000000000000000",
+              "log_upper": "666113569924807425516579703165863788142051129/500000000000000000000000000000000000000000000",
+              "multiplicity": 648
+            },
+            {
+              "child": 20,
+              "contribution_lower": "1376194270784411367058144487545168888349508179/19344375000000000000000000000000000000000000000",
+              "contribution_upper": "3669851388758430312155051966787117035598688481/51585000000000000000000000000000000000000000000",
+              "exp_lower": "125108570071310124278013135231378989849955289/125000000000000000000000000000000000000000000",
+              "exp_upper": "1000868560570480994224105081851031918799642313/1000000000000000000000000000000000000000000000",
+              "log_lower": "256186769092412863521392652415408067568975979/200000000000000000000000000000000000000000000",
+              "log_upper": "160116730682758039700870407759630042230609987/125000000000000000000000000000000000000000000",
+              "multiplicity": 5280
+            },
+            {
+              "child": 21,
+              "contribution_lower": "8767819079685492434805108853633788360681785571329/41268000000000000000000000000000000000000000000000",
+              "contribution_upper": "17535638159370984869610217707267576721363571160179/82536000000000000000000000000000000000000000000000",
+              "exp_lower": "500417731846669278854238277132229231247176849/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000835463693338557708476554264458462494353699/1000000000000000000000000000000000000000000000",
+              "log_lower": "1232143681292632314541588857853875679236906231/1000000000000000000000000000000000000000000000",
+              "log_upper": "154017960161579039317698607231734459904613279/125000000000000000000000000000000000000000000",
+              "multiplicity": 15018
+            },
+            {
+              "child": 22,
+              "contribution_lower": "61209167000676788286637868915423995035962800537/619020000000000000000000000000000000000000000000",
+              "contribution_upper": "255038195836153284527657787147599979316511669159/2579250000000000000000000000000000000000000000000",
+              "exp_lower": "40032156311757219284916853443704378702395553/40000000000000000000000000000000000000000000",
+              "exp_upper": "500401953896965241061460668046304733779944413/500000000000000000000000000000000000000000000",
+              "log_lower": "118562366565773945756301113879627524562427453/100000000000000000000000000000000000000000000",
+              "log_upper": "1185623665657739457563011138796275245624274531/1000000000000000000000000000000000000000000000",
+              "multiplicity": 6672
+            },
+            {
+              "child": 60,
+              "contribution_lower": "733423958987024449128825365436025534734788111/8253600000000000000000000000000000000000000000",
+              "contribution_upper": "2750339846201341684233095120385095755255455419/30951000000000000000000000000000000000000000000",
+              "exp_lower": "200024716087370304307861463300734236745851303/200000000000000000000000000000000000000000000",
+              "exp_upper": "250030895109212880384826829125917795932314129/250000000000000000000000000000000000000000000",
+              "log_lower": "182321556793954626211718025154514633197389337/1000000000000000000000000000000000000000000000",
+              "log_upper": "91160778396977313105859012577257316598694669/500000000000000000000000000000000000000000000",
+              "multiplicity": 2200
+            }
+          ],
+          "upper": "247607999999182720263673570524402262142038012691201/247608000000000000000000000000000000000000000000000"
+        },
+        "saving": "677773948354561/1000000000000000000",
+        "strict_gap_lower": "1096960749330367936545998316872597948340150283/604511718750000000000000000000000000000000000000000000000000000",
+        "upper": "604511718749999998903039250669632063454001683127402051659849717/604511718750000000000000000000000000000000000000000000000000000"
+      },
+      "atom_beta": "677340914792209011107/1000000000000000000000000",
+      "atom_grid": 1000000000000000000000000,
+      "atom_lower_gap": "842533550323109027/1000000000000000000000000000000000000000000",
+      "atom_threshold": "677773948354561/1000639314048354561",
+      "atom_upper_gap": "998645318170415581977786842533550323109027/1000000000000000000000000000000000000000000",
+      "coarse_grid": 1000000000000000000,
+      "coarse_saving": "677773948354561/1000000000000000000",
+      "controls": {
+        "next_coarse_grid_rejected": true,
+        "previous_atom_grid_rejected": true
+      },
+      "old_atom_saving": "384599/10000000000",
+      "ordinary_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000",
+      "rejected": {
+        "bad_fraction": "1/10000000000000000",
+        "edge_count": 294746,
+        "fallback_children_per_edge": 165888,
+        "fallback_lower": "44340239095665503112752912611541335189267919771031/13433593750000000000000000000000000000000000000000000000000000",
+        "fallback_upper": "221701195478327515563764563057706675946339635108913/67167968750000000000000000000000000000000000000000000000000000",
+        "lower": "362707031250000000039805296271292744207821944826366581490067837/362707031250000000000000000000000000000000000000000000000000000",
+        "raw": {
+          "lower": "742823999997548162220487327103484755081851553333773/742824000000000000000000000000000000000000000000000",
+          "saving": "338886974177281/500000000000000000",
+          "strict_gap_lower": "408639629918778816085874153024739085093/123804000000000000000000000000000000000000000000000",
+          "terms": [
+            {
+              "child": 1,
+              "contribution_lower": "350380814487856691769081233093024528176589762123/4126800000000000000000000000000000000000000000000",
+              "contribution_upper": "5255712217317850376536218496395367922648847291287/61902000000000000000000000000000000000000000000000",
+              "exp_lower": "100290281792154381767698091716350881073348849/100000000000000000000000000000000000000000000",
+              "exp_upper": "501451408960771908838490458581754405366744327/500000000000000000000000000000000000000000000",
+              "log_lower": "2138333059508027655521093419109790556760740759/500000000000000000000000000000000000000000000",
+              "log_upper": "4276666119016055311042186838219581113521481519/1000000000000000000000000000000000000000000000",
+              "multiplicity": 125772
+            },
+            {
+              "child": 2,
+              "contribution_lower": "14699158226290795263378361235038462747621926678163/185706000000000000000000000000000000000000000000000",
+              "contribution_upper": "653295921168479789483482721557265011005418974553/8253600000000000000000000000000000000000000000000",
+              "exp_lower": "501215883871203848446085901559602507846759869/500000000000000000000000000000000000000000000",
+              "exp_upper": "200486353548481539378434360623841003138703951/200000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/125000000000000000000000000000000000000000000",
+              "log_upper": "716703787691222000324990943352280909089196277/200000000000000000000000000000000000000000000",
+              "multiplicity": 58654
+            },
+            {
+              "child": 3,
+              "contribution_lower": "3398760426493487742326620741379094277746822923/54300000000000000000000000000000000000000000000",
+              "contribution_upper": "344407723218006757889097568459748220145011391249/5502400000000000000000000000000000000000000000000",
+              "exp_lower": "62634770226359133951703001053542959531706727/62500000000000000000000000000000000000000000",
+              "exp_upper": "1002156323621746143227248016856687352507307637/1000000000000000000000000000000000000000000000",
+              "log_lower": "39725672879349320245586770016213192610924887/12500000000000000000000000000000000000000000",
+              "log_upper": "3178053830347945619646941601297055408873990961/1000000000000000000000000000000000000000000000",
+              "multiplicity": 30930
+            },
+            {
+              "child": 4,
+              "contribution_lower": "40028339505431770178108807196032306932572735869/1547550000000000000000000000000000000000000000000",
+              "contribution_upper": "133427798351439233927029357320107689775242453163/5158500000000000000000000000000000000000000000000",
+              "exp_lower": "50098046940465294340561711133957830954408931/50000000000000000000000000000000000000000000",
+              "exp_upper": "500980469404652943405617111339578309544089311/500000000000000000000000000000000000000000000",
+              "log_lower": "462459481263386350753235615248516476379277/160000000000000000000000000000000000000000",
+              "log_upper": "2890371757896164692207722595303227977370481251/1000000000000000000000000000000000000000000000",
+              "multiplicity": 9588
+            },
+            {
+              "child": 5,
+              "contribution_lower": "89828910681793987447163451971081995480110079153/3301440000000000000000000000000000000000000000000",
+              "contribution_upper": "269486732045381962341490355913245986440330237997/9904320000000000000000000000000000000000000000000",
+              "exp_lower": "1001809412808111384169109129789018536952900511/1000000000000000000000000000000000000000000000",
+              "exp_upper": "1001809412808111384169109129789018536952900513/1000000000000000000000000000000000000000000000",
+              "log_lower": "666807051645488734110356876248348368498970041/250000000000000000000000000000000000000000000",
+              "log_upper": "533445641316390987288285500998678694799176033/200000000000000000000000000000000000000000000",
+              "multiplicity": 8070
+            },
+            {
+              "child": 6,
+              "contribution_lower": "173291612962570650156011159090966457720248713363/10317000000000000000000000000000000000000000000000",
+              "contribution_upper": "902560484180055469562558120265450300626295383/53734375000000000000000000000000000000000000000",
+              "exp_lower": "1001685624061102024023185890699228079307796031/1000000000000000000000000000000000000000000000",
+              "exp_upper": "15651337875954719125362279542175438739184313/15625000000000000000000000000000000000000000",
+              "log_lower": "1242453324894000155114854739919439420399245413/500000000000000000000000000000000000000000000",
+              "log_upper": "2484906649788000310229709479838878840798490827/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4152
+            },
+            {
+              "child": 7,
+              "contribution_lower": "59594067958969049907742674750915694087307787623/3095100000000000000000000000000000000000000000000",
+              "contribution_upper": "7945875727862539987699023300122092544974371691/412680000000000000000000000000000000000000000000",
+              "exp_lower": "500790487050160083258341804629543647792502417/500000000000000000000000000000000000000000000",
+              "exp_upper": "200316194820064033303336721851817459117000967/200000000000000000000000000000000000000000000",
+              "log_lower": "2330755969960742005936834094776401383884396789/1000000000000000000000000000000000000000000000",
+              "log_upper": "233075596996074200593683409477640138388439679/100000000000000000000000000000000000000000000",
+              "multiplicity": 4080
+            },
+            {
+              "child": 8,
+              "contribution_lower": "209812224348338470215653195542378976261841360047/15475500000000000000000000000000000000000000000000",
+              "contribution_upper": "46624938744075215603478487898306439169298080057/3439000000000000000000000000000000000000000000000",
+              "exp_lower": "500745165509161026767668724444818559097473413/500000000000000000000000000000000000000000000",
+              "exp_upper": "1001490331018322053535337448889637118194946827/1000000000000000000000000000000000000000000000",
+              "log_lower": "439444915467243876558098094769010281858996223/200000000000000000000000000000000000000000000",
+              "log_upper": "549306144334054845697622618461262852323745279/250000000000000000000000000000000000000000000",
+              "multiplicity": 2514
+            },
+            {
+              "child": 9,
+              "contribution_lower": "73102958102281770684891484821286970594216793543/6878000000000000000000000000000000000000000000000",
+              "contribution_upper": "4568934881392610667805717801330435662138549601/429875000000000000000000000000000000000000000000",
+              "exp_lower": "1001410384962763981984814860565574939646805391/1000000000000000000000000000000000000000000000",
+              "exp_upper": "62588149060172748874050928785348433727925337/62500000000000000000000000000000000000000000",
+              "log_lower": "2079441541679835928251696364374529704226500403/1000000000000000000000000000000000000000000000",
+              "log_upper": "519860385419958982062924091093632426056625101/250000000000000000000000000000000000000000000",
+              "multiplicity": 1752
+            },
+            {
+              "child": 10,
+              "contribution_lower": "168725600637490073767789747843176894742431632513/12380400000000000000000000000000000000000000000000",
+              "contribution_upper": "337451201274980147535579495686353789484863265363/24760800000000000000000000000000000000000000000000",
+              "exp_lower": "500669438093442355394034860068774168375168049/500000000000000000000000000000000000000000000",
+              "exp_upper": "1001338876186884710788069720137548336750336099/1000000000000000000000000000000000000000000000",
+              "log_lower": "197408102602200962702419538353521690592038003/100000000000000000000000000000000000000000000",
+              "log_upper": "1974081026022009627024195383535216905920380031/1000000000000000000000000000000000000000000000",
+              "multiplicity": 2022
+            },
+            {
+              "child": 11,
+              "contribution_lower": "370805209485262361754478721214145988918857274587/41268000000000000000000000000000000000000000000000",
+              "contribution_upper": "139051953556973385657929520455304745844571478109/15475500000000000000000000000000000000000000000000",
+              "exp_lower": "1001274193029511327869879535231717341815096151/1000000000000000000000000000000000000000000000",
+              "exp_upper": "125159274128688915983734941903964667726887019/125000000000000000000000000000000000000000000",
+              "log_lower": "234846355777210595872530407531806476712471833/125000000000000000000000000000000000000000000",
+              "log_upper": "375754169243536953396048652050890362739954933/200000000000000000000000000000000000000000000",
+              "multiplicity": 1212
+            },
+            {
+              "child": 12,
+              "contribution_lower": "677822653558886284371893315501806719057087836701/20634000000000000000000000000000000000000000000000",
+              "contribution_upper": "112970442259814380728648885916967786509514639563/3439000000000000000000000000000000000000000000000",
+              "exp_lower": "1001215145581811350623180672823939023718002713/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500607572790905675311590336411969511859001357/500000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/250000000000000000000000000000000000000000000",
+              "log_upper": "1791759469228055000812477358380702272722990693/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4062
+            },
+            {
+              "child": 13,
+              "contribution_lower": "3527089605042755650885035385753316005622697399413/247608000000000000000000000000000000000000000000000",
+              "contribution_upper": "146962066876781485453543141073054833567612391789/10317000000000000000000000000000000000000000000000",
+              "exp_lower": "1001160830270438731446220660162735170486147431/1000000000000000000000000000000000000000000000",
+              "exp_upper": "125145103783804841430777582520341896310768429/125000000000000000000000000000000000000000000",
+              "log_lower": "1711716761554518574988699396654262508716213573/1000000000000000000000000000000000000000000000",
+              "log_upper": "855858380777259287494349698327131254358106787/500000000000000000000000000000000000000000000",
+              "multiplicity": 1626
+            },
+            {
+              "child": 14,
+              "contribution_lower": "11913215482807397988395364845293391009448059303/343900000000000000000000000000000000000000000000",
+              "contribution_upper": "119132154828073979883953648452933910094480593149/3439000000000000000000000000000000000000000000000",
+              "exp_lower": "100111054477373092339456847439440260583597137/100000000000000000000000000000000000000000000",
+              "exp_upper": "1001110544773730923394568474394402605835971371/1000000000000000000000000000000000000000000000",
+              "log_lower": "818804394700398348259800986659112407904448327/500000000000000000000000000000000000000000000",
+              "log_upper": "327521757880159339303920394663644963161779331/200000000000000000000000000000000000000000000",
+              "multiplicity": 3672
+            },
+            {
+              "child": 15,
+              "contribution_lower": "750797799274887060915902298803110995205267329/85975000000000000000000000000000000000000000000",
+              "contribution_upper": "3003191197099548243663609195212443980821069319/343900000000000000000000000000000000000000000000",
+              "exp_lower": "250265933091629020305300766267703665068422443/250000000000000000000000000000000000000000000",
+              "exp_upper": "1001063732366516081221203065070814660273689773/1000000000000000000000000000000000000000000000",
+              "log_lower": "784307958956922622523091134035433884674194803/500000000000000000000000000000000000000000000",
+              "log_upper": "1568615917913845245046182268070867769348389607/1000000000000000000000000000000000000000000000",
+              "multiplicity": 864
+            },
+            {
+              "child": 16,
+              "contribution_lower": "20771163843510964929314070781488664010322226501/644812500000000000000000000000000000000000000000",
+              "contribution_upper": "27694885124681286572418761041984885347096302029/859750000000000000000000000000000000000000000000",
+              "exp_lower": "250254986066397167823061093752875470003882247/250000000000000000000000000000000000000000000",
+              "exp_upper": "1001019944265588671292244375011501880015528989/1000000000000000000000000000000000000000000000",
+              "log_lower": "1504077396776274073373258352386874841219480981/1000000000000000000000000000000000000000000000",
+              "log_upper": "752038698388137036686629176193437420609740491/500000000000000000000000000000000000000000000",
+              "multiplicity": 2988
+            },
+            {
+              "child": 17,
+              "contribution_lower": "1922880300564514466128803075851214370735079050661/123804000000000000000000000000000000000000000000000",
+              "contribution_upper": "320480050094085744354800512641869061789179842097/20634000000000000000000000000000000000000000000000",
+              "exp_lower": "1000978813412032517505883954113073592261883941/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500489406706016258752941977056536796130941971/500000000000000000000000000000000000000000000",
+              "log_lower": "721726387479919615396326110173227288966639253/500000000000000000000000000000000000000000000",
+              "log_upper": "1443452774959839230792652220346454577933278507/1000000000000000000000000000000000000000000000",
+              "multiplicity": 1356
+            },
+            {
+              "child": 18,
+              "contribution_lower": "33656608702417717721865529610005938590399900833/1719500000000000000000000000000000000000000000000",
+              "contribution_upper": "269252869619341741774924236880047508723199206933/13756000000000000000000000000000000000000000000000",
+              "exp_lower": "125117504469954340973477805241657764276579557/125000000000000000000000000000000000000000000",
+              "exp_upper": "1000940035759634727787822441933262114212636457/1000000000000000000000000000000000000000000000",
+              "log_lower": "346573590279972654708616060729088284037750067/250000000000000000000000000000000000000000000",
+              "log_upper": "1386294361119890618834464242916353136151000269/1000000000000000000000000000000000000000000000",
+              "multiplicity": 1614
+            },
+            {
+              "child": 19,
+              "contribution_lower": "750677517472288912099774268266786383149318727/90500000000000000000000000000000000000000000000",
+              "contribution_upper": "3002710069889155648399097073067145532597274911/362000000000000000000000000000000000000000000000",
+              "exp_lower": "250225839157429637366591422755595461049772909/250000000000000000000000000000000000000000000",
+              "exp_upper": "1000903356629718549466365691022381844199091637/1000000000000000000000000000000000000000000000",
+              "log_lower": "1332227139849614851033159406331727576284102257/1000000000000000000000000000000000000000000000",
+              "log_upper": "666113569924807425516579703165863788142051129/500000000000000000000000000000000000000000000",
+              "multiplicity": 648
+            },
+            {
+              "child": 20,
+              "contribution_lower": "440382166651011638022706658215650039862604459/6190200000000000000000000000000000000000000000",
+              "contribution_upper": "5504777083137645475283833227695625498282555743/77377500000000000000000000000000000000000000000",
+              "exp_lower": "40034742422819239820246059837786367260236769/40000000000000000000000000000000000000000000",
+              "exp_upper": "500434280285240497753075747972329590752959613/500000000000000000000000000000000000000000000",
+              "log_lower": "256186769092412863521392652415408067568975979/200000000000000000000000000000000000000000000",
+              "log_upper": "160116730682758039700870407759630042230609987/125000000000000000000000000000000000000000000",
+              "multiplicity": 5280
+            },
+            {
+              "child": 21,
+              "contribution_lower": "140285105274967879129733147702164008464416469009/660288000000000000000000000000000000000000000000",
+              "contribution_upper": "8767819079685492445608321731385250529026029321823/41268000000000000000000000000000000000000000000000",
+              "exp_lower": "8006683709546708471533197174942298297152929/8000000000000000000000000000000000000000000",
+              "exp_upper": "500417731846669279470824823433893643572058063/500000000000000000000000000000000000000000000",
+              "log_lower": "1232143681292632314541588857853875679236906231/1000000000000000000000000000000000000000000000",
+              "log_upper": "154017960161579039317698607231734459904613279/125000000000000000000000000000000000000000000",
+              "multiplicity": 15018
+            },
+            {
+              "child": 22,
+              "contribution_lower": "510076391672306569660074215555192921572711189931/5158500000000000000000000000000000000000000000000",
+              "contribution_upper": "765114587508459854490111323332789382359066785661/7737750000000000000000000000000000000000000000000",
+              "exp_lower": "1000803907793930483309498133855839610672422217/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500401953896965241654749066927919805336211109/500000000000000000000000000000000000000000000",
+              "log_lower": "118562366565773945756301113879627524562427453/100000000000000000000000000000000000000000000",
+              "log_upper": "1185623665657739457563011138796275245624274531/1000000000000000000000000000000000000000000000",
+              "multiplicity": 6672
+            },
+            {
+              "child": 60,
+              "contribution_lower": "440054375392214669557526618057115216800669839/4952160000000000000000000000000000000000000000",
+              "contribution_upper": "1833559897467561123156360908571313403336124331/20634000000000000000000000000000000000000000000",
+              "exp_lower": "40004943217474060868866056187010474254606349/40000000000000000000000000000000000000000000",
+              "exp_upper": "500061790218425760860825702337630928182579363/500000000000000000000000000000000000000000000",
+              "log_lower": "182321556793954626211718025154514633197389337/1000000000000000000000000000000000000000000000",
+              "log_upper": "91160778396977313105859012577257316598694669/500000000000000000000000000000000000000000000",
+              "multiplicity": 2200
+            }
+          ],
+          "upper": "123803999999591360370081221183914125846975260914907/123804000000000000000000000000000000000000000000000"
+        },
+        "saving": "338886974177281/500000000000000000",
+        "strict_gap_lower": "-3491692655376556509458065856294020665972643/31816406250000000000000000000000000000000000000000000000000000",
+        "upper": "31816406250000000003491692655376556509458065856294020665972643/31816406250000000000000000000000000000000000000000000000000000"
+      },
+      "scope": "Adjacent coarse exclusion for this fixed worst-case bad-class envelope and least atom on the stated grid; no true bad-fraction or global optimality claim."
+    },
+    "foreign_producer_replays": 0,
+    "formal": [
+      {
+        "all_dirty_and_source_columns_restored": true,
+        "defining_decoder": true,
+        "formal_variables": 20668,
+        "identity": true,
+        "ring": "2",
+        "target_contract": "F2 identity"
+      },
+      {
+        "all_dirty_and_source_columns_restored": true,
+        "defining_decoder": true,
+        "formal_variables": 20668,
+        "identity": false,
+        "ring": "0",
+        "target_contract": "integer defining decoder"
+      }
+    ],
+    "overridden_profile": {
+      "R": 17148,
+      "W_per_vertex": 20668,
+      "changed_operation_frames": 7282,
+      "child_histogram": {
+        "1": 125772,
+        "10": 2022,
+        "11": 1212,
+        "12": 4062,
+        "13": 1626,
+        "14": 3672,
+        "15": 864,
+        "16": 2988,
+        "17": 1356,
+        "18": 1614,
+        "19": 648,
+        "2": 58654,
+        "20": 5280,
+        "21": 15120,
+        "22": 6672,
+        "3": 31032,
+        "4": 9588,
+        "5": 8070,
+        "6": 4152,
+        "60": 2200,
+        "7": 4080,
+        "8": 2514,
+        "9": 1752
+      },
+      "deficit_per_vertex": 1936,
+      "foreign_producer_replays": 0,
+      "frames_not_contained_in_original": 84,
+      "h": 24,
+      "loss": 528,
+      "m": 72,
+      "maxchild": 60,
+      "physical_internal_histogram": {
+        "1": 35764,
+        "10": 674,
+        "11": 404,
+        "12": 1354,
+        "13": 542,
+        "14": 1224,
+        "15": 288,
+        "16": 996,
+        "17": 452,
+        "18": 538,
+        "19": 216,
+        "2": 17498,
+        "21": 4160,
+        "22": 1344,
+        "3": 10344,
+        "4": 3196,
+        "5": 2690,
+        "6": 1384,
+        "7": 1360,
+        "8": 838,
+        "9": 584
+      },
+      "physical_target_histogram": {
+        "1": 4400,
+        "20": 880,
+        "21": 880
+      },
+      "rank_per_vertex": 1486160,
+      "reused_registers": 1760,
+      "selected_rank_histogram": {
+        "20": 2200
+      },
+      "selected_roles": 2200,
+      "v": 1760,
+      "virtual_R": 18908
+    },
+    "parent_profile": {
+      "package_checker": {
+        "W": 22428,
+        "roles": 18908
+      },
+      "package_profile": {
+        "R": 18908,
+        "W_per_vertex": 22428,
+        "deficit_per_vertex": 1936,
+        "loss": 528,
+        "m": 72,
+        "rank_per_vertex": 1612880
+      }
+    },
+    "prime_witnesses": {
+      "adverse_controls": [
+        "zero determinant",
+        "incorrect factor identity",
+        "residual above retained prime lower bound"
+      ],
+      "all_remaining_factors_below_retained_prime_lower_bound": true,
+      "h": 24,
+      "input_sha256": {
+        "research/paired-cube-diagonal-bit-168/selected/bit/frames_p12.json.gz": "ad8e2705652b68476713d7647a8592505e222f2b3ccd1728dedce153aac6d462",
+        "research/paired-cube-diagonal-bit-168/selected/bit/graph_p12.json": "31a09a55920e64c8bfbac8b845dc01754c112aa6e207812e2fd1f4939d8f64cb",
+        "research/paired-cube-diagonal-bit-168/selected/bit/kchron_p12.json": "0fab548e84cf5ca7c04e8bd19b5810850463f36e0f92180efe73aeff17105e39",
+        "research/paired-cube-diagonal-bit-168/selected/bit/profile_p12.json": "c44ef8640cbcbcc9bac3a30e13373bd79efddde55d7cea514354ca2cdb60d66d",
+        "research/paired-cube-diagonal-bit-168/selected/bit/word_p12.json.gz": "1cb7e8ed45cf542e304fddc4b12247dbb248a0dc84dedbd832f336b2d172793a"
+      },
+      "maximum_determinant_bits": 118,
+      "rule": "Every q>2^80 avoids every nonzero used-frame determinant, so the original prime range is unchanged.",
+      "scope": "Exact integer cleared-Gram factors for all physical frames including every changed operation, gauge, source, root, partner-mix, delivery and ambient frame. Uniform split-rank and fallback arguments remain the retained local-ring interface.",
+      "script_sha256": "98cd03bc9582e7bd0ab194c191ea8eea940539e510051443ab9fd3e572a364ab",
+      "source_commit": "4a3c769e5c5430e7114c4d3e099ff34664677f17",
+      "status": "PASS exact prime witnesses for every used physical frame",
+      "stripped_primes": [
+        2,
+        3,
+        5,
+        7,
+        11,
+        13,
+        17,
+        19,
+        23,
+        29,
+        31
+      ],
+      "total_operation_frames": 7282,
+      "total_used_frames": 24401,
+      "unique_used_bases": 24401,
+      "witness_file": "bit/prime-witnesses.json.gz",
+      "witness_sha256": "612f0b91c7689b0cebcacb28278579aa2c88801df640798d7a119f11eca836c3"
+    },
+    "profile": {
+      "R": 17114,
+      "W_per_vertex": 20634,
+      "active_virtual_R": 18874,
+      "changed_operation_frames": 7282,
+      "child_histogram": {
+        "1": 125772,
+        "10": 2022,
+        "11": 1212,
+        "12": 4062,
+        "13": 1626,
+        "14": 3672,
+        "15": 864,
+        "16": 2988,
+        "17": 1356,
+        "18": 1614,
+        "19": 648,
+        "2": 58654,
+        "20": 5280,
+        "21": 15018,
+        "22": 6672,
+        "3": 30930,
+        "4": 9588,
+        "5": 8070,
+        "6": 4152,
+        "60": 2200,
+        "7": 4080,
+        "8": 2514,
+        "9": 1752
+      },
+      "deficit_per_vertex": 1936,
+      "foreign_producer_replays": 0,
+      "frames_not_contained_in_original": 84,
+      "h": 24,
+      "loss": 528,
+      "m": 72,
+      "maxchild": 60,
+      "physical_internal_histogram": {
+        "1": 35764,
+        "10": 674,
+        "11": 404,
+        "12": 1354,
+        "13": 542,
+        "14": 1207,
+        "15": 288,
+        "16": 993,
+        "17": 452,
+        "18": 533,
+        "19": 208,
+        "2": 17469,
+        "21": 4160,
+        "22": 1344,
+        "3": 10301,
+        "4": 3196,
+        "5": 2673,
+        "6": 1384,
+        "7": 1359,
+        "8": 838,
+        "9": 583
+      },
+      "physical_target_histogram": {
+        "1": 4400,
+        "14": 17,
+        "16": 3,
+        "18": 5,
+        "19": 8,
+        "2": 29,
+        "20": 880,
+        "21": 846,
+        "3": 9,
+        "5": 17,
+        "7": 1,
+        "9": 1
+      },
+      "rank_per_vertex": 1483712,
+      "reused_registers": 1760,
+      "scalar_role_reserve": 18908,
+      "selected_rank_histogram": {
+        "20": 2200
+      },
+      "selected_roles": 2200,
+      "terminal_sinks": 34,
+      "v": 1760,
+      "virtual_R": 18908
+    },
+    "scope": "Complete F2 identity, integer defining decoder, exact physical frame geometry and retained weighted-compiler contracts.",
+    "status": "PASS",
+    "terminal": {
+      "all_original_adjoint_responses_retained": true,
+      "base_exceeds_twice_bound": true,
+      "baseline_profile": {
+        "R": 17148,
+        "W_per_vertex": 20668,
+        "changed_operation_frames": 7282,
+        "child_histogram": {
+          "1": 125772,
+          "10": 2022,
+          "11": 1212,
+          "12": 4062,
+          "13": 1626,
+          "14": 3672,
+          "15": 864,
+          "16": 2988,
+          "17": 1356,
+          "18": 1614,
+          "19": 648,
+          "2": 58654,
+          "20": 5280,
+          "21": 15120,
+          "22": 6672,
+          "3": 31032,
+          "4": 9588,
+          "5": 8070,
+          "6": 4152,
+          "60": 2200,
+          "7": 4080,
+          "8": 2514,
+          "9": 1752
+        },
+        "deficit_per_vertex": 1936,
+        "foreign_producer_replays": 0,
+        "frames_not_contained_in_original": 84,
+        "h": 24,
+        "loss": 528,
+        "m": 72,
+        "maxchild": 60,
+        "physical_internal_histogram": {
+          "1": 35764,
+          "10": 674,
+          "11": 404,
+          "12": 1354,
+          "13": 542,
+          "14": 1224,
+          "15": 288,
+          "16": 996,
+          "17": 452,
+          "18": 538,
+          "19": 216,
+          "2": 17498,
+          "21": 4160,
+          "22": 1344,
+          "3": 10344,
+          "4": 3196,
+          "5": 2690,
+          "6": 1384,
+          "7": 1360,
+          "8": 838,
+          "9": 584
+        },
+        "physical_target_histogram": {
+          "1": 4400,
+          "20": 880,
+          "21": 880
+        },
+        "rank_per_vertex": 1486160,
+        "reused_registers": 1760,
+        "selected_rank_histogram": {
+          "20": 2200
+        },
+        "selected_roles": 2200,
+        "v": 1760,
+        "virtual_R": 18908
+      },
+      "child_delta": {
+        "21": -102,
+        "3": -102
+      },
+      "controls": {
+        "omit-ancestor-response": "REJECTED",
+        "omit-pre-target": "REJECTED",
+        "omit-write": "REJECTED"
+      },
+      "foreign_producer_replays": 0,
+      "formal": [
+        {
+          "all_outputs": true,
+          "all_sources_and_dirty_restored": true,
+          "direction": 1,
+          "dirty_columns": 17114,
+          "formal_columns": 20634,
+          "mode": "F2",
+          "partner_mix_unmix_at_original_anchors": true,
+          "retained_cleanup_literal_reverse": true,
+          "source_columns": 1760,
+          "target_columns": 1760
+        },
+        {
+          "all_outputs": true,
+          "all_sources_and_dirty_restored": true,
+          "direction": 1,
+          "dirty_columns": 17114,
+          "formal_columns": 20634,
+          "mode": "Z",
+          "partner_mix_unmix_at_original_anchors": true,
+          "retained_cleanup_literal_reverse": true,
+          "source_columns": 1760,
+          "target_columns": 1760
+        },
+        {
+          "all_outputs": true,
+          "all_sources_and_dirty_restored": true,
+          "direction": -1,
+          "dirty_columns": 17114,
+          "formal_columns": 20634,
+          "mode": "Z",
+          "partner_mix_unmix_at_original_anchors": true,
+          "retained_cleanup_literal_reverse": true,
+          "source_columns": 1760,
+          "target_columns": 1760
+        }
+      ],
+      "integer_residual_bound": 39780,
+      "literal_sandwich_inverse": true,
+      "new_frames_added": 0,
+      "original_partner_delivery_anchors_retained": true,
+      "packed_digit_bits": 24,
+      "profile": {
+        "R": 17114,
+        "W_per_vertex": 20634,
+        "active_virtual_R": 18874,
+        "changed_operation_frames": 7282,
+        "child_histogram": {
+          "1": 125772,
+          "10": 2022,
+          "11": 1212,
+          "12": 4062,
+          "13": 1626,
+          "14": 3672,
+          "15": 864,
+          "16": 2988,
+          "17": 1356,
+          "18": 1614,
+          "19": 648,
+          "2": 58654,
+          "20": 5280,
+          "21": 15018,
+          "22": 6672,
+          "3": 30930,
+          "4": 9588,
+          "5": 8070,
+          "6": 4152,
+          "60": 2200,
+          "7": 4080,
+          "8": 2514,
+          "9": 1752
+        },
+        "deficit_per_vertex": 1936,
+        "foreign_producer_replays": 0,
+        "frames_not_contained_in_original": 84,
+        "h": 24,
+        "loss": 528,
+        "m": 72,
+        "maxchild": 60,
+        "physical_internal_histogram": {
+          "1": 35764,
+          "10": 674,
+          "11": 404,
+          "12": 1354,
+          "13": 542,
+          "14": 1207,
+          "15": 288,
+          "16": 993,
+          "17": 452,
+          "18": 533,
+          "19": 208,
+          "2": 17469,
+          "21": 4160,
+          "22": 1344,
+          "3": 10301,
+          "4": 3196,
+          "5": 2673,
+          "6": 1384,
+          "7": 1359,
+          "8": 838,
+          "9": 583
+        },
+        "physical_target_histogram": {
+          "1": 4400,
+          "14": 17,
+          "16": 3,
+          "18": 5,
+          "19": 8,
+          "2": 29,
+          "20": 880,
+          "21": 846,
+          "3": 9,
+          "5": 17,
+          "7": 1,
+          "9": 1
+        },
+        "rank_per_vertex": 1483712,
+        "reused_registers": 1760,
+        "scalar_role_reserve": 18908,
+        "selected_rank_histogram": {
+          "20": 2200
+        },
+        "selected_roles": 2200,
+        "terminal_sinks": 34,
+        "v": 1760,
+        "virtual_R": 18908
+      },
+      "scalar_addition_delta": -158,
+      "scalar_bill": "Retain the original conservative full-word scalar inventory: removed old root reads/old root corrections and deleted inverse gates dominate the new pre/post target shears.",
+      "selected": [
+        {
+          "deleted_path": [
+            3,
+            9,
+            2,
+            7,
+            3
+          ],
+          "pivot": 8,
+          "role": 8660,
+          "root": 30,
+          "root_frame": 25212,
+          "root_rank": 21,
+          "targets": [
+            8,
+            9,
+            10,
+            11
+          ],
+          "writes": [
+            9837,
+            22811,
+            24471,
+            31019
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 136,
+          "role": 12631,
+          "root": 510,
+          "root_frame": 25564,
+          "root_rank": 21,
+          "targets": [
+            136,
+            137,
+            138,
+            139
+          ],
+          "writes": [
+            17498,
+            28429,
+            31006
+          ]
+        },
+        {
+          "deleted_path": [
+            16,
+            3,
+            2,
+            3
+          ],
+          "pivot": 160,
+          "role": 14425,
+          "root": 600,
+          "root_frame": 25630,
+          "root_rank": 21,
+          "targets": [
+            160,
+            161,
+            162,
+            163
+          ],
+          "writes": [
+            26491,
+            28438,
+            31056
+          ]
+        },
+        {
+          "deleted_path": [
+            3,
+            18,
+            3
+          ],
+          "pivot": 288,
+          "role": 8939,
+          "root": 1080,
+          "root_frame": 25982,
+          "root_rank": 21,
+          "targets": [
+            288,
+            289,
+            290,
+            291
+          ],
+          "writes": [
+            10386,
+            31059
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 344,
+          "role": 12634,
+          "root": 1290,
+          "root_frame": 26136,
+          "root_rank": 21,
+          "targets": [
+            344,
+            345,
+            346,
+            347
+          ],
+          "writes": [
+            17505,
+            28468,
+            31040
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 400,
+          "role": 14698,
+          "root": 1500,
+          "root_frame": 26290,
+          "root_rank": 21,
+          "targets": [
+            400,
+            401,
+            402,
+            403
+          ],
+          "writes": [
+            28437,
+            31026
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 416,
+          "role": 14076,
+          "root": 1560,
+          "root_frame": 26334,
+          "root_rank": 21,
+          "targets": [
+            416,
+            417,
+            418,
+            419
+          ],
+          "writes": [
+            24448,
+            28444,
+            30985
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 496,
+          "role": 12705,
+          "root": 1860,
+          "root_frame": 26554,
+          "root_rank": 21,
+          "targets": [
+            496,
+            497,
+            498,
+            499
+          ],
+          "writes": [
+            17700,
+            28593,
+            31231
+          ]
+        },
+        {
+          "deleted_path": [
+            16,
+            3,
+            2,
+            3
+          ],
+          "pivot": 520,
+          "role": 14437,
+          "root": 1950,
+          "root_frame": 26620,
+          "root_rank": 21,
+          "targets": [
+            520,
+            521,
+            522,
+            523
+          ],
+          "writes": [
+            26609,
+            28602,
+            31287
+          ]
+        },
+        {
+          "deleted_path": [
+            3,
+            18,
+            3
+          ],
+          "pivot": 648,
+          "role": 9811,
+          "root": 2430,
+          "root_frame": 26972,
+          "root_rank": 21,
+          "targets": [
+            648,
+            649,
+            650,
+            651
+          ],
+          "writes": [
+            12068,
+            31290
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 704,
+          "role": 12708,
+          "root": 2640,
+          "root_frame": 27126,
+          "root_rank": 21,
+          "targets": [
+            704,
+            705,
+            706,
+            707
+          ],
+          "writes": [
+            17707,
+            28632,
+            31269
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 760,
+          "role": 14708,
+          "root": 2850,
+          "root_frame": 27280,
+          "root_rank": 21,
+          "targets": [
+            760,
+            761,
+            762,
+            763
+          ],
+          "writes": [
+            28601,
+            31254
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 776,
+          "role": 14094,
+          "root": 2910,
+          "root_frame": 27324,
+          "root_rank": 21,
+          "targets": [
+            776,
+            777,
+            778,
+            779
+          ],
+          "writes": [
+            24562,
+            28608,
+            31209
+          ]
+        },
+        {
+          "deleted_path": [
+            16,
+            3,
+            2,
+            3
+          ],
+          "pivot": 808,
+          "role": 14449,
+          "root": 3030,
+          "root_frame": 27412,
+          "root_rank": 21,
+          "targets": [
+            808,
+            809,
+            810,
+            811
+          ],
+          "writes": [
+            26727,
+            28766,
+            31539
+          ]
+        },
+        {
+          "deleted_path": [
+            3,
+            18,
+            3
+          ],
+          "pivot": 936,
+          "role": 10525,
+          "root": 3510,
+          "root_frame": 27764,
+          "root_rank": 21,
+          "targets": [
+            936,
+            937,
+            938,
+            939
+          ],
+          "writes": [
+            13430,
+            31542
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 992,
+          "role": 12782,
+          "root": 3720,
+          "root_frame": 27918,
+          "root_rank": 21,
+          "targets": [
+            992,
+            993,
+            994,
+            995
+          ],
+          "writes": [
+            17909,
+            28796,
+            31520
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1048,
+          "role": 14718,
+          "root": 3930,
+          "root_frame": 28072,
+          "root_rank": 21,
+          "targets": [
+            1048,
+            1049,
+            1050,
+            1051
+          ],
+          "writes": [
+            28765,
+            31502
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1064,
+          "role": 14112,
+          "root": 3990,
+          "root_frame": 28116,
+          "root_rank": 21,
+          "targets": [
+            1064,
+            1065,
+            1066,
+            1067
+          ],
+          "writes": [
+            24676,
+            28772,
+            31454
+          ]
+        },
+        {
+          "deleted_path": [
+            3,
+            18,
+            3
+          ],
+          "pivot": 1160,
+          "role": 11085,
+          "root": 4350,
+          "root_frame": 28380,
+          "root_rank": 21,
+          "targets": [
+            1160,
+            1161,
+            1162,
+            1163
+          ],
+          "writes": [
+            14494,
+            31809
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 1216,
+          "role": 12856,
+          "root": 4560,
+          "root_frame": 28534,
+          "root_rank": 21,
+          "targets": [
+            1216,
+            1217,
+            1218,
+            1219
+          ],
+          "writes": [
+            18111,
+            28960,
+            31785
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1272,
+          "role": 14728,
+          "root": 4770,
+          "root_frame": 28688,
+          "root_rank": 21,
+          "targets": [
+            1272,
+            1273,
+            1274,
+            1275
+          ],
+          "writes": [
+            28929,
+            31767
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1288,
+          "role": 14130,
+          "root": 4830,
+          "root_frame": 28732,
+          "root_rank": 21,
+          "targets": [
+            1288,
+            1289,
+            1290,
+            1291
+          ],
+          "writes": [
+            24790,
+            28936,
+            31716
+          ]
+        },
+        {
+          "deleted_path": [
+            3,
+            18,
+            3
+          ],
+          "pivot": 1328,
+          "role": 11089,
+          "root": 4980,
+          "root_frame": 28842,
+          "root_rank": 21,
+          "targets": [
+            1328,
+            1329,
+            1330,
+            1331
+          ],
+          "writes": [
+            14502,
+            32093
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 1384,
+          "role": 12930,
+          "root": 5190,
+          "root_frame": 28996,
+          "root_rank": 21,
+          "targets": [
+            1384,
+            1385,
+            1386,
+            1387
+          ],
+          "writes": [
+            18313,
+            29124,
+            32066
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1440,
+          "role": 14738,
+          "root": 5400,
+          "root_frame": 29150,
+          "root_rank": 21,
+          "targets": [
+            1440,
+            1441,
+            1442,
+            1443
+          ],
+          "writes": [
+            29093,
+            32048
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1456,
+          "role": 14148,
+          "root": 5460,
+          "root_frame": 29194,
+          "root_rank": 21,
+          "targets": [
+            1456,
+            1457,
+            1458,
+            1459
+          ],
+          "writes": [
+            24904,
+            29100,
+            31994
+          ]
+        },
+        {
+          "deleted_path": [
+            5,
+            14,
+            2,
+            3
+          ],
+          "pivot": 1504,
+          "role": 13004,
+          "root": 5640,
+          "root_frame": 29326,
+          "root_rank": 21,
+          "targets": [
+            1504,
+            1505,
+            1506,
+            1507
+          ],
+          "writes": [
+            18515,
+            29288,
+            32360
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1560,
+          "role": 14748,
+          "root": 5850,
+          "root_frame": 29480,
+          "root_rank": 21,
+          "targets": [
+            1560,
+            1561,
+            1562,
+            1563
+          ],
+          "writes": [
+            29257,
+            32341
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1576,
+          "role": 14166,
+          "root": 5910,
+          "root_frame": 29524,
+          "root_rank": 21,
+          "targets": [
+            1576,
+            1577,
+            1578,
+            1579
+          ],
+          "writes": [
+            25018,
+            29264,
+            32286
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1640,
+          "role": 14758,
+          "root": 6150,
+          "root_frame": 29700,
+          "root_rank": 21,
+          "targets": [
+            1640,
+            1641,
+            1642,
+            1643
+          ],
+          "writes": [
+            29421,
+            32647
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1656,
+          "role": 14184,
+          "root": 6210,
+          "root_frame": 29744,
+          "root_rank": 21,
+          "targets": [
+            1656,
+            1657,
+            1658,
+            1659
+          ],
+          "writes": [
+            25132,
+            29428,
+            32591
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1688,
+          "role": 14768,
+          "root": 6330,
+          "root_frame": 29832,
+          "root_rank": 21,
+          "targets": [
+            1688,
+            1689,
+            1690,
+            1691
+          ],
+          "writes": [
+            29585,
+            32962
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1704,
+          "role": 14202,
+          "root": 6390,
+          "root_frame": 29876,
+          "root_rank": 21,
+          "targets": [
+            1704,
+            1705,
+            1706,
+            1707
+          ],
+          "writes": [
+            25246,
+            29592,
+            32905
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1728,
+          "role": 14220,
+          "root": 6480,
+          "root_frame": 29942,
+          "root_rank": 21,
+          "targets": [
+            1728,
+            1729,
+            1730,
+            1731
+          ],
+          "writes": [
+            25360,
+            29756,
+            33227
+          ]
+        }
+      ],
+      "status": "PASS complete terminal bit word, exact geometry/ledger/F2/integer columns",
+      "target_events": 16810
+    },
+    "word_controls": [
+      "omit_compensation",
+      "missing_partner",
+      "stale",
+      "zero_operation_frame"
+    ]
+  },
+  "complex": {
+    "moment": {
+      "accepted": {
+        "lower": "28958599999999972643161690227622507425401034850261/28958600000000000000000000000000000000000000000000",
+        "saving": "665489485337/1000000000000000",
+        "strict_gap_lower": "6839209577443094373143649741194477/7239650000000000000000000000000000000000000000000",
+        "terms": [
+          {
+            "child": 1,
+            "contribution_lower": "19554445203974510661879082169868440022400954857/180991250000000000000000000000000000000000000000",
+            "contribution_upper": "19554445203974510661879082169868440022400956807/180991250000000000000000000000000000000000000000",
+            "exp_lower": "501396030871141299022540568458165128779511663/500000000000000000000000000000000000000000000",
+            "exp_upper": "501396030871141299022540568458165128779511713/500000000000000000000000000000000000000000000",
+            "log_lower": "2094827371013212772437210468172915786272348773/500000000000000000000000000000000000000000000",
+            "log_upper": "4189654742026425544874420936345831572544697547/1000000000000000000000000000000000000000000000",
+            "multiplicity": 93600
+          },
+          {
+            "child": 2,
+            "contribution_lower": "284360907044751102414242635607473432559626590831/2895860000000000000000000000000000000000000000000",
+            "contribution_upper": "71090226761187775603560658901868358139906648417/723965000000000000000000000000000000000000000000",
+            "exp_lower": "100232959832481883120987887066434061529653363/100000000000000000000000000000000000000000000",
+            "exp_upper": "25058239958120470780246971766608515382413341/25000000000000000000000000000000000000000000",
+            "log_lower": "3496507561466480235457188814887655004469197411/1000000000000000000000000000000000000000000000",
+            "log_upper": "874126890366620058864297203721913751117299353/250000000000000000000000000000000000000000000",
+            "multiplicity": 42555
+          },
+          {
+            "child": 3,
+            "contribution_lower": "3685949412113871892547126185129066073969827080471/36198250000000000000000000000000000000000000000000",
+            "contribution_upper": "29487595296910975140377009481032528591758616732049/289586000000000000000000000000000000000000000000000",
+            "exp_lower": "125257396680391201704119556364191595268624973/125000000000000000000000000000000000000000000",
+            "exp_upper": "1002059173443129613632956450913532762148999787/1000000000000000000000000000000000000000000000",
+            "log_lower": "772760613339578963369793924855826466974301747/250000000000000000000000000000000000000000000",
+            "log_upper": "3091042453358315853479175699423305867897206989/1000000000000000000000000000000000000000000000",
+            "multiplicity": 29427
+          },
+          {
+            "child": 4,
+            "contribution_lower": "18083705634726347850960500630149793348832701261/361982500000000000000000000000000000000000000000",
+            "contribution_upper": "180837056347263478509605006301497933488327012971/3619825000000000000000000000000000000000000000000",
+            "exp_lower": "50093367409214259974959835540581145010616901/50000000000000000000000000000000000000000000",
+            "exp_upper": "500933674092142599749598355405811450106169011/500000000000000000000000000000000000000000000",
+            "log_lower": "2803360380906534926039956693429478436393697277/1000000000000000000000000000000000000000000000",
+            "log_upper": "1401680190453267463019978346714739218196848639/500000000000000000000000000000000000000000000",
+            "multiplicity": 10830
+          },
+          {
+            "child": 5,
+            "contribution_lower": "588008807776444355592419854799690204006330237353/14479300000000000000000000000000000000000000000000",
+            "contribution_upper": "588008807776444355592419854799690204006330238527/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "1001718582242665001009233142759267809210102619/1000000000000000000000000000000000000000000000",
+            "exp_upper": "1001718582242665001009233142759267809210102621/1000000000000000000000000000000000000000000000",
+            "log_lower": "2580216829592325170273661603119643933019096191/1000000000000000000000000000000000000000000000",
+            "log_upper": "20157943981190040392762981274372218226711689/7812500000000000000000000000000000000000000",
+            "multiplicity": 7044
+          },
+          {
+            "child": 6,
+            "contribution_lower": "4414038190606526990615966079295032806964090649467/144793000000000000000000000000000000000000000000000",
+            "contribution_upper": "2207019095303263495307983039647516403482045326937/72396500000000000000000000000000000000000000000000",
+            "exp_lower": "1001597048016003401546622663783760564321327581/1000000000000000000000000000000000000000000000",
+            "exp_upper": "500798524008001700773311331891880282160663791/500000000000000000000000000000000000000000000",
+            "log_lower": "2397895272798370544061943577965129299821706853/1000000000000000000000000000000000000000000000",
+            "log_upper": "1198947636399185272030971788982564649910853427/500000000000000000000000000000000000000000000",
+            "multiplicity": 4407
+          },
+          {
+            "child": 7,
+            "contribution_lower": "298996124398096747456040246004140991499091240029/14479300000000000000000000000000000000000000000000",
+            "contribution_upper": "5979922487961934949120804920082819829981824806551/289586000000000000000000000000000000000000000000000",
+            "exp_lower": "50074715189766663449345209513337965416025999/50000000000000000000000000000000000000000000",
+            "exp_upper": "1001494303795333268986904190266759308320519981/1000000000000000000000000000000000000000000000",
+            "log_lower": "140234037060694514985566762056415740181725801/62500000000000000000000000000000000000000000",
+            "log_upper": "2243744592971112239769068192902651842907612817/1000000000000000000000000000000000000000000000",
+            "multiplicity": 2559
+          },
+          {
+            "child": 8,
+            "contribution_lower": "4460805477263077618368946182293341164081358457/131630000000000000000000000000000000000000000000",
+            "contribution_upper": "12267215062473463450514602001306688201223735769/361982500000000000000000000000000000000000000000",
+            "exp_lower": "1001405311222323546980783836841362302140713123/1000000000000000000000000000000000000000000000",
+            "exp_upper": "250351327805580886745195959210340575535178281/250000000000000000000000000000000000000000000",
+            "log_lower": "2110213200346589616622724571971301868318197143/1000000000000000000000000000000000000000000000",
+            "log_upper": "263776650043323702077840571496412733539774643/125000000000000000000000000000000000000000000",
+            "multiplicity": 3675
+          },
+          {
+            "child": 9,
+            "contribution_lower": "79485323033018237947989360316065340698677862807/5791720000000000000000000000000000000000000000000",
+            "contribution_upper": "361296922877355627036315274163933366812172104029/26326000000000000000000000000000000000000000000000",
+            "exp_lower": "20026536415474486759382554879331151599566103/20000000000000000000000000000000000000000000",
+            "exp_upper": "1001326820773724337969127743966557579978305151/1000000000000000000000000000000000000000000000",
+            "log_lower": "199243016469020616208393046250078016324971643/100000000000000000000000000000000000000000000",
+            "log_upper": "1992430164690206162083930462500780163249716431/1000000000000000000000000000000000000000000000",
+            "multiplicity": 1323
+          },
+          {
+            "child": 10,
+            "contribution_lower": "172816891557060762738705998269665965895947070231/5791720000000000000000000000000000000000000000000",
+            "contribution_upper": "432042228892651906846764995674164914739867676009/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "200251322777590686835117031598685939624504137/200000000000000000000000000000000000000000000",
+            "exp_upper": "500628306943976717087792578996714849061260343/500000000000000000000000000000000000000000000",
+            "log_lower": "1887069649032379860856429481661467364943596057/1000000000000000000000000000000000000000000000",
+            "log_upper": "943534824516189930428214740830733682471798029/500000000000000000000000000000000000000000000",
+            "multiplicity": 2589
+          },
+          {
+            "child": 11,
+            "contribution_lower": "164696266311249937804736233258673708911790905903/13163000000000000000000000000000000000000000000000",
+            "contribution_upper": "65878506524499975121894493303469483564716362427/5265200000000000000000000000000000000000000000000",
+            "exp_lower": "500596554137537804877617730269524951099668407/500000000000000000000000000000000000000000000",
+            "exp_upper": "200238621655015121951047092107809980439867363/200000000000000000000000000000000000000000000",
+            "log_lower": "447939867307013750203119339595175568180747673/250000000000000000000000000000000000000000000",
+            "log_upper": "1791759469228055000812477358380702272722990693/1000000000000000000000000000000000000000000000",
+            "multiplicity": 987
+          },
+          {
+            "child": 12,
+            "contribution_lower": "177951770372440833367515713017253441048563914213/3619825000000000000000000000000000000000000000000",
+            "contribution_upper": "711807081489763333470062852069013764194255657563/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "250283783927483591234199315073492884737783283/250000000000000000000000000000000000000000000",
+            "exp_upper": "1001135135709934364936797260293971538951133133/1000000000000000000000000000000000000000000000",
+            "log_lower": "1704748092238425234644711456506952731746206719/1000000000000000000000000000000000000000000000",
+            "log_upper": "332958611765317428641545206349014205419181/195312500000000000000000000000000000000000",
+            "multiplicity": 3555
+          },
+          {
+            "child": 13,
+            "contribution_lower": "1392504796435802101823810468285558086781709367561/144793000000000000000000000000000000000000000000000",
+            "contribution_upper": "174063099554475262727976308535694760847713671119/18099125000000000000000000000000000000000000000000",
+            "exp_lower": "1001081809083969879096916224504355202574916871/1000000000000000000000000000000000000000000000",
+            "exp_upper": "125135226135496234887114528063044400321864609/125000000000000000000000000000000000000000000",
+            "log_lower": "1624705384564888808820933494780512967739429601/1000000000000000000000000000000000000000000000",
+            "log_upper": "812352692282444404410466747390256483869714801/500000000000000000000000000000000000000000000",
+            "multiplicity": 642
+          },
+          {
+            "child": 14,
+            "contribution_lower": "1250790032371077515616152101965053044974389729571/36198250000000000000000000000000000000000000000000",
+            "contribution_upper": "2501580064742155031232304203930106089948779461641/72396500000000000000000000000000000000000000000000",
+            "exp_lower": "500516219436205488441837575816347757092592929/500000000000000000000000000000000000000000000",
+            "exp_upper": "1001032438872410976883675151632695514185185859/1000000000000000000000000000000000000000000000",
+            "log_lower": "775298706205583465175918035722237637416056341/500000000000000000000000000000000000000000000",
+            "log_upper": "1550597412411166930351836071444475274832112683/1000000000000000000000000000000000000000000000",
+            "multiplicity": 2142
+          },
+          {
+            "child": 15,
+            "contribution_lower": "651642197499310476834266983652297662569304394601/11583440000000000000000000000000000000000000000000",
+            "contribution_upper": "162910549374827619208566745913074415642326098813/2895860000000000000000000000000000000000000000000",
+            "exp_lower": "1000986478493564480544188914980487960935951451/1000000000000000000000000000000000000000000000",
+            "exp_upper": "250246619623391120136047228745121990233987863/250000000000000000000000000000000000000000000",
+            "log_lower": "740802270462107739439208183098559114185802817/500000000000000000000000000000000000000000000",
+            "log_upper": "296320908184843095775683273239423645674321127/200000000000000000000000000000000000000000000",
+            "multiplicity": 3255
+          },
+          {
+            "child": 16,
+            "contribution_lower": "50047174367031053906114007076104443302925003/8226875000000000000000000000000000000000000000",
+            "contribution_upper": "1000943487340621078122280141522088866058500061/164537500000000000000000000000000000000000000000",
+            "exp_lower": "50047174367031053906114007076104443302925003/50000000000000000000000000000000000000000000",
+            "exp_upper": "1000943487340621078122280141522088866058500061/1000000000000000000000000000000000000000000000",
+            "log_lower": "88566626236665269200343278157070331265168563/62500000000000000000000000000000000000000000",
+            "log_upper": "1417066019786644307205492450513125300242697009/1000000000000000000000000000000000000000000000",
+            "multiplicity": 330
+          },
+          {
+            "child": 17,
+            "contribution_lower": "3403070557142207346773934991622940700360183833/1316300000000000000000000000000000000000000000000",
+            "contribution_upper": "8507676392855518366934837479057351750900459591/3290750000000000000000000000000000000000000000000",
+            "exp_lower": "200180621008365138045525587742525923550599049/200000000000000000000000000000000000000000000",
+            "exp_upper": "500451552520912845113813969356314808876497623/500000000000000000000000000000000000000000000",
+            "log_lower": "1356441397970209464624886318472705036956494533/1000000000000000000000000000000000000000000000",
+            "log_upper": "678220698985104732312443159236352518478247267/500000000000000000000000000000000000000000000",
+            "multiplicity": 132
+          },
+          {
+            "child": 18,
+            "contribution_lower": "531459332570745507840722756443447013890223446131/3290750000000000000000000000000000000000000000000",
+            "contribution_upper": "265729666285372753920361378221723506945111723331/1645375000000000000000000000000000000000000000000",
+            "exp_lower": "1000865033089916210622830049799335242731117601/1000000000000000000000000000000000000000000000",
+            "exp_upper": "500432516544958105311415024899667621365558801/500000000000000000000000000000000000000000000",
+            "log_lower": "162410373016282606583337292630325449396777037/125000000000000000000000000000000000000000000",
+            "log_upper": "1299282984130260852666698341042603595174216297/1000000000000000000000000000000000000000000000",
+            "multiplicity": 7788
+          },
+          {
+            "child": 19,
+            "contribution_lower": "36947604984708453597376640085717897148571094226019/289586000000000000000000000000000000000000000000000",
+            "contribution_upper": "4618450623088556699672080010714737143571386782867/36198250000000000000000000000000000000000000000000",
+            "exp_lower": "1000829021445633545449972643652460848621802807/1000000000000000000000000000000000000000000000",
+            "exp_upper": "125103627680704193181246580456557606077725351/125000000000000000000000000000000000000000000",
+            "log_lower": "311303940714996271216348376114494508826829571/250000000000000000000000000000000000000000000",
+            "log_upper": "249043152571997016973078700891595607061463657/200000000000000000000000000000000000000000000",
+            "multiplicity": 5829
+          },
+          {
+            "child": 20,
+            "contribution_lower": "4253378148972909456145938223738660874824909493/329075000000000000000000000000000000000000000000",
+            "contribution_upper": "17013512595891637824583752894954643499299637989/1316300000000000000000000000000000000000000000000",
+            "exp_lower": "250198714645465262126231660219921227930877029/250000000000000000000000000000000000000000000",
+            "exp_upper": "1000794858581861048504926640879684911723508117/1000000000000000000000000000000000000000000000",
+            "log_lower": "1193922468472434551439197360203290796868095923/1000000000000000000000000000000000000000000000",
+            "log_upper": "298480617118108637859799340050822699217023981/250000000000000000000000000000000000000000000",
+            "multiplicity": 561
+          }
+        ],
+        "upper": "7239649999999993160790422556905626856350258805523/7239650000000000000000000000000000000000000000000"
+      },
+      "complex_saving": "665489485337/1000000000000000",
+      "denominator": 1000000000000000,
+      "iterations": 45,
+      "method": {
+        "exp_degree": 12,
+        "log_base": "4/3",
+        "log_terms": 80,
+        "outward_grid": 1000000000000000000000000000000000000000000000
+      },
+      "rejected": {
+        "lower": "144793000000000194100193959420325446256537624666829/144793000000000000000000000000000000000000000000000",
+        "saving": "332744742669/500000000000000",
+        "strict_gap_lower": "-551421005566535015472319709166267/411343750000000000000000000000000000000000000000",
+        "terms": [
+          {
+            "child": 1,
+            "contribution_lower": "39108890407949185176506317395485545073026535187/361982500000000000000000000000000000000000000000",
+            "contribution_upper": "39108890407949185176506317395485545073026539087/361982500000000000000000000000000000000000000000",
+            "exp_lower": "1002792061742286799397597881935526796744270133/1000000000000000000000000000000000000000000000",
+            "exp_upper": "1002792061742286799397597881935526796744270233/1000000000000000000000000000000000000000000000",
+            "log_lower": "2094827371013212772437210468172915786272348773/500000000000000000000000000000000000000000000",
+            "log_upper": "4189654742026425544874420936345831572544697547/1000000000000000000000000000000000000000000000",
+            "multiplicity": 93600
+          },
+          {
+            "child": 2,
+            "contribution_lower": "1421804535223760483421521515241747482470059591059/14479300000000000000000000000000000000000000000000",
+            "contribution_upper": "355451133805940120855380378810436870617514901311/3619825000000000000000000000000000000000000000000",
+            "exp_lower": "501164799162411167931449247529695975491737607/500000000000000000000000000000000000000000000",
+            "exp_upper": "125291199790602791982862311882423993872934403/125000000000000000000000000000000000000000000",
+            "log_lower": "3496507561466480235457188814887655004469197411/1000000000000000000000000000000000000000000000",
+            "log_upper": "874126890366620058864297203721913751117299353/250000000000000000000000000000000000000000000",
+            "multiplicity": 42555
+          },
+          {
+            "child": 3,
+            "contribution_lower": "268069048153736966252599269836456320374002649627/2632600000000000000000000000000000000000000000000",
+            "contribution_upper": "29487595296911066287785919682010195241140291547251/289586000000000000000000000000000000000000000000000",
+            "exp_lower": "100205917344313271104040234077582476097258611/100000000000000000000000000000000000000000000",
+            "exp_upper": "1002059173443132711040402340775824760972586113/1000000000000000000000000000000000000000000000",
+            "log_lower": "772760613339578963369793924855826466974301747/250000000000000000000000000000000000000000000",
+            "log_upper": "3091042453358315853479175699423305867897206989/1000000000000000000000000000000000000000000000",
+            "multiplicity": 29427
+          },
+          {
+            "child": 4,
+            "contribution_lower": "180837056347263985461044169983273093136227249403/3619825000000000000000000000000000000000000000000",
+            "contribution_upper": "45209264086815996365261042495818273284056812441/904956250000000000000000000000000000000000000000",
+            "exp_lower": "500933674092144004047213767266684468521405123/500000000000000000000000000000000000000000000",
+            "exp_upper": "125233418523036001011803441816671117130351281/125000000000000000000000000000000000000000000",
+            "log_lower": "2803360380906534926039956693429478436393697277/1000000000000000000000000000000000000000000000",
+            "log_upper": "1401680190453267463019978346714739218196848639/500000000000000000000000000000000000000000000",
+            "multiplicity": 10830
+          },
+          {
+            "child": 5,
+            "contribution_lower": "58800880777644587278264162810186081409541852409/1447930000000000000000000000000000000000000000000",
+            "contribution_upper": "3340959135093442458992281977851481898269423439/82268750000000000000000000000000000000000000000",
+            "exp_lower": "100171858224266758566037756065052949590360907/100000000000000000000000000000000000000000000",
+            "exp_upper": "62607411390166724103773597540658093493975567/62500000000000000000000000000000000000000000",
+            "log_lower": "2580216829592325170273661603119643933019096191/1000000000000000000000000000000000000000000000",
+            "log_upper": "20157943981190040392762981274372218226711689/7812500000000000000000000000000000000000000",
+            "multiplicity": 7044
+          },
+          {
+            "child": 6,
+            "contribution_lower": "882807638121307515003455457234335566608450813843/28958600000000000000000000000000000000000000000000",
+            "contribution_upper": "200638099573024435228058058462348992411011548801/6581500000000000000000000000000000000000000000000",
+            "exp_lower": "200319409603201160654289870032751433312559749/200000000000000000000000000000000000000000000",
+            "exp_upper": "500798524008002901635724675081878583281399373/500000000000000000000000000000000000000000000",
+            "log_lower": "2397895272798370544061943577965129299821706853/1000000000000000000000000000000000000000000000",
+            "log_upper": "1198947636399185272030971788982564649910853427/500000000000000000000000000000000000000000000",
+            "multiplicity": 4407
+          },
+          {
+            "child": 7,
+            "contribution_lower": "5979922487961948366539553671050437336100965253249/289586000000000000000000000000000000000000000000000",
+            "contribution_upper": "298996124398097418326977683552521866805048262961/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "1001494303795335516084333222416753866370953819/1000000000000000000000000000000000000000000000",
+            "exp_upper": "50074715189766775804216661120837693318547691/50000000000000000000000000000000000000000000",
+            "log_lower": "140234037060694514985566762056415740181725801/62500000000000000000000000000000000000000000",
+            "log_upper": "2243744592971112239769068192902651842907612817/1000000000000000000000000000000000000000000000",
+            "multiplicity": 2559
+          },
+          {
+            "child": 8,
+            "contribution_lower": "12267215062473489336953758323350589678682448017/361982500000000000000000000000000000000000000000",
+            "contribution_upper": "49068860249893957347815033293402358714729792117/1447930000000000000000000000000000000000000000000",
+            "exp_lower": "250351327805581415039872618843889585279233633/250000000000000000000000000000000000000000000",
+            "exp_upper": "1001405311222325660159490475375558341116934533/1000000000000000000000000000000000000000000000",
+            "log_lower": "2110213200346589616622724571971301868318197143/1000000000000000000000000000000000000000000000",
+            "log_upper": "263776650043323702077840571496412733539774643/125000000000000000000000000000000000000000000",
+            "multiplicity": 3675
+          },
+          {
+            "child": 9,
+            "contribution_lower": "3974266151650919815847231072349405628245304864377/289586000000000000000000000000000000000000000000000",
+            "contribution_upper": "1987133075825459907923615536174702814122652434173/144793000000000000000000000000000000000000000000000",
+            "exp_lower": "1001326820773726333042890166880676651107408633/1000000000000000000000000000000000000000000000",
+            "exp_upper": "500663410386863166521445083440338325553704317/500000000000000000000000000000000000000000000",
+            "log_lower": "199243016469020616208393046250078016324971643/100000000000000000000000000000000000000000000",
+            "log_upper": "1992430164690206162083930462500780163249716431/1000000000000000000000000000000000000000000000",
+            "multiplicity": 1323
+          },
+          {
+            "child": 10,
+            "contribution_lower": "864084457785305444281084478597387921924302943123/28958600000000000000000000000000000000000000000000",
+            "contribution_upper": "432042228892652722140542239298693960962151471993/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "1001256613887955323616552118884574648811475021/1000000000000000000000000000000000000000000000",
+            "exp_upper": "500628306943977661808276059442287324405737511/500000000000000000000000000000000000000000000",
+            "log_lower": "1887069649032379860856429481661467364943596057/1000000000000000000000000000000000000000000000",
+            "log_upper": "943534824516189930428214740830733682471798029/500000000000000000000000000000000000000000000",
+            "multiplicity": 2589
+          },
+          {
+            "child": 11,
+            "contribution_lower": "1646962663112502329008309429465225142441159993/131630000000000000000000000000000000000000000000",
+            "contribution_upper": "329392532622500465801661885893045028488231998929/26326000000000000000000000000000000000000000000000",
+            "exp_lower": "5005965541375387018262338691383663046933617/5000000000000000000000000000000000000000000",
+            "exp_upper": "1001193108275077403652467738276732609386723401/1000000000000000000000000000000000000000000000",
+            "log_lower": "447939867307013750203119339595175568180747673/250000000000000000000000000000000000000000000",
+            "log_upper": "1791759469228055000812477358380702272722990693/1000000000000000000000000000000000000000000000",
+            "multiplicity": 987
+          },
+          {
+            "child": 12,
+            "contribution_lower": "355903540744882273460913531772689384798872460423/7239650000000000000000000000000000000000000000000",
+            "contribution_upper": "711807081489764546921827063545378769597744921557/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "500567567854968035810004967331489992684771393/500000000000000000000000000000000000000000000",
+            "exp_upper": "1001135135709936071620009934662979985369542787/1000000000000000000000000000000000000000000000",
+            "log_lower": "1704748092238425234644711456506952731746206719/1000000000000000000000000000000000000000000000",
+            "log_upper": "332958611765317428641545206349014205419181/195312500000000000000000000000000000000000",
+            "multiplicity": 3555
+          },
+          {
+            "child": 13,
+            "contribution_lower": "126591345130527669475804660906314262671565048097/13163000000000000000000000000000000000000000000000",
+            "contribution_upper": "696252398217902182116925634984728444693607765229/72396500000000000000000000000000000000000000000000",
+            "exp_lower": "1001081809083971505559921833191557792514173637/1000000000000000000000000000000000000000000000",
+            "exp_upper": "500540904541985752779960916595778896257086819/500000000000000000000000000000000000000000000",
+            "log_lower": "1624705384564888808820933494780512967739429601/1000000000000000000000000000000000000000000000",
+            "log_upper": "812352692282444404410466747390256483869714801/500000000000000000000000000000000000000000000",
+            "multiplicity": 642
+          },
+          {
+            "child": 14,
+            "contribution_lower": "625395016185539727543969883119537102713368427529/18099125000000000000000000000000000000000000000000",
+            "contribution_upper": "500316012948431782035175906495629682170694742523/14479300000000000000000000000000000000000000000000",
+            "exp_lower": "250258109718103132270496151708498240381499971/250000000000000000000000000000000000000000000",
+            "exp_upper": "200206487774482505816396921366798592305199977/200000000000000000000000000000000000000000000",
+            "log_lower": "775298706205583465175918035722237637416056341/500000000000000000000000000000000000000000000",
+            "log_upper": "1550597412411166930351836071444475274832112683/1000000000000000000000000000000000000000000000",
+            "multiplicity": 2142
+          },
+          {
+            "child": 15,
+            "contribution_lower": "651642197499311442310305856465867855834576894233/11583440000000000000000000000000000000000000000000",
+            "contribution_upper": "162910549374827860577576464116466963958644223721/2895860000000000000000000000000000000000000000000",
+            "exp_lower": "1000986478493565963610300854786279348440210283/1000000000000000000000000000000000000000000000",
+            "exp_upper": "250246619623391490902575213696569837110052571/250000000000000000000000000000000000000000000",
+            "log_lower": "740802270462107739439208183098559114185802817/500000000000000000000000000000000000000000000",
+            "log_upper": "296320908184843095775683273239423645674321127/200000000000000000000000000000000000000000000",
+            "multiplicity": 3255
+          },
+          {
+            "child": 16,
+            "contribution_lower": "250235871835155624131320944665099541136973787/41134375000000000000000000000000000000000000000",
+            "contribution_upper": "1000943487340622496525283778660398164547895149/164537500000000000000000000000000000000000000000",
+            "exp_lower": "250235871835155624131320944665099541136973787/250000000000000000000000000000000000000000000",
+            "exp_upper": "1000943487340622496525283778660398164547895149/1000000000000000000000000000000000000000000000",
+            "log_lower": "88566626236665269200343278157070331265168563/62500000000000000000000000000000000000000000",
+            "log_upper": "1417066019786644307205492450513125300242697009/1000000000000000000000000000000000000000000000",
+            "multiplicity": 330
+          },
+          {
+            "child": 17,
+            "contribution_lower": "17015352785711059814198594564306979295385664951/6581500000000000000000000000000000000000000000000",
+            "contribution_upper": "2126919098213882476774824320538372411923208121/822687500000000000000000000000000000000000000000",
+            "exp_lower": "1000903105041827047894034974370998782081509703/1000000000000000000000000000000000000000000000",
+            "exp_upper": "125112888130228380986754371796374847760188713/125000000000000000000000000000000000000000000",
+            "log_lower": "1356441397970209464624886318472705036956494533/1000000000000000000000000000000000000000000000",
+            "log_upper": "678220698985104732312443159236352518478247267/500000000000000000000000000000000000000000000",
+            "multiplicity": 132
+          },
+          {
+            "child": 18,
+            "contribution_lower": "132864833142686549589197580709713988002006854283/822687500000000000000000000000000000000000000000",
+            "contribution_upper": "531459332570746198356790322838855952008027417663/3290750000000000000000000000000000000000000000000",
+            "exp_lower": "250216258272479377757434238624696775898317993/250000000000000000000000000000000000000000000",
+            "exp_upper": "1000865033089917511029736954498787103593271973/1000000000000000000000000000000000000000000000",
+            "log_lower": "162410373016282606583337292630325449396777037/125000000000000000000000000000000000000000000",
+            "log_upper": "1299282984130260852666698341042603595174216297/1000000000000000000000000000000000000000000000",
+            "multiplicity": 7788
+          },
+          {
+            "child": 19,
+            "contribution_lower": "36947604984708499605116766968871144376710501427419/289586000000000000000000000000000000000000000000000",
+            "contribution_upper": "2309225311544281225319797935554446523544406341521/18099125000000000000000000000000000000000000000000",
+            "exp_lower": "1000829021445634791698046075490184586415757007/1000000000000000000000000000000000000000000000",
+            "exp_upper": "62551813840352174481127879718136536650984813/62500000000000000000000000000000000000000000",
+            "log_lower": "311303940714996271216348376114494508826829571/250000000000000000000000000000000000000000000",
+            "log_upper": "249043152571997016973078700891595607061463657/200000000000000000000000000000000000000000000",
+            "multiplicity": 5829
+          },
+          {
+            "child": 20,
+            "contribution_lower": "2126689074486457267174838596096106649596502193/164537500000000000000000000000000000000000000000",
+            "contribution_upper": "17013512595891658137398708768768853196772017561/1316300000000000000000000000000000000000000000000",
+            "exp_lower": "125099357322732780422049329182123920564500129/125000000000000000000000000000000000000000000",
+            "exp_upper": "1000794858581862243376394633456991364516001033/1000000000000000000000000000000000000000000000",
+            "log_lower": "1193922468472434551439197360203290796868095923/1000000000000000000000000000000000000000000000",
+            "log_upper": "298480617118108637859799340050822699217023981/250000000000000000000000000000000000000000000",
+            "multiplicity": 561
+          }
+        ],
+        "upper": "411343750000000551421005566535015472319709166267/411343750000000000000000000000000000000000000000"
+      },
+      "scope": "Strict contraction and adjacent point exclusion for this fixed complete complex profile."
+    },
+    "physical": {
+      "before_terminal_sinks": {
+        "R": 12877,
+        "W_per_vertex": 13207,
+        "changed_operation_frames": 13364,
+        "checks": {
+          "donor_frames_inside_gauges": true,
+          "pair_chronology": true,
+          "role_chains_nested": true,
+          "target_chains_nested_in_read_order": true,
+          "telescoping_deficit": true,
+          "value_spans_inside_frames": true
+        },
+        "child_histogram": {
+          "1": 93600,
+          "10": 2589,
+          "11": 987,
+          "12": 3555,
+          "13": 642,
+          "14": 2142,
+          "15": 3255,
+          "16": 330,
+          "17": 132,
+          "18": 7920,
+          "19": 5829,
+          "2": 42555,
+          "20": 561,
+          "3": 29427,
+          "4": 10962,
+          "5": 7044,
+          "6": 4407,
+          "7": 2559,
+          "8": 3675,
+          "9": 1323
+        },
+        "deficit_per_vertex": 1320,
+        "h": 22,
+        "late_pairs": 1261,
+        "local_histogram": {
+          "1": 25920,
+          "10": 863,
+          "11": 329,
+          "12": 1185,
+          "13": 214,
+          "14": 714,
+          "15": 1085,
+          "16": 110,
+          "17": 44,
+          "19": 1943,
+          "2": 11985,
+          "20": 187,
+          "3": 9809,
+          "4": 3654,
+          "5": 2348,
+          "6": 1469,
+          "7": 853,
+          "8": 1225,
+          "9": 441
+        },
+        "loss": 440,
+        "m": 66,
+        "pairs": 2310,
+        "physical_R": 10567,
+        "physical_gauge_histogram": {},
+        "rank_per_vertex": 870342,
+        "scalar_replay": {
+          "modulus": "2^61-1",
+          "rejected_controls": [
+            "flipped_signed_operation",
+            "late_read_before_donor_death",
+            "omitted_recipient_read"
+          ],
+          "seeds_restored_and_y_plus_x": true,
+          "slots": 10567
+        },
+        "source_data_histogram": {
+          "1": 1320,
+          "18": 1320,
+          "2": 1320
+        },
+        "target_data_histogram": {
+          "0": 6270,
+          "1": 3960,
+          "18": 1320
+        },
+        "v": 1320
+      },
+      "exact_adjoint": {
+        "L1": 5845250,
+        "gauge_supports_contained": true,
+        "max_numerator_over_6": 6,
+        "nonzeros": 4280534
+      },
+      "foreign_producer_replays": 0,
+      "formal": [
+        {
+          "columns": 13163,
+          "direction": 1,
+          "dirty": 10523,
+          "outputs": true,
+          "restored": true
+        },
+        {
+          "columns": 13163,
+          "direction": -1,
+          "dirty": 10523,
+          "outputs": true,
+          "restored": true
+        }
+      ],
+      "input_sha256": {
+        "baseline.json.gz": "5975dc6981aa18ac4ba4a1ca290d9163beedc8bc48e9600f4de5390758b57ef9",
+        "frames.json.gz": "05cf2b64cdc6142294512fcd963285ed535599b433691a547eaf775424f7b104",
+        "graph.json.gz": "4720aa3bf8960d89fca62cf8dc71dc7c5f8b3b85c59ecae727184ae12e1f7c18",
+        "physical-frames.json.gz": "bbbe32fb7a5d2415b7b2f130c46d1e20de392ea1cf6587fca6bc015879a3ca4f",
+        "physical-pairs.json.gz": "33b847e6f40e40809dce1c3eb25afe357b88b0b14c9a5ccca95b78553a595065",
+        "profile-before.json.gz": "e41fd008059d8a08d8f3078831e577201acd9f4aa115dd0197e28286cf281c80",
+        "profile.json.gz": "67de497a9c1ea64bb0cf9dc3ca655e7f9c704452a615f3e7eb45d124ed40c2c1",
+        "word.json.gz": "b70c03e2401df03f67bbba36e0c33704bde377902e446831a4df94833e935cc8"
+      },
+      "mutations": {
+        "early-read": "REJECTED",
+        "missing-read": "REJECTED"
+      },
+      "original_formal": {
+        "absolute_coefficient_bound": 394506,
+        "base_exceeds_twice_bound": true,
+        "columns": [
+          {
+            "K_and_inverse": true,
+            "all_aliases_and_deadline_reads": true,
+            "all_physical_dirty_slots_restored": true,
+            "direction": 1,
+            "dirty_columns": 10567,
+            "every_formal_column": true,
+            "source_columns": 1320,
+            "target_columns": 1320
+          },
+          {
+            "K_and_inverse": true,
+            "all_aliases_and_deadline_reads": true,
+            "all_physical_dirty_slots_restored": true,
+            "direction": -1,
+            "dirty_columns": 10567,
+            "every_formal_column": true,
+            "source_columns": 1320,
+            "target_columns": 1320
+          }
+        ],
+        "packed_digit_bits": 24
+      },
+      "physical": {
+        "R": 12877,
+        "W_per_vertex": 13163,
+        "changed_operation_frames": 13364,
+        "checks": {
+          "donor_frames_inside_gauges": true,
+          "pair_chronology": true,
+          "role_chains_nested": true,
+          "target_chains_nested_in_read_order": true,
+          "telescoping_deficit": true,
+          "value_spans_inside_frames": true
+        },
+        "child_histogram": {
+          "1": 93600,
+          "10": 2589,
+          "11": 987,
+          "12": 3555,
+          "13": 642,
+          "14": 2142,
+          "15": 3255,
+          "16": 330,
+          "17": 132,
+          "18": 7788,
+          "19": 5829,
+          "2": 42555,
+          "20": 561,
+          "3": 29427,
+          "4": 10830,
+          "5": 7044,
+          "6": 4407,
+          "7": 2559,
+          "8": 3675,
+          "9": 1323
+        },
+        "deficit_per_vertex": 1320,
+        "h": 22,
+        "late_pairs": 1261,
+        "local_histogram": {
+          "1": 25920,
+          "10": 855,
+          "11": 327,
+          "12": 1179,
+          "13": 212,
+          "14": 710,
+          "15": 1073,
+          "16": 103,
+          "17": 44,
+          "19": 1943,
+          "2": 11962,
+          "20": 187,
+          "3": 9793,
+          "4": 3603,
+          "5": 2346,
+          "6": 1462,
+          "7": 850,
+          "8": 1220,
+          "9": 440
+        },
+        "loss": 440,
+        "m": 66,
+        "pairs": 2310,
+        "physical_R": 10523,
+        "physical_gauge_histogram": {},
+        "rank_per_vertex": 867438,
+        "scalar_replay": {
+          "modulus": "2^61-1",
+          "rejected_controls": [
+            "flipped_signed_operation",
+            "late_read_before_donor_death",
+            "omitted_recipient_read"
+          ],
+          "seeds_restored_and_y_plus_x": true,
+          "slots": 10567
+        },
+        "source_data_histogram": {
+          "1": 1320,
+          "18": 1320,
+          "2": 1320
+        },
+        "target_data_histogram": {
+          "0": 6270,
+          "1": 3960,
+          "10": 8,
+          "11": 2,
+          "12": 6,
+          "13": 2,
+          "14": 4,
+          "15": 12,
+          "16": 7,
+          "18": 1276,
+          "2": 23,
+          "3": 16,
+          "4": 7,
+          "5": 2,
+          "6": 7,
+          "7": 3,
+          "8": 5,
+          "9": 1
+        },
+        "terminal_sinks": 44,
+        "v": 1320
+      },
+      "pre_reuse_finite": {
+        "K_involution_and_inverse_exact": true,
+        "K_source_itinerary_verified": true,
+        "center_phase_closed": true,
+        "conservative_source_supports": true,
+        "decoder_identity_exact": true,
+        "full_backward_intersections": true,
+        "full_gauge_intersections": true,
+        "physical_signed_M_replayed": true,
+        "positive_rank_ledger_recounted": true,
+        "reverse_target_chains": true,
+        "scalar_H_exact": true,
+        "selected_roles": 2310,
+        "selected_sources_untouched": true,
+        "signed_scalar_pairs_checked": 1742400
+      },
+      "scalar_bound": {
+        "M_operations": 33466,
+        "binary_dirty_read_bits": 33482,
+        "c": 21909,
+        "decoder_coefficients": [
+          "-1/2",
+          "-1/6",
+          "1/2",
+          "1/3"
+        ],
+        "fixed_odd_divisor": 3,
+        "gate_and_inverse_coefficients": [
+          -1,
+          1
+        ],
+        "handoffs": 2310,
+        "local_group_upper": 4552920126520,
+        "logical_R": 12877,
+        "physical_R": 10523,
+        "q": 3157,
+        "scalar_denominators_divide": 6,
+        "scope": "Conservative inherited virtual-word bill retained after aliasing, including all compensated reads. Alias and frame route choices are finite permutations/Clifford adapters; their separate global movement bill remains an assembly obligation.",
+        "terminal_original_scalar_reserve_retained": true,
+        "terminal_scalar_gate_delta": -202,
+        "terminal_sinks": 44,
+        "three_q_less_than_2pow15": true
+      },
+      "scope": "Finite candidate audit only. General exact Clifford and shared cover contracts, analytic supplier bridge, and paid global multiplication assembly remain separate obligations.",
+      "source_sha256": {
+        "research/paired-cube-diagonal-bit-168/complex/check_sinks.py": "d70903464b3caabc0920aee8953978a27a6874a655ecb66cadacf77a31df11af",
+        "research/paired-cube-diagonal-bit-168/complex/formal_sinks.py": "d7fefe86e637584ad1bf53c8f7714b88d5abed92eaa29d110ef099536e51f516",
+        "research/paired-cube-diagonal-bit-168/complex/physical.py": "01961fad4b04aaa940d2dc99c87690bc861b3861200296974c5e065ce3446659",
+        "research/paired-cube-diagonal-bit-168/complex/prove.py": "3eecae7856aa212d1d7e607e2663b8ce0766ed6067b388c6be2ed5485886bd43",
+        "research/paired-cube-diagonal-bit-168/complex/verify_fused.py": "75c3dcd80fcdbc461651fa2d2fa463e6b41a569d695fc74700d240223ef198e9",
+        "research/paired-cube-diagonal-bit-168/references/pr168-v4/notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+        "research/paired-cube-diagonal-bit-168/references/pr168-v4/scripts/paired_cube/frames.py": "7d897418dbfee47de0723ea4983098a982610ccba45e1bac9000a79626d8421c",
+        "research/paired-cube-diagonal-bit-168/references/pr168-v4/scripts/paired_cube_physical.py": "9c9ea1ea29e551ab6116d7c8ca09f4703ff9e2fa102032d5055327fde07ba319"
+      },
+      "status": "PASS exact fused physical candidate, all formal source/target/dirty columns",
+      "terminal_compiler": {
+        "all_formal_source_and_dirty_coefficients": true,
+        "all_new_target_events_replayed": true,
+        "child_histogram": {
+          "1": 93600,
+          "10": 2589,
+          "11": 987,
+          "12": 3555,
+          "13": 642,
+          "14": 2142,
+          "15": 3255,
+          "16": 330,
+          "17": 132,
+          "18": 7788,
+          "19": 5829,
+          "2": 42555,
+          "20": 561,
+          "3": 29427,
+          "4": 10830,
+          "5": 7044,
+          "6": 4407,
+          "7": 2559,
+          "8": 3675,
+          "9": 1323
+        },
+        "chronological_inverse_by_literal_reverse": true,
+        "deficit": 1320,
+        "dirty_coefficient_nonzero_range": [
+          701,
+          721
+        ],
+        "eligible_count": 44,
+        "formal_original_source_dirty_target_columns": 13207,
+        "full_old_physical_histogram_verified": true,
+        "h": 22,
+        "input_pins": {
+          "frames.json.gz": "05cf2b64cdc6142294512fcd963285ed535599b433691a547eaf775424f7b104",
+          "graph.json.gz": "4720aa3bf8960d89fca62cf8dc71dc7c5f8b3b85c59ecae727184ae12e1f7c18",
+          "physical-frames.json.gz": "bbbe32fb7a5d2415b7b2f130c46d1e20de392ea1cf6587fca6bc015879a3ca4f",
+          "physical-pairs.json.gz": "33b847e6f40e40809dce1c3eb25afe357b88b0b14c9a5ccca95b78553a595065",
+          "profile-before.json.gz": "e41fd008059d8a08d8f3078831e577201acd9f4aa115dd0197e28286cf281c80",
+          "profile.json.gz": "67de497a9c1ea64bb0cf9dc3ca655e7f9c704452a615f3e7eb45d124ed40c2c1",
+          "word.json.gz": "b70c03e2401df03f67bbba36e0c33704bde377902e446831a4df94833e935cc8"
+        },
+        "local_histogram": {
+          "1": 25920,
+          "10": 855,
+          "11": 327,
+          "12": 1179,
+          "13": 212,
+          "14": 710,
+          "15": 1073,
+          "16": 103,
+          "17": 44,
+          "19": 1943,
+          "2": 11962,
+          "20": 187,
+          "3": 9793,
+          "4": 3603,
+          "5": 2346,
+          "6": 1462,
+          "7": 850,
+          "8": 1220,
+          "9": 440
+        },
+        "new_W": 13163,
+        "new_kappa_claimed": false,
+        "new_odd_denominator": false,
+        "new_physical_R": 10523,
+        "new_rank": 867438,
+        "old_W": 13207,
+        "old_physical_R": 10567,
+        "old_rank": 870342,
+        "rejected_conditions": {
+          "center_phase_touch": 13,
+          "no_uncorrected_pivot": 4,
+          "retained_producer_consumer": 119
+        },
+        "remaining_formal_columns": 13163,
+        "scalar_gate_delta": -202,
+        "scalar_sandwich_literal_reverse_checked": true,
+        "scope": "Only all-eight disjoint roots; retained full proof contracts unchanged",
+        "shared_child_delta": {
+          "18": -132,
+          "4": -132
+        },
+        "simultaneous_compatible": true,
+        "sinks": [
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 26877,
+            "last_write_chronology": 24995,
+            "pivot": 40,
+            "post_after_op": 24819,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              10,
+              4,
+              4
+            ],
+            "role": 10080,
+            "root_index": 55,
+            "targets": [
+              40,
+              41,
+              42,
+              43,
+              44,
+              45,
+              46,
+              47
+            ],
+            "write_ranks": [
+              10,
+              14,
+              18
+            ],
+            "writes": [
+              16836,
+              20644,
+              24819
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27021,
+            "last_write_chronology": 25424,
+            "pivot": 72,
+            "post_after_op": 25248,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10435,
+            "root_index": 99,
+            "targets": [
+              72,
+              73,
+              74,
+              75,
+              76,
+              77,
+              78,
+              79
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21268,
+              25248
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27237,
+            "last_write_chronology": 25002,
+            "pivot": 120,
+            "post_after_op": 24826,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              8,
+              10
+            ],
+            "role": 9708,
+            "root_index": 165,
+            "targets": [
+              120,
+              121,
+              122,
+              123,
+              124,
+              125,
+              126,
+              127
+            ],
+            "write_ranks": [
+              8,
+              18
+            ],
+            "writes": [
+              14887,
+              24826
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27309,
+            "last_write_chronology": 25347,
+            "pivot": 136,
+            "post_after_op": 25171,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10466,
+            "root_index": 187,
+            "targets": [
+              136,
+              137,
+              138,
+              139,
+              140,
+              141,
+              142,
+              143
+            ],
+            "write_ranks": [
+              16,
+              18
+            ],
+            "writes": [
+              22350,
+              25171
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27417,
+            "last_write_chronology": 25432,
+            "pivot": 160,
+            "post_after_op": 25256,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              10,
+              2,
+              6
+            ],
+            "role": 10066,
+            "root_index": 220,
+            "targets": [
+              160,
+              161,
+              162,
+              163,
+              164,
+              165,
+              166,
+              167
+            ],
+            "write_ranks": [
+              10,
+              12,
+              18
+            ],
+            "writes": [
+              16779,
+              20665,
+              25256
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27453,
+            "last_write_chronology": 25411,
+            "pivot": 168,
+            "post_after_op": 25235,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              10,
+              2,
+              6
+            ],
+            "role": 10057,
+            "root_index": 231,
+            "targets": [
+              168,
+              169,
+              170,
+              171,
+              172,
+              173,
+              174,
+              175
+            ],
+            "write_ranks": [
+              10,
+              12,
+              18
+            ],
+            "writes": [
+              16744,
+              19066,
+              25235
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27705,
+            "last_write_chronology": 25025,
+            "pivot": 224,
+            "post_after_op": 24849,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              9,
+              2,
+              7
+            ],
+            "role": 10050,
+            "root_index": 308,
+            "targets": [
+              224,
+              225,
+              226,
+              227,
+              228,
+              229,
+              230,
+              231
+            ],
+            "write_ranks": [
+              9,
+              11,
+              18
+            ],
+            "writes": [
+              16132,
+              18181,
+              24849
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27921,
+            "last_write_chronology": 25026,
+            "pivot": 272,
+            "post_after_op": 24850,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              6,
+              2,
+              8,
+              2
+            ],
+            "role": 8956,
+            "root_index": 374,
+            "targets": [
+              272,
+              273,
+              274,
+              275,
+              276,
+              277,
+              278,
+              279
+            ],
+            "write_ranks": [
+              6,
+              8,
+              16,
+              18
+            ],
+            "writes": [
+              13006,
+              16158,
+              22414,
+              24850
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28029,
+            "last_write_chronology": 24927,
+            "pivot": 296,
+            "post_after_op": 24751,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              13,
+              5
+            ],
+            "role": 10335,
+            "root_index": 407,
+            "targets": [
+              296,
+              297,
+              298,
+              299,
+              300,
+              301,
+              302,
+              303
+            ],
+            "write_ranks": [
+              13,
+              18
+            ],
+            "writes": [
+              19761,
+              24751
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28245,
+            "last_write_chronology": 25380,
+            "pivot": 344,
+            "post_after_op": 25204,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10425,
+            "root_index": 473,
+            "targets": [
+              344,
+              345,
+              346,
+              347,
+              348,
+              349,
+              350,
+              351
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21184,
+              25204
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27341,
+            "last_write_chronology": 25147,
+            "pivot": 432,
+            "post_after_op": 24971,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10471,
+            "root_index": 594,
+            "targets": [
+              432,
+              433,
+              434,
+              435,
+              436,
+              437,
+              438,
+              439
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              22467,
+              24971
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27449,
+            "last_write_chronology": 25144,
+            "pivot": 456,
+            "post_after_op": 24968,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              10,
+              8
+            ],
+            "role": 10089,
+            "root_index": 627,
+            "targets": [
+              456,
+              457,
+              458,
+              459,
+              460,
+              461,
+              462,
+              463
+            ],
+            "write_ranks": [
+              10,
+              18
+            ],
+            "writes": [
+              16876,
+              24968
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27485,
+            "last_write_chronology": 25389,
+            "pivot": 464,
+            "post_after_op": 25213,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              12,
+              6
+            ],
+            "role": 10289,
+            "root_index": 638,
+            "targets": [
+              464,
+              465,
+              466,
+              467,
+              468,
+              469,
+              470,
+              471
+            ],
+            "write_ranks": [
+              12,
+              18
+            ],
+            "writes": [
+              18895,
+              25213
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27521,
+            "last_write_chronology": 25281,
+            "pivot": 472,
+            "post_after_op": 25105,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10431,
+            "root_index": 649,
+            "targets": [
+              472,
+              473,
+              474,
+              475,
+              476,
+              477,
+              478,
+              479
+            ],
+            "write_ranks": [
+              16,
+              18
+            ],
+            "writes": [
+              21248,
+              25105
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27593,
+            "last_write_chronology": 25324,
+            "pivot": 488,
+            "post_after_op": 25148,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10433,
+            "root_index": 671,
+            "targets": [
+              488,
+              489,
+              490,
+              491,
+              492,
+              493,
+              494,
+              495
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21254,
+              25148
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27809,
+            "last_write_chronology": 25338,
+            "pivot": 536,
+            "post_after_op": 25162,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10464,
+            "root_index": 737,
+            "targets": [
+              536,
+              537,
+              538,
+              539,
+              540,
+              541,
+              542,
+              543
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              22339,
+              25162
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27917,
+            "last_write_chronology": 25160,
+            "pivot": 560,
+            "post_after_op": 24984,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              14,
+              2,
+              2
+            ],
+            "role": 10354,
+            "root_index": 770,
+            "targets": [
+              560,
+              561,
+              562,
+              563,
+              564,
+              565,
+              566,
+              567
+            ],
+            "write_ranks": [
+              14,
+              16,
+              18
+            ],
+            "writes": [
+              20599,
+              22490,
+              24984
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27953,
+            "last_write_chronology": 25068,
+            "pivot": 568,
+            "post_after_op": 24892,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              10,
+              8
+            ],
+            "role": 10102,
+            "root_index": 781,
+            "targets": [
+              568,
+              569,
+              570,
+              571,
+              572,
+              573,
+              574,
+              575
+            ],
+            "write_ranks": [
+              10,
+              18
+            ],
+            "writes": [
+              16943,
+              24892
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28025,
+            "last_write_chronology": 24940,
+            "pivot": 584,
+            "post_after_op": 24764,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              12,
+              6
+            ],
+            "role": 10293,
+            "root_index": 803,
+            "targets": [
+              584,
+              585,
+              586,
+              587,
+              588,
+              589,
+              590,
+              591
+            ],
+            "write_ranks": [
+              12,
+              18,
+              18
+            ],
+            "writes": [
+              18919,
+              24737,
+              24764
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28061,
+            "last_write_chronology": 24992,
+            "pivot": 592,
+            "post_after_op": 24816,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10441,
+            "root_index": 814,
+            "targets": [
+              592,
+              593,
+              594,
+              595,
+              596,
+              597,
+              598,
+              599
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21286,
+              24816
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28277,
+            "last_write_chronology": 25326,
+            "pivot": 640,
+            "post_after_op": 25150,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10432,
+            "root_index": 880,
+            "targets": [
+              640,
+              641,
+              642,
+              643,
+              644,
+              645,
+              646,
+              647
+            ],
+            "write_ranks": [
+              16,
+              18,
+              18
+            ],
+            "writes": [
+              21250,
+              25019,
+              25150
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27379,
+            "last_write_chronology": 24965,
+            "pivot": 664,
+            "post_after_op": 24789,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              11,
+              5,
+              2
+            ],
+            "role": 10252,
+            "root_index": 913,
+            "targets": [
+              664,
+              665,
+              666,
+              667,
+              668,
+              669,
+              670,
+              671
+            ],
+            "write_ranks": [
+              11,
+              16,
+              18,
+              18
+            ],
+            "writes": [
+              18105,
+              22356,
+              24787,
+              24789
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27415,
+            "last_write_chronology": 25358,
+            "pivot": 672,
+            "post_after_op": 25182,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              4,
+              12,
+              2
+            ],
+            "role": 8926,
+            "root_index": 924,
+            "targets": [
+              672,
+              673,
+              674,
+              675,
+              676,
+              677,
+              678,
+              679
+            ],
+            "write_ranks": [
+              4,
+              16,
+              18
+            ],
+            "writes": [
+              12966,
+              22387,
+              25182
+            ]
+          },
+          {
+            "first_any_old_read": 25714,
+            "first_pivot_old_read": 27595,
+            "last_write_chronology": 25040,
+            "pivot": 712,
+            "post_after_op": 24864,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              6,
+              10,
+              2
+            ],
+            "role": 10048,
+            "root_index": 979,
+            "targets": [
+              712,
+              713,
+              714,
+              715,
+              716,
+              717,
+              718,
+              719
+            ],
+            "write_ranks": [
+              6,
+              16,
+              18
+            ],
+            "writes": [
+              16124,
+              22336,
+              24864
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27667,
+            "last_write_chronology": 25106,
+            "pivot": 728,
+            "post_after_op": 24930,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10460,
+            "root_index": 1001,
+            "targets": [
+              728,
+              729,
+              730,
+              731,
+              732,
+              733,
+              734,
+              735
+            ],
+            "write_ranks": [
+              15,
+              18,
+              18
+            ],
+            "writes": [
+              21378,
+              24929,
+              24930
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27883,
+            "last_write_chronology": 25294,
+            "pivot": 776,
+            "post_after_op": 25118,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10426,
+            "root_index": 1067,
+            "targets": [
+              776,
+              777,
+              778,
+              779,
+              780,
+              781,
+              782,
+              783
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21206,
+              25118
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27955,
+            "last_write_chronology": 25114,
+            "pivot": 792,
+            "post_after_op": 24938,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              13,
+              3,
+              2
+            ],
+            "role": 10344,
+            "root_index": 1089,
+            "targets": [
+              792,
+              793,
+              794,
+              795,
+              796,
+              797,
+              798,
+              799
+            ],
+            "write_ranks": [
+              13,
+              16,
+              18,
+              18
+            ],
+            "writes": [
+              19809,
+              22417,
+              24877,
+              24938
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27991,
+            "last_write_chronology": 25356,
+            "pivot": 800,
+            "post_after_op": 25180,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10474,
+            "root_index": 1100,
+            "targets": [
+              800,
+              801,
+              802,
+              803,
+              804,
+              805,
+              806,
+              807
+            ],
+            "write_ranks": [
+              16,
+              18
+            ],
+            "writes": [
+              22520,
+              25180
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28171,
+            "last_write_chronology": 25415,
+            "pivot": 840,
+            "post_after_op": 25239,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10450,
+            "root_index": 1155,
+            "targets": [
+              840,
+              841,
+              842,
+              843,
+              844,
+              845,
+              846,
+              847
+            ],
+            "write_ranks": [
+              16,
+              18
+            ],
+            "writes": [
+              21331,
+              25239
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28207,
+            "last_write_chronology": 25374,
+            "pivot": 848,
+            "post_after_op": 25198,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              14,
+              2,
+              2
+            ],
+            "role": 10327,
+            "root_index": 1166,
+            "targets": [
+              848,
+              849,
+              850,
+              851,
+              852,
+              853,
+              854,
+              855
+            ],
+            "write_ranks": [
+              14,
+              16,
+              18
+            ],
+            "writes": [
+              19070,
+              22564,
+              25198
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27599,
+            "last_write_chronology": 25386,
+            "pivot": 880,
+            "post_after_op": 25210,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              14,
+              2,
+              2
+            ],
+            "role": 10297,
+            "root_index": 1210,
+            "targets": [
+              880,
+              881,
+              882,
+              883,
+              884,
+              885,
+              886,
+              887
+            ],
+            "write_ranks": [
+              14,
+              16,
+              18
+            ],
+            "writes": [
+              18950,
+              22536,
+              25210
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27707,
+            "last_write_chronology": 25301,
+            "pivot": 904,
+            "post_after_op": 25125,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              11,
+              7
+            ],
+            "role": 10255,
+            "root_index": 1243,
+            "targets": [
+              904,
+              905,
+              906,
+              907,
+              908,
+              909,
+              910,
+              911
+            ],
+            "write_ranks": [
+              11,
+              18,
+              18
+            ],
+            "writes": [
+              18115,
+              24878,
+              25125
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27815,
+            "last_write_chronology": 25365,
+            "pivot": 928,
+            "post_after_op": 25189,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              8,
+              7,
+              3
+            ],
+            "role": 9586,
+            "root_index": 1276,
+            "targets": [
+              928,
+              929,
+              930,
+              931,
+              932,
+              933,
+              934,
+              935
+            ],
+            "write_ranks": [
+              8,
+              15,
+              18
+            ],
+            "writes": [
+              14591,
+              22510,
+              25189
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27923,
+            "last_write_chronology": 25332,
+            "pivot": 952,
+            "post_after_op": 25156,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              12,
+              3,
+              3
+            ],
+            "role": 10291,
+            "root_index": 1309,
+            "targets": [
+              952,
+              953,
+              954,
+              955,
+              956,
+              957,
+              958,
+              959
+            ],
+            "write_ranks": [
+              12,
+              15,
+              18
+            ],
+            "writes": [
+              18902,
+              22403,
+              25156
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27959,
+            "last_write_chronology": 25321,
+            "pivot": 960,
+            "post_after_op": 25145,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              12,
+              4,
+              2
+            ],
+            "role": 10339,
+            "root_index": 1320,
+            "targets": [
+              960,
+              961,
+              962,
+              963,
+              964,
+              965,
+              966,
+              967
+            ],
+            "write_ranks": [
+              12,
+              16,
+              18,
+              18
+            ],
+            "writes": [
+              19776,
+              22491,
+              25050,
+              25145
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28031,
+            "last_write_chronology": 25188,
+            "pivot": 976,
+            "post_after_op": 25012,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              10,
+              4,
+              4
+            ],
+            "role": 10054,
+            "root_index": 1342,
+            "targets": [
+              976,
+              977,
+              978,
+              979,
+              980,
+              981,
+              982,
+              983
+            ],
+            "write_ranks": [
+              10,
+              10,
+              14,
+              18
+            ],
+            "writes": [
+              16738,
+              16959,
+              22416,
+              25012
+            ]
+          },
+          {
+            "first_any_old_read": 26054,
+            "first_pivot_old_read": 28211,
+            "last_write_chronology": 25387,
+            "pivot": 1016,
+            "post_after_op": 25211,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10473,
+            "root_index": 1397,
+            "targets": [
+              1016,
+              1017,
+              1018,
+              1019,
+              1020,
+              1021,
+              1022,
+              1023
+            ],
+            "write_ranks": [
+              16,
+              18
+            ],
+            "writes": [
+              22489,
+              25211
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28247,
+            "last_write_chronology": 25299,
+            "pivot": 1024,
+            "post_after_op": 25123,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              16,
+              2
+            ],
+            "role": 10456,
+            "root_index": 1408,
+            "targets": [
+              1024,
+              1025,
+              1026,
+              1027,
+              1028,
+              1029,
+              1030,
+              1031
+            ],
+            "write_ranks": [
+              16,
+              18
+            ],
+            "writes": [
+              21356,
+              25123
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 27997,
+            "last_write_chronology": 25229,
+            "pivot": 1088,
+            "post_after_op": 25053,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10458,
+            "root_index": 1496,
+            "targets": [
+              1088,
+              1089,
+              1090,
+              1091,
+              1092,
+              1093,
+              1094,
+              1095
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21365,
+              25053
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28177,
+            "last_write_chronology": 25241,
+            "pivot": 1128,
+            "post_after_op": 25065,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10457,
+            "root_index": 1551,
+            "targets": [
+              1128,
+              1129,
+              1130,
+              1131,
+              1132,
+              1133,
+              1134,
+              1135
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21362,
+              25065
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28213,
+            "last_write_chronology": 25028,
+            "pivot": 1136,
+            "post_after_op": 24852,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              12,
+              6
+            ],
+            "role": 10331,
+            "root_index": 1562,
+            "targets": [
+              1136,
+              1137,
+              1138,
+              1139,
+              1140,
+              1141,
+              1142,
+              1143
+            ],
+            "write_ranks": [
+              12,
+              18
+            ],
+            "writes": [
+              19736,
+              24852
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28059,
+            "last_write_chronology": 25182,
+            "pivot": 1184,
+            "post_after_op": 25006,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              4,
+              14
+            ],
+            "role": 8962,
+            "root_index": 1628,
+            "targets": [
+              1184,
+              1185,
+              1186,
+              1187,
+              1188,
+              1189,
+              1190,
+              1191
+            ],
+            "write_ranks": [
+              4,
+              18,
+              18
+            ],
+            "writes": [
+              13014,
+              24950,
+              25006
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28107,
+            "last_write_chronology": 25248,
+            "pivot": 1240,
+            "post_after_op": 25072,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10351,
+            "root_index": 1705,
+            "targets": [
+              1240,
+              1241,
+              1242,
+              1243,
+              1244,
+              1245,
+              1246,
+              1247
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              20585,
+              25072
+            ]
+          },
+          {
+            "first_any_old_read": 11146,
+            "first_pivot_old_read": 28289,
+            "last_write_chronology": 25311,
+            "pivot": 1304,
+            "post_after_op": 25135,
+            "pre_at_phase_cut_after_center_before_old_reads": true,
+            "prefix_children": [
+              15,
+              3
+            ],
+            "role": 10463,
+            "root_index": 1793,
+            "targets": [
+              1304,
+              1305,
+              1306,
+              1307,
+              1308,
+              1309,
+              1310,
+              1311
+            ],
+            "write_ranks": [
+              15,
+              18
+            ],
+            "writes": [
+              21387,
+              25135
+            ]
+          }
+        ],
+        "status": "AUTHOR_EXACT_FINITE_COMPILER_CHECK_PASS",
+        "target_histogram": {
+          "0": 6270,
+          "1": 3960,
+          "10": 8,
+          "11": 2,
+          "12": 6,
+          "13": 2,
+          "14": 4,
+          "15": 12,
+          "16": 7,
+          "18": 1276,
+          "2": 23,
+          "3": 16,
+          "4": 7,
+          "5": 2,
+          "6": 7,
+          "7": 3,
+          "8": 5,
+          "9": 1
+        },
+        "targets_disjoint": true,
+        "v": 1320
+      },
+      "terminal_formal": {
+        "absolute_residual_bound": 394518,
+        "columns": [
+          {
+            "columns": 13163,
+            "direction": 1,
+            "dirty": 10523,
+            "outputs": true,
+            "restored": true
+          },
+          {
+            "columns": 13163,
+            "direction": -1,
+            "dirty": 10523,
+            "outputs": true,
+            "restored": true
+          }
+        ],
+        "controls": {
+          "omit-ancestor-response": "REJECTED",
+          "omit-first-write": "REJECTED",
+          "omit-pre-shear": "REJECTED"
+        },
+        "digit_bits": 24,
+        "input_pins": {
+          "baseline.json.gz": "5975dc6981aa18ac4ba4a1ca290d9163beedc8bc48e9600f4de5390758b57ef9",
+          "frames.json.gz": "05cf2b64cdc6142294512fcd963285ed535599b433691a547eaf775424f7b104",
+          "graph.json.gz": "4720aa3bf8960d89fca62cf8dc71dc7c5f8b3b85c59ecae727184ae12e1f7c18",
+          "physical-frames.json.gz": "bbbe32fb7a5d2415b7b2f130c46d1e20de392ea1cf6587fca6bc015879a3ca4f",
+          "physical-pairs.json.gz": "33b847e6f40e40809dce1c3eb25afe357b88b0b14c9a5ccca95b78553a595065",
+          "physical.py": "01961fad4b04aaa940d2dc99c87690bc861b3861200296974c5e065ce3446659",
+          "profile-before.json.gz": "e41fd008059d8a08d8f3078831e577201acd9f4aa115dd0197e28286cf281c80",
+          "profile.json.gz": "67de497a9c1ea64bb0cf9dc3ca655e7f9c704452a615f3e7eb45d124ed40c2c1",
+          "sinks.json": "d56196c9a6c4ed0d0eac660dbf5a7bdfbb118222e954cf2126a90ac0b1c84e6a",
+          "word.json.gz": "b70c03e2401df03f67bbba36e0c33704bde377902e446831a4df94833e935cc8"
+        },
+        "source_sha256": "d7fefe86e637584ad1bf53c8f7714b88d5abed92eaa29d110ef099536e51f516",
+        "status": "PASS full modified finite word"
+      }
+    },
+    "profile": {
+      "R": 10523,
+      "W_per_vertex": 13163,
+      "c": 21909,
+      "child_histogram": {
+        "1": 93600,
+        "10": 2589,
+        "11": 987,
+        "12": 3555,
+        "13": 642,
+        "14": 2142,
+        "15": 3255,
+        "16": 330,
+        "17": 132,
+        "18": 7788,
+        "19": 5829,
+        "2": 42555,
+        "20": 561,
+        "3": 29427,
+        "4": 10830,
+        "5": 7044,
+        "6": 4407,
+        "7": 2559,
+        "8": 3675,
+        "9": 1323
+      },
+      "deficit_per_vertex": 1320,
+      "h": 22,
+      "loss": 440,
+      "m": 66,
+      "matched": 12189,
+      "maxchild": 20,
+      "q": 3157,
+      "rank_per_vertex": 867438,
+      "reuse_pairs": 2310,
+      "scalar_role_reserve": 12877,
+      "terminal_sinks": 44,
+      "total_M_operations": 33466,
+      "v": 1320
+    },
+    "status": "PASS"
+  },
+  "kappa": "166261725903847/250000000000000000",
+  "scope": "Finite word, paid moments, full finite bridge and 47 strict arithmetic constraints; source-specified all-size contracts remain assumptions.",
+  "status": "PASS conditional finite witness"
+}
diff --git a/research/composed-diagonal-bit-bootstrap/levers.json b/research/composed-diagonal-bit-bootstrap/levers.json
new file mode 100644
index 0000000000..11c6825322
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/levers.json
@@ -0,0 +1,61 @@
+{
+ "claim": {
+  "kappa": "1693287/2500000000",
+  "kappa_decimal": 0.0006773148
+ },
+ "copies": 3,
+ "gain_vs_claim": 0.008484237169919048,
+ "method": "PR200's exact interval arithmetic on the 10^-18 grid, three-copy rows; the three published values are reproduced exactly, not to a tolerance",
+ "pr200_banked": {
+  "W_per_vertex": "56402/3",
+  "W_per_vertex_decimal": 18800.666666666668,
+  "W_three_copies": 56402,
+  "ceiling": "683528191056257/1000683528191056257",
+  "ceiling_decimal": 0.0006830612994018963,
+  "coarse": "683528191056257/1000000000000000000",
+  "coarse_decimal": 0.000683528191056257,
+  "deficit_three_copies": "5808",
+  "ledger_share_of_rank60": 0.08896605271103826,
+  "rank60_children_per_copy": 2200,
+  "rank60_mass_per_copy": 132000
+ },
+ "pr200_unpacked": {
+  "ceiling": "677773948354561/1000677773948354561",
+  "ceiling_decimal": 0.000677314881972727,
+  "coarse": "677773948354561/1000000000000000000",
+  "coarse_decimal": 0.000677773948354561
+ },
+ "status": "MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's certified word, but the bank construction on PR200's word is not built here and no claim is made about it.",
+ "validations": [
+  {
+   "W": 63324,
+   "deficit": "5808",
+   "maxchild": 60,
+   "model": "167724995262213/250000000000000000",
+   "model_decimal": 0.000670899981048852,
+   "name": "PR187 unpacked row",
+   "published": "167724995262213/250000000000000000",
+   "published_decimal": 0.000670899981048852
+  },
+  {
+   "W": 57824,
+   "deficit": "5808",
+   "maxchild": 22,
+   "model": "676537710350481/1000000000000000000",
+   "model_decimal": 0.000676537710350481,
+   "name": "PR187 banked row (PR197)",
+   "published": "676537710350481/1000000000000000000",
+   "published_decimal": 0.000676537710350481
+  },
+  {
+   "W": 61902,
+   "deficit": "5808",
+   "maxchild": 60,
+   "model": "677773948354561/1000000000000000000",
+   "model_decimal": 0.000677773948354561,
+   "name": "PR200 unpacked row",
+   "published": "677773948354561/1000000000000000000",
+   "published_decimal": 0.000677773948354561
+  }
+ ]
+}
diff --git a/research/composed-diagonal-bit-bootstrap/levers.py b/research/composed-diagonal-bit-bootstrap/levers.py
new file mode 100644
index 0000000000..920661fcea
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/levers.py
@@ -0,0 +1,195 @@
+#!/usr/bin/env python3
+"""Where the next gain is on this word, modelled exactly.
+
+The bit branch's coarse saving is the largest `a` on the 10^-18 grid whose paid
+moment is below 1:
+
+    sum_r n_r * r/(W*m) * exp(a*ln(m/r))  +  BAD * 32 m^2 * edges/(W*m) * exp(a*ln m) < 1,
+
+with `m*W - sum n_r r = D` the row identity. The moment increases in `a`, so two
+words with the same `D` differ only through the child ledger.
+
+PR197 lowered a word's ledger by *banking* the rank-60 exterior corrections: the
+rank-60 children, one per selected gauge, are replaced by shared banks, so those
+entries leave the ledger and the stock falls to what the identity still requires.
+This script models that transformation exactly -- drop the rank-60 entries, keep
+`D`, set `W = (mass + D)/m` -- checks the model against the three published values
+it can be checked on, and then applies it to this package's bit word.
+
+Everything is exact rational arithmetic, on the enclosure implementation of the
+supplier whose certificate is being reproduced (`references/pr200/interval_moment.py`,
+the arithmetic PR200's own `bit/prove.py` prices with). The reported grid points
+are therefore identical on every platform, and the three checks are *exact*
+reproductions rather than tolerances. Rows are taken over the family's three
+copies so that the stock stays integral, which leaves the saving unchanged.
+
+The transformation is accounting, validated on another word of the same family. On
+PR200's word it is a *prediction*: the bank construction is not built here.
+
+    python3 -B levers.py [--out levers.json]
+"""
+import argparse
+import importlib.util
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+COPIES = 3
+RANK60 = 60
+GRID = 10 ** 18
+BAD = Q(1, 10 ** 16)
+CLAIM = Q(1693287, 2500000000)
+
+# Published values the model is checked against, exactly.
+PR187_COARSE = Q(167724995262213, 250000000000000000)
+PR187_PACKED = Q(676537710350481, GRID)         # PR197's certified banked word
+PR200_COARSE = Q(677773948354561, GRID)         # PR200's certified bit word
+
+
+def module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    loaded = importlib.util.module_from_spec(spec)
+    sys.modules[name] = loaded
+    spec.loader.exec_module(loaded)
+    return loaded
+
+
+def three_copies(profile):
+    """The family's three-copy row: integral stock, same saving as one copy."""
+    m = int(profile["m"])
+    W = Q(profile["W_per_vertex"] if "W_per_vertex" in profile else profile["W"])
+    D = Q(profile["deficit_per_vertex"] if "deficit_per_vertex" in profile else profile["N"])
+    key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram"
+    hist = {int(r): COPIES * int(n) for r, n in profile[key].items() if n}
+    mass = sum(r * n for r, n in hist.items())
+    D, W = D * COPIES, W * COPIES
+    assert m * W - mass == D, "row identity"
+    assert W.denominator == 1, "three-copy stock must be integral"
+    return row(m, int(W), D, hist)
+
+
+def row(m, W, D, hist):
+    return dict(m=m, W=W, N=D, L=0, total_rank=sum(r * n for r, n in hist.items()),
+                maxchild=max(hist), child_multiplicities=dict(sorted(hist.items())))
+
+
+def paid_moment(interval, profile, a):
+    """PR200's `bit/prove.py` price: the child ledger plus the rare-class fallback."""
+    raw = interval.moment(profile, a)
+    m, W = profile["m"], profile["W"]
+    edges = sum(profile["child_multiplicities"].values())
+    low, high = interval.log_interval(Q(m))
+    exp_low, exp_high = interval.exp_interval(a * low, a * high)
+    weight = BAD * Q(32 * m * m * edges, W * m)
+    return dict(upper=raw["upper"] + weight * exp_high,
+                lower=raw["lower"] + weight * exp_low)
+
+
+def certified(interval, profile):
+    """The largest 10^-18 grid point that pays, as PR200's own `certify` finds it."""
+    low, high = 0, GRID // 100
+    assert paid_moment(interval, profile, Q(low, GRID))["upper"] < 1, "zero-saving contraction"
+    assert paid_moment(interval, profile, Q(high, GRID))["lower"] > 1, "upper bracket"
+    while high - low > 1:
+        mid = (low + high) // 2
+        if paid_moment(interval, profile, Q(mid, GRID))["upper"] < 1:
+            low = mid
+        else:
+            high = mid
+    accepted = paid_moment(interval, profile, Q(low, GRID))["upper"]
+    rejected = paid_moment(interval, profile, Q(high, GRID))["lower"]
+    assert accepted < 1 < rejected, "adjacent grid exclusion"
+    return Q(low, GRID)
+
+
+def banked(profile):
+    """PR197's accounting: the rank-60 exterior corrections become banked roles."""
+    hist = profile["child_multiplicities"]
+    assert hist.get(RANK60), "no rank-60 exterior corrections to bank"
+    trimmed = {r: n for r, n in hist.items() if r != RANK60}
+    mass = sum(r * n for r, n in trimmed.items())
+    packed = row(profile["m"], (mass + profile["N"]) // profile["m"], profile["N"], trimmed)
+    assert packed["W"] * packed["m"] - mass == packed["N"], "banked row identity"
+    assert packed["W"] < profile["W"], "the stock must fall"
+    return packed
+
+
+def check(interval, name, profile, published):
+    model = certified(interval, profile)
+    assert model == published, (name, str(model), str(published))
+    return dict(name=name, published=str(published), published_decimal=float(published),
+                model=str(model), model_decimal=float(model),
+                W=profile["W"], deficit=str(profile["N"]),
+                maxchild=profile["maxchild"])
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--out", type=Path, default=HERE / "levers.json")
+    args = parser.parse_args()
+    if hasattr(sys, "set_int_max_str_digits"):
+        sys.set_int_max_str_digits(0)
+    assert not sys.flags.optimize, "assertions must stay enabled"
+    interval = module("levers_interval_moment", HERE / "references/pr200/interval_moment.py")
+
+    validations = []
+    pr187 = three_copies(json.loads((HERE / "references/pr187/certificate.json").read_text())["profile"])
+    validations.append(check(interval, "PR187 unpacked row", pr187, PR187_COARSE))
+    validations.append(check(interval, "PR187 banked row (PR197)", banked(pr187), PR187_PACKED))
+
+    bit = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text())["bit"]["profile"]
+    per_copy = {int(r): int(n) for r, n in bit["child_histogram"].items() if n}
+    pr200 = three_copies(bit)
+    validations.append(check(interval, "PR200 unpacked row", pr200, PR200_COARSE))
+
+    packed = banked(pr200)
+    packed_saving = certified(interval, packed)
+    now = Q(validations[-1]["model"])
+    ceiling_now, ceiling_packed = now / (1 + now), packed_saving / (1 + packed_saving)
+    gain = ceiling_packed / CLAIM - 1
+    for v in validations:
+        print("[validated] {name}: model {model} = published {published} exactly "
+              "(W={W}, N={deficit}, maxchild={maxchild})".format(**v))
+    print("[PR200 now]     coarse {} ({:.10g}) -> ceiling {:.10g}".format(
+        now, float(now), float(ceiling_now)))
+    print("[PR200 banked]  W={} (= {:d}/3 per vertex) -> coarse {} ({:.10g}) -> "
+          "ceiling {:.10g}".format(packed["W"], 3 * packed["W"], packed_saving,
+                                   float(packed_saving), float(ceiling_packed)))
+    print("[lever]         banking the rank-60 exterior corrections is worth {:.4f}% of "
+          "kappa ({:.10g} -> {:.10g})".format(float(ceiling_packed / ceiling_now - 1) * 100,
+                                              float(ceiling_now), float(ceiling_packed)))
+    print("[vs the claim]  {} ({:.10g}) -> {:.4f}%".format(
+        CLAIM, float(CLAIM), float(gain) * 100))
+
+    out = dict(
+        status="MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's "
+               "certified word, but the bank construction on PR200's word is not built here "
+               "and no claim is made about it.",
+        method="PR200's exact interval arithmetic on the 10^-18 grid, three-copy rows; the "
+               "three published values are reproduced exactly, not to a tolerance",
+        copies=COPIES,
+        validations=validations,
+        pr200_unpacked=dict(coarse=str(now), coarse_decimal=float(now),
+                            ceiling=str(ceiling_now), ceiling_decimal=float(ceiling_now)),
+        pr200_banked=dict(W_three_copies=packed["W"],
+                          W_per_vertex=str(Q(packed["W"], COPIES)),
+                          W_per_vertex_decimal=float(Q(packed["W"], COPIES)),
+                          coarse=str(packed_saving), coarse_decimal=float(packed_saving),
+                          ceiling=str(ceiling_packed), ceiling_decimal=float(ceiling_packed),
+                          rank60_children_per_copy=per_copy[RANK60],
+                          rank60_mass_per_copy=RANK60 * per_copy[RANK60],
+                          ledger_share_of_rank60=float(
+                              Q(RANK60 * per_copy[RANK60],
+                                sum(r * n for r, n in per_copy.items()))),
+                          deficit_three_copies=str(pr200["N"])),
+        claim=dict(kappa=str(CLAIM), kappa_decimal=float(CLAIM)),
+        gain_vs_claim=float(gain),
+    )
+    args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n")
+    print("[write] " + str(args.out))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py b/research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt b/research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt
new file mode 100644
index 0000000000..c1a8843611
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt
@@ -0,0 +1,141 @@
+FINITE ROUTER, ROW-STOCK, AND SEMANTIC BRIDGE FOR ROUND 13
+
+Prepared for icekylinx by GPT-6 Astra, 9 October 2026. Apache-2.0.
+
+This bridge applies to a completed, physically proved round-13 profile.
+It cannot make a numerically attractive but unconstructed profile valid.
+The local source/target flags, controlled injections, old-response
+subtraction, inverse cleanup, and retained alias boundaries are separate
+construction obligations. assemble_profiles.py records their role as
+proof dependencies and independently checks the exact arithmetic.
+
+1. The inherited uniform interfaces
+
+Retain the three completed-core cover of PR144/PR168 and all of its
+analytic and fixed-tape assumptions. The complex cover is O(m,2), m<=72,
+with order V<2^(m*m)<=2^5184. No new independent cover coordinates are
+introduced by common-frame scalar lifts or source-controlled local
+rewrites. Every stage still uses one completed invocation at each vertex.
+
+For a supplied profile with W0<10^7 roles per cover vertex, the full
+physical stock W=V W0 is less than2^5208. Its total rank s is less
+than mW<2^5215. The profile's actual proper-child maximum is retained;
+the selected complex maximum must be less than m/2. The script checks
+these inequalities rather than assuming that fewer auxiliary rows imply
+a better contraction or a shorter recursion.
+
+The bit word uses the same weighted q-adic frame interface and the same
+internally borrowed selectors as its pinned parent. New source controls
+must use existing nondegenerate source-meeting planes or separately
+certified new frames. All zero-rank adapters remain charged scalar work.
+The group-size factor is not omitted and is not inserted into an external
+polynomial row reserve. The inherited ordinary leaf saving is exactly
+384599/10^10. The bad-row allowance is1/10^16; the charged fallback per
+edge is32m^2. Its inequality2m^3/2^80<1/10^16 is checked explicitly.
+
+2. A deliberately loose finite scalar bound
+
+The pinned words and round-13 modifications are finite straight-line
+programs with fewer than2^40 stored nodes, roles, coefficients, and
+boundary entries. Scalar sum/difference lifts use actual invertible
+matrices and are executed pointwise at common frame representatives.
+For the selected dyadic rewrite, new elementary coefficients are
+dyadic; the inherited center scatters retain their fixed odd divisor3.
+No unrecorded new odd denominator may be included under this bridge.
+
+Fixed integer multipliers can be expanded into scalar doublings and
+additions; dyadic divisions can be expanded into halvings. The explicit
+low words and full-frame inverses are much smaller than2^4096 primitive
+scalar/movement groups per invocation. Even constructing their fixed
+old-response matrices by exact elimination is dominated by this bound:
+matrix order is below2^40, original finite-word coefficient bit lengths
+are below2^80, and the elementary elimination and coefficient expansion
+bounds are below2^1024. No input-size-dependent dense elimination is
+being performed. These are constants of the chosen finite construction.
+
+Consequently all3V invocation words, endpoint adapters, and finite role
+bookkeeping fit within K<2^9300 logical groups. The retained universal
+router is overcharged by a full W-role permutation for every group:
+
+    64 (m+1)^3 (K+1) (W+1)^2 < 2^20000.
+
+Choose the exact dominating scalar/router budget G=2^30000. This also
+dominates the primitive arithmetic required to realize the fixed scalar
+coefficients and source-controlled inverse cleanup. The router still
+uses a fixed number of tapes, with sequential reuse of row stock.
+
+3. Explicit semantic constants
+
+Choose the exact integer E=2^100000 and put B=s+E. Then
+
+    2 G W^2 + 8s + 4W + 4 + 32m < 2^40500 < E,
+    E <= B < 2^100001.
+
+For the actual maximum child r<m, the induction gap obeys
+
+    2B(m-r)-s-E >= s+E >= 1.
+
+Choose C0=2^210000 and C1=1. These dominate both the retained semantic
+requirement32m B^2 and2B+18. The reported strict_literal_gap=1 and
+induction_gap_lower=1 are proved lower bounds on the positive actual
+integer gaps; they are not claims that those gaps equal one.
+
+Use the inherited common dyadic grid with fixed3^(-K') exposure and
+retain its precision/rounding contract. No child receives an independent
+rounding allowance and no source-controlled injection is treated as an
+unpaid numerical operation.
+
+4. External rows and stopping
+
+The complex child maximum below m/2 gives halving degree1, while
+log2 W<5208<10000. Keep the deliberately conservative inherited bit
+coarse reserve9909 and ordinary-leaf reserve252. Thus the external
+row coefficient is bounded by
+
+    A=10000+9909+252=20161.
+
+Choose degree D=1000000 and suffix slope4D. The exact row gap is
+
+    D - (51/25)A > 0.
+
+The q-adic selector fields and source-control labels remain internally
+borrowed and restored. Increasing these finite overcharges changes
+constants and the all-size bridge, not the selected exponent saving.
+
+5. Exact supplier moments and balanced assembly
+
+For each actual histogram, assemble_profiles.py proves
+
+    sum_r n_r r exp(a log(m/r))/(mW0) + bad_allowance < 1
+
+using rational upper bounds, with upward rounding on the2^120 grid.
+The bit atom stop is the first10^(-12) grid point above
+a/(1+a-old), which implies both required strict toll inequalities.
+Its effective saving is(1-beta)a+beta*old. This stopping rule is the
+already reviewed PR158 edge rule, not a new local-word contribution.
+
+The final assembly uses the substantial PR168 balanced-prefix adapter,
+with eta=10^(-8) and phase stop10^(-9), retaining all47 strict
+constraints and all7 margins. The selected final kappa is rounded
+down on the10^(-10) grid below the minimum complete margin. The
+script checks every constraint exactly and reports whether the fixed
+target0.0009218338 is reached.
+
+This is a conditional bound of the retained theorem form
+
+    T(n)=O(n (log n)^(1-kappa)).
+
+The improvement ratio refers to kappa, the logarithmic exponent saving.
+It is not a measurement of practical multiplication throughput.
+
+Credits
+
+The base supplier, scalar/frame verification, and actual profiles are
+pinned to PR168 fd25adb7fbaa12ee761d02c733c54d1d2a7687ee, eumemic
+(Anthropic Claude assistance), building on icekylinx's PR144. The
+balanced prefix is RaD/hipotures; the semantic constraints are retained
+from the reviewed PR23 line; completed-core sharing is credited to
+an664 PR128; the atom-edge stop is credited to geckods PR158. Existing
+source notices retain their more detailed upstream attributions.
+The new source-controlled boundary construction, this conservative
+bridge, and its integration are GPT-6 Astra's round-13 work.
diff --git a/research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py b/research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py
new file mode 100644
index 0000000000..1f5672db45
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py
@@ -0,0 +1,248 @@
+#!/usr/bin/env python3
+"""Price complete supplied profiles and perform the exact balanced assembly.
+
+New integration for icekylinx: GPT-6 Astra, 2026-10-09. Apache-2.0.
+The rational enclosures are retained from icekylinx's three_stage_cover_network.py;
+the balanced assembly is PR168's paired_cube_assembly.py (eumemic, Anthropic
+Claude assistance), retaining the RaD/hipotures balanced prefix and PR23 gates.
+
+This tool certifies arithmetic and binds the supplied construction receipts.
+It is not a substitute for regenerating their exact flow and boundary checks.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import importlib.util
+import json
+import math
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PIN = HERE.parent / "public/pr168_fd25adb7"
+GRID = 1 << 120
+SELECT_GRID = 10**10
+OLD = Q(384599, SELECT_GRID)
+BAD = Q(1, 10**16)
+BASE = Q(4609169, SELECT_GRID)
+
+
+def serial(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): serial(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [serial(v) for v in x]
+    return x
+
+
+def up(x):
+    return Q((x.numerator*GRID+x.denominator-1)//x.denominator, GRID)
+
+
+def log_upper(x):
+    assert x >= 1
+    p = 0
+    while x >= 2:
+        x /= 2
+        p += 1
+    def small(y):
+        z = (y-1)/(y+1)
+        return (2*sum((z**(2*j+1)/(2*j+1) for j in range(32)), Q(0))
+                + 2*z**65/(65*(1-z*z)))
+    return up(p*small(Q(2))+small(x))
+
+
+def exp_upper(u):
+    assert 0 <= u < 3
+    return up(1+u+u*u/(2*(1-u/3)))
+
+
+def normalize(data):
+    p = data.get("combined_fixed_boundary_profile") or data
+    m = int(p.get("m", 3*int(p.get("h",0))))
+    W = Q(p.get("W_per_vertex", p.get("W", p.get("new_W"))))
+    hist = {int(r): Q(n) for r, n in p["child_histogram"].items() if int(r) and n}
+    delta = Q(p.get("deficit_per_vertex", p.get("delta", p.get("deficit"))))
+    assert all(0 < r < m and n > 0 for r, n in hist.items())
+    mass = sum((r*n for r, n in hist.items()), Q(0))
+    assert m*W-mass == delta > 0
+    return dict(m=m, W=W, delta=delta, histogram=hist,
+                mass=mass, edge_count=sum(hist.values()), maxchild=max(hist))
+
+
+def numerical_root(p):
+    lo, hi = 0., .02
+    while sum(float(n)*r*math.expm1(hi*math.log(p['m']/r))
+              for r, n in p['histogram'].items()) < float(p['delta']):
+        hi *= 2
+    for _ in range(85):
+        a = (lo+hi)/2
+        excess = math.fsum(float(n)*r*math.expm1(a*math.log(p['m']/r))
+                           for r, n in p['histogram'].items())
+        if excess < float(p['delta']):
+            lo = a
+        else:
+            hi = a
+    return lo
+
+
+def moment(p, a, bit=False):
+    m, W = p['m'], p['W']
+    good = sum((n*r/(W*m)*exp_upper(a*log_upper(Q(m, r)))
+                for r, n in p['histogram'].items()), Q(0))
+    extra = (BAD*32*m*m*p['edge_count']/(W*m)*exp_upper(a*log_upper(Q(m)))) if bit else Q(0)
+    return dict(saving=a, ideal_moment_upper=good, bad_moment_upper=extra,
+                strict_gap_lower=1-good-extra,
+                strict_gap_lower_decimal=float(1-good-extra))
+
+
+def select(p, bit=False):
+    root = numerical_root(p)
+    ticks = int(root*SELECT_GRID)
+    while True:
+        result = moment(p, Q(ticks, SELECT_GRID), bit)
+        if result['strict_gap_lower'] > 0:
+            break
+        ticks -= 1
+    result['numerical_root_for_discovery_only'] = root
+    result['counts'] = p
+    if bit:
+        assert Q(2*p['m']**3, 2**80) < BAD
+        a = result['saving']
+        edge = a/(1+a-OLD)
+        beta = Q(edge.numerator*10**12//edge.denominator+1, 10**12)
+        effective = (1-beta)*a+beta*OLD
+        assert effective < beta < 1-effective
+        result.update(atom_exponent=beta, ordinary_leaf_saving=OLD,
+                      effective_saving=effective,
+                      effective_saving_decimal=float(effective))
+    return result
+
+
+def construction_receipts(cdata, bdata, bit_lifts, proof):
+    """Reject a raw modular screen and bind the selected constructive proofs."""
+    checks = cdata['contract_checks']
+    for name in ('all_fresh_columns_equal_identity',
+                 'source_controls_at_paid_parity_frames',
+                 'original_source_V_before_all_controls',
+                 'controls_before_original_K', 'all_centers_in_phase1',
+                 'all_target_cap_reads_in_phase2', 'target_chains_nested'):
+        assert checks[name] is True, name
+    assert checks['checked_source_columns'] == checks['checked_target_rows'] == cdata['v']
+    assert cdata['scalar_denominator_lcm'] == '2'
+    assert cdata['terminal_sink_substitutions'] == 0
+    cp = Path(cdata['exact_lift_certificate_path'])
+    if not cp.is_file():
+        cp = HERE.parent / cp
+    assert cp.is_file(), 'The exact complex lift certificate must be present'
+    assert sha256(cp.read_bytes()).hexdigest() == cdata['exact_lift_certificate_sha256']
+    low = bdata['source_aligned_rewrite']
+    assert low['exact_high_boundary_and_suffix_unchanged'] is True
+    assert low['exact_rank3_resource_counts_unchanged'] is True
+    chosen = bdata['combined_fixed_boundary_profile']
+    assert chosen['paired_donors_deleted'] == 0
+    assert chosen['retained_gauges'] == 3960 and chosen['retained_pairs'] == 1760
+    assert chosen['child_histogram']['60'] == 2200
+    lifts = json.loads(bit_lifts.read_text())
+    assert lifts['source_commit'] == 'fd25adb7fbaa12ee761d02c733c54d1d2a7687ee'
+    assert lifts['instances'] == 2640
+    assert all(value is True for value in lifts['checks'].values())
+    proof_paths = (proof, HERE/'COMMON_FRAME_LIFT_AND_GLOBAL_CONTRACT.txt',
+                   HERE.parent/'bit/SOURCE_ALIGNED_BIT_WORD.txt', bit_lifts)
+    def label(path):
+        try:
+            return str(path.resolve().relative_to(HERE.parent))
+        except ValueError:
+            return path.name
+    return dict(
+        status='Constructive exact flow and fixed-boundary proofs; literal globally renumbered program/replay remains a downstream integration task',
+        complex_lift_certificate_sha256=cdata['exact_lift_certificate_sha256'],
+        complex_endpoint_checks=checks,
+        bit_high_boundary_sha256=low['high_boundary_and_suffix_sha256'],
+        bit_low_instances_sha256=lifts['instance_sha256'],
+        bit_low_checks=lifts['checks'],
+        proof_sha256={label(p):sha256(p.read_bytes()).hexdigest()
+                      for p in proof_paths})
+
+
+def assemble(c, b, source, proof):
+    # The finite bridge is deliberately overcharged. Its derivation is in
+    # FINITE_BRIDGE.txt; the integers below are exact powers, not estimates.
+    assert proof.is_file(), 'The physical/finite bridge proof must be present'
+    assert c['counts']['m'] <= 72 and b['counts']['m'] <= 72
+    assert c['counts']['W'] < 10**7 and b['counts']['W'] < 10**7
+    assert 2*c['counts']['maxchild'] < c['counts']['m']
+    coefficient, degree = 20161, 10**6
+    bridge = dict(
+        proof=proof.name,
+        representation='Exact powers of two with proved dominating bounds',
+        semantic=dict(G=dict(base=2, exponent=30000),
+                      E=dict(base=2, exponent=100000),
+                      B_upper=dict(base=2, exponent=100001),
+                      C0=dict(base=2, exponent=210000), C1=1,
+                      strict_literal_gap=1, induction_gap_lower=1),
+        rows=dict(coefficient=coefficient, degree=degree,
+                  suffix_slope=4*degree,
+                  degree_gap=Q(degree)-Q(51*coefficient,25)))
+    eta, stop = Q(1,10**8), Q(1,10**9)
+    a = min(b['effective_saving'], (1-stop)*c['saving']-Q(1,SELECT_GRID))
+    q = a*(1-2*eta)
+    minimum = (1-eta)*q/(1+q)
+    kappa = Q(minimum.numerator*SELECT_GRID//minimum.denominator, SELECT_GRID)
+    if kappa == minimum:
+        kappa -= Q(1, SELECT_GRID)
+    ap = source / 'scripts/paired_cube_assembly.py'
+    spec = importlib.util.spec_from_file_location('retained_balanced_assembly', ap)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    out = module.assembly(a,c['saving'],bridge,kappa,eta=eta,beta=stop)
+    assert len(out['strict_constraints']) == 47 and len(out['margins']) == 7
+    assert out['minimum_margin'] == minimum
+    return dict(finite_bridge=bridge, assembly=out,
+                kappa=kappa, kappa_decimal=float(kappa),
+                reviewed_baseline=BASE, fixed_doubling_target=2*BASE,
+                ratio_to_reviewed_baseline=kappa/BASE,
+                ratio_to_reviewed_baseline_decimal=float(kappa/BASE),
+                doubling_achieved=kappa >= 2*BASE,
+                assembly_source_sha256=sha256(ap.read_bytes()).hexdigest())
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--complex', type=Path, required=True)
+    parser.add_argument('--bit', type=Path, required=True)
+    parser.add_argument('--source', type=Path, default=PIN)
+    parser.add_argument('--proof', type=Path, default=HERE/'FINITE_BRIDGE.txt')
+    parser.add_argument('--bit-lifts', type=Path, default=HERE.parent/'bit/source_aligned_lifts.json')
+    parser.add_argument('--output', type=Path, default=HERE/'global_certificate.json')
+    parser.add_argument('--moments-only', action='store_true')
+    args = parser.parse_args()
+    paths = dict(complex=args.complex,bit=args.bit)
+    data = {kind: json.loads(path.read_text()) for kind,path in paths.items()}
+    profiles = {kind: normalize(value) for kind,value in data.items()}
+    c,b = select(profiles['complex']),select(profiles['bit'],True)
+    out = dict(author='GPT-6 Astra',
+               status='Exact arithmetic; construction and finite bridge are explicit proof dependencies',
+               complex=c,bit=b,
+               source_sha256={kind:sha256(path.read_bytes()).hexdigest() for kind,path in paths.items()},
+               arithmetic='32-term rational logarithm enclosure; rational exponential majorant; upward 2^120 rounding')
+    if not args.moments_only:
+        out['construction_receipts'] = construction_receipts(data['complex'],data['bit'],args.bit_lifts,args.proof)
+        out.update(assemble(c,b,args.source,args.proof))
+    args.output.parent.mkdir(parents=True,exist_ok=True)
+    args.output.write_text(json.dumps(serial(out),indent=2)+'\n')
+    summary = dict(complex_saving=float(c['saving']),
+                   complex_gap=c['strict_gap_lower_decimal'],
+                   bit_coarse_saving=float(b['saving']),
+                   bit_gap=b['strict_gap_lower_decimal'],
+                   bit_effective_saving=b['effective_saving_decimal'])
+    if not args.moments_only:
+        summary.update(kappa=out['kappa_decimal'],
+                       ratio=out['ratio_to_reviewed_baseline_decimal'],
+                       doubling_achieved=out['doubling_achieved'])
+    print(json.dumps(summary,indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json b/research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json
new file mode 100644
index 0000000000..1c77667185
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json
@@ -0,0 +1,231 @@
+{
+  "status": "PASS conditional finite source-assisted bit supplier and assembly",
+  "source_sha256": {
+    "emitted-physical.json": "5f1f1d978937b816a14b07fee5ac8fc31f3a9aaf05046a477e8be57bb6d07ce6",
+    "scalar-cost.json": "253a203c74aaafdc393094f742fec88949e1604d6a3bbd594ffea9af6fc7b975",
+    "independent-all-columns.json": "a1093cbbcea4b9ac36b7dd09b555a75f5fd776e249f97a39c5dbadfc4a2b260c"
+  },
+  "profile": {
+    "m": 72,
+    "W": 21108,
+    "N": 1936,
+    "L": 0,
+    "total_rank": 1517840,
+    "maxchild": 60,
+    "child_multiplicities": {
+      "1": 120168,
+      "2": 64228,
+      "3": 29616,
+      "4": 8970,
+      "5": 7800,
+      "6": 3660,
+      "7": 3312,
+      "8": 2802,
+      "9": 1812,
+      "10": 2508,
+      "11": 1158,
+      "12": 4320,
+      "13": 1590,
+      "14": 3234,
+      "15": 1230,
+      "16": 3216,
+      "17": 1164,
+      "18": 1332,
+      "19": 918,
+      "20": 5280,
+      "21": 11160,
+      "22": 11952,
+      "60": 2200
+    }
+  },
+  "word_sha256": "3c188c2527b3b96443e241f2f0d07c120feb1e784c2ff7f49c3e1e10eaea5f0b",
+  "scalar_guard": {
+    "local_scalar_group_upper": 17663702937368,
+    "actual_F2_unit_shears": 890560,
+    "expanded_readout_bits_per_coefficient": 64840,
+    "logical_scalar_reserve": 19348,
+    "forward_unit_updates": 64824,
+    "integer_majorants": {
+      "maximum_aux_old_read_row_l1": 2820,
+      "sum_aux_old_read_row_l1": 5442384,
+      "maximum_X_adjoint_row_l1": 3049,
+      "maximum_forward_and_inverse_row_l1": 442955,
+      "interpretation": "Noncancelling defining-integer-word coefficient majorants, not exact coefficient maxima or an integer identity. F2 adjoints are separately stored in emitted word."
+    },
+    "scope": "Fixed local bit-word/scalar toll in the uniform recurrence. Complex precision/group bounds remain unchanged; no integer decoder identity is asserted."
+  },
+  "profile_origin": "Actual newly emitted elementary-word physical histogram; independently replayed source/target/dirty columns",
+  "coarse": "167724995262213/250000000000000000",
+  "accepted": {
+    "lower": "82453124999999999989205572896937038584170512932039742846004063/82453125000000000000000000000000000000000000000000000000000000",
+    "upper": "27484374999999999996401857632312346194723504686885643461352837/27484375000000000000000000000000000000000000000000000000000000"
+  },
+  "next_coarse_excluded": {
+    "lower": "247359375000000000437697138375814169267365282480510092612153899/247359375000000000000000000000000000000000000000000000000000000",
+    "upper": "742078125000000001313091415127442507802095857661807621928951729/742078125000000000000000000000000000000000000000000000000000000"
+  },
+  "ordinary_chain": [
+    "41290795370408974880561882669886564377/62500000000000000000000000000000000000000",
+    "10482704783837260008462102001556104083601218468819986301/15625000000000000000000000000000000000000000000000000000000",
+    "2620703032955050571154178221888936860701775524669750066156599988562944113/3906250000000000000000000000000000000000000000000000000000000000000000000000",
+    "655175762739997625388892048465518856359612684797421550872147594576395840411339259699702069/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "atom_exponent": "167724995262213/250000000000000000",
+  "transfer_saving": "132438677972999999999999867361322027/200000000000000000000000000000000000000",
+  "complex_saving": "132438677973/200000000000000",
+  "kappa": "330877589979561/500000000000000000",
+  "improvement_over185": "375948628277/220209111358097",
+  "assembly": {
+    "parameters": {
+      "a_bit": "132438677972999999999999867361322027/200000000000000000000000000000000000000",
+      "a_complex": "132438677973/200000000000000",
+      "tau": "199867561322027000000000000132638677973/200000000000000000000000000000000000000",
+      "sigma": "199867561322027/200000000000000",
+      "beta": "1/1000000000000000000000000",
+      "h": "1/1000000000000000000000000",
+      "q": "66219338986499999999999801241983040500000000000132638677973/100000000000000000000000000000000000000000000000000000000000000",
+      "c": "66219338986500000000024801241983040500000000000132638677973/100000000000000000000000000000000000000000000000000000000000000",
+      "epsilon": "99999900000099999900000000000000000000000000000000000000/100066119272867227132772867028374954665545334454665677973",
+      "lambda_": "199867561322027000000000000265077355945999999999999867361322027/200000000000000000000000000000000000000000000000000000000000000",
+      "lambda_prime": "99933780661013500000000000198758016959499999999999867361322027/100000000000000000000000000000000000000000000000000000000000000",
+      "alpha_squared_power": "132438545534454465545633990630636463863536136464327571045334454665545334322027/200132238545734454265545734056749909331090668909331355946000000000000000000000000",
+      "delta": "1/8000000000000000000000000",
+      "C0": 628527618122649248682757650146876240355084858156873576455411140848847129754468654378106151495900839472854370729649793654143457444860130252966983704112892628648140779720071789063074328885897315863317306969510319083326450824232988437078706753970138361551599623222242957713739055304249294570220956354137189755614318912892657261352398740904375429859773125667460879494195403553749965561261487647113317863536655211591647773113465846178111417790230369803174014983668008558503247471590322186981578414736792722823258083620998358930902572151126379332319453650133350342704928914214005609101059291838819726623704841887326096950671354115211238102145489284816797253377393993409407204797307473786441815237469544063081967927275853257836025383277644739908517335326170219033741209859126692670559777488639453055535377861835278857790878490150974232023447690023689409148090345620688503979404514782629463140984816734823474475267446745999177133614077964249361868378965420389012058107296801760423043782337668449127750481325064650996546604170760737480881135850800964938249000411607184673458848693633471017715707501804503978124950887142016640619147582877586832275393906959678822665873037743296825607007958465958226110583553125597297932060298517903053804941860695690866603931935213418587816431208295586111642378791333424092952958355087462219759148985635375945699604663556012919921357823329519989088231365257074902150161582485904771382825739528668118048600550102312040379165112741080138359820519467511395153738006590774015029974630551179662402529165698804322673596451536592575582578658341452190425820075353115047807063314064232753057033455029555026718879411085747711178102161920578548824205283445836503059854386922425421243979423854133972165833454392490615885957527456202057131178782047266750703106996995699822897612665713855474716612603065710448268493480892784114613485129881891303071672863424748311197367982889247837816134790622301262041760333789918121163870779905348537211539790812379830807702437631156909847652007057651666142000683676376404049627413935348616830394777745045398147420029914894037194502236124125867606213182036114140397453859882538927202042640783343877109420600135411348373375203904512426300797553719439423129620556743106957140858600072906050771555822670952382456032548086719677333825230837435999346258118721646360967384881202161559548597947112032619279426467503511691685787814811651604167677531455597112863799616089973187467545657720868001138456002249223647718897041153811089277268833927268858101603024264609960135565443776635778664741360824317942318239225181832387758188551721853467268748984908078571778833621334649278828936852190064270440578912580378077466933204405384344184782301472493091865675647418975710660783087711556534575312755838217475556876557477051683292246634463888400605189971688951903437806451477613991328928672058892036792524967240582139796588302232535584084652279806887721330440448575480050273626621192637935974517026589482460620838972832681402818102175482026875161938770948195549798191027650693922385425951987277985285335616705644078141911231255865273209448332618510884576236834628878409690523441776606993751185468060765782246371420752252705872689329641984523409850184429207513907054337643606620558225310201803923643262610284927299454876997343379943246848027267396558078170456389210400696180857092653955290054328182296446362220810673583184305942041490315998030184287242440995275901097224808465864144028692108282526997284741535232319380720841363368625290993041231445948551414508787847163038493077496396424567572523556598724230424655684002306756607075700765284021903659536250768800528723448116047115217906012521136086494619788435583705271334623035767866983532149832295551537152482429278784941994957498387241399680403063843219505356894350975676780648909480048467907004718355901515440281560604233653795202874299864201927701911408751332292705111334765050042136982798155805592358642792427706158241691004823990491022288954137679124596937593692575526681462593716088428788715342917188595577178931494899800742614803183865943649593943052372352301672863260436336220337902174991929942632740926148007646746243855923365367595359296174335950961110063566986553351717321124619379651427187829182638867061831617782800445307654937528915601490261483971501350050835896352144554891296094107783704353205725635071477015290579882003661990414882325588490292787138838949900775963064084695088695311796194931371124622133507277188166017690379610419980052373058899845557995220368696251370864711697007871718522173304739890082505142320723616369832221744942371495407161202344897230972877897361383560111255812623636828740605586547621644311136821334726280042093496418959510556780467379001074147962192799963490517401942658255499796216321598806381146662810090786856551297390652835745893315168503431659153510943534013881404790865334819841948831676386749297887729154622820041807813112059415884585571361893494188060737471026568354376410678623485590233406403084787410357806054451884922506835406425391204430352734923828044884813075123999320838510241563104892554229921855073618369682738561429699060296567387933946361355661789501064447814664449100238942791899608721387505500835407982541553251181791427425443267686991028251201602458114564139406689067656679855545519873156431062944013782142639561182473198723168751095241096862601134967246661816980906967688174874472593117631255080521276279679926752003432837220277004637123566600281528102779381532735060567673376479317499532040633376356438495797708955786719881310190268416549798982268642707589434254532919951936758959805704083893405484170503888007209759134785835363914709385094566268441377075206283499412916467314611322244460828585925523572643636649497661217612262548807589845184642044547665679827892517558375563965790160423573040410143133667253615455466287718408743469636088553889205222769817444373757295101226383707549944920347709143679308379560937900753516970386506706830014747982170691322055137631480921958774620273738472263195409936069137694189149317075037317864991519698460746771547937879266539021726676148697701304368723499304990768407532176562428041282393650770852776831092292612308426780152741331413270975140805826381214307714656581317444535435313367608879330711601080156428557854534572818200419184294896670900126751902861518550408798780376272475690045806199507902464558669760799995071387163276901415949137165430386243914414590038378684932939137057937566219522860317945380284272711944406422563621286325557461560412032750353196757256035396352066193985928861871768498586897635757060907681855980687239327003166314096983279224547891934939986931606579015249822595747191012625652641221396993797384870844391355118290774118983502397642154552056150274560230680190211484928830874653583423180914325538535735093902230137624479491896961965340068064429711948176059969411194420168089518163639572023332779517831580428264320435174645483013273704918931110319203447354494284798374550545056168191192058404938694128984070397392684319791664169621079255763843605056318598001644216105760970168598775125018408342065029476140104993580594811839842297075023426401852361993483183897485876533769556704633789344240059221647165578616462651803003513343940055733991608807334757990142207001765496244493221081746525264280758437494517971427189031925040899764259877560827653337605289095481732335888657739398893558880781713671129362588030126775697093678552563613324022956310682179447528960704290644974574635743663163021324820165038451314663704482118616569199211127577513485563623529966150688706859282153390397075062657519947364864228738579534549034877054103594915553605688829018366553644963354448176504219030051148360253152789576444670458919108717920612023891474658296714868464121957377097300197493316264758487590294609537811880115894084411334377251410463047035022733328322732195374174187163741865784195392849712247429612802629950557984815202681298135842549599299940667307855681606169360830550303121499817720159716098432955371908389879319529254898775004890553047926042190419989178415262031407292380567648830368612180513457421864592358575085178052899462299686627669555671857333554373810521129076969564349156554934769214685419102843505434769861001034260649523394203910650214490861809365984547460468197176682006761543705281581595569627383556118359737841778526577647601855965859816250381395437441196153952734987868242875836300739543005659428724356834427841245708230608300714842163544408921963499251964844135002091212491781252316264846834707857792993775796727229055633215696842884716757523410919089112769674906960913386263830377354863603339279773872377065427201150438592514012508102819040883624750417018100828935576525362427670028371198528569904322508764618464268558860647481547980184612170085713653719104636511778378115288202605222382085888938644507924328288047938207809280055630677069250491234781833632345738327688998165994374000679785941520188200414241690942721374940262304206354056956339611808085225187446260725476567446490953341138745363793593306117852435420701047770971744999956910700077397208445217464049591958823056369023716164531297387128309010044082492194218616979519034919532301055799719158738476613659615222950259777881564947446829846957735966254673950912073236967431393128166965222718064872951988601560396258682304759510251382967143006886318794257459472656893592648830260421116733242395393126630349122586559483889751175542204054271836230906453208451719111223112180410634946320729847598426546497183643061619323643477436049539025470356501813517654752561093076003889359581436003131139561714702396251420238469344388750554215226975136996407326639423884765224786565434832647936121735884312949397635312607167368123956916955047425249530586294346043664444242084069270753630295413784079878312263947923958886417730092004316354041492941394855280411334309176434704741678884265474154577639045279600785232311334546490945523892215929079842239034597673801382162666601622855666089217503579654439995150900254730014571087409622046920336960143320123347607470317737072925598563722464023768038148329773157583283762151675809372778130207926954780806664893457100839197536676290084144253706706891125067921756297271871808956862588518790175877103344467583519284986480372242165108165450619399364573034437748737668968718310512965772389260295576453855607553784286254171996689319040379516718657070240826783133887666348821793826547697090066179018354567902436002295745117467440212258021950582692334178238224747290286995318772714377526154826100732558073062525223730767666079955785485034243179230911277440310247121266007874216552934259581449457069586655131076583567441737885247703399877020984922231397439472050207548840382625542790326979657945767935910473015178275018248927909990450762874111342365769186739155874659351250590100375736672529220542166932188683977789727307075404693702770675359677982987943418353159763677827176580167621562368772051192219266149202462733219905872320820976495391772118438461435409829753489603521415038659539309192356319881762019467796437683834610171258586084529071215238909693349042027907030313611717617074029250528732090425820020755615460618115178849482027238800843068335311311018304417788959686202890999447925993216820421374916707558210290560149752768056495906419967682792646885829737687136445438640157308164996022268753097542889537492416505250680597309911672094483897810316254838579201475818784628819822169781510326095163854737101744322897963701316133361340223979891065755601882595107299357199946637706303583783236848826686853713309996118570974168641551278797832663572615752606650396696434773175772378791556823848865806233919061685505233152889280701360176368729211306203499479904774408355000139252595643709434852098997287801206187050414873422869316815402606483973130740991293198067525452729430446695922680022795638568807986783872994088619227865626291608893494696114483917208383040757211754460606815395619536284636413952,
+      "C1": "1",
+      "kappa": "330877589979561/500000000000000000"
+    },
+    "constraints": {
+      "a_positive": "132438677972999999999999867361322027/200000000000000000000000000000000000000",
+      "a_below_b": "132638677973/200000000000000000000000000000000000000",
+      "b_below_one_over32": "6117561322027/200000000000000",
+      "beta_positive": "1/1000000000000000000000000",
+      "beta_below_one": "999999999999999999999999/1000000000000000000000000",
+      "phase_leaf_above_bit": "1/1000000000000000000000000000000",
+      "q_positive": "66219338986499999999999801241983040500000000000132638677973/100000000000000000000000000000000000000000000000000000000000000",
+      "q_below_internal": "132438677972999999999999867361322027/100000000000000000000000000000000000000000000000000000000000000",
+      "q_below_leaf": "132538677972999999999999867361322027/100000000000000000000000000000000000000000000000000000000000000",
+      "c_positive": "66219338986500000000024801241983040500000000000132638677973/100000000000000000000000000000000000000000000000000000000000000",
+      "c_below_one": "99933780661013499999999975198758016959499999999999867361322027/100000000000000000000000000000000000000000000000000000000000000",
+      "q_below_reservations": "1/4000000000000000000000000",
+      "lambda_above_tau": "132438677972999999999999867361322027/200000000000000000000000000000000000000000000000000000000000000",
+      "lambda_above_sigma": "265077355945999999999999867361322027/200000000000000000000000000000000000000000000000000000000000000",
+      "lambda_above_internal": "132438677972999999999999867361322027/200000000000000000000000000000000000000000000000000000000000000",
+      "lambda_prime_above_lambda": "132438677972999999999999867361322027/200000000000000000000000000000000000000000000000000000000000000",
+      "compact_leaf": "132538677972999999999999867361322027/100000000000000000000000000000000000000000000000000000000000000",
+      "compact_reservations": "1/4000000000000000000000000",
+      "lambda_prime_below_one": "66219338986499999999999801241983040500000000000132638677973/100000000000000000000000000000000000000000000000000000000000000",
+      "epsilon_positive": "99999900000099999900000000000000000000000000000000000000/100066119272867227132772867028374954665545334454665677973",
+      "epsilon_below_one": "66219272767227232772867028374954665545334454665677973/100066119272867227132772867028374954665545334454665677973",
+      "guard_width": "66219272767227232772867028374954665545334454665677973/100066119272867227132772867028374954665545334454665677973",
+      "K_geometry": "75066144272842227157772867028374954665545334454665677973/100066119272867227132772867028374954665545334454665677973000000000000000000000000",
+      "K_dominates_log": "66219272767227232772791962230681823318176681798649598045334454665545334322027/100066119272867227132772867028374954665545334454665677973000000000000000000000000",
+      "record_suffix": "66219272767227232772867028374954665545334454665677973/100066119272867227132772867028374954665545334454665677973",
+      "phase_local": "529754182137817862182836160880364457135542864458395409045334454665545334322027/800528954182937817062182936226999637324362675637325423784000000000000000000000000",
+      "phase_boundary": "105950836427563572436487179280654597645402354598056381845334454665545334322027/160105790836587563412436587245399927464872535127465084756800000000000000000000000",
+      "gamma_sublinear": "1/2000000000000000000000000",
+      "cell_above_band": "199999800000199999799999899933880727132772867227132971625045334454665545334322027/400264477091468908531091468113499818662181337818662711892000000000000000000000000",
+      "prime_interval_packing": "66219272767227232772867028374954665545334454665677973/100066119272867227132772867028374954665545334454665677973",
+      "alpha_positive": "132438545534454465545633990630636463863536136464327571045334454665545334322027/200132238545734454265545734056749909331090668909331355946000000000000000000000000",
+      "alpha_below_one": "199999800000199999800000100066119272867227132772867028374954665545334454665677973/200132238545734454265545734056749909331090668909331355946000000000000000000000000",
+      "alpha_below_one_fourth": "49900621090899159100840799523556840868909131090868511415454665545334454665677973/200132238545734454265545734056749909331090668909331355946000000000000000000000000",
+      "delta_positive": "1/8000000000000000000000000",
+      "delta_below_one_eighth": "999999999999999999999999/8000000000000000000000000",
+      "short_record_fallback": "19986727375473612908389377259421714870167196423581034375036133198993012535164982428036466388729/20013223854573445426554573405674990933109066890933135594600000000000000000000000000000000000000",
+      "small_field_exposure": "1/1000000000000000000000000",
+      "artificial_boundary": "5604232433462702537297463790014354917196582803417204475396863996636003363997033919/800528954182937817062182936226999637324362675637325423784000000000000000000000000",
+      "literal_scalar_guard": "545525713450195936959791755649507653812391934109146114224022993194486781261556406929876345400494106460145101416556571651175783299240521688320914949372392465260417618851561997293614853486640710618177089795064142340680092394904003439794736151877038259684233672253731321519953303044044380382536240561401005420713467104554948572910819207534048809700459453672343813537393180839707008102181675890082333760137858773829409024112844334963945352198782614232724287788614299537908012049163820380801509398126446396497167685076878142141568867219871974944072678079428719256937903926230267896857348469446273933068334913806093153489855307207340138448252603645594011997726559874755418215639592393116850847987285537951904659067422760615811791271884825860615205798679231787711415101076164097305180233986762348107201867870755754687425974700930642612152200312927350935204771694450499076477483436060079961562797581415663344077707308140979425676965426890833119517775606025910009430831080523396389874972492806680449638961848298404197000244396707451088923325770250040355052164667308150858388845507482995331150981168649021887838310309455275361192089833277913356672539741016396954625098564516026112115467904951447876939589291954639180752797450962666174304476355291001009850424782308752107661873261141769243592391436863721975883596558948892981218674104762176074543808353380778960628914216078006254911176564071074322725759441049227095831793594030274056246771887722234219369229172486030898883795510338739934914365625328700189338839786512133704101106849186278410502682208711482389973928221750273946542632812188279515629624057021759231429953414305957907040470489318960929210049767547183120833945594509087646118179356291494651775337529584886279578937932878626639329471903897968199284723070551990251145357589521729131643957609226054727271343138714064750914042579697755594977938542310869549530295036146975789029236872336066543810501844268746616107099817071895171108390409742682848357400365732965742918300791567469603495773480761459388356127350704843079228245418814353582949754309339102155594691875011167509541038573928335074372460840720437733423130594302813854665935897729925044845291030027367196062292356667811027900606906878919200842556461248850236788439418073999603579529409522642692323714575329216163290874636831663597830690443826878210104659199624925748153881262880137305346291702187043764617398340053742816308263077954317024115625399587523033505226368237950805644517149753560695212077687074235569132351340946901661863545827463020354642519738016161194602215971246443638307038558344103590742612464959249234949518292001975393108493417690310190740177962598399429470974333833628026332331105911030748197774708970739071292009255752386635463588567874554456387228664429701029690265033287249809349420871758785285758338173555670315082101513140818035781315997399537424905476530081805965467263925586723865600960927299937436655636875288799718355640170693879035972903332253237737085257926218585036063374177819618929646495714573525541534107407491268194178366694264395510205516523436081870561139308079122444475787906178441108464608370897693627176385567109711496912760548819746325481119840955332223679101954180842683229724810751085116334265998105864553517834968114799676714624721350745282109447287724236060521541378025821206918628241365879081401263562123323230080596407101840922626694665058079572209943427490049542175213888409863317024505310523290684196981177438645600788099649180501943674291567329592958349980245083833899820013575056704757919615016092162831924250850493158886669372241577105304040676844718683901256206797442003757285688487057114934248753646753347707013787838101393788310575676645556693669318504164040996748969396331281572283657027783017006201532116741378020520741693831124339816228183376200490137726696069173582109276430446303379355215411843251842715591492969536836461621599207742197057409636705299408252938760886625393672328509776873684118777058540694123832109892512192214751761012290271939932644256257160765278139916041521743322612251604845176781202905953275275745094912065293414736081866531636859988728295988563519810072977989549734235054571537198555946859296149025407362108660079346771698779714176036279075373459494510228428475183683738496281182705529887715686937964092344995950201110161294197934778788210726887617989060238890112456866552790503070508988003265072565482502689133731986220458319157181414887184736543754468536013107068460656072910378865748245546482304371749666293319447975479433655173677628385151480017590976725191998729308376813437889521890069998865654108492953861676378033747968557952202649011373780432293078276783320764034196389205641757904334457280762813519259809584696612541831410308497596054329256987972268821571310553860237005946191269168585599141950385463249321969425231824308793322412468921178898671070144454094010634555502125915344401574218014907405115476898227717579433323214999525825784388198127237176012868634137861800239504251979559010015321172226681631752643053155374223351166467038876634516787605297577752887645249563270307884253812883174318102607657950762310087455194141825926956739324626285196665268176635543088038205259836499362161330754641352789992953379592421242587008995194111415981171138517743419613675358770966009594950595568670105194256228961311813465988335838711839039859569092848421340011062670038170518106550408522201196836746136098503136829087807981902696738364545484049957427460310332751589690114557159687176369478862599088644852917913664939118913669054700258102872033972711644847967755760351774288155133777646559883131009918505685139827597885936122524875656407329984516045297914548526240936297243697997834431803241028870445227917865915135377958034048340902067120665027326649490360811668402564293442831761787384310771015508782019650922553063825331417061297491720511810304372484150708498788059558589882504138991705746634109741846511969572192716091627177270040786694670532209479466620",
+      "row_product_gap": "224336/5",
+      "g1_above_kappa": "7294577151183104910785765286731144323807496586722090147/50033059636433613566386433514187477332772667227332838986500000000000000000",
+      "g2_above_kappa": "87641981175599999999867361322027/200000000000000000000000000000000000000",
+      "g3_above_kappa": "14589054236246936954344397800595260272660327628109725628322027/100066119272867227132772867028374954665545334454665677973000000000000000000000000",
+      "g4_above_kappa": "87641981175599999999867361322027/200000000000000000000000000000000000000",
+      "g5_above_kappa": "23342546817666662847287316144672633461229323532176233804722027/160105790836587563412436587245399927464872535127465084756800000000000000000000000",
+      "g6_above_kappa": "116713134352810405705345111814831280805965279842218987686322027/800528954182937817062182936226999637324362675637325423784000000000000000000000000",
+      "g7_above_kappa": "49966840363666386340908143636995627578013098059398305337307496586722090147/50033059636433613566386433514187477332772667227332838986500000000000000000"
+    },
+    "margins": {
+      "g1": "66219272767227232772867028374954665545334454665677973/100066119272867227132772867028374954665545334454665677973",
+      "g2": "132438677972999999999999867361322027/200000000000000000000000000000000000000",
+      "g3": "66219272767227232772766962255681798318201681798649598045334454665545334322027/100066119272867227132772867028374954665545334454665677973000000000000000000000000",
+      "g4": "132438677972999999999999867361322027/200000000000000000000000000000000000000",
+      "g5": "105950836427563572436487179280654597645402354598056381845334454665545334322027/160105790836587563412436587245399927464872535127465084756800000000000000000000000",
+      "g6": "529754182137817862182836160880364457135542864458395409045334454665545334322027/800528954182937817062182936226999637324362675637325423784000000000000000000000000",
+      "g7": "99999900000099999900000000000000000000000000000000000000/100066119272867227132772867028374954665545334454665677973"
+    },
+    "minimum_margin": "66219272767227232772766962255681798318201681798649598045334454665545334322027/100066119272867227132772867028374954665545334454665677973000000000000000000000000",
+    "absorption_gap": "14589054236246936954344397800595260272660327628109725628322027/100066119272867227132772867028374954665545334454665677973000000000000000000000000",
+    "scoped_limit": "132438677972999999999999867361322027/200132438677972999999999999867361322027",
+    "recurrence": {
+      "internal": "199867561322027000000000000132638677973/200000000000000000000000000000000000000",
+      "leaf": "199867561322027000000000000132438677973/200000000000000000000000000000000000000",
+      "reservations": "99933780661013499999999975198758016959499999999999867361322027/100000000000000000000000000000000000000000000000000000000000000"
+    },
+    "finite_bridge": {
+      "complex": {
+        "m": 66,
+        "W": 46993014508907546545619280249174112657461900835901030815261504418863694290567174681810611945720444150660152817763059801639245973345112004897278366859154750334212500439512936840627848244394765451284074456532617330107411313215968707402530219517117844943749718652926156476700283889177946425077003557843877389276428634874323005085014508575892059245742828042621769981353800662281169324045925646130349280697840930356148460214115622656770692246981506552181976330172235709092174881040687715319309680026164838937259505461229837578427933481128739708869451568634392001589375469155812523061199192023353874976910265961141812249619087818311598080000000000000000000,
+        "s": 3096884787483474455456234332435219089300960116851386599182698578422247214799316131747100177750656232740173372157877610253165939171388470666072682578531488111610759085086773618649082885114253117444135545412468540990289793210860996611303238493999931160995933589809973376790756823815567776684051199051162750567856168218179349970761601387188334379741507103017699128465075107150367263659259437343515713011462577181711822086055203077496705325623257254424136472548583391798882936593240183044791313973440974688931967805578562483537323676366509880778202855445341255850239569108094725521856014700741923942130825336218319753120005564621997998080000000000000000000,
+        "N": 4654170104423616554638164010272346091525338318081434624560713222756608378117397252400210666893081203396713814484336655024295069388921657147689634172725410447265943921080212832355099015801402340613368718684202796799353461392938077263755994129846605291547841283152950671461912870176687371031035766533157124388121683525968364849356178820541530477519547795337690304275736560189911727771655301087339514594924221793976288076428017850160362677522178019873965242784165001200605555445206166283124908285904680927159554862606796638919933387986940007180948084528616254659211856188901000183131972799431806345252217217039855354854231386567475200000000000000000000,
+        "maxchild": 20,
+        "invocations_per_stage": 3525886442745164056544063644145716736004044180364723200424782744512582104634391857878947474919000911664177132185103526533556870749183073596734571342973795793383290849303191539662953799849547227737400544457729391514661713176468240351330298583217125220869576729661326266259024901649005584114421035252391760900092184489369973370724377894349644301151172572225522957784648909234781611948223712944954177723427440753012339451839407462242698998122862136268155486957700758485307238973641035062973415368109606762999662774702118665848434384838590914531021276158042617166069588021894697108433312726842277534281982740181708602162296504975360000000000000000000,
+        "stages": 3,
+        "auxiliary_banks_after_sharing": 1,
+        "halving_degree": 1,
+        "wire_bits": 2159,
+        "original_X_involution_scalar_group_upper": 42240,
+        "local_group_upper": 4543086018280,
+        "logical_group_upper": 48055240874671078945188109455239520058125488875232627175138628358868780177925699722126530175705817333026189386759058850796056608167194243611166862233989266394079390943072014584949304299869954384886421723421911987945115273191975273130673021312190153197265258374805576467982195036600831887640610122364350378680566893667391453290004779060967383005112312464513344677405467841885406083074150167310709790096664383418384887308487025537224681862534621594326666444261335797898775105432540768232639941539591520899074988764992625395530881862776285446393870890377790644933526724019631227104238724960296923222769054605565181302065531301311730953696051200000000000000000000,
+        "finite_group_router_upper": 2042733685541310236593996563124710993412165863603306313097532902018433466683431743715259007829146987095378627302512247296273579196724865635466424495886986981070240397155989611901227274057344115006992368238295067937096681914939897329330375897850947653624154670627567536540399720617344588251455630430130931283214971866771632648027119764337342344652974886259123204570638608969527856002307906428308648271283107654233784029920261562062441634609575222294256530335686672972094697601933339431796932668405898134579255702844363845882474708468208758785148433016193063510518755982063138558376100687934874724673882718386824464636056802379731693082380370257615524198097971706920300670514785149198047112812589262598451026696606105144349263419777761388556924150378882153660586083231627698985439717349132380289334640425239716030365051552310444048834985873630612831601761031016998447678647208392850918363259427684972030870622102919784360657161485751852158581374304190237691268858704247599964760134258277434684030263792385403474393413555973632021332993606819195569256783157695772555762218961654961483071898813478715114933642408814572455099487524946213727616776758529362493007012128742175516659103497256150398688067237295539038286054433070958988450327523496660474475015177485962957043001891810348130524968091565530711246863869435913581520796765892701707248466483246004653153934614453923325331090272046405694531720642794739801349300597117009558972642063469652020414157994463402891269148057505219538790196840956548422975773514132792507087108642926872500370530948765817617814354169836284740013615891292828792176460677144382290379101394591548513381424766141758112339957037071338204348324849159760547862762023937163784970360528440141699170517172479674484353402002874845101145390769252570862957716099987600419158072752037560685304580963211038225882927995606707773197948561882380706350507940215524792066837493717985086348682434583749147435614934783671039459572748018799083520000000000019248832,
+        "scalar_group_upper": 2042733685541310236593996563124710993412165863603306313097532902018433466683431743715259007829146987095378627302512247296273579196724865635466424495886986981070240397155989611901227274057344115006992368238295067937096681914939897329330375897850947653624154670627567536540399720617344588251455630430130931283214971866771632648027119764337342344652974886259123204570638608969527856002307906428308648271283107654233784029920261562062441634609575222294256530335686672972094697601933339431796932668405898134579255702844363845882474708468208758785148433016193063510518755982063138558376100687934874724673882718386824464636056802379731693082380370257615524198097971706920300670514785149198047112812589262598451026696606105144349263419777761388556924150378882153660586083231627698985439717349132380289334640425239716030365051552310444048834985873630612831601761031016998447678647208392850918363259427684972030870622102919784360657161485751852158581374304190237691268858704247599964760134258277434684030263792385403474393413555973632021332993606819195569256783157695772555762218961654961483071898813478715114933642408814572455099487524946213727616776758529362493007012128742175516659103497256150398688067237295539038286054433070958988450327523496660474475015177485962957043001891810348130524968091565530711246863869435913581520796765892701707248466483246004653153934614453923325331090272046405694531720642794739801349300597117009558972642063469652020414157994463402891269148057505219538790196840956548422975773514132792507087108642926872500370530948765817617814354169836284740013615891292828792176460677144382290379101394591548513381424766141758112339957037071338204348324849159760547862762023937163784970360528440141699170517172479674484353402002874845101145390769252570862957716099987600419158072752037560685304580963211038225882927995606707773197948561882380706350507940215524792066837493717985086348682434583749147435614934783671039459572748018799083520000000000019248832,
+        "coefficient_bound": 26,
+        "coefficient_denominator_divides": 6,
+        "physical_roles_per_vertex": 10688,
+        "scalar_role_reserve": 13042,
+        "reuse_pairs": 2310,
+        "terminal_sinks": 44
+      },
+      "semantic": {
+        "E": 545525713450195936959791755649507653812391934109146114224022993194486781261556406929876345400494106460145101416556571651175783299240521688320914949372392465260417618851561997293614853486640710618177089795064142340680092394904003439794736151877038259684233672253731321519953303044044380382536240561401005420713467104554948572910819207534048809700459453672343813537393180839707008102181675890082333760137858773829409024112844334963945352198782614232724287788614299537908012049163820380801509398126446396497167685076878142141568867219871974944072678079428719256937903926230267896857348469446273933068334913806093153489855307207340138448252603645594011997726559874755418215639592393116850847987285537951904659067422760615811791271884825860615205798679231787711415101076164097305180233986762348107201867870755754687425974700930642612152200312927350935204771694450499076477483436060079961562797581415663344077707308140979425676965426890833119517775606025910009430831080523396389874972492806680449638961848298404197000244396707451088923325770250040355052164667308150858388845507482995331150981168649021887838310309455275361192089833277913356672539741016396954625098564516026112115467904951447876939589291954639180752797450962666174304476355291001009850424782308752107661873261141769243592391436863721975883596558948892981218674104762176074543808353380778960628914216078006254911176564071074322725759441049227095831793594030274056246771887722234219369229172486030898883795510338739934914365625328700189338839786512133704101106849186278410502682208711482389973928221750273946542632812188279515629624057021759231429953414305957907040470489318960929210049767547183120833945594509087646118179356291494651775337529584886279578937932878626639329471903897968199284723070551990251145357589521729131643957609226054727271343138714064750914042579697755594977938542310869549530295036146975789029236872336066543810501844268746616107099817071895171108390409742682848357400365732965742918300791567469603495773480761459388356127350704843079228245418814353582949754309339102155594691875011167509541038573928335074372460840720437733423130594302813854665935897729925044845291030027367196062292356667811027900606906878919200842556461248850236788439418073999603579529409522642692323714575329216163290874636831663597830690443826878210104659199624925748153881262880137305346291702187043764617398340053742816308263077954317024115625399587523033505226368237950805644517149753560695212077687074235569132351340946901661863545827463020354642519738016161194602215971246443638307038558344103590742612464959249234949518292001975393108493417690310190740177962598399429470983355948584489397361000132403544297410530351609443075397691970864350662146556828873400722400856526678559332866751960043756037304548960773780114994380817295974560389215613200495104238123893468475988295292128475233289219477245972367408694405933775023353027356296204165754779857293614976794258089536988109549117151633247805615999775353475812435065242270955955241017833710866998422018536271117493454801836197366311840739921024969366342045933214598468730861375979464034241249019627748402549143924603790218200909179281804169820287487911906598901164323917389679560767404995073694876750172443881112497446222998710707424642879910695575392581080119177883486047681709861915409814809478988096593002308326690264058199105287676294033919035906591016568850802596451351686647294993410558704814647667414315048331778789663176538750169713479696444836596806223219224583342413081575242619928243564934733766476980538581755113540745119675595825768359707674246673422748974559131441760334920424088039664741875322215715629086183218101829240962485985572795335976194473029242078461606929593754455231919392812664068609244957222174107935814077442467642614154483555909204937603800473825458018724816885509979327413795978789978878740401336430132818952243803525579530661090728503394325270425640721903067803379764474515184157760388806512837057644318149181934695802708310732752494564569885914477001301866651100813942120912028175428602662914262666878111955123804723391352158371492336786684977136273753470228002798904164613992705924079270747974807180638269315239260586804598359482619619381838545718768618855793666337720587620998164727919892236872105672363222146234229091368970895124360976065406826285223975911567655253414129230495420541795897246053256604094369223530290653344796356906338790148268413826760748674524519292251453343975714502885987935234369874493101913001157760200550459084674336032925861769577597385785068262226499285230533047656911900405637490685123547691480324695214864475727940289819447547206994135288934903737746499121319555412987525437969560022764086123106848012781641391968141340535694042507876216277847081503499716481084272998177330515512180003888852553694830145197018146106980839516275318257413795995672534660363087687715821526077652256859829810711730239991834210920241607164318679532269804573482330048565180923824166173320949735476758239824179586636600885549424586171281739412405981671379196797766158587665954811758729095611687255655121992287138505307177792544918124503095309881786914092691677202140899294733598606005652984905151694759575125655467108943050484304157150126642948513335799234398896059133654916356802749473250274211891185271868189309394957667655975497022452274842407074738899072398876513918395441392927811698574781919277408672876792497107796922618155916706833536909977530542826541814375168093518085000519446687617246155743065552553064269824405898496392219028041375370238852976267724433706568720999961058335888456682860800204304951475826290099538667564468983217765182666287253650412270477311778624014133603263491035040948870177650885178837699975099462285988802058105773711986269595777415191242928820664833303521163337702532621138895868697870160183847704469602599048293690879730106501995114957106598943750461745190894753760367890559650148045519271163654670532209479468736,
+        "literal_charge": 9022114956463065029894221372796099635821380870371783388436218477715198557988954318944335172192096977529642601718672793946687883677201988494356656207261625659478287702472382459322922126493931051082818762046669267821955551659248501807733478633837586697390481007404447399139686599735940821354757283750372463859225414662769552625597533856882788569527697430413706910426219598804243651842006721983249285312761284441279600612945846921866258027036157360266253005081770407064863452518036905636383375784043892719789338326471946141185533731063915671439513166304563226501406889209141358915204329081435782821501647965425315195592186459514871039702093356676567419440343982834008551247355664866512405901224849341431504440229596721823975608416541474393636914186588034662141984470119874507833470228768714260232129609161232864458602383886738094856351722389319404569767356376817323004912151402102809515626487379695085741299168014371555148923641023772990466625306970801845753273277805489839286017988527615201927790984789429791253564316929291903476831812153476280272682130325357310097427448902386611131951867866936701432414104689737626239459237953993418182508868430218364549027572421437530294567484161953263198485909203564874808533611210046746115942825361682475564633438645031968393393290929695645697456643463636556696620324865429566388169644423862775666476495333799291745998435479558544038849209096944130825269475327387169167754812818540387722856859715298382764040798121457326200775480678268563849593076794149977219974598949399818529609235892488888024884183446340544008379051208540190380609982599224306438292634840204205298908013327367271945124067797171036116336150249177788837224985085799110788700623626159986432538530824680570753914960637237309832334187614942019154053604513945290747641606063863219341074478227468956403683563484703581173653937521724105026872830699522856015334885044385598656476691448788609763340463048791257791912683629008745513943511766743012215464354159857526369270423673371254738514532104741216985098132224711918709750438067473581275437704284045337638884352563425220936565662417610075557308447312498673856226945052262858034463620729386036822784549224928082168446130864163403161440170408745018686113497806618672536779961602093132296916776834685094457218966191442356256935939344468248325676671844607163305628563250076608071536533481226662198258119132405104895618376373801443910120909024395646927504916212437369153047464041524828417851983650718991167763770683596590248824515041659052861089473762106643491654150510341969582172275874687700463475308963038710661777374818055814785220700362688906761852153904580169017634956310556375843406621828944136457162883181993985734727836402360705995811845032870726614861828645820774271843788984515205100184253610432656876109449667197791236851699818008406341715521656847598972393237829400613434150600769705640393520185055329730522271097215915950145551434943353401175204878538177175660376707065539703765223882260234484467172467268117761012714115026779313944192210892574393045807123082955042272927144789359073032341620961475408615412900317867031483972359481141436354062288012381318051610068075070537280808862692127192659298226564142982380942046943405232452967607238003827635449048241790795697843558520868249230376960000000000000002116,
+        "strict_literal_gap": 545525713450195936959791755649507653812391934109146114224022993194486781261556406929876345400494106460145101416556571651175783299240521688320914949372392465260417618851561997293614853486640710618177089795064142340680092394904003439794736151877038259684233672253731321519953303044044380382536240561401005420713467104554948572910819207534048809700459453672343813537393180839707008102181675890082333760137858773829409024112844334963945352198782614232724287788614299537908012049163820380801509398126446396497167685076878142141568867219871974944072678079428719256937903926230267896857348469446273933068334913806093153489855307207340138448252603645594011997726559874755418215639592393116850847987285537951904659067422760615811791271884825860615205798679231787711415101076164097305180233986762348107201867870755754687425974700930642612152200312927350935204771694450499076477483436060079961562797581415663344077707308140979425676965426890833119517775606025910009430831080523396389874972492806680449638961848298404197000244396707451088923325770250040355052164667308150858388845507482995331150981168649021887838310309455275361192089833277913356672539741016396954625098564516026112115467904951447876939589291954639180752797450962666174304476355291001009850424782308752107661873261141769243592391436863721975883596558948892981218674104762176074543808353380778960628914216078006254911176564071074322725759441049227095831793594030274056246771887722234219369229172486030898883795510338739934914365625328700189338839786512133704101106849186278410502682208711482389973928221750273946542632812188279515629624057021759231429953414305957907040470489318960929210049767547183120833945594509087646118179356291494651775337529584886279578937932878626639329471903897968199284723070551990251145357589521729131643957609226054727271343138714064750914042579697755594977938542310869549530295036146975789029236872336066543810501844268746616107099817071895171108390409742682848357400365732965742918300791567469603495773480761459388356127350704843079228245418814353582949754309339102155594691875011167509541038573928335074372460840720437733423130594302813854665935897729925044845291030027367196062292356667811027900606906878919200842556461248850236788439418073999603579529409522642692323714575329216163290874636831663597830690443826878210104659199624925748153881262880137305346291702187043764617398340053742816308263077954317024115625399587523033505226368237950805644517149753560695212077687074235569132351340946901661863545827463020354642519738016161194602215971246443638307038558344103590742612464959249234949518292001975393108493417690310190740177962598399429470974333833628026332331105911030748197774708970739071292009255752386635463588567874554456387228664429701029690265033287249809349420871758785285758338173555670315082101513140818035781315997399537424905476530081805965467263925586723865600960927299937436655636875288799718355640170693879035972903332253237737085257926218585036063374177819618929646495714573525541534107407491268194178366694264395510205516523436081870561139308079122444475787906178441108464608370897693627176385567109711496912760548819746325481119840955332223679101954180842683229724810751085116334265998105864553517834968114799676714624721350745282109447287724236060521541378025821206918628241365879081401263562123323230080596407101840922626694665058079572209943427490049542175213888409863317024505310523290684196981177438645600788099649180501943674291567329592958349980245083833899820013575056704757919615016092162831924250850493158886669372241577105304040676844718683901256206797442003757285688487057114934248753646753347707013787838101393788310575676645556693669318504164040996748969396331281572283657027783017006201532116741378020520741693831124339816228183376200490137726696069173582109276430446303379355215411843251842715591492969536836461621599207742197057409636705299408252938760886625393672328509776873684118777058540694123832109892512192214751761012290271939932644256257160765278139916041521743322612251604845176781202905953275275745094912065293414736081866531636859988728295988563519810072977989549734235054571537198555946859296149025407362108660079346771698779714176036279075373459494510228428475183683738496281182705529887715686937964092344995950201110161294197934778788210726887617989060238890112456866552790503070508988003265072565482502689133731986220458319157181414887184736543754468536013107068460656072910378865748245546482304371749666293319447975479433655173677628385151480017590976725191998729308376813437889521890069998865654108492953861676378033747968557952202649011373780432293078276783320764034196389205641757904334457280762813519259809584696612541831410308497596054329256987972268821571310553860237005946191269168585599141950385463249321969425231824308793322412468921178898671070144454094010634555502125915344401574218014907405115476898227717579433323214999525825784388198127237176012868634137861800239504251979559010015321172226681631752643053155374223351166467038876634516787605297577752887645249563270307884253812883174318102607657950762310087455194141825926956739324626285196665268176635543088038205259836499362161330754641352789992953379592421242587008995194111415981171138517743419613675358770966009594950595568670105194256228961311813465988335838711839039859569092848421340011062670038170518106550408522201196836746136098503136829087807981902696738364545484049957427460310332751589690114557159687176369478862599088644852917913664939118913669054700258102872033972711644847967755760351774288155133777646559883131009918505685139827597885936122524875656407329984516045297914548526240936297243697997834431803241028870445227917865915135377958034048340902067120665027326649490360811668402564293442831761787384310771015508782019650922553063825331417061297491720511810304372484150708498788059558589882504138991705746634109741846511969572192716091627177270040786694670532209479466620,
+        "B": 545525713450195936959791755649507653812391934109146114224022993194486781261556406929876345400494106460145101416556571651175783299240521688320914949372392465260417618851561997293614853486640710618177089795064142340680092394904003439794736151877038259684233672253731321519953303044044380382536240561401005420713467104554948572910819207534048809700459453672343813537393180839707008102181675890082333760137858773829409024112844334963945352198782614232724287788614299537908012049163820380801509398126446396497167685076878142141568867219871974944072678079428719256937903926230267896857348469446273933068334913806093153489855307207340138448252603645594011997726559874755418215639592393116850847987285537951904659067422760615811791271884825860615205798679231787711415101076164097305180233986762348107201867870755754687425974700930642612152200312927350935204771694450499076477483436060079961562797581415663344077707308140979425676965426890833119517775606025910009430831080523396389874972492806680449638961848298404197000244396707451088923325770250040355052164667308150858388845507482995331150981168649021887838310309455275361192089833277913356672539741016396954625098564516026112115467904951447876939589291954639180752797450962666174304476355291001009850424782308752107661873261141769243592391436863721975883596558948892981218674104762176074543808353380778960628914216078006254911176564071074322725759441049227095831793594030274056246771887722234219369229172486030898883795510338739934914365625328700189338839786512133704101106849186278410502682208711482389973928221750273946542632812188279515629624057021759231429953414305957907040470489318960929210049767547183120833945594509087646118179356291494651775337529584886279578937932878626639329471903897968199284723070551990251145357589521729131643957609226054727271343138714064750914042579697755594977938542310869549530295036146975789029236872336066543810501844268746616107099817071895171108390409742682848357400365732965742918300791567469603495773480761459388356127350704843079228245418814353582949754309339102155594691875011167509541038573928335074372460840720437733423130594302813854665935897729925044845291030027367196062292356667811027900606906878919200842556461248850236788439418073999603579529409522642692323714575329216163290874636831663597830690443826878210104659199624925748153881262880137305346291702187043764617398340053742816308263077954317024115625399587523033505226368237950805644517149753560695212077687074235569132351340946901661863545827463020354642519738016161194602215971246443638307038558344103590742612464959249234949518292001975393108493417690310190740177962598399429470983355948584489397361000132403544297410530351609443075397691970864350662146556828873400722400856526678559332866751960043756037304548960773780114994380817295974560389215613200495104238123893468475988295292128475233289219477245972367408694405933775023353027356296204165754779857293614976794258089536988109549117151633247805615999775353475812435065242270955955241017833710866998422018536271117493454801836197366311840739921024969366342045933214598468730861375979464034241249019627748402549143924603790218200909179281804169820287487911906598901164323917389679560767404995073694876750172443881112497446222998710707424642879910695575392581080119177883486047681709861915409814809478988096593002308326690264058199105287676294033919035906591016568850802596451351686647294993410558704814647667414315048331778789663176538750169713479696444836596806223219224583342413081575242619928243564934733766476980538581755113540745119675595825768359707674246673422748974559131441760334920424088039664741875322215715629086183218101829240962485985572795335976194473029242078461606929593754455231919392812664068609244957222174107935814077442467642614154483555909204937603800473825458018724816885509979327413795978789978878740401336430132818952243803525579530661090728503394325270425640721903067803379764474515184157760388806512837057644318149181934695802708310732752494564569885914477001301866651100813942120912028175428602662914262666878111955123804723391352158371492336786684977136273753470228002798904164613992705924079270747974807180638269315239260586804598359482619619381838545718768618855793666337720587620998164727919892236872105672363222146234229091368970895124360976065406826285223975911567655253414129230495420541795897246053256604094369223530290653344796356906338790148268413826760748674524519292251453343975714502885987935234369874493101913001157760200550459084674336032925861769577597385785068262226499285230533047656911900405637490685123547691480324695214864475727940289819447547206994135288934903737746499121319555412987525437969560022764086123106848012781641391968141340535694042507876216277847081503499716481084272998177330515512180003888852553694830145197018146106980839516275318257413795995672534660363087687715821526077652256859829810711730239991834210920241607164318679532269804573482330048565180923824166173320949735476758239824179586636600885549424586171281739412405981671379196797766158587665954811758729095611687255655121992287138505307177792544918124503095309881786914092691677202140899294733598606005652984905151694759575125655467108943050484304157150126642948513335799234398896059133654916356802749473250274211894282156655672783850413901988410716111753234959258461338081770977298761133194757524674911876325438152017582045034670107360962861789544387372906219488509018654437300899461941712167167885633699805061381701155534093543354063035266895107695457522041306531234786566077697810497325544815528835019939655734023550772161119694005640070300268951657317597506689769304952778877345584462145887673393040607006748052411447359362707264892903052596167611612059312529910184534852987576298127836169003709624617494604312391464588944474431181407483860214214350380801903739032135580346071103209682628454958451203669133025579096586210312770153610141269161734670532209479468736,
+        "C0": 628527618122649248682757650146876240355084858156873576455411140848847129754468654378106151495900839472854370729649793654143457444860130252966983704112892628648140779720071789063074328885897315863317306969510319083326450824232988437078706753970138361551599623222242957713739055304249294570220956354137189755614318912892657261352398740904375429859773125667460879494195403553749965561261487647113317863536655211591647773113465846178111417790230369803174014983668008558503247471590322186981578414736792722823258083620998358930902572151126379332319453650133350342704928914214005609101059291838819726623704841887326096950671354115211238102145489284816797253377393993409407204797307473786441815237469544063081967927275853257836025383277644739908517335326170219033741209859126692670559777488639453055535377861835278857790878490150974232023447690023689409148090345620688503979404514782629463140984816734823474475267446745999177133614077964249361868378965420389012058107296801760423043782337668449127750481325064650996546604170760737480881135850800964938249000411607184673458848693633471017715707501804503978124950887142016640619147582877586832275393906959678822665873037743296825607007958465958226110583553125597297932060298517903053804941860695690866603931935213418587816431208295586111642378791333424092952958355087462219759148985635375945699604663556012919921357823329519989088231365257074902150161582485904771382825739528668118048600550102312040379165112741080138359820519467511395153738006590774015029974630551179662402529165698804322673596451536592575582578658341452190425820075353115047807063314064232753057033455029555026718879411085747711178102161920578548824205283445836503059854386922425421243979423854133972165833454392490615885957527456202057131178782047266750703106996995699822897612665713855474716612603065710448268493480892784114613485129881891303071672863424748311197367982889247837816134790622301262041760333789918121163870779905348537211539790812379830807702437631156909847652007057651666142000683676376404049627413935348616830394777745045398147420029914894037194502236124125867606213182036114140397453859882538927202042640783343877109420600135411348373375203904512426300797553719439423129620556743106957140858600072906050771555822670952382456032548086719677333825230837435999346258118721646360967384881202161559548597947112032619279426467503511691685787814811651604167677531455597112863799616089973187467545657720868001138456002249223647718897041153811089277268833927268858101603024264609960135565443776635778664741360824317942318239225181832387758188551721853467268748984908078571778833621334649278828936852190064270440578912580378077466933204405384344184782301472493091865675647418975710660783087711556534575312755838217475556876557477051683292246634463888400605189971688951903437806451477613991328928672058892036792524967240582139796588302232535584084652279806887721330440448575480050273626621192637935974517026589482460620838972832681402818102175482026875161938770948195549798191027650693922385425951987277985285335616705644078141911231255865273209448332618510884576236834628878409690523441776606993751185468060765782246371420752252705872689329641984523409850184429207513907054337643606620558225310201803923643262610284927299454876997343379943246848027267396558078170456389210400696180857092653955290054328182296446362220810673583184305942041490315998030184287242440995275901097224808465864144028692108282526997284741535232319380720841363368625290993041231445948551414508787847163038493077496396424567572523556598724230424655684002306756607075700765284021903659536250768800528723448116047115217906012521136086494619788435583705271334623035767866983532149832295551537152482429278784941994957498387241399680403063843219505356894350975676780648909480048467907004718355901515440281560604233653795202874299864201927701911408751332292705111334765050042136982798155805592358642792427706158241691004823990491022288954137679124596937593692575526681462593716088428788715342917188595577178931494899800742614803183865943649593943052372352301672863260436336220337902174991929942632740926148007646746243855923365367595359296174335950961110063566986553351717321124619379651427187829182638867061831617782800445307654937528915601490261483971501350050835896352144554891296094107783704353205725635071477015290579882003661990414882325588490292787138838949900775963064084695088695311796194931371124622133507277188166017690379610419980052373058899845557995220368696251370864711697007871718522173304739890082505142320723616369832221744942371495407161202344897230972877897361383560111255812623636828740605586547621644311136821334726280042093496418959510556780467379001074147962192799963490517401942658255499796216321598806381146662810090786856551297390652835745893315168503431659153510943534013881404790865334819841948831676386749297887729154622820041807813112059415884585571361893494188060737471026568354376410678623485590233406403084787410357806054451884922506835406425391204430352734923828044884813075123999320838510241563104892554229921855073618369682738561429699060296567387933946361355661789501064447814664449100238942791899608721387505500835407982541553251181791427425443267686991028251201602458114564139406689067656679855545519873156431062944013782142639561182473198723168751095241096862601134967246661816980906967688174874472593117631255080521276279679926752003432837220277004637123566600281528102779381532735060567673376479317499532040633376356438495797708955786719881310190268416549798982268642707589434254532919951936758959805704083893405484170503888007209759134785835363914709385094566268441377075206283499412916467314611322244460828585925523572643636649497661217612262548807589845184642044547665679827892517558375563965790160423573040410143133667253615455466287718408743469636088553889205222769817444373757295101226383707549944920347709143679308379560937900753516970386506706830014747982170691322055137631480921958774620273738472263195409936069137694189149317075037317864991519698460746771547937879266539021726676148697701304368723499304990768407532176562428041282393650770852776831092292612308426780152741331413270975140805826381214307714656581317444535435313367608879330711601080156428557854534572818200419184294896670900126751902861518550408798780376272475690045806199507902464558669760799995071387163276901415949137165430386243914414590038378684932939137057937566219522860317945380284272711944406422563621286325557461560412032750353196757256035396352066193985928861871768498586897635757060907681855980687239327003166314096983279224547891934939986931606579015249822595747191012625652641221396993797384870844391355118290774118983502397642154552056150274560230680190211484928830874653583423180914325538535735093902230137624479491896961965340068064429711948176059969411194420168089518163639572023332779517831580428264320435174645483013273704918931110319203447354494284798374550545056168191192058404938694128984070397392684319791664169621079255763843605056318598001644216105760970168598775125018408342065029476140104993580594811839842297075023426401852361993483183897485876533769556704633789344240059221647165578616462651803003513343940055733991608807334757990142207001765496244493221081746525264280758437494517971427189031925040899764259877560827653337605289095481732335888657739398893558880781713671129362588030126775697093678552563613324022956310682179447528960704290644974574635743663163021324820165038451314663704482118616569199211127577513485563623529966150688706859282153390397075062657519947364864228738579534549034877054103594915553605688829018366553644963354448176504219030051148360253152789576444670458919108717920612023891474658296714868464121957377097300197493316264758487590294609537811880115894084411334377251410463047035022733328322732195374174187163741865784195392849712247429612802629950557984815202681298135842549599299940667307855681606169360830550303121499817720159716098432955371908389879319529254898775004890553047926042190419989178415262031407292380567648830368612180513457421864592358575085178052899462299686627669555671857333554373810521129076969564349156554934769214685419102843505434769861001034260649523394203910650214490861809365984547460468197176682006761543705281581595569627383556118359737841778526577647601855965859816250381395437441196153952734987868242875836300739543005659428724356834427841245708230608300714842163544408921963499251964844135002091212491781252316264846834707857792993775796727229055633215696842884716757523410919089112769674906960913386263830377354863603339279773872377065427201150438592514012508102819040883624750417018100828935576525362427670028371198528569904322508764618464268558860647481547980184612170085713653719104636511778378115288202605222382085888938644507924328288047938207809280055630677069250491234781833632345738327688998165994374000679785941520188200414241690942721374940262304206354056956339611808085225187446260725476567446490953341138745363793593306117852435420701047770971744999956910700077397208445217464049591958823056369023716164531297387128309010044082492194218616979519034919532301055799719158738476613659615222950259777881564947446829846957735966254673950912073236967431393128166965222718064872951988601560396258682304759510251382967143006886318794257459472656893592648830260421116733242395393126630349122586559483889751175542204054271836230906453208451719111223112180410634946320729847598426546497183643061619323643477436049539025470356501813517654752561093076003889359581436003131139561714702396251420238469344388750554215226975136996407326639423884765224786565434832647936121735884312949397635312607167368123956916955047425249530586294346043664444242084069270753630295413784079878312263947923958886417730092004316354041492941394855280411334309176434704741678884265474154577639045279600785232311334546490945523892215929079842239034597673801382162666601622855666089217503579654439995150900254730014571087409622046920336960143320123347607470317737072925598563722464023768038148329773157583283762151675809372778130207926954780806664893457100839197536676290084144253706706891125067921756297271871808956862588518790175877103344467583519284986480372242165108165450619399364573034437748737668968718310512965772389260295576453855607553784286254171996689319040379516718657070240826783133887666348821793826547697090066179018354567902436002295745117467440212258021950582692334178238224747290286995318772714377526154826100732558073062525223730767666079955785485034243179230911277440310247121266007874216552934259581449457069586655131076583567441737885247703399877020984922231397439472050207548840382625542790326979657945767935910473015178275018248927909990450762874111342365769186739155874659351250590100375736672529220542166932188683977789727307075404693702770675359677982987943418353159763677827176580167621562368772051192219266149202462733219905872320820976495391772118438461435409829753489603521415038659539309192356319881762019467796437683834610171258586084529071215238909693349042027907030313611717617074029250528732090425820020755615460618115178849482027238800843068335311311018304417788959686202890999447925993216820421374916707558210290560149752768056495906419967682792646885829737687136445438640157308164996022268753097542889537492416505250680597309911672094483897810316254838579201475818784628819822169781510326095163854737101744322897963701316133361340223979891065755601882595107299357199946637706303583783236848826686853713309996118570974168641551278797832663572615752606650396696434773175772378791556823848865806233919061685505233152889280701360176368729211306203499479904774408355000139252595643709434852098997287801206187050414873422869316815402606483973130740991293198067525452729430446695922680022795638568807986783872994088619227865626291608893494696114483917208383040757211754460606815395619536284636413952,
+        "C1": 1,
+        "induction_gap": 49642839923967830263341049764105196496927666003932296394386092380698297094801633030618747431444963687873204228906648020256996280230887473637203260392887714338698003315492141753718951667284304666254115171350836953001888407936264313021320989820810481631265264175089550258315750577008038614810797891087491493284925506514500320134884547885598441682741810284183287031902779456413337737298532505997492372172545148418476221194268834481719027050089217895177910188763901257949629096473907654652937355229506622081242259341995910934882766917008349719910613705228013452381349257286954378614018710719610927909218477156354476967576832955867952598790986931749055091793116948602743057623202907773633427166842983953623323975135471216038873005741519153315983727679810092681738774197930932854771401292795373677755369976238773676555763697784688477705850228476388935103634224194995415959450992681467276502214579908825364311071365040829127736603853847065813876117580148357810858205628327629071478622496845407920917145528195154781927022240100378049092022645092753672309746984725041728113384941180952575134739286347060991793286238160430057868480174828290115457201116432492122870883969370958376202507579350581756801502625567872165448504568037602621861707348331481091896388655190096441797230466763901001166907620754598699805407286864349261290899343533358022783486560157650885417231193663098569196917067330467763368044109135479665720693217056754939118456241782723313962599854696228811798425391440825334077207271904911717229834420572604167073200723275951335355744080992744897487627468179274929135379585909133435922295789188980090060125760701842169540682814528025444558114528846793663995889049100326975796754321422526013311555715192224651441683351891955024178981943254715106134909799420231112854227540646477350979600142439570980181692225622979892333177874752495759142992407350289129007256848289374796801660555382582055486755667828455942065746083353542460570863527286584139200523433281699882605565372032639733918115386749292804340407588914140720209770333112106176048427642149858296159116960626016243368234510227478491767893936505559833741504884081556060774600166693423179080921483732490414841668604456770803538955228525981647276672637973645371547747987044733963925737176266560485001458026354958670859469591951681387402592830388245917119523987165868243082003194922092494786512544899020982580183248944890596284051940093842849194521911362464596048975599509653523313651060627574023264299069523755436791043972026168051229582670299134852272469296159470668708801653383426371085940508809313426757577734311291680380406164572179760772872901009818227357356194596454348081859485391321188535159851012048722531064358261996459319861189969348655910255336671427479465738477943927748899290874428363981799394713955430413990464488654373933684995418620801245054485669274305631314934871583691246229318972429383485434191190939973527125125489422954579083684967013718962888277486147865917968969660798625550311055979557166298931590937046656991926932622867688896856403686800671691904386967093960334377507332813272212337126179922528460654508385214131227115953660786125104631972097138944909856282735314644179453646161399983500500005953476482460840029833854551706233784265692393181237267606292882674375642502071873297360724878290845187397230339035597434302293147662587916789963210057728814029296118581178542757086632267499782507765423036277073003484903844400360842138132937734702669398191869859349065026265443926652376480130309366312949437084159590423347078413470164409060772749405229010939715332207805890479220144920733398356447281470156684880961200190477758592011609491510654321630122246842672847266460927586224687124375573833697045661029140006230593031655426104664745952430243441291107217843822159081047264555477888058003587737649321945843118116679703958336581408118794655434069888077965376521615142086524654186120827737290159256293808883599608733305693179170107558567180881758356195381392668172245632951575556057318046456276680477005375859618217407118469865250174068733002994563964002842325197902685908187916266229828613046411805802647588332919400911565790748254700278979873336239091213638065707453438082507686772713399218450712918385363747307660407944315877223636732573473510832990240710193555361616185053215307314847314576351456316848821952021191955381807952656628060685759975083269303426649390846350972587599341256449454376468478476829903492425658235228129381731255594882254301790019762624902106327658578872274083105356178250091776705364578996253421031561362106441211862611434955978507336778982936913011652346242839924709547264552667291242566373569726795836466311293076240134931420040079542581864814855229962071531837202723169163129366669100861988748157868216735681284084416818474199778668842834137076911608380353885582386229543212928651295735256395981053961424655435606200654093040979582139758873066355374244512774767451839256913193741986251952999837436552216186892034419431464067999121772206425928384999824000342383930680584997637341586638286528944332095506908596720431477601887870044347700663540264616101298129603982953179121587549329781673199242609182434942625394821835820757473146514421626368804223121336434647506913817594071678300661524508314713557730330299541381162597388469050202065774953282379676255666223330387665080945375166169544381292519981765441158934187263120722934745416980745614871833599966098154979769847620422848539250934465973454320697553794381851036695807212277592666682260585734805153602512445219736209287454800286634505758894342365577513070500755256624578213123986814508671796143120266661892154513246397324474600815901373108769006750702877838448186055275778278766695237614072769441709702006361105254177786251252656697397440221826792671621869443129633091379337575840192008992427623277593947173237508081031279493505884652973240251924337811492470392081119189401219059533891105327697789345138462083978522855493717855018431062631654976,
+        "fixed_odd_divisor": 3
+      },
+      "rows": {
+        "coefficient": 12320,
+        "complex_coefficient": 2159,
+        "degree": 70000,
+        "suffix_slope": 280000,
+        "degree_gap": "224336/5"
+      },
+      "bit_uniform": {
+        "coarse_saving": "167724995262213/250000000000000000",
+        "atom_beta": "167724995262213/250000000000000000",
+        "old_atom_saving": "2620703032955050571154178221888936860701775524669750066156599988562944113/3906250000000000000000000000000000000000000000000000000000000000000000000000",
+        "ordinary_saving": "655175762739997625388892048465518856359612684797421550872147594576395840411339259699702069/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+      },
+      "conservative_old_coarse_row_reserve": 9909,
+      "ordinary_leaf_row_degree": 252
+    }
+  },
+  "controls_rejected": [
+    "next final grid",
+    "complex supplier overstated",
+    "bit supplier overstated",
+    "rank mass changed",
+    "changed word digest",
+    "omitted scalar work",
+    "missing dirty column",
+    "false integer decoder claim"
+  ],
+  "source_interface_obligations": [
+    "Retained general weighted compiler and all-size ordinary supplier",
+    "Finite-frame good-prime selection",
+    "Completed ordinary spectator and restored-row contract",
+    "Analytic and fixed-tape composition"
+  ],
+  "scope": "New bit scalar/geometry receipts are rederived by verify.py --full. Exact finite arithmetic preserves the conditional framework; F2 endpoint correctness is distinct from signed integer inverse and coefficient bounds."
+}
diff --git a/research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json b/research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json
new file mode 100644
index 0000000000..344976a1eb
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json
@@ -0,0 +1,577 @@
+{
+  "assembly": {
+    "arithmetic": "PR184 assemble_profiles: 32-term rational logarithm enclosure; rational exponential majorant; upward 2^120 rounding",
+    "assembly": {
+      "absorption_gap": "252613160861230973365700389/4169449492628652010667996046250000000",
+      "margins": {
+        "Gaussian_arithmetic": "356203720907863262581885385603163/533689535056467457365503493920000000",
+        "balanced_prefix": "2226294102921608534396837/3335559594102921608534396837",
+        "bulk_exposure": "133575648846809489/200000000000000000000",
+        "compact_phase_layer": "222626074732566750518075165603163/333555959410292160853439683700000000",
+        "coordinate_movement": "133575648846809489/200000000000000000000",
+        "dimension": "3333333300000000000000000000/3335559594102921608534396837",
+        "scalar_work": "1781031946777692724595861065603163/2668447675282337286827517469600000000"
+      },
+      "minimum_margin": "222626074732566750518075165603163/333555959410292160853439683700000000",
+      "parameters": {
+        "C0": {
+          "base": 2,
+          "exponent": 210000
+        },
+        "C1": 1,
+        "a_bit": "133575648846809489/200000000000000000000",
+        "a_complex": "219037/312500000",
+        "alpha_squared_power": "445255485024727603957758865603163/667111918820584321706879367400000000",
+        "beta": "1/1000000000",
+        "c": "6678807308764825603190511/10000000000000000000000000000",
+        "delta": "1/800000000",
+        "epsilon": "3333333300000000000000000000/3335559594102921608534396837",
+        "eta": "1/100000000",
+        "kappa": "1668581/2500000000",
+        "lambda_": "19986642435248894699946809489/20000000000000000000000000000",
+        "lambda_prime": "9993321217691235174396809489/10000000000000000000000000000",
+        "q": "6678782308764825603190511/10000000000000000000000000000",
+        "sigma": "312280963/312500000",
+        "tau": "199866424351153190511/200000000000000000000"
+      },
+      "recurrence": {
+        "internal": "199866424351153190511/200000000000000000000",
+        "leaf": "312280963000219037/312500000000000000",
+        "reservations": "9993321192691235174396809489/10000000000000000000000000000"
+      },
+      "strict_constraints": {
+        "Gaussian_arithmetic_above_kappa": "254208780131498816213930968999/66711191882058432170687936740000000000",
+        "K_dominates_log": "222626908065891750518075165603163/333555959410292160853439683700000000",
+        "K_geometry": "2502226269102921608534396837/333555959410292160853439683700000000",
+        "alpha_below_one": "666666663335559594102921608534396837/667111918820584321706879367400000000",
+        "alpha_below_one_fourth": "166332724220121352822762082984396837/667111918820584321706879367400000000",
+        "alpha_positive": "445255485024727603957758865603163/667111918820584321706879367400000000",
+        "artificial_boundary": "18680914772265377076928904582403190511/2668447675282337286827517469600000000",
+        "balanced_prefix_above_kappa": "83894216174295502160091321703/8338898985257304021335992092500000000",
+        "beta_below_one": "999999999/1000000000",
+        "beta_positive": "1/1000000000",
+        "bit_positive": "133575648846809489/200000000000000000000",
+        "bulk_exposure_above_kappa": "89168846809489/200000000000000000000",
+        "c_below_one": "9993321192691235174396809489/10000000000000000000000000000",
+        "c_positive": "6678807308764825603190511/10000000000000000000000000000",
+        "cell_above_band": "666666656664440405897078391465603163/1334223837641168643413758734800000000",
+        "compact_leaf": "330401684225990396809489/10000000000000000000000000000",
+        "compact_phase_layer_above_kappa": "252613160861230973365700389/4169449492628652010667996046250000000",
+        "compact_reservations": "1/400000000",
+        "complex_above_bit": "6608031153190511/200000000000000000000",
+        "complex_below_one_over32": "2386647/78125000",
+        "coordinate_movement_above_kappa": "89168846809489/200000000000000000000",
+        "delta_below_one_eighth": "99999999/800000000",
+        "delta_positive": "1/800000000",
+        "dimension_above_kappa": "8327767598636912152959510067591321703/8338898985257304021335992092500000000",
+        "epsilon_below_one": "2226294102921608534396837/3335559594102921608534396837",
+        "epsilon_positive": "3333333300000000000000000000/3335559594102921608534396837",
+        "gamma_sublinear": "1/200000000",
+        "guard_width": "2226294102921608534396837/3335559594102921608534396837",
+        "lambda_above_internal": "133575648846809489/20000000000000000000000000000",
+        "lambda_above_sigma": "660803248894699946809489/20000000000000000000000000000",
+        "lambda_above_tau": "133575648846809489/20000000000000000000000000000",
+        "lambda_prime_above_lambda": "133575648846809489/20000000000000000000000000000",
+        "lambda_prime_below_one": "6678782308764825603190511/10000000000000000000000000000",
+        "leaf_saving_above_bit": "6608031013006831/200000000000000000000",
+        "literal_scalar_guard": "1",
+        "phase_boundary": "356203720907863262581885385603163/533689535056467457365503493920000000",
+        "phase_local": "1781031946777692724595861065603163/2668447675282337286827517469600000000",
+        "prime_interval_packing": "2226294102921608534396837/3335559594102921608534396837",
+        "q_below_internal": "133575648846809489/10000000000000000000000000000",
+        "q_below_leaf": "330401684225990396809489/10000000000000000000000000000",
+        "q_below_reservations": "1/400000000",
+        "q_positive": "6678782308764825603190511/10000000000000000000000000000",
+        "record_suffix": "2226294102921608534396837/3335559594102921608534396837",
+        "row_product_gap": "23971789/25",
+        "scalar_work_above_kappa": "587764739541790977067370652699/66711191882058432170687936740000000000",
+        "short_record_fallback": "666221110462950501752035473151478503999536813707/667111918820584321706879367400000000000000000000",
+        "small_field_exposure": "1/100000000"
+      }
+    },
+    "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "bit": {
+      "atom_exponent": "133575649/200000000000",
+      "bad_moment_upper": "89247857896954790902471195679381717922243/27355615999190739360912919910496075776000000000000000",
+      "counts": {
+        "W": "21074",
+        "delta": "1936",
+        "edge_count": "297560",
+        "histogram": {
+          "1": "127290",
+          "10": "2544",
+          "11": "1266",
+          "12": "4158",
+          "13": "1578",
+          "14": "3426",
+          "15": "1170",
+          "16": "3006",
+          "17": "1032",
+          "18": "1614",
+          "19": "648",
+          "2": "59368",
+          "20": "5280",
+          "21": "13698",
+          "22": "9312",
+          "3": "30726",
+          "4": "9108",
+          "5": "7686",
+          "6": "3936",
+          "60": "2200",
+          "7": "3762",
+          "8": "2808",
+          "9": "1944"
+        },
+        "m": 72,
+        "mass": "1515392",
+        "maxchild": 60
+      },
+      "effective_saving": "133575648846809489/200000000000000000000",
+      "effective_saving_decimal": "6.678782442340e-04",
+      "ideal_moment_upper": "168072904686372575392663389853985508233749/168072904699027902633448979930087889567744",
+      "ordinary_leaf_saving": "384599/10000000000",
+      "saving": "6682989/10000000000",
+      "strict_gap_lower": "5911615430598974531639452298701600939983271/82066847997572218082738759731488227328000000000000000",
+      "strict_gap_lower_decimal": "7.203414746444e-11"
+    },
+    "bit_source": "research/paired-cube-twin-local-168/certificate.json bit.profile (PR189)",
+    "complex": {
+      "bad_moment_upper": "0",
+      "counts": {
+        "W": "12052",
+        "delta": "1320",
+        "edge_count": "213147",
+        "histogram": {
+          "1": "87534",
+          "10": "2790",
+          "11": "1062",
+          "12": "3591",
+          "13": "381",
+          "14": "2226",
+          "15": "5637",
+          "16": "264",
+          "17": "243",
+          "18": "7959",
+          "19": "501",
+          "2": "39834",
+          "20": "66",
+          "3": "29769",
+          "4": "12627",
+          "5": "5850",
+          "6": "4815",
+          "7": "2118",
+          "8": "4593",
+          "9": "1287"
+        },
+        "m": 66,
+        "mass": "794112",
+        "maxchild": 20
+      },
+      "ideal_moment_upper": "8009927901769221530141375505975603941953/8009927902599903050118341345249356414976",
+      "saving": "219037/312500000",
+      "strict_gap_lower": "830681519976965839273752473023/8009927902599903050118341345249356414976",
+      "strict_gap_lower_decimal": "1.037064915038e-10"
+    },
+    "construction_receipts": {
+      "complex_endpoint_checks": {
+        "all_centers_in_phase1": true,
+        "all_fresh_columns_equal_identity": true,
+        "all_target_cap_reads_in_phase2": true,
+        "arithmetic": "integers, endpoint scaled by 6",
+        "checked_source_columns": 1320,
+        "checked_target_rows": 1320,
+        "controls_before_original_K": true,
+        "original_source_V_before_all_controls": true,
+        "positive_target_data_histogram": {
+          "1": 3960,
+          "18": 1320
+        },
+        "read_counts": {
+          "center": 22,
+          "deferred": 2310,
+          "side": 3135
+        },
+        "source_controls_at_paid_parity_frames": true,
+        "target_chains_nested": true,
+        "target_data_histogram": {
+          "0": 6270,
+          "1": 3960,
+          "18": 1320
+        }
+      },
+      "complex_lift_certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2"
+    },
+    "finite_bridge": {
+      "proof": "FINITE_BRIDGE.txt",
+      "representation": "Exact powers of two with proved dominating bounds",
+      "rows": {
+        "coefficient": 20161,
+        "degree": 1000000,
+        "degree_gap": "23971789/25",
+        "suffix_slope": 4000000
+      },
+      "semantic": {
+        "B_upper": {
+          "base": 2,
+          "exponent": 100001
+        },
+        "C0": {
+          "base": 2,
+          "exponent": 210000
+        },
+        "C1": 1,
+        "E": {
+          "base": 2,
+          "exponent": 100000
+        },
+        "G": {
+          "base": 2,
+          "exponent": 30000
+        },
+        "induction_gap_lower": 1,
+        "strict_literal_gap": 1
+      }
+    },
+    "kappa": "1668581/2500000000",
+    "kappa_decimal": "6.674324000000e-04",
+    "source_sha256": {
+      "bit_certificate": "a781a738228609937165cfbc50d2eb9bfb0ecca2a28084d4deef6fb4f3bc9139",
+      "complex": "7374c75b7d6eaec051d0a451fbc1487acf443ecc3f6c39424af5ebcf0ee8f0cb"
+    },
+    "status": "Exact arithmetic; construction and finite bridge are explicit proof dependencies"
+  },
+  "binding_supplier": "bit",
+  "bit_effective_saving": "133575648846809489/200000000000000000000",
+  "complex_gain_over_pr184": "13701/205336",
+  "complex_profile": {
+    "W_per_vertex": 12052,
+    "child_histogram": {
+      "1": 87534,
+      "10": 2790,
+      "11": 1062,
+      "12": 3591,
+      "13": 381,
+      "14": 2226,
+      "15": 5637,
+      "16": 264,
+      "17": 243,
+      "18": 7959,
+      "19": 501,
+      "2": 39834,
+      "20": 66,
+      "3": 29769,
+      "4": 12627,
+      "5": 5850,
+      "6": 4815,
+      "7": 2118,
+      "8": 4593,
+      "9": 1287
+    },
+    "contract_checks": {
+      "all_centers_in_phase1": true,
+      "all_fresh_columns_equal_identity": true,
+      "all_target_cap_reads_in_phase2": true,
+      "arithmetic": "integers, endpoint scaled by 6",
+      "checked_source_columns": 1320,
+      "checked_target_rows": 1320,
+      "controls_before_original_K": true,
+      "original_source_V_before_all_controls": true,
+      "positive_target_data_histogram": {
+        "1": 3960,
+        "18": 1320
+      },
+      "read_counts": {
+        "center": 22,
+        "deferred": 2310,
+        "side": 3135
+      },
+      "source_controls_at_paid_parity_frames": true,
+      "target_chains_nested": true,
+      "target_data_histogram": {
+        "0": 6270,
+        "1": 3960,
+        "18": 1320
+      }
+    },
+    "deficit_per_vertex": 1320,
+    "entropy": "1.881413992826e+06",
+    "exact_lift_certificate_path": "research/source-assisted-v4/.work/lift.certificate.json.gz",
+    "exact_lift_certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2",
+    "exact_scalar_program_sha256": "3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027",
+    "h": 22,
+    "local_histogram": {
+      "1": 23898,
+      "10": 930,
+      "11": 354,
+      "12": 1197,
+      "13": 127,
+      "14": 742,
+      "15": 1879,
+      "16": 88,
+      "17": 81,
+      "18": 13,
+      "19": 167,
+      "2": 11078,
+      "20": 22,
+      "3": 9923,
+      "4": 4209,
+      "5": 1950,
+      "6": 1605,
+      "7": 706,
+      "8": 1531,
+      "9": 429
+    },
+    "loss": 440,
+    "m": 66,
+    "numerical_local_root": "7.009184438594e-04",
+    "physical_R": 9412,
+    "physical_gauge_histogram": {},
+    "proof_chain_sha256": {
+      "research/source-assisted-v4/.work/aligned/cache/frames.json": "434b81507ebb6e20aa73508d9ac01011fa1b785204363a5eee2eea59256e4b70",
+      "research/source-assisted-v4/.work/aligned/cache/graph.json": "a4d350feb76f2ddcffa409d079bf479c04afd65af2d6b6e96a2ea157019d78d5",
+      "research/source-assisted-v4/.work/aligned/cache/record.json": "2065cbaa22c87198a4d535119534e05fab4a258445ecda00cf3cbb9151cfcc30",
+      "research/source-assisted-v4/.work/aligned/cache/selection.json": "dfc2cd63e23473ee2a55aca490bde08566b5a8828a9826b9bea8e2ca84fbe22a",
+      "research/source-assisted-v4/.work/aligned/references/paired-cube/physical/frames.json": "1a6c215cdc58216f7ec96fb898a471e25d094fd86de085f6c06e86fd8997bfad",
+      "research/source-assisted-v4/.work/aligned/references/paired-cube/physical/pairs.json": "abf341935148071a2222fe61c430e4e2fe3d16a64db14ab4eed9cd9a5a0f54d3",
+      "research/source-assisted-v4/.work/flow.json": "ecc1b61843c40303516f05721d708e3f8183ba9c7fea2551da45028d557f7af3",
+      "research/source-assisted-v4/.work/flow.witness.json": "51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457",
+      "research/source-assisted-v4/.work/lift.certificate.json.gz": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2",
+      "research/source-assisted-v4/.work/lift.json": "c41fee34c5c6e036ed9242ea6c19f32988aa21753b83e79513c890804cc469ae",
+      "research/source-assisted-v4/contract_v4.py": "67da183217adbe28915391c8cd0c8c4ec9c9dedead54a641a2de23834df2342c",
+      "research/source-assisted-v4/data/kernel-pairs.json": "f1535677d1ec225a3a132b2da0f6da9613b7b814227647b288c4e298ec26d8d3",
+      "research/source-assisted-v4/data/physical-pairs.json": "7095501f054e9ec18aa212bfed1b01e497ca2ae997f4c9ece2779909b3fd72e2",
+      "research/source-assisted-v4/source_aligned_local_v4.py": "3e11a7418bf1f3b51674b45e4dded184cf1599338c4c3911e145f58c8c15a969",
+      "research/source-assisted-v4/verify.py": "41e73269755771828a33c85ba9d171ff9df36315430205889b321b35c4193aaa",
+      "research/source-assisted/decision/complex_frame_flow.py": "5ea4f32f4eb0b19816a0b98272592f9dc0e9cbc448ce5eb7907ba113233dcc86",
+      "research/source-assisted/decision/exact_complex_flow_lift.py": "9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e"
+    },
+    "rank_per_vertex": 794112,
+    "regeneration": "Run source_aligned_local_v4.py, PR184 complex_frame_flow.py with source purification and frozen kernel reuse, PR184 exact_complex_flow_lift.py, and this checker on the PR168 v4 producer cache. No frozen large cache is required.",
+    "scalar_coefficients": [
+      [
+        -2,
+        1
+      ],
+      [
+        -1,
+        1
+      ],
+      [
+        -1,
+        2
+      ],
+      [
+        1,
+        2
+      ],
+      [
+        1,
+        1
+      ],
+      [
+        2,
+        1
+      ]
+    ],
+    "scalar_denominator_lcm": "2",
+    "signature": "GPT-6 Astra",
+    "source_data_histogram": {
+      "1": 1320,
+      "18": 1320,
+      "2": 1320
+    },
+    "status": "Exact local invertible flow, exact all-column fresh identity, paid source controls, target read chains, and integer histogram certified. A literal globally renumbered operation program is not exported; dense initial dirty-response subtraction is defined by the exact certified flow.",
+    "target_data_histogram": {
+      "0": 6270,
+      "1": 3960,
+      "18": 1320
+    },
+    "terminal_sink_substitutions": 0,
+    "v": 1320
+  },
+  "complex_saving": "219037/312500000",
+  "flow": {
+    "baseline_entropy": "2.264636168006e+06",
+    "birth_histogram": {
+      "1:1": 2640,
+      "1:10": 22,
+      "1:3": 2016,
+      "1:5": 154,
+      "1:6": 88,
+      "2:10": 74,
+      "2:11": 5,
+      "2:12": 57,
+      "2:13": 11,
+      "2:14": 92,
+      "2:15": 47,
+      "2:16": 37,
+      "2:17": 39,
+      "2:3": 1548,
+      "2:4": 503,
+      "2:5": 396,
+      "2:6": 94,
+      "2:7": 23,
+      "2:8": 241,
+      "2:9": 5
+    },
+    "cache_sha256": {
+      "frames.json": "434b81507ebb6e20aa73508d9ac01011fa1b785204363a5eee2eea59256e4b70",
+      "graph.json": "a4d350feb76f2ddcffa409d079bf479c04afd65af2d6b6e96a2ea157019d78d5",
+      "record.json": "2065cbaa22c87198a4d535119534e05fab4a258445ecda00cf3cbb9151cfcc30",
+      "selection.json": "dfc2cd63e23473ee2a55aca490bde08566b5a8828a9826b9bea8e2ca84fbe22a"
+    },
+    "child_histogram": {
+      "1": 87534,
+      "10": 2790,
+      "11": 1062,
+      "12": 3591,
+      "13": 381,
+      "14": 2226,
+      "15": 5637,
+      "16": 264,
+      "17": 243,
+      "18": 7959,
+      "19": 501,
+      "2": 39834,
+      "20": 66,
+      "3": 29769,
+      "4": 12627,
+      "5": 5850,
+      "6": 4815,
+      "7": 2118,
+      "8": 4593,
+      "9": 1287
+    },
+    "deficit": 1320,
+    "edge_basis_values": 42787,
+    "edge_distinct_values": 42787,
+    "edge_nullity_histogram": {
+      "0": 41912
+    },
+    "edge_removed_values": 0,
+    "entropy": "1.881413992826e+06",
+    "entropy_ratio": "8.307798044588e-01",
+    "field_prime": 1000003,
+    "frames": 18532,
+    "h": 22,
+    "incoming_dependencies": 24,
+    "kernel_reuses": 0,
+    "local_histogram": {
+      "1": 23898,
+      "10": 930,
+      "11": 354,
+      "12": 1197,
+      "13": 127,
+      "14": 742,
+      "15": 1879,
+      "16": 88,
+      "17": 81,
+      "18": 13,
+      "19": 167,
+      "2": 11078,
+      "20": 22,
+      "3": 9923,
+      "4": 4209,
+      "5": 1950,
+      "6": 1605,
+      "7": 706,
+      "8": 1531,
+      "9": 429
+    },
+    "loss": 440,
+    "new_R": 9412,
+    "new_W": 12052,
+    "numerical_local_root": "7.009184438594e-04",
+    "original_physical_roles": 13372,
+    "original_role_crossings": 46747,
+    "outgoing_dependencies": 8116,
+    "retirement_histogram": {
+      "1:12": 66,
+      "1:20": 198,
+      "1:3": 84,
+      "1:6": 4,
+      "2:10": 63,
+      "2:11": 1,
+      "2:12": 103,
+      "2:13": 26,
+      "2:14": 117,
+      "2:15": 87,
+      "2:16": 293,
+      "2:17": 177,
+      "2:18": 651,
+      "2:19": 3410,
+      "2:20": 1320,
+      "2:21": 2640,
+      "2:3": 83,
+      "2:4": 13,
+      "2:5": 42,
+      "2:6": 3,
+      "2:8": 30,
+      "2:9": 1
+    },
+    "source_control_erasures": 0,
+    "source_sha256": {
+      "references/paired-cube/physical/frames.json": "1a6c215cdc58216f7ec96fb898a471e25d094fd86de085f6c06e86fd8997bfad",
+      "references/paired-cube/physical/pairs.json": "abf341935148071a2222fe61c430e4e2fe3d16a64db14ab4eed9cd9a5a0f54d3"
+    },
+    "status": "Modular equal-frame flow price, retaining dirty kernel lifts and complete full-frame cleanup. Not an exact supplier certificate.",
+    "v": 1320,
+    "vectors": 26200
+  },
+  "gain_over_pr186": "2773425370201/330942774629799",
+  "gain_over_pr191": "48017/6626307",
+  "gain_over_pr193": "6613/1661968",
+  "kappa": "1668581/2500000000",
+  "lift": {
+    "all_actual_coefficients_dyadic": true,
+    "certificate_path": "research/source-assisted-v4/.work/lift.certificate.json.gz",
+    "certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2",
+    "checker_path": "research/source-assisted/decision/exact_complex_flow_lift.py",
+    "checker_sha256": "9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e",
+    "coefficient_numerator_lcm": "2",
+    "coefficients": [
+      [
+        -2,
+        1
+      ],
+      [
+        -1,
+        1
+      ],
+      [
+        -1,
+        2
+      ],
+      [
+        1,
+        2
+      ],
+      [
+        1,
+        1
+      ],
+      [
+        2,
+        1
+      ]
+    ],
+    "denominator_lcm": "2",
+    "exact_scalar_program_sha256": "3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027",
+    "inverse_elementary_gates": 58165,
+    "kernel_reuses": 0,
+    "max_abs_numerator": "2",
+    "max_denominator": "2",
+    "nodes": 18532,
+    "physical_R": 9412,
+    "signature": "GPT-6 Astra",
+    "source_control_vertices": 0,
+    "source_erasures": 0,
+    "status": "Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.",
+    "witness_path": "research/source-assisted-v4/.work/flow.witness.json",
+    "witness_sha256": "51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457"
+  },
+  "lift_certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2",
+  "scope": "PR184 contract and finite bridge unchanged; the bit supplier is PR189 (verified by its own verify.py); the complex supplier is PR184's source-parity local word and frame flow on PR168 v4's query modules and physical layer, with donor/recipient pairs that avoid parity purification. No new flattened bit transcript or full Clifford/router replay, as in PR184.",
+  "status": "PASS conditional finite witness",
+  "witness_sha256": "51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457"
+}
diff --git a/research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py b/research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py
new file mode 100644
index 0000000000..c135d98d86
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py
@@ -0,0 +1,76 @@
+"""Independent exact interval moments; no floating point or producer execution.
+
+Positive atanh series, range reduction by 4/3, explicit geometric tails,
+80 logarithm terms and degree-12 exponential enclosures. The final rounding
+is outward on the 10^-45 grid. Prepared with OpenAI Codex assistance.
+"""
+from fractions import Fraction as Q
+from functools import lru_cache
+from math import factorial
+GRID = 10**45
+LOG_TERMS = 80
+EXP_DEGREE = 12
+
+def require(ok, reason):
+    if not ok: raise ValueError(reason)
+
+def lower(x):return Q((x*GRID).numerator//(x*GRID).denominator,GRID)
+def upper(x):
+    y=x*GRID
+    return Q(-((-y.numerator)//y.denominator),GRID)
+
+@lru_cache(None)
+def log_interval(x):
+    x=Q(x);require(x>=1,'log interval domain')
+    base=Q(4,3);k=0
+    while x>base:x/=base;k+=1
+    def short(y):
+        z=(y-1)/(y+1);power=z;s=Q(0)
+        for j in range(LOG_TERMS):s+=power/Q(2*j+1);power*=z*z
+        lo=2*s;tail=2*power/(Q(2*LOG_TERMS+1)*(1-z*z))
+        return lo,lo+tail
+    lo,hi=short(x);blo,bhi=short(base)
+    return lower(k*blo+lo),upper(k*bhi+hi)
+
+def exp_interval(lo,hi):
+    require(0<=lo<=hi<Q(1,4),'exp enclosure domain')
+    def poly(x):
+        value=term=Q(1)
+        for j in range(1,EXP_DEGREE+1):term=term*x/j;value+=term
+        return value
+    low=poly(lo);high=poly(hi)
+    tail=hi**(EXP_DEGREE+1)/factorial(EXP_DEGREE+1)/(1-hi/Q(EXP_DEGREE+2))
+    return lower(low),upper(high+tail)
+
+def prepare(profile):
+    m,W=profile['m'],profile['W'];require(type(m) is int and type(W) is int and m>1 and W>0,'profile dimensions')
+    raw=profile['child_multiplicities'];hist={int(t):n for t,n in raw.items()}
+    require(len(hist)==len(raw),'aliased histogram keys')
+    require(all(0<t<m and type(n) is int and n>0 for t,n in hist.items()),'invalid child or multiplicity')
+    mass=sum(t*n for t,n in hist.items());require(mass==profile['total_rank']==W*m-profile['N']+profile['L'],'rank mass')
+    require(max(hist)==profile['maxchild'],'maximum child')
+    require(0<mass<W*m,'rank-moment contraction')
+    return [(t,n,*log_interval(Q(m,t))) for t,n in sorted(hist.items())]
+
+def moment(profile,a,details=False):
+    a=Q(a);require(a>=0,'nonnegative saving');lo=hi=Q(0);rows=[]
+    for t,n,L,U in prepare(profile):
+        E,F=exp_interval(a*L,a*U);w=Q(t*n,profile['m']*profile['W']);lo+=w*E;hi+=w*F
+        if details:rows.append(dict(child=t,multiplicity=n,log_lower=L,log_upper=U,exp_lower=E,exp_upper=F,contribution_lower=w*E,contribution_upper=w*F))
+    result=dict(saving=a,lower=lo,upper=hi,strict_gap_lower=1-hi)
+    if details:result['terms']=rows
+    return result
+
+def saving_grid(profile,denominator=10**24):
+    require(type(denominator) is int and denominator>0,'positive saving grid')
+    prepare(profile);lo=0;hi=denominator//32;iterations=0
+    require(moment(profile,Q(lo,denominator))['upper']<1,'initial contraction')
+    require(moment(profile,Q(hi,denominator))['lower']>1,'initial exclusion')
+    while hi-lo>1:
+        mid=(hi+lo)//2;m=moment(profile,Q(mid,denominator));iterations+=1
+        if m['upper']<1:lo=mid
+        elif m['lower']>1:hi=mid
+        else:raise ValueError('Moment interval overlaps one; increase enclosure precision')
+    accepted=moment(profile,Q(lo,denominator),True);rejected=moment(profile,Q(hi,denominator),True)
+    require(accepted['upper']<1<rejected['lower'],'adjacent saving proof failed')
+    return dict(accepted=accepted,rejected=rejected,denominator=denominator,iterations=iterations,method=dict(log_base='4/3',log_terms=LOG_TERMS,exp_degree=EXP_DEGREE,outward_grid=GRID))
diff --git a/research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json b/research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json
new file mode 100644
index 0000000000..5d81d4d857
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json
@@ -0,0 +1,318 @@
+{
+  "arithmetic": {
+    "after_packing": {
+      "assembly": {
+        "absorption_gap": "1230914396526348070057671757694860242218455432936619316060414825083637894961901056119952178599407157762533482930751316362407/18531176447982486686713516168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593000000000000000000000000",
+        "margins": {
+          "Gaussian_arithmetic": "20252687142349069112007337816608950117057419648998374718731303825288364153083931753428238433576128978304538856753404536645113737856655362407/29649882316771978698741625868993056932603744133165166495379314181165371592382143543824791466790821367818019429351420148800000000000000000000000",
+          "balanced_prefix": "12657929463968168195016168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593/18531176447982486686713516168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593",
+          "bulk_exposure": "683528191054281082529874445572053583938529554073260363159021491390399389418070922129694784989/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "compact_phase_layer": "12657929463968168194997636944212600390653369712060938951488485888274017009780102819131438387018116046547252849970848736645113737856655362407/18531176447982486686713516168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593000000000000000000000000",
+          "coordinate_movement": "683528191054281082529874445572053583938529554073260363159021491390399389418070922129694784989/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "dimension": "18518518518518518518518500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/18531176447982486686713516168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593",
+          "scalar_work": "101263435711745345560110813788836680532033952309664356235988028486774733681658107052594105596861600250382256262433999736645113737856655362407/148249411583859893493708129344965284663018720665825832476896570905826857961910717719123957333954106839090097146757100744000000000000000000000000"
+        },
+        "minimum_constraint": "683528191054281082529874445572053583938529554073260363159021491390399389418070922129694784989/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "minimum_margin": "12657929463968168194997636944212600390653369712060938951488485888274017009780102819131438387018116046547252849970848736645113737856655362407/18531176447982486686713516168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593000000000000000000000000",
+        "parameters": {
+          "C0": {
+            "base": 2,
+            "exponent": 210000
+          },
+          "C1": 1,
+          "a_bit": "683528191054281082529874445572053583938529554073260363159021491390399389418070922129694784989/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "a_complex": "700918443859411/1000000000000000000",
+          "alpha_squared_power": "25315858927936336390013805064873183267993452940289998563559849116631262248619817709626105131281470932809396194608441736645113737856655362407/37062352895964973373427032336241321165754680166456458119224142726456714490477679429780989333488526709772524286689275186000000000000000000000000",
+          "beta": "1/1000000000000000000000000",
+          "c": "341764095527140541265061539257835737688182247162184609525926807165645621448672302043356002095110581929077870305215011/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "delta": "1/8000000000000000000000000",
+          "epsilon": "18518518518518518518518500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/18531176447982486686713516168120660582877340083228229059612071363228357245238839714890494666744263354886262143344637593",
+          "eta": "1/1000000000000000000000000",
+          "kappa": "683061299399923/1000000000000000000",
+          "lambda_": "999316471808945718917470126237956137470342552975801185208894562447139154683842292236891796605410389418070922129694784989/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "lambda_prime": "499658235904472859458735063460742164262311817752837815390474073192834354378551327697956643997904889418070922129694784989/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "q": "341764095527140541264936539257835737688182247162184609525926807165645621448672302043356002095110581929077870305215011/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "sigma": "999299081556140589/1000000000000000000",
+          "tau": "999316471808945718917470125554427946416061470445926739636840978508609600610581929077870305215011/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        },
+        "recurrence": {
+          "internal": "999316471808945718917470125554427946416061470445926739636840978508609600610581929077870305215011/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "leaf": "999299081556140589000000000700918443859411/1000000000000000000000000000000000000000000",
+          "reservations": "499658235904472859458734938460742164262311817752837815390474073192834354378551327697956643997904889418070922129694784989/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        },
+        "strict_constraint_count": 47
+      },
+      "binding": "bit",
+      "kappa": "683061299399923/1000000000000000000"
+    },
+    "before_packing": {
+      "binding": "bit",
+      "kappa": "676882434624733/1000000000000000000"
+    },
+    "bit_after": {
+      "accepted": {
+        "lower": "1652402343749999999056756952997375000419712810964287699571400017/1652402343750000000000000000000000000000000000000000000000000000",
+        "saving": "683528191056257/1000000000000000000",
+        "strict_gap_lower": "811199161762180042666927876792094464411/225608000000000000000000000000000000000000000000000",
+        "upper": "550800781249999999685585650999125000139904281294428908032975471/550800781250000000000000000000000000000000000000000000000000000"
+      },
+      "next_excluded": {
+        "lower": "3304804687500000005034672763894061432592377001145339332563639737/3304804687500000000000000000000000000000000000000000000000000000",
+        "saving": "341764095528129/500000000000000000",
+        "strict_gap_lower": "811198689277735346876494889239815434533/225608000000000000000000000000000000000000000000000",
+        "upper": "1101601562500000001678224254631353810864125688930806470956230843/1101601562500000000000000000000000000000000000000000000000000000"
+      },
+      "saving": "683528191056257/1000000000000000000"
+    },
+    "bit_before": {
+      "accepted": {
+        "lower": "3627070312499999993418235504017792380724010039202009964239458157/3627070312500000000000000000000000000000000000000000000000000000",
+        "saving": "677773948354561/1000000000000000000",
+        "strict_gap_lower": "817279736326429475597737857961987308799/247608000000000000000000000000000000000000000000000",
+        "upper": "604511718749999998903039250669632063454001683127402051659849717/604511718750000000000000000000000000000000000000000000000000000"
+      },
+      "next_excluded": {
+        "lower": "362707031250000000039805296271292744207821944826366581490067837/362707031250000000000000000000000000000000000000000000000000000",
+        "saving": "338886974177281/500000000000000000",
+        "strict_gap_lower": "408639629918778816085874153024739085093/123804000000000000000000000000000000000000000000000",
+        "upper": "31816406250000000003491692655376556509458065856294020665972643/31816406250000000000000000000000000000000000000000000000000000"
+      },
+      "saving": "677773948354561/1000000000000000000"
+    },
+    "bit_coarse_relative_gain": "5754242701696/677773948354561",
+    "comparison_pr199_kappa": "1693287/2500000000",
+    "comparison_pr202_kappa": "6768823/10000000000",
+    "complex": {
+      "accepted": {
+        "lower": "265143999999999999505356323836919762528275607173151/265144000000000000000000000000000000000000000000000",
+        "saving": "700918443859411/1000000000000000000",
+        "strict_gap_lower": "44967606923916385224702216933483/24104000000000000000000000000000000000000000000000",
+        "upper": "24103999999999999955032393076083614775297783066517/24104000000000000000000000000000000000000000000000"
+      },
+      "next_excluded": {
+        "lower": "66286000000000000033428585232057842908390904631703/66286000000000000000000000000000000000000000000000",
+        "saving": "175229610964853/250000000000000000",
+        "strict_gap_lower": "-1162733399375924970726640217937/2305600000000000000000000000000000000000000000000",
+        "upper": "2305600000000000001162733399375924970726640217937/2305600000000000000000000000000000000000000000000"
+      },
+      "saving": "700918443859411/1000000000000000000"
+    },
+    "complex_profile": {
+      "L": 0,
+      "N": 1320,
+      "W": 12052,
+      "child_multiplicities": {
+        "1": 87534,
+        "10": 2790,
+        "11": 1062,
+        "12": 3591,
+        "13": 381,
+        "14": 2226,
+        "15": 5637,
+        "16": 264,
+        "17": 243,
+        "18": 7959,
+        "19": 501,
+        "2": 39834,
+        "20": 66,
+        "3": 29769,
+        "4": 12627,
+        "5": 5850,
+        "6": 4815,
+        "7": 2118,
+        "8": 4593,
+        "9": 1287
+      },
+      "m": 66,
+      "maxchild": 20,
+      "total_rank": 794112
+    },
+    "controls": [
+      "changed rank mass"
+    ],
+    "extra_selector_calls": 5368513266,
+    "kappa_gain_from_packing": "617886477519/100000000000000000",
+    "ordinary_chain": [
+      "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000",
+      "683523961878504669962213417174292289938411338392698468061/1000000000000000000000000000000000000000000000000000000000000",
+      "683528188165494781294482383962566136580856823964900515238146164645368707677/1000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "683528191054281082529874445572053583938529554073260363159021491390399389418070922129694784989/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+    ],
+    "packed_profile": {
+      "L": 0,
+      "N": 5808,
+      "W": 56402,
+      "child_multiplicities": {
+        "1": 377316,
+        "10": 6066,
+        "11": 3636,
+        "12": 12186,
+        "13": 4878,
+        "14": 11016,
+        "15": 2592,
+        "16": 8964,
+        "17": 4068,
+        "18": 4842,
+        "19": 1944,
+        "2": 175962,
+        "20": 15840,
+        "21": 45054,
+        "22": 20016,
+        "3": 92790,
+        "4": 28764,
+        "5": 24210,
+        "6": 12456,
+        "7": 12240,
+        "8": 7542,
+        "9": 5256
+      },
+      "m": 72,
+      "maxchild": 22,
+      "total_rank": 4055136
+    },
+    "relative_gain_over_pr202": "6178999399923/676882300000000",
+    "scope": "Conditional composition; physical and finite bridge proof dependencies are separate",
+    "selector_toll_gap": "998632943617889461917470125554427946416061470445926739636840978508609600610581929077870305215011/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "source_commits": {
+      "bit": "a1175449f34d39ff933d9d8ab23ced1f32b290ec",
+      "complex": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "stock_relative_reduction": "2750/30951",
+    "unpacked_profile": {
+      "L": 0,
+      "N": 1936,
+      "W": 20634,
+      "child_multiplicities": {
+        "1": 125772,
+        "10": 2022,
+        "11": 1212,
+        "12": 4062,
+        "13": 1626,
+        "14": 3672,
+        "15": 864,
+        "16": 2988,
+        "17": 1356,
+        "18": 1614,
+        "19": 648,
+        "2": 58654,
+        "20": 5280,
+        "21": 15018,
+        "22": 6672,
+        "3": 30930,
+        "4": 9588,
+        "5": 8070,
+        "6": 4152,
+        "60": 2200,
+        "7": 4080,
+        "8": 2514,
+        "9": 1752
+      },
+      "m": 72,
+      "maxchild": 60,
+      "total_rank": 1483712
+    }
+  },
+  "bank_controls": {
+    "formal_columns_per_case": 144,
+    "rejected": [
+      "repeated block mod 9",
+      "omitted block mod 9",
+      "repeated block mod 25",
+      "omitted block mod 25",
+      "repeated block mod 125",
+      "omitted block mod 125"
+    ],
+    "weighted_partition_cases": 12
+  },
+  "independent": {
+    "adjacent_final_grids_checked": 2,
+    "finite_leaf_levels": 3,
+    "moment_intervals": {
+      "bit_after": {
+        "accepted_lower": "10372297619510143600774466115808210752618127629978432765365716852883069087083/10372297619510143606695298683039808628935694876327943591690240000000000000000",
+        "accepted_upper": "4148919047804057440309786446323284301047251051991373106147069580996984743701/4148919047804057442678119473215923451574277950531177436676096000000000000000",
+        "next_lower": "2593074404877535905624218813677885842824923268658416555605315352918239909111/2593074404877535901673824670759952157233923719081985897922560000000000000000",
+        "next_upper": "10372297619510143622496875254711543371299693074633666222423064981008908984557/10372297619510143606695298683039808628935694876327943591690240000000000000000"
+      },
+      "bit_before": {
+        "accepted_lower": "569187233824081511627730252557041692036672752449752559704939563312903258519/569187233824081512660590386047950634506203134848456051392512000000000000000",
+        "accepted_upper": "11383744676481630232554605051140833840733455048995051194100755968406514607593/11383744676481630253211807720959012690124062696969121027850240000000000000000",
+        "next_lower": "711484042280101890903819824529348498672355089122208648154739471157301989689/711484042280101890825737982559938293132753918560570064240640000000000000000",
+        "next_upper": "1264860519609070028273457465829952886528631269550593152275310693407253474693/1264860519609070028134645302328779187791562521885457891983360000000000000000"
+      },
+      "complex": {
+        "accepted_lower": "151303260229760552849231624798695928011617003747957445895984727/151303260229760553131497868256997591293731175633361087898845184",
+        "accepted_upper": "1664335862527366081341547872785655208127787041227531904856155057/1664335862527366084446476550826973504231042931966971966887297024",
+        "next_lower": "1664335862527366085285815072313660921079442613294059590682498373/1664335862527366084446476550826973504231042931966971966887297024",
+        "next_upper": "72362428805537655881991959665811344394758374491046069160122671/72362428805537655845498980470737978444827953563781389864665088"
+      }
+    },
+    "status": "PASS"
+  },
+  "physical": {
+    "W": 56402,
+    "banks": 45842,
+    "chart_sha256": "22662b8580d62f26f50a7773ac45a40d4ffa8352bba5317ec3b2c0ce5897a810",
+    "child_histogram": {
+      "1": 377316,
+      "10": 6066,
+      "11": 3636,
+      "12": 12186,
+      "13": 4878,
+      "14": 11016,
+      "15": 2592,
+      "16": 8964,
+      "17": 4068,
+      "18": 4842,
+      "19": 1944,
+      "2": 175962,
+      "20": 15840,
+      "21": 45054,
+      "22": 20016,
+      "3": 92790,
+      "4": 28764,
+      "5": 24210,
+      "6": 12456,
+      "7": 12240,
+      "8": 7542,
+      "9": 5256
+    },
+    "color_stats": {
+      "longest_swapped_path": 11,
+      "swaps": 733
+    },
+    "conflicting_assignment_rejected": true,
+    "conservative_selector_calls": 5368513266,
+    "copies": 3,
+    "deficit": 5808,
+    "distinct_gauges": 220,
+    "gauge_roles": 2200,
+    "incidence_sha256": "76bff256b747bd188fdfa679059c8340cab7d8e1208db4b818d770ea08711117",
+    "incidences": 154026,
+    "interior_splices": 1760,
+    "m": 72,
+    "max_chart_factors": 171,
+    "max_den": 18,
+    "max_num": 5,
+    "maxchild": 22,
+    "patterns": [
+      {
+        "count": 3300,
+        "rank24": 2,
+        "rank4": 6
+      },
+      {
+        "count": 42542,
+        "rank24": 3,
+        "rank4": 0
+      }
+    ],
+    "physical_roles": 17114,
+    "rank_mass": 4055136,
+    "source_package": "research/paired-cube-diagonal-bit-168",
+    "status": "PASS exact actual-chain chart and incidence checks",
+    "terminal_sinks": 34,
+    "word_sha256": "0728ed1c7320430a87709b1034485cbabefec85d532b48897f74136cf3954218"
+  },
+  "pinned_bit_files": 2242
+}
diff --git a/research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json b/research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json
new file mode 100644
index 0000000000..a19c4e16fb
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json
@@ -0,0 +1,1114 @@
+{
+  "assembly": {
+    "with_leaf": {
+      "assembly": {
+        "absorption_gap": "220118718583721391004594231219861532824106005649531611111667/2501708820215823243203862220695933445243831026251421693142030000000000",
+        "margins": {
+          "Gaussian_arithmetic": "27341273282289869679471210748713054307951895639644465130310685797/40027341123453171891261795531134935123901296420022747090272480000000",
+          "balanced_prefix": "170884521582324320386222069593344524383102625142169314203/250170882021582324320386222069593344524383102625142169314203",
+          "bulk_exposure": "3417640499999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000",
+          "compact_phase_layer": "17088201987350410456297886573112382844965738131114306278130685797/25017088202158232432038622206959334452438310262514216931420300000000",
+          "coordinate_movement": "3417640499999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000",
+          "dimension": "249999997500000000000000000000000000000000000000000000000000/250170882021582324320386222069593344524383102625142169314203",
+          "scalar_work": "136707367094977434726653335288453549913137575730632826220230685797/200136705617265859456308977655674675619506482100113735451362400000000"
+        },
+        "minimum_margin": "17088201987350410456297886573112382844965738131114306278130685797/25017088202158232432038622206959334452438310262514216931420300000000",
+        "parameters": {
+          "C0": {
+            "base": 2,
+            "exponent": 210000
+          },
+          "C1": 1,
+          "a_bit": "3417640499999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000",
+          "a_complex": "219037/312500000",
+          "alpha_squared_power": "34176654145582842494920093532446835283276000645331237698430685797/50034176404316464864077244413918668904876620525028433862840600000000",
+          "beta": "1/1000000000",
+          "c": "170882646582324320386222069593344524383102625142169314203/250000000000000000000000000000000000000000000000000000000000",
+          "delta": "1/800000000",
+          "epsilon": "249999997500000000000000000000000000000000000000000000000000/250170882021582324320386222069593344524383102625142169314203",
+          "eta": "1/100000000",
+          "kappa": "6830611/10000000000",
+          "lambda_": "499658235953417710859228259453102941405159513340567980685797/500000000000000000000000000000000000000000000000000000000000",
+          "lambda_prime": "249829117978417675679613777930406655475616897374857830685797/250000000000000000000000000000000000000000000000000000000000",
+          "q": "170882021582324320386222069593344524383102625142169314203/250000000000000000000000000000000000000000000000000000000000",
+          "sigma": "312280963/312500000",
+          "tau": "4996582359500000703592289630453925718590852319314203/5000000000000000000000000000000000000000000000000000"
+        },
+        "recurrence": {
+          "internal": "4996582359500000703592289630453925718590852319314203/5000000000000000000000000000000000000000000000000000",
+          "leaf": "312280963000219037/312500000000000000",
+          "reservations": "249829117353417675679613777930406655475616897374857830685797/250000000000000000000000000000000000000000000000000000000000"
+        },
+        "strict_constraints": {
+          "Gaussian_arithmetic_above_kappa": "19203053588786117106038155117659223904976944708184725920788559/5003417640431646486407724441391866890487662052502843386284060000000000",
+          "K_dominates_log": "17088264487349785456297886573112382844965738131114306278130685797/25017088202158232432038622206959334452438310262514216931420300000000",
+          "K_geometry": "187670882646582324320386222069593344524383102625142169314203/25017088202158232432038622206959334452438310262514216931420300000000",
+          "alpha_below_one": "49999999750170882021582324320386222069593344524383102625142169314203/50034176404316464864077244413918668904876620525028433862840600000000",
+          "alpha_below_one_fourth": "12474367446933533373524391009947220390935879130611777228011719314203/50034176404316464864077244413918668904876620525028433862840600000000",
+          "alpha_positive": "34176654145582842494920093532446835283276000645331237698430685797/50034176404316464864077244413918668904876620525028433862840600000000",
+          "artificial_boundary": "1401093647688639521715218794206556071164831890374059191486325707942609/200136705617265859456308977655674675619506482100113735451362400000000",
+          "balanced_prefix_above_kappa": "25237206920741953823043216438179195985262416268163748542531967/2501708820215823243203862220695933445243831026251421693142030000000000",
+          "beta_below_one": "999999999/1000000000",
+          "beta_positive": "1/1000000000",
+          "bit_positive": "3417640499999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000",
+          "bulk_exposure_above_kappa": "2334999999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000",
+          "c_below_one": "249829117353417675679613777930406655475616897374857830685797/250000000000000000000000000000000000000000000000000000000000",
+          "c_positive": "170882646582324320386222069593344524383102625142169314203/250000000000000000000000000000000000000000000000000000000000",
+          "cell_above_band": "49999999249829117978417675679613777930406655475616897374857830685797/100068352808632929728154488827837337809753241050056867725681200000000",
+          "compact_leaf": "4347578242446079613777930406655475616897374857830685797/250000000000000000000000000000000000000000000000000000000000",
+          "compact_phase_layer_above_kappa": "220118718583721391004594231219861532824106005649531611111667/2501708820215823243203862220695933445243831026251421693142030000000000",
+          "compact_reservations": "1/400000000",
+          "complex_above_bit": "86951500000703592289630453925718590852319314203/5000000000000000000000000000000000000000000000000000",
+          "complex_below_one_over32": "2386647/78125000",
+          "coordinate_movement_above_kappa": "2334999999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000",
+          "delta_below_one_eighth": "99999999/800000000",
+          "delta_positive": "1/800000000",
+          "dimension_above_kappa": "2498291155021383677538091602347282992935364959010994575021718542531967/2501708820215823243203862220695933445243831026251421693142030000000000",
+          "epsilon_below_one": "170884521582324320386222069593344524383102625142169314203/250170882021582324320386222069593344524383102625142169314203",
+          "epsilon_positive": "249999997500000000000000000000000000000000000000000000000000/250170882021582324320386222069593344524383102625142169314203",
+          "gamma_sublinear": "1/200000000",
+          "guard_width": "170884521582324320386222069593344524383102625142169314203/250170882021582324320386222069593344524383102625142169314203",
+          "lambda_above_internal": "3417640499999296407710369546074281409147680685797/500000000000000000000000000000000000000000000000000000000000",
+          "lambda_above_sigma": "8695153417710859228259453102941405159513340567980685797/500000000000000000000000000000000000000000000000000000000000",
+          "lambda_above_tau": "3417640499999296407710369546074281409147680685797/500000000000000000000000000000000000000000000000000000000000",
+          "lambda_prime_above_lambda": "3417640499999296407710369546074281409147680685797/500000000000000000000000000000000000000000000000000000000000",
+          "lambda_prime_below_one": "170882021582324320386222069593344524383102625142169314203/250000000000000000000000000000000000000000000000000000000000",
+          "leaf_saving_above_bit": "86951496496111592289630453925718590852319314203/5000000000000000000000000000000000000000000000000000",
+          "literal_scalar_guard": "1",
+          "phase_boundary": "27341273282289869679471210748713054307951895639644465130310685797/40027341123453171891261795531134935123901296420022747090272480000000",
+          "phase_local": "136707367094977434726653335288453549913137575730632826220230685797/200136705617265859456308977655674675619506482100113735451362400000000",
+          "prime_interval_packing": "170884521582324320386222069593344524383102625142169314203/250170882021582324320386222069593344524383102625142169314203",
+          "q_below_internal": "3417640499999296407710369546074281409147680685797/250000000000000000000000000000000000000000000000000000000000",
+          "q_below_leaf": "4347578242446079613777930406655475616897374857830685797/250000000000000000000000000000000000000000000000000000000000",
+          "q_below_reservations": "1/400000000",
+          "q_positive": "170882021582324320386222069593344524383102625142169314203/250000000000000000000000000000000000000000000000000000000000",
+          "record_suffix": "170884521582324320386222069593344524383102625142169314203/250170882021582324320386222069593344524383102625142169314203",
+          "row_product_gap": "23971789/25",
+          "scalar_work_above_kappa": "44220141790944349538076777324618558357415254970698942852208859/5003417640431646486407724441391866890487662052502843386284060000000000",
+          "short_record_fallback": "1249144993361682494392622193507082605477152780852343078632209596124179499543531138532992146810869027211787525209/1250854410107911621601931110347966722621915513125710846571015000000000000000000000000000000000000000000000000000",
+          "small_field_exposure": "1/100000000"
+        }
+      },
+      "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+      "doubling_achieved": false,
+      "finite_bridge": {
+        "proof": "FINITE_BRIDGE.txt",
+        "representation": "Exact powers of two with proved dominating bounds",
+        "rows": {
+          "coefficient": 20161,
+          "degree": 1000000,
+          "degree_gap": "23971789/25",
+          "suffix_slope": 4000000
+        },
+        "semantic": {
+          "B_upper": {
+            "base": 2,
+            "exponent": 100001
+          },
+          "C0": {
+            "base": 2,
+            "exponent": 210000
+          },
+          "C1": 1,
+          "E": {
+            "base": 2,
+            "exponent": 100000
+          },
+          "G": {
+            "base": 2,
+            "exponent": 30000
+          },
+          "induction_gap_lower": 1,
+          "strict_literal_gap": 1
+        }
+      },
+      "fixed_doubling_target": "4609169/5000000000",
+      "kappa": "6830611/10000000000",
+      "kappa_decimal": 0.0006830611,
+      "ratio_to_reviewed_baseline": "6830611/4609169",
+      "ratio_to_reviewed_baseline_decimal": 1.4819614989166159,
+      "reviewed_baseline": "4609169/10000000000"
+    },
+    "without_leaf": {
+      "assembly": {
+        "absorption_gap": "129004488966564671495137678387/2501707718620845126958509998830000000000",
+        "margins": {
+          "Gaussian_arithmetic": "27323647762750169251647285429000117/40027323497933522031336159981280000000",
+          "balanced_prefix": "170774362084512695850999883/250170771862084512695850999883",
+          "bulk_exposure": "3415437309999000117/5000000000000000000000",
+          "compact_phase_layer": "17077186037679407500587292449000117/25017077186208451269585099988300000000",
+          "coordinate_movement": "3415437309999000117/5000000000000000000000",
+          "dimension": "249999997500000000000000000000/250170771862084512695850999883",
+          "scalar_work": "136619239496838294596287210549000117/200136617489667610156680799906400000000"
+        },
+        "minimum_margin": "17077186037679407500587292449000117/25017077186208451269585099988300000000",
+        "parameters": {
+          "C0": {
+            "base": 2,
+            "exponent": 210000
+          },
+          "C1": 1,
+          "a_bit": "3415437309999000117/5000000000000000000000",
+          "a_complex": "219037/312500000",
+          "alpha_squared_power": "34154622246130677085687280749000117/50034154372416902539170199976600000000",
+          "beta": "1/1000000000",
+          "c": "170772487084512695850999883/250000000000000000000000000000",
+          "delta": "1/800000000",
+          "epsilon": "249999997500000000000000000000/250170771862084512695850999883",
+          "eta": "1/100000000",
+          "kappa": "6826211/10000000000",
+          "lambda_": "499658456272415537298299000117/500000000000000000000000000000",
+          "lambda_prime": "249829228137915487304149000117/250000000000000000000000000000",
+          "q": "170771862084512695850999883/250000000000000000000000000000",
+          "sigma": "312280963/312500000",
+          "tau": "4996584562690000999883/5000000000000000000000"
+        },
+        "recurrence": {
+          "internal": "4996584562690000999883/5000000000000000000000",
+          "leaf": "312280963000219037/312500000000000000",
+          "reservations": "249829227512915487304149000117/250000000000000000000000000000"
+        },
+        "strict_constraints": {
+          "Gaussian_arithmetic_above_kappa": "19020816867589467795179100347999/5003415437241690253917019997660000000000",
+          "K_dominates_log": "17077248537678782500587292449000117/25017077186208451269585099988300000000",
+          "K_geometry": "187670772487084512695850999883/25017077186208451269585099988300000000",
+          "alpha_below_one": "49999999750170771862084512695850999883/50034154372416902539170199976600000000",
+          "alpha_below_one_fourth": "12474383970858094957706862713400999883/50034154372416902539170199976600000000",
+          "alpha_positive": "34154622246130677085687280749000117/50034154372416902539170199976600000000",
+          "artificial_boundary": "1401092942667853196839699937338752999649/200136617489667610156680799906400000000",
+          "balanced_prefix_above_kappa": "25146081675175015941080237666687/2501707718620845126958509998830000000000",
+          "beta_below_one": "999999999/1000000000",
+          "beta_positive": "1/1000000000",
+          "bit_positive": "3415437309999000117/5000000000000000000000",
+          "bulk_exposure_above_kappa": "2331809999000117/5000000000000000000000",
+          "c_below_one": "249829227512915487304149000117/250000000000000000000000000000",
+          "c_positive": "170772487084512695850999883/250000000000000000000000000000",
+          "cell_above_band": "49999999249829228137915487304149000117/100068308744833805078340399953200000000",
+          "compact_leaf": "4457737740257704149000117/250000000000000000000000000000",
+          "compact_phase_layer_above_kappa": "129004488966564671495137678387/2501707718620845126958509998830000000000",
+          "compact_reservations": "1/400000000",
+          "complex_above_bit": "89154690000999883/5000000000000000000000",
+          "complex_below_one_over32": "2386647/78125000",
+          "coordinate_movement_above_kappa": "2331809999000117/5000000000000000000000",
+          "delta_below_one_eighth": "99999999/800000000",
+          "delta_positive": "1/800000000",
+          "dimension_above_kappa": "2498292256525236548216505942250237666687/2501707718620845126958509998830000000000",
+          "epsilon_below_one": "170774362084512695850999883/250170771862084512695850999883",
+          "epsilon_positive": "249999997500000000000000000000/250170771862084512695850999883",
+          "gamma_sublinear": "1/200000000",
+          "guard_width": "170774362084512695850999883/250170771862084512695850999883",
+          "lambda_above_internal": "3415437309999000117/500000000000000000000000000000",
+          "lambda_above_sigma": "8915472415537298299000117/500000000000000000000000000000",
+          "lambda_above_tau": "3415437309999000117/500000000000000000000000000000",
+          "lambda_prime_above_lambda": "3415437309999000117/500000000000000000000000000000",
+          "lambda_prime_below_one": "170771862084512695850999883/250000000000000000000000000000",
+          "leaf_saving_above_bit": "89154686496407883/5000000000000000000000",
+          "literal_scalar_guard": "1",
+          "phase_boundary": "27323647762750169251647285429000117/40027323497933522031336159981280000000",
+          "phase_local": "136619239496838294596287210549000117/200136617489667610156680799906400000000",
+          "prime_interval_packing": "170774362084512695850999883/250170771862084512695850999883",
+          "q_below_internal": "3415437309999000117/250000000000000000000000000000",
+          "q_below_leaf": "4457737740257704149000117/250000000000000000000000000000",
+          "q_below_reservations": "1/400000000",
+          "q_positive": "170771862084512695850999883/250000000000000000000000000000",
+          "record_suffix": "170774362084512695850999883/250170771862084512695850999883",
+          "row_product_gap": "23971789/25",
+          "scalar_work_above_kappa": "44037894053797919064764200336299/5003415437241690253917019997660000000000",
+          "short_record_fallback": "1249145544911910988522467303589447604030855316013689/1250853859310422563479254999415000000000000000000000",
+          "small_field_exposure": "1/100000000"
+        }
+      },
+      "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+      "doubling_achieved": false,
+      "finite_bridge": {
+        "proof": "FINITE_BRIDGE.txt",
+        "representation": "Exact powers of two with proved dominating bounds",
+        "rows": {
+          "coefficient": 20161,
+          "degree": 1000000,
+          "degree_gap": "23971789/25",
+          "suffix_slope": 4000000
+        },
+        "semantic": {
+          "B_upper": {
+            "base": 2,
+            "exponent": 100001
+          },
+          "C0": {
+            "base": 2,
+            "exponent": 210000
+          },
+          "C1": 1,
+          "E": {
+            "base": 2,
+            "exponent": 100000
+          },
+          "G": {
+            "base": 2,
+            "exponent": 30000
+          },
+          "induction_gap_lower": 1,
+          "strict_literal_gap": 1
+        }
+      },
+      "fixed_doubling_target": "4609169/5000000000",
+      "kappa": "6826211/10000000000",
+      "kappa_decimal": 0.0006826211,
+      "ratio_to_reviewed_baseline": "6826211/4609169",
+      "ratio_to_reviewed_baseline_decimal": 1.4810068799820533,
+      "reviewed_baseline": "4609169/10000000000"
+    }
+  },
+  "banks": {
+    "charts": {
+      "chart_sha256": "3468876360ddb34e3d29cc7aa83e38213b93c1ad1d5b8bfd50e01a1475d3f236",
+      "distinct_entrance_frames": 220,
+      "entrance_roles": 2200,
+      "entry_bound": "2^79",
+      "max_chart_factors": 186,
+      "max_den": 18,
+      "max_entry": 18,
+      "max_num": 5,
+      "slot_separation": "Distinct bank slots place the residual in disjoint coordinate blocks of an invertible chart; every difference of two slot charts is a nonzero integer matrix over the common denominator with entries below 2^80, so no prime q > 2^80 identifies two charts of one bank group."
+    },
+    "fixed_selector_calls": "5701209426",
+    "projector_checks": [
+      {
+        "ambient": 72,
+        "blocks": 18,
+        "controls_rejected": {
+          "0:omit_block": true,
+          "0:repeat_block": true,
+          "2:omit_block": true,
+          "2:repeat_block": true
+        },
+        "endpoint": "partialSwap(P)(x,y)=(x-Px+Py,y-Py+Px)",
+        "formal_columns": 288,
+        "inverse_columns": 288,
+        "projectors_disjoint": true,
+        "projectors_idempotent": true,
+        "rings": [
+          2,
+          0
+        ],
+        "sum_is_identity": true,
+        "width": 4
+      },
+      {
+        "ambient": 72,
+        "blocks": 3,
+        "controls_rejected": {
+          "0:omit_block": true,
+          "0:repeat_block": true,
+          "2:omit_block": true,
+          "2:repeat_block": true
+        },
+        "endpoint": "partialSwap(P)(x,y)=(x-Px+Py,y-Py+Px)",
+        "formal_columns": 288,
+        "inverse_columns": 288,
+        "projectors_disjoint": true,
+        "projectors_idempotent": true,
+        "rings": [
+          2,
+          0
+        ],
+        "sum_is_identity": true,
+        "width": 24
+      }
+    ],
+    "schedule_diagnostic": {
+      "duplicate_embedding_collides": true,
+      "full_endpoint_basis_checks": 15552,
+      "high_lifts_per_batch": 81,
+      "invocation_vertices": 3888,
+      "modulus": 9,
+      "residue_batches": 48,
+      "role_visits": 7776,
+      "scope": "finite scheduling diagnostic; general proof and PR186 word checks are separate",
+      "status": "PASS"
+    },
+    "weighted_controls": {
+      "formal_columns_per_case": 144,
+      "rejected": [
+        "repeated block mod 9",
+        "omitted block mod 9",
+        "repeated block mod 25",
+        "omitted block mod 25",
+        "repeated block mod 125",
+        "omitted block mod 125"
+      ],
+      "weighted_partition_cases": 12
+    }
+  },
+  "binding": "bit",
+  "bit": {
+    "coarse": {
+      "accepted": {
+        "bad_fraction": "1/10000000000000000",
+        "edge_count": 877638,
+        "fallback_children_per_edge": 165888,
+        "fallback_lower": "1980466389106598368917304526603730670432325638383339/550800781250000000000000000000000000000000000000000000000000000",
+        "fallback_upper": "1980466389106598368917304526603730670432326001725471/550800781250000000000000000000000000000000000000000000000000000",
+        "lower": "1652402343749999999056756952997375000419712810964287699571400017/1652402343750000000000000000000000000000000000000000000000000000",
+        "raw": {
+          "lower": "135364799999513280502942691974399843273924740624629/135364800000000000000000000000000000000000000000000",
+          "saving": "683528191056257/1000000000000000000",
+          "strict_gap_lower": "811199161762180042666927876792094464411/225608000000000000000000000000000000000000000000000",
+          "terms": [
+            {
+              "child": 1,
+              "contribution_lower": "5255841556598824852013717815655632544220637923329/56402000000000000000000000000000000000000000000000",
+              "contribution_upper": "5255841556598824852013717815655632544220638887581/56402000000000000000000000000000000000000000000000",
+              "exp_lower": "501463749317701064021917547529399155063509009/500000000000000000000000000000000000000000000",
+              "exp_upper": "501463749317701064021917547529399155063509101/500000000000000000000000000000000000000000000",
+              "log_lower": "2138333059508027655521093419109790556760740759/500000000000000000000000000000000000000000000",
+              "log_upper": "4276666119016055311042186838219581113521481519/1000000000000000000000000000000000000000000000",
+              "multiplicity": 377316
+            },
+            {
+              "child": 2,
+              "contribution_lower": "29398922664984588045866918557294583056787535159359/338412000000000000000000000000000000000000000000000",
+              "contribution_upper": "9799640888328196015288972852431527685595845248633/112804000000000000000000000000000000000000000000000",
+              "exp_lower": "1002452438537340609195175727394366387860590417/1000000000000000000000000000000000000000000000",
+              "exp_upper": "1002452438537340609195175727394366387860590437/1000000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/125000000000000000000000000000000000000000000",
+              "log_upper": "716703787691222000324990943352280909089196277/200000000000000000000000000000000000000000000",
+              "multiplicity": 175962
+            },
+            {
+              "child": 3,
+              "contribution_lower": "3099726194045063647471569502134132940654496743629/45121600000000000000000000000000000000000000000000",
+              "contribution_upper": "3099726194045063647471569502134132940654496756001/45121600000000000000000000000000000000000000000000",
+              "exp_lower": "1002174650515701146935521985817695745442772953/1000000000000000000000000000000000000000000000",
+              "exp_upper": "1002174650515701146935521985817695745442772957/1000000000000000000000000000000000000000000000",
+              "log_lower": "39725672879349320245586770016213192610924887/12500000000000000000000000000000000000000000",
+              "log_upper": "3178053830347945619646941601297055408873990961/1000000000000000000000000000000000000000000000",
+              "multiplicity": 92790
+            },
+            {
+              "child": 4,
+              "contribution_lower": "100072513145829206071557586354402127799104032527/3525125000000000000000000000000000000000000000000",
+              "contribution_upper": "400290052583316824286230345417608511196416130907/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "125247200432827542016968193184483263828665873/125000000000000000000000000000000000000000000",
+              "exp_upper": "500988801731310168067872772737933055314663493/500000000000000000000000000000000000000000000",
+              "log_lower": "462459481263386350753235615248516476379277/160000000000000000000000000000000000000000",
+              "log_upper": "2890371757896164692207722595303227977370481251/1000000000000000000000000000000000000000000000",
+              "multiplicity": 28764
+            },
+            {
+              "child": 5,
+              "contribution_lower": "1684317925792043387624010655455555004789516247/56402000000000000000000000000000000000000000000",
+              "contribution_upper": "134745434063363471009920852436444400383161300029/4512160000000000000000000000000000000000000000000",
+              "exp_lower": "6261404928594956831316024741470464701819763/6250000000000000000000000000000000000000000",
+              "exp_upper": "500912394287596546505281979317637176145581041/500000000000000000000000000000000000000000000",
+              "log_lower": "666807051645488734110356876248348368498970041/250000000000000000000000000000000000000000000",
+              "log_upper": "533445641316390987288285500998678694799176033/200000000000000000000000000000000000000000000",
+              "multiplicity": 24210
+            },
+            {
+              "child": 6,
+              "contribution_lower": "519882272504305405754061486945103504053852879807/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "259941136252152702877030743472551752026926440163/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "1001699947021783055402815967138927753475631753/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500849973510891527701407983569463876737815877/500000000000000000000000000000000000000000000",
+              "log_lower": "1242453324894000155114854739919439420399245413/500000000000000000000000000000000000000000000",
+              "log_upper": "2484906649788000310229709479838878840798490827/1000000000000000000000000000000000000000000000",
+              "multiplicity": 12456
+            },
+            {
+              "child": 7,
+              "contribution_lower": "11918973444841480470869233758634600202085781817/564020000000000000000000000000000000000000000000",
+              "contribution_upper": "119189734448414804708692337586346002020857818289/5640200000000000000000000000000000000000000000000",
+              "exp_lower": "100159440712953617402262468559954623546939343/100000000000000000000000000000000000000000000",
+              "exp_upper": "1001594407129536174022624685599546235469393431/1000000000000000000000000000000000000000000000",
+              "log_lower": "2330755969960742005936834094776401383884396789/1000000000000000000000000000000000000000000000",
+              "log_upper": "233075596996074200593683409477640138388439679/100000000000000000000000000000000000000000000",
+              "multiplicity": 12240
+            },
+            {
+              "child": 8,
+              "contribution_lower": "419629754194649914248191456342743921628439285019/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "209814877097324957124095728171371960814219642719/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "1001502993304653733289239752607980719876943401/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500751496652326866644619876303990359938471701/500000000000000000000000000000000000000000000",
+              "log_lower": "439444915467243876558098094769010281858996223/200000000000000000000000000000000000000000000",
+              "log_upper": "549306144334054845697622618461262852323745279/250000000000000000000000000000000000000000000",
+              "multiplicity": 7542
+            },
+            {
+              "child": 9,
+              "contribution_lower": "657934495461879261525647552942368606847323603287/56402000000000000000000000000000000000000000000000",
+              "contribution_upper": "82241811932734907690705944117796075855915450493/7050250000000000000000000000000000000000000000000",
+              "exp_lower": "1001422367521886242809204798999038975414495591/1000000000000000000000000000000000000000000000",
+              "exp_upper": "125177795940235780351150599874879871926811949/125000000000000000000000000000000000000000000",
+              "log_lower": "2079441541679835928251696364374529704226500403/1000000000000000000000000000000000000000000000",
+              "log_upper": "519860385419958982062924091093632426056625101/250000000000000000000000000000000000000000000",
+              "multiplicity": 5256
+            },
+            {
+              "child": 10,
+              "contribution_lower": "13498201380805255396439172324108854434681299409/902432000000000000000000000000000000000000000000",
+              "contribution_upper": "168727517260065692455489654051360680433516242781/11280400000000000000000000000000000000000000000000",
+              "exp_lower": "40054010032063072392994576629403128886294657/40000000000000000000000000000000000000000000",
+              "exp_upper": "500675125400788404912432207867539111078683213/500000000000000000000000000000000000000000000",
+              "log_lower": "197408102602200962702419538353521690592038003/100000000000000000000000000000000000000000000",
+              "log_upper": "1974081026022009627024195383535216905920380031/1000000000000000000000000000000000000000000000",
+              "multiplicity": 6066
+            },
+            {
+              "child": 11,
+              "contribution_lower": "278106913684681931054308623215948913761896786793/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "556213827369363862108617246431897827523793574697/56402000000000000000000000000000000000000000000000",
+              "exp_lower": "250321254441657903739251686062960318417548863/250000000000000000000000000000000000000000000",
+              "exp_upper": "500642508883315807478503372125920636835097727/500000000000000000000000000000000000000000000",
+              "log_lower": "234846355777210595872530407531806476712471833/125000000000000000000000000000000000000000000",
+              "log_upper": "375754169243536953396048652050890362739954933/200000000000000000000000000000000000000000000",
+              "multiplicity": 3636
+            },
+            {
+              "child": 12,
+              "contribution_lower": "2033488926284435672546524015796730120462568328733/56402000000000000000000000000000000000000000000000",
+              "contribution_upper": "508372231571108918136631003949182530115642082691/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "1001225468382292305537431814769438759459659443/1000000000000000000000000000000000000000000000",
+              "exp_upper": "250306367095573076384357953692359689864914861/250000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/250000000000000000000000000000000000000000000",
+              "log_upper": "1791759469228055000812477358380702272722990693/1000000000000000000000000000000000000000000000",
+              "multiplicity": 12186
+            },
+            {
+              "child": 13,
+              "contribution_lower": "110222635804825693505225526943823250465386371321/7050250000000000000000000000000000000000000000000",
+              "contribution_upper": "705424869150884438433443372440468802978472777159/45121600000000000000000000000000000000000000000000",
+              "exp_lower": "31286584105826197418457430299126667744929427/31250000000000000000000000000000000000000000",
+              "exp_upper": "200234138277287663478127553914410673567548333/200000000000000000000000000000000000000000000",
+              "log_lower": "1711716761554518574988699396654262508716213573/1000000000000000000000000000000000000000000000",
+              "log_upper": "855858380777259287494349698327131254358106787/500000000000000000000000000000000000000000000",
+              "multiplicity": 4878
+            },
+            {
+              "child": 14,
+              "contribution_lower": "1072199496953672691655236089832726147016800117489/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "6701246855960454322845225561454538418855000741/176256250000000000000000000000000000000000000000",
+              "exp_lower": "1001119978481487107054375434017484731108123359/1000000000000000000000000000000000000000000000",
+              "exp_upper": "6256999865509294419089846462609279569425771/6250000000000000000000000000000000000000000",
+              "log_lower": "818804394700398348259800986659112407904448327/500000000000000000000000000000000000000000000",
+              "log_upper": "327521757880159339303920394663644963161779331/200000000000000000000000000000000000000000000",
+              "multiplicity": 11016
+            },
+            {
+              "child": 15,
+              "contribution_lower": "6757241185386791830665961872385264004039400099/705025000000000000000000000000000000000000000000",
+              "contribution_upper": "27028964741547167322663847489541056016157600423/2820100000000000000000000000000000000000000000000",
+              "exp_lower": "250268192051362660395035624903157926075533337/250000000000000000000000000000000000000000000",
+              "exp_upper": "1001072768205450641580142499612631704302133349/1000000000000000000000000000000000000000000000",
+              "log_lower": "784307958956922622523091134035433884674194803/500000000000000000000000000000000000000000000",
+              "log_upper": "1568615917913845245046182268070867769348389607/1000000000000000000000000000000000000000000000",
+              "multiplicity": 2592
+            },
+            {
+              "child": 16,
+              "contribution_lower": "249256123381269024482414701770930553547286385737/7050250000000000000000000000000000000000000000000",
+              "contribution_upper": "124628061690634512241207350885465276773643192993/3525125000000000000000000000000000000000000000000",
+              "exp_lower": "1001028607956903712780781934823014271274242513/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500514303978451856390390967411507135637121257/500000000000000000000000000000000000000000000",
+              "log_lower": "1504077396776274073373258352386874841219480981/1000000000000000000000000000000000000000000000",
+              "log_upper": "752038698388137036686629176193437420609740491/500000000000000000000000000000000000000000000",
+              "multiplicity": 8964
+            },
+            {
+              "child": 17,
+              "contribution_lower": "1922896272031539119039714206442668968884595872733/112804000000000000000000000000000000000000000000000",
+              "contribution_upper": "961448136015769559519857103221334484442297937327/56402000000000000000000000000000000000000000000000",
+              "exp_lower": "1000987127554158833440767416159640275317332573/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500493563777079416720383708079820137658666287/500000000000000000000000000000000000000000000",
+              "log_lower": "721726387479919615396326110173227288966639253/500000000000000000000000000000000000000000000",
+              "log_upper": "1443452774959839230792652220346454577933278507/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4068
+            },
+            {
+              "child": 18,
+              "contribution_lower": "30291189466278455973716276325671796769895630763/1410050000000000000000000000000000000000000000000",
+              "contribution_upper": "2423295157302276477897302106053743741591650463461/112804000000000000000000000000000000000000000000000",
+              "exp_lower": "12511850254555330844162030700401403044153503/12500000000000000000000000000000000000000000",
+              "exp_upper": "1000948020364426467532962456032112243532280241/1000000000000000000000000000000000000000000000",
+              "log_lower": "346573590279972654708616060729088284037750067/250000000000000000000000000000000000000000000",
+              "log_upper": "1386294361119890618834464242916353136151000269/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4842
+            },
+            {
+              "child": 19,
+              "contribution_lower": "513467358155312429927165741263826369097115463793/56402000000000000000000000000000000000000000000000",
+              "contribution_upper": "256733679077656214963582870631913184548557732153/28201000000000000000000000000000000000000000000000",
+              "exp_lower": "1000911029542519356583169086284261928064552561/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500455514771259678291584543142130964032276281/500000000000000000000000000000000000000000000",
+              "log_lower": "1332227139849614851033159406331727576284102257/1000000000000000000000000000000000000000000000",
+              "log_upper": "666113569924807425516579703165863788142051129/500000000000000000000000000000000000000000000",
+              "multiplicity": 1944
+            },
+            {
+              "child": 20,
+              "contribution_lower": "5504817657921398114228480071373269987852091523/70502500000000000000000000000000000000000000000",
+              "contribution_upper": "11009635315842796228456960142746539975704183057/141005000000000000000000000000000000000000000000",
+              "exp_lower": "500437968901945283111680006488479089804735593/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000875937803890566223360012976958179609471187/1000000000000000000000000000000000000000000000",
+              "log_lower": "256186769092412863521392652415408067568975979/200000000000000000000000000000000000000000000",
+              "log_upper": "160116730682758039700870407759630042230609987/125000000000000000000000000000000000000000000",
+              "multiplicity": 15840
+            },
+            {
+              "child": 21,
+              "contribution_lower": "105214574930576685262642186837461064049194681539/451216000000000000000000000000000000000000000000",
+              "contribution_upper": "52607287465288342631321093418730532024597340822063/225608000000000000000000000000000000000000000000000",
+              "exp_lower": "2001685119391524175991518498515325686303953/2000000000000000000000000000000000000000000",
+              "exp_upper": "1000842559695762087995759249257662843151976501/1000000000000000000000000000000000000000000000",
+              "log_lower": "1232143681292632314541588857853875679236906231/1000000000000000000000000000000000000000000000",
+              "log_upper": "154017960161579039317698607231734459904613279/125000000000000000000000000000000000000000000",
+              "multiplicity": 45054
+            },
+            {
+              "child": 22,
+              "contribution_lower": "765119807418262538621198527041709502823912817821/7050250000000000000000000000000000000000000000000",
+              "contribution_upper": "1530239614836525077242397054083419005647825637171/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "500405367834050057960234484657756378563710149/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000810735668100115920468969315512757127420299/1000000000000000000000000000000000000000000000",
+              "log_lower": "118562366565773945756301113879627524562427453/100000000000000000000000000000000000000000000",
+              "log_upper": "1185623665657739457563011138796275245624274531/1000000000000000000000000000000000000000000000",
+              "multiplicity": 20016
+            }
+          ],
+          "upper": "225607999999188800838237819957333072123207905535589/225608000000000000000000000000000000000000000000000"
+        },
+        "saving": "683528191056257/1000000000000000000",
+        "strict_gap_lower": "314414349000874999860095718705571091967024529/550800781250000000000000000000000000000000000000000000000000000",
+        "upper": "550800781249999999685585650999125000139904281294428908032975471/550800781250000000000000000000000000000000000000000000000000000"
+      },
+      "atom_beta": "170771888233960718837/250000000000000000000000",
+      "atom_grid": 1000000000000000000000000,
+      "atom_lower_gap": "177693025726613109/250000000000000000000000000000000000000000",
+      "atom_threshold": "683528191056257/1000645068291056257",
+      "atom_upper_gap": "249658456223532078562326177693025726613109/250000000000000000000000000000000000000000",
+      "coarse_grid": 1000000000000000000,
+      "coarse_saving": "683528191056257/1000000000000000000",
+      "controls": {
+        "next_coarse_grid_rejected": true,
+        "previous_atom_grid_rejected": true
+      },
+      "old_atom_saving": "384599/10000000000",
+      "ordinary_saving": "170771888233960718836822306974273386891/250000000000000000000000000000000000000000",
+      "rejected": {
+        "bad_fraction": "1/10000000000000000",
+        "edge_count": 877638,
+        "fallback_children_per_edge": 165888,
+        "fallback_lower": "3960932778213196754774196065491975232237134292046579/1101601562500000000000000000000000000000000000000000000000000000",
+        "fallback_upper": "3960932778213196754774196065491975232237135018730843/1101601562500000000000000000000000000000000000000000000000000000",
+        "lower": "3304804687500000005034672763894061432592377001145339332563639737/3304804687500000000000000000000000000000000000000000000000000000",
+        "raw": {
+          "lower": "676823999997566403932166793959370515332280540251879/676824000000000000000000000000000000000000000000000",
+          "saving": "341764095528129/500000000000000000",
+          "strict_gap_lower": "811198689277735346876494889239815434533/225608000000000000000000000000000000000000000000000",
+          "terms": [
+            {
+              "child": 1,
+              "contribution_lower": "10511683113197649748982394655356863766173753874969/112804000000000000000000000000000000000000000000000",
+              "contribution_upper": "10511683113197649748982394655356863766173755803473/112804000000000000000000000000000000000000000000000",
+              "exp_lower": "1002927498635402132333021148302343647187649449/1000000000000000000000000000000000000000000000",
+              "exp_upper": "1002927498635402132333021148302343647187649633/1000000000000000000000000000000000000000000000",
+              "log_lower": "2138333059508027655521093419109790556760740759/500000000000000000000000000000000000000000000",
+              "log_upper": "4276666119016055311042186838219581113521481519/1000000000000000000000000000000000000000000000",
+              "multiplicity": 377316
+            },
+            {
+              "child": 2,
+              "contribution_lower": "29398922664984588151218514697473426650542808947899/338412000000000000000000000000000000000000000000000",
+              "contribution_upper": "1224955111041024506300771445728059443772617062713/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "1002452438537340612787483025794436070874716437/1000000000000000000000000000000000000000000000",
+              "exp_upper": "125306554817167576598435378224304508859339557/125000000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/125000000000000000000000000000000000000000000",
+              "log_upper": "716703787691222000324990943352280909089196277/200000000000000000000000000000000000000000000",
+              "multiplicity": 175962
+            },
+            {
+              "child": 3,
+              "contribution_lower": "774931548511265914330666551537226706267952858051/11280400000000000000000000000000000000000000000000",
+              "contribution_upper": "3099726194045063657322666206148906825071811447669/45121600000000000000000000000000000000000000000000",
+              "exp_lower": "250543662628925287530121743141683383856434807/250000000000000000000000000000000000000000000",
+              "exp_upper": "1002174650515701150120486972566733535425739233/1000000000000000000000000000000000000000000000",
+              "log_lower": "39725672879349320245586770016213192610924887/12500000000000000000000000000000000000000000",
+              "log_upper": "3178053830347945619646941601297055408873990961/1000000000000000000000000000000000000000000000",
+              "multiplicity": 92790
+            },
+            {
+              "child": 4,
+              "contribution_lower": "800580105166633650886434816742396325870941169353/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "800580105166633650886434816742396325870941170951/28201000000000000000000000000000000000000000000000",
+              "exp_lower": "1001977603462620339031833312568706290201428247/1000000000000000000000000000000000000000000000",
+              "exp_upper": "1001977603462620339031833312568706290201428249/1000000000000000000000000000000000000000000000",
+              "log_lower": "462459481263386350753235615248516476379277/160000000000000000000000000000000000000000",
+              "log_upper": "2890371757896164692207722595303227977370481251/1000000000000000000000000000000000000000000000",
+              "multiplicity": 28764
+            },
+            {
+              "child": 5,
+              "contribution_lower": "134745434063363471369317674878376412486299423793/4512160000000000000000000000000000000000000000000",
+              "contribution_upper": "53898173625345388547727069951350564994519769571/1804864000000000000000000000000000000000000000000",
+              "exp_lower": "500912394287596547841329646388016403294793397/500000000000000000000000000000000000000000000",
+              "exp_upper": "200364957715038619136531858555206561317917359/200000000000000000000000000000000000000000000",
+              "log_lower": "666807051645488734110356876248348368498970041/250000000000000000000000000000000000000000000",
+              "log_upper": "533445641316390987288285500998678694799176033/200000000000000000000000000000000000000000000",
+              "multiplicity": 24210
+            },
+            {
+              "child": 6,
+              "contribution_lower": "259941136252152703522960201498974640780078277823/14100500000000000000000000000000000000000000000000",
+              "contribution_upper": "103976454500861081409184080599589856312031311233/5640200000000000000000000000000000000000000000000",
+              "exp_lower": "500849973510891528945973413292822043892251017/500000000000000000000000000000000000000000000",
+              "exp_upper": "200339989404356611578389365317128817556900407/200000000000000000000000000000000000000000000",
+              "log_lower": "1242453324894000155114854739919439420399245413/500000000000000000000000000000000000000000000",
+              "log_upper": "2484906649788000310229709479838878840798490827/1000000000000000000000000000000000000000000000",
+              "multiplicity": 12456
+            },
+            {
+              "child": 7,
+              "contribution_lower": "14898716806051850623311815338753039446050619549/705025000000000000000000000000000000000000000000",
+              "contribution_upper": "119189734448414804986494522710024315568404956511/5640200000000000000000000000000000000000000000000",
+              "exp_lower": "125199300891192022044637103687000331479416971/125000000000000000000000000000000000000000000",
+              "exp_upper": "1001594407129536176357096829496002651835335769/1000000000000000000000000000000000000000000000",
+              "log_lower": "2330755969960742005936834094776401383884396789/1000000000000000000000000000000000000000000000",
+              "log_upper": "233075596996074200593683409477640138388439679/100000000000000000000000000000000000000000000",
+              "multiplicity": 12240
+            },
+            {
+              "child": 8,
+              "contribution_lower": "419629754194649915170212265640785213094301847399/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "209814877097324957585106132820392606547150923909/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "1001502993304653735489766743772757071824109421/1000000000000000000000000000000000000000000000",
+              "exp_upper": "500751496652326867744883371886378535912054711/500000000000000000000000000000000000000000000",
+              "log_lower": "439444915467243876558098094769010281858996223/200000000000000000000000000000000000000000000",
+              "log_upper": "549306144334054845697622618461262852323745279/250000000000000000000000000000000000000000000",
+              "multiplicity": 7542
+            },
+            {
+              "child": 9,
+              "contribution_lower": "657934495461879262893783874509963835063776109839/56402000000000000000000000000000000000000000000000",
+              "contribution_upper": "20560452983183726965430746078436369845743003453/1762562500000000000000000000000000000000000000000",
+              "exp_lower": "1001422367521886244891604070791421362349735327/1000000000000000000000000000000000000000000000",
+              "exp_upper": "31294448985058945152862627212231917573429229/31250000000000000000000000000000000000000000",
+              "log_lower": "2079441541679835928251696364374529704226500403/1000000000000000000000000000000000000000000000",
+              "log_upper": "519860385419958982062924091093632426056625101/250000000000000000000000000000000000000000000",
+              "multiplicity": 5256
+            },
+            {
+              "child": 10,
+              "contribution_lower": "33745503452013138557714288888451500295165494849/2256080000000000000000000000000000000000000000000",
+              "contribution_upper": "337455034520131385577142888884515002951654948827/22560800000000000000000000000000000000000000000000",
+              "exp_lower": "100135025080157681180161094624485164080609777/100000000000000000000000000000000000000000000",
+              "exp_upper": "1001350250801576811801610946244851640806097771/1000000000000000000000000000000000000000000000",
+              "log_lower": "197408102602200962702419538353521690592038003/100000000000000000000000000000000000000000000",
+              "log_upper": "1974081026022009627024195383535216905920380031/1000000000000000000000000000000000000000000000",
+              "multiplicity": 6066
+            },
+            {
+              "child": 11,
+              "contribution_lower": "139053456842340965788403892389153700900793289263/14100500000000000000000000000000000000000000000000",
+              "contribution_upper": "222485530947745545261446227822645921441269263043/22560800000000000000000000000000000000000000000000",
+              "exp_lower": "125160627220828952104773980548293160126726633/125000000000000000000000000000000000000000000",
+              "exp_upper": "200257003553326323367638368877269056202762613/200000000000000000000000000000000000000000000",
+              "log_lower": "234846355777210595872530407531806476712471833/125000000000000000000000000000000000000000000",
+              "log_upper": "375754169243536953396048652050890362739954933/200000000000000000000000000000000000000000000",
+              "multiplicity": 3636
+            },
+            {
+              "child": 12,
+              "contribution_lower": "2033488926284435676190047055037258046069305218257/56402000000000000000000000000000000000000000000000",
+              "contribution_upper": "31773264473194307440469485234957156969832894067/881281250000000000000000000000000000000000000000",
+              "exp_lower": "1001225468382292307331387028575705586444758847/1000000000000000000000000000000000000000000000",
+              "exp_upper": "15644147943473317302052922321495399788199357/15625000000000000000000000000000000000000000",
+              "log_lower": "447939867307013750203119339595175568180747673/250000000000000000000000000000000000000000000",
+              "log_upper": "1791759469228055000812477358380702272722990693/1000000000000000000000000000000000000000000000",
+              "multiplicity": 12186
+            },
+            {
+              "child": 13,
+              "contribution_lower": "176356217287721109910232736245860182113911727773/11280400000000000000000000000000000000000000000000",
+              "contribution_upper": "3527124345754422198204654724917203642278234558983/225608000000000000000000000000000000000000000000000",
+              "exp_lower": "50058534569321915955217921159767295519134751/50000000000000000000000000000000000000000000",
+              "exp_upper": "1001170691386438319104358423195345910382695021/1000000000000000000000000000000000000000000000",
+              "log_lower": "1711716761554518574988699396654262508716213573/1000000000000000000000000000000000000000000000",
+              "log_upper": "855858380777259287494349698327131254358106787/500000000000000000000000000000000000000000000",
+              "multiplicity": 4878
+            },
+            {
+              "child": 14,
+              "contribution_lower": "268049874238418173352769852508793322631851244227/7050250000000000000000000000000000000000000000000",
+              "contribution_upper": "1072199496953672693411079410035173290527404977979/28201000000000000000000000000000000000000000000000",
+              "exp_lower": "250279994620371777173454577505876118237022637/250000000000000000000000000000000000000000000",
+              "exp_upper": "1001119978481487108693818310023504472948090549/1000000000000000000000000000000000000000000000",
+              "log_lower": "818804394700398348259800986659112407904448327/500000000000000000000000000000000000000000000",
+              "log_upper": "327521757880159339303920394663644963161779331/200000000000000000000000000000000000000000000",
+              "multiplicity": 11016
+            },
+            {
+              "child": 15,
+              "contribution_lower": "27028964741547167365061911827864024825587317413/2820100000000000000000000000000000000000000000000",
+              "contribution_upper": "84465514817334898015818474462075077579960367/8812812500000000000000000000000000000000000000",
+              "exp_lower": "1001072768205450643150441178809778697243974719/1000000000000000000000000000000000000000000000",
+              "exp_upper": "3128352400642033259845128683780558428887421/3125000000000000000000000000000000000000000",
+              "log_lower": "784307958956922622523091134035433884674194803/500000000000000000000000000000000000000000000",
+              "log_upper": "1568615917913845245046182268070867769348389607/1000000000000000000000000000000000000000000000",
+              "multiplicity": 2592
+            },
+            {
+              "child": 16,
+              "contribution_lower": "249256123381269024857315202956775449558601790791/7050250000000000000000000000000000000000000000000",
+              "contribution_upper": "778925385566465702679110009239923279870630597/22032031250000000000000000000000000000000000000",
+              "exp_lower": "1001028607956903714286406437577411444010448959/1000000000000000000000000000000000000000000000",
+              "exp_upper": "3128214399865324107145020117429410762532653/3125000000000000000000000000000000000000000",
+              "log_lower": "1504077396776274073373258352386874841219480981/1000000000000000000000000000000000000000000000",
+              "log_upper": "752038698388137036686629176193437420609740491/500000000000000000000000000000000000000000000",
+              "multiplicity": 8964
+            },
+            {
+              "child": 17,
+              "contribution_lower": "240362034003942390226915520783315500799503694047/14100500000000000000000000000000000000000000000000",
+              "contribution_upper": "1922896272031539121815324166266524006396029554297/112804000000000000000000000000000000000000000000000",
+              "exp_lower": "125123390944269854360705632890846174283968607/125000000000000000000000000000000000000000000",
+              "exp_upper": "1000987127554158834885645063126769394271748857/1000000000000000000000000000000000000000000000",
+              "log_lower": "721726387479919615396326110173227288966639253/500000000000000000000000000000000000000000000",
+              "log_upper": "1443452774959839230792652220346454577933278507/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4068
+            },
+            {
+              "child": 18,
+              "contribution_lower": "2423295157302276481256702517951027953719710729807/112804000000000000000000000000000000000000000000000",
+              "contribution_upper": "605823789325569120314175629487756988429927683057/28201000000000000000000000000000000000000000000000",
+              "exp_lower": "1000948020364426468920571052437434099016815667/1000000000000000000000000000000000000000000000",
+              "exp_upper": "250237005091106617230142763109358524754203917/250000000000000000000000000000000000000000000",
+              "log_lower": "346573590279972654708616060729088284037750067/250000000000000000000000000000000000000000000",
+              "log_upper": "1386294361119890618834464242916353136151000269/1000000000000000000000000000000000000000000000",
+              "multiplicity": 4842
+            },
+            {
+              "child": 19,
+              "contribution_lower": "256733679077656215305610445612608029367647776653/28201000000000000000000000000000000000000000000000",
+              "contribution_upper": "513467358155312430611220891225216058735295553819/56402000000000000000000000000000000000000000000000",
+              "exp_lower": "500455514771259678958304962207812922743952781/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000911029542519357916609924415625845487905563/1000000000000000000000000000000000000000000000",
+              "log_lower": "1332227139849614851033159406331727576284102257/1000000000000000000000000000000000000000000000",
+              "log_upper": "666113569924807425516579703165863788142051129/500000000000000000000000000000000000000000000",
+              "multiplicity": 1944
+            },
+            {
+              "child": 20,
+              "contribution_lower": "688102207240174765159973415312750125157608663/8812812500000000000000000000000000000000000000",
+              "contribution_upper": "11009635315842796242559574645004002002521738619/141005000000000000000000000000000000000000000000",
+              "exp_lower": "62554746112743160469088492301159102287055333/62500000000000000000000000000000000000000000",
+              "exp_upper": "1000875937803890567505415876818545636592885329/1000000000000000000000000000000000000000000000",
+              "log_lower": "256186769092412863521392652415408067568975979/200000000000000000000000000000000000000000000",
+              "log_upper": "160116730682758039700870407759630042230609987/125000000000000000000000000000000000000000000",
+              "multiplicity": 15840
+            },
+            {
+              "child": 21,
+              "contribution_lower": "52607287465288342696140830259030662573398196361933/225608000000000000000000000000000000000000000000000",
+              "contribution_upper": "1643977733290260709254400945594708205418693637953/7050250000000000000000000000000000000000000000000",
+              "exp_lower": "1000842559695762089228941085155540257850544991/1000000000000000000000000000000000000000000000",
+              "exp_upper": "31276329990492565288404408911110633057829531/31250000000000000000000000000000000000000000",
+              "log_lower": "1232143681292632314541588857853875679236906231/1000000000000000000000000000000000000000000000",
+              "log_upper": "154017960161579039317698607231734459904613279/125000000000000000000000000000000000000000000",
+              "multiplicity": 45054
+            },
+            {
+              "child": 22,
+              "contribution_lower": "765119807418262539528342677780293609435951597177/7050250000000000000000000000000000000000000000000",
+              "contribution_upper": "1530239614836525079056685355560587218871903195883/14100500000000000000000000000000000000000000000000",
+              "exp_lower": "500405367834050058553526931183972275628483713/500000000000000000000000000000000000000000000",
+              "exp_upper": "1000810735668100117107053862367944551256967427/1000000000000000000000000000000000000000000000",
+              "log_lower": "118562366565773945756301113879627524562427453/100000000000000000000000000000000000000000000",
+              "log_upper": "1185623665657739457563011138796275245624274531/1000000000000000000000000000000000000000000000",
+              "multiplicity": 20016
+            }
+          ],
+          "upper": "225607999999188801310722264653123505110760184565467/225608000000000000000000000000000000000000000000000"
+        },
+        "saving": "341764095528129/500000000000000000",
+        "strict_gap_lower": "-1678224254631353810864125688930806470956230843/1101601562500000000000000000000000000000000000000000000000000000",
+        "upper": "1101601562500000001678224254631353810864125688930806470956230843/1101601562500000000000000000000000000000000000000000000000000000"
+      },
+      "scope": "Adjacent coarse exclusion for this fixed worst-case bad-class envelope and least atom on the stated grid; no true bad-fraction or global optimality claim."
+    },
+    "independent_moment_gap": "5708313417552449916044781731/10000000000000000000000000000000000000000000000",
+    "leaf_chain": [
+      "3415437309999000117/5000000000000000000000",
+      "34176389940577246775518727877/50000000000000000000000000000000",
+      "341764049897064613783917014425801828437/500000000000000000000000000000000000000000",
+      "3417640499999296407710369546074281409147680685797/5000000000000000000000000000000000000000000000000000"
+    ],
+    "pr184": {
+      "atom_exponent": "683087463/1000000000000",
+      "bad_moment_upper": "2632491368089083391024603745163036852599241/732139818537703369760942634901679636480000000000000000",
+      "counts": {
+        "W": "56402/3",
+        "delta": "1936",
+        "edge_count": "292546",
+        "histogram": {
+          "1": "125772",
+          "10": "2022",
+          "11": "1212",
+          "12": "4062",
+          "13": "1626",
+          "14": "3672",
+          "15": "864",
+          "16": "2988",
+          "17": "1356",
+          "18": "1614",
+          "19": "648",
+          "2": "58654",
+          "20": "5280",
+          "21": "15018",
+          "22": "6672",
+          "3": "30930",
+          "4": "9588",
+          "5": "8070",
+          "6": "4152",
+          "7": "4080",
+          "8": "2514",
+          "9": "1752"
+        },
+        "m": 72,
+        "mass": "1351712",
+        "maxchild": 22
+      },
+      "effective_saving": "3415437309999000117/5000000000000000000000",
+      "effective_saving_decimal": 0.0006830874619998,
+      "ideal_moment_upper": "899653408844498940210600447043678369429283/899653409019129900762246309767183937306624",
+      "numerical_root_for_discovery_only": 0.0006835281927731371,
+      "ordinary_leaf_saving": "384599/10000000000",
+      "saving": "6835281/10000000000",
+      "strict_gap_lower": "418447644430024406866734704090050440223452277/2196419455613110109282827904705038909440000000000000000",
+      "strict_gap_lower_decimal": 1.9051353937001922e-10
+    },
+    "profile": {
+      "R": 17114,
+      "W_per_vertex": "56402/3",
+      "active_virtual_R": 18874,
+      "bank": {
+        "deleted_terminal_sinks": 34,
+        "entrance_gauges": 2200,
+        "entrance_rank": 20,
+        "moment_normalization_scale": 3,
+        "physical_chains_spliced": true,
+        "physical_replica_count": 9,
+        "selected_banks_per_stage": 1100,
+        "selected_blocks": 18,
+        "selected_width": 4,
+        "stages": 3,
+        "undeferred_banks_per_stage": 44742,
+        "undeferred_blocks": 3,
+        "undeferred_physical_roles": 14914,
+        "undeferred_width": 24
+      },
+      "bank_roles_per_vertex": "45842/3",
+      "changed_operation_frames": 7282,
+      "child_histogram": {
+        "1": 125772,
+        "10": 2022,
+        "11": 1212,
+        "12": 4062,
+        "13": 1626,
+        "14": 3672,
+        "15": 864,
+        "16": 2988,
+        "17": 1356,
+        "18": 1614,
+        "19": 648,
+        "2": 58654,
+        "20": 5280,
+        "21": 15018,
+        "22": 6672,
+        "3": 30930,
+        "4": 9588,
+        "5": 8070,
+        "6": 4152,
+        "7": 4080,
+        "8": 2514,
+        "9": 1752
+      },
+      "deficit_per_vertex": 1936,
+      "foreign_producer_replays": 0,
+      "frames_not_contained_in_original": 84,
+      "h": 24,
+      "loss": 528,
+      "m": 72,
+      "maxchild": 22,
+      "physical_internal_histogram": {
+        "1": 35764,
+        "10": 674,
+        "11": 404,
+        "12": 1354,
+        "13": 542,
+        "14": 1207,
+        "15": 288,
+        "16": 993,
+        "17": 452,
+        "18": 533,
+        "19": 208,
+        "2": 17469,
+        "21": 4160,
+        "22": 1344,
+        "3": 10301,
+        "4": 3196,
+        "5": 2673,
+        "6": 1384,
+        "7": 1359,
+        "8": 838,
+        "9": 583
+      },
+      "physical_roles_before_banks": 17114,
+      "physical_target_histogram": {
+        "1": 4400,
+        "14": 17,
+        "16": 3,
+        "18": 5,
+        "19": 8,
+        "2": 29,
+        "20": 880,
+        "21": 846,
+        "3": 9,
+        "5": 17,
+        "7": 1,
+        "9": 1
+      },
+      "rank_per_vertex": 1351712,
+      "reused_registers": 1760,
+      "scalar_role_reserve": 18908,
+      "selected_rank_histogram": {
+        "20": 2200
+      },
+      "selected_roles": 2200,
+      "terminal_sinks": 34,
+      "v": 1760,
+      "virtual_R": 18908
+    },
+    "unpacked": {
+      "R": 17114,
+      "W_per_vertex": 20634,
+      "maxchild": 60,
+      "rank_per_vertex": 1483712
+    }
+  },
+  "complex": {
+    "saving": "219037/312500000",
+    "source": "research/source-assisted-v4/certificate.json complex_profile"
+  },
+  "controls": {
+    "unpacked_pr200_kappa_pr199_leaf": "1693287/2500000000",
+    "unpacked_pr200_kappa_pr202": "6768823/10000000000"
+  },
+  "gain_over_pr194": "156287/6674324",
+  "gain_over_pr202": "61788/6768823",
+  "kappa": "6830611/10000000000",
+  "kappa_decimal": 0.0006830611,
+  "kappa_without_leaf": "6826211/10000000000",
+  "mutations_rejected": [
+    "sink role counted as a live bank chain",
+    "live chain added to the deleted sinks",
+    "corrupted packed rank mass",
+    "missing rank60 exterior",
+    "wrong entrance chart residual"
+  ],
+  "references": {
+    "git_blobs_verified": true,
+    "ported_pr186_functions": [
+      "bank_projectors",
+      "certify",
+      "independent_bank_moment",
+      "paid_moment"
+    ],
+    "vendored_files": 14
+  },
+  "scope": "Finite checks of the literal PR200 word, the completed bank endpoints, exact charts and paid moments; the bank schedule, weighted compiler, routing, stage cover and all-size transfer remain the conditional contracts of PR186, the round-8 supplement and PR184.",
+  "status": "PASS conditional finite witness",
+  "terminal_word": {
+    "controls": {
+      "omit-ancestor-response": "REJECTED",
+      "omit-pre-target": "REJECTED",
+      "omit-write": "REJECTED"
+    },
+    "deleted_sink_roles": [
+      8660,
+      8939,
+      9811,
+      10525,
+      11085,
+      11089,
+      12631,
+      12634,
+      12705,
+      12708,
+      12782,
+      12856,
+      12930,
+      13004,
+      14076,
+      14094,
+      14112,
+      14130,
+      14148,
+      14166,
+      14184,
+      14202,
+      14220,
+      14425,
+      14437,
+      14449,
+      14698,
+      14708,
+      14718,
+      14728,
+      14738,
+      14748,
+      14758,
+      14768
+    ],
+    "formal": [
+      {
+        "all_outputs": true,
+        "all_sources_and_dirty_restored": true,
+        "direction": 1,
+        "dirty_columns": 17114,
+        "formal_columns": 20634,
+        "mode": "F2",
+        "partner_mix_unmix_at_original_anchors": true,
+        "retained_cleanup_literal_reverse": true,
+        "source_columns": 1760,
+        "target_columns": 1760
+      },
+      {
+        "all_outputs": true,
+        "all_sources_and_dirty_restored": true,
+        "direction": 1,
+        "dirty_columns": 17114,
+        "formal_columns": 20634,
+        "mode": "Z",
+        "partner_mix_unmix_at_original_anchors": true,
+        "retained_cleanup_literal_reverse": true,
+        "source_columns": 1760,
+        "target_columns": 1760
+      },
+      {
+        "all_outputs": true,
+        "all_sources_and_dirty_restored": true,
+        "direction": -1,
+        "dirty_columns": 17114,
+        "formal_columns": 20634,
+        "mode": "Z",
+        "partner_mix_unmix_at_original_anchors": true,
+        "retained_cleanup_literal_reverse": true,
+        "source_columns": 1760,
+        "target_columns": 1760
+      }
+    ],
+    "integer_residual_bound": 39780,
+    "status": "PASS complete terminal bit word, exact geometry/ledger/F2/integer columns"
+  }
+}
diff --git a/research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json b/research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json
new file mode 100644
index 0000000000..ebf70ec2ae
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json
@@ -0,0 +1,199 @@
+{
+  "a_bit": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "a_complex": "700918443859411/1000000000000000000",
+  "adjacent_kappa_rejected": true,
+  "assembly": {
+    "absorption_gap": "134281643351448469855595122809435201472739986862783885293176478497632435149777090241037553043786318538250810999419972289/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711000000000000000000000000",
+    "margins": {
+      "Gaussian_arithmetic": "269255886111883479314991099644648533713048750891109557636200948729645684632351887487203757789591105011931098889929870370327450919972289/394115409732265729633160997421775731199794069476514498167468200820023068506193706555112716272207407476078528044337600000000000000000000000",
+      "balanced_prefix": "168284928819927174572023388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "bulk_exposure": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "compact_phase_layer": "168284928819927174571777066478749333790272697198172744835625641220994994809711929319935155711813301482483082263329870370327450919972289/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711000000000000000000000000",
+      "coordinate_movement": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "dimension": "246153846153846153846153600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "scalar_work": "1346279430559417396575940786747573332889326656949102227509004228821919709407178107938068846619221009326043276240329870370327450919972289/1970577048661328648165804987108878655998970347382572490837341004100115342530968532775563581361037037380392640221688000000000000000000000000"
+    },
+    "minimum_margin": "168284928819927174571777066478749333790272697198172744835625641220994994809711929319935155711813301482483082263329870370327450919972289/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711000000000000000000000000",
+    "parameters": {
+      "C0": {
+        "base": 2,
+        "exponent": 210000
+      },
+      "C1": 1,
+      "a_bit": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "a_complex": "700918443859411/1000000000000000000",
+      "alpha_squared_power": "336569857639854349143800455088581333661566120019734099503251153735412811180778526265382825841442974031563109974329870370327450919972289/492644262165332162041451246777219663999742586845643122709335251025028835632742133193890895340259259345098160055422000000000000000000000000",
+      "beta": "1/1000000000000000000000000",
+      "c": "2187704074659053269433904051927815998326814496680297610679131662687431612823865760290819711685185743138040360243/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "delta": "1/8000000000000000000000000",
+      "epsilon": "246153846153846153846153600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "eta": "1/1000000000000000000000000",
+      "kappa": "1366380910073/2000000000000000",
+      "lambda_": "6395624591850681893461133787520736218685239832140422550106711103807918410980047703259889301788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "lambda_prime": "3197812295925340946730566895948072184001673185503319702389320868337312568387176134239709180288314814256861959639757/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "q": "2187704074659053269433104051927815998326814496680297610679131662687431612823865760290819711685185743138040360243/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "sigma": "999299081556140589/1000000000000000000",
+      "tau": "6395624591850681893461133783145328069367133293274205695434780470941211685185743138040360243/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+    },
+    "recurrence": {
+      "internal": "6395624591850681893461133783145328069367133293274205695434780470941211685185743138040360243/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "leaf": "999299081556140589000000000700918443859411/1000000000000000000000000000000000000000000",
+      "reservations": "3197812295925340946730566095948072184001673185503319702389320868337312568387176134239709180288314814256861959639757/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+    },
+    "strict_constraints": {
+      "Gaussian_arithmetic_above_kappa": "214850777155596201368600808930470355522283178903230270162019178396787203748294034208300043037326711738979101128519972289/394115409732265729633160997421775731199794069476514498167468200820023068506193706555112716272207407476078528044337600000000000000000000000",
+      "K_dominates_log": "168284928819927174571838604940287795328734235598172744835625641220994994809711929319935155711813301482483082263329870370327450919972289/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711000000000000000000000000",
+      "K_geometry": "184783669544204542559187223388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711000000000000000000000000",
+      "alpha_below_one": "492307692307692307692307446322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/492644262165332162041451246777219663999742586845643122709335251025028835632742133193890895340259259345098160055422000000000000000000000000",
+      "alpha_below_one_fourth": "122824495683693186161219011239216334666274080591391046577830561602521796097004754772207341009223371862242976903881170129629672549080027711/492644262165332162041451246777219663999742586845643122709335251025028835632742133193890895340259259345098160055422000000000000000000000000",
+      "alpha_positive": "336569857639854349143800455088581333661566120019734099503251153735412811180778526265382825841442974031563109974329870370327450919972289/492644262165332162041451246777219663999742586845643122709335251025028835632742133193890895340259259345098160055422000000000000000000000000",
+      "artificial_boundary": "13795385620059859954557211835837422495990005841237450092528224032414803008712432326207385188431549748156340912609847010388889017647240083133/1970577048661328648165804987108878655998970347382572490837341004100115342530968532775563581361037037380392640221688000000000000000000000000",
+      "balanced_prefix_above_kappa": "268563779347159105043352287070117180165143973468154616229475666330515895328389813224208299978467977335760967097/492644262165332162041451246777219663999742586845643122709335251025028835632742133193890895340259259345098160055422000000000000000",
+      "beta_below_one": "999999999999999999999999/1000000000000000000000000",
+      "beta_positive": "1/1000000000000000000000000",
+      "bit_positive": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "bulk_exposure_above_kappa": "2989237084506538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "c_below_one": "3197812295925340946730566095948072184001673185503319702389320868337312568387176134239709180288314814256861959639757/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "c_positive": "2187704074659053269433904051927815998326814496680297610679131662687431612823865760290819711685185743138040360243/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cell_above_band": "492307692307692307692306953677868917333918979274376611390168000128706577178438645332374487485582183628933403054552329870370327450919972289/985288524330664324082902493554439327999485173691286245418670502050057671265484266387781790680518518690196320110844000000000000000000000000",
+      "compact_leaf": "55234945691061930566893705133163651557985503319702389320868337312568387176134239709180288314814256861959639757/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "compact_phase_layer_above_kappa": "134281643351448469855595122809435201472739986862783885293176478497632435149777090241037553043786318538250810999419972289/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711000000000000000000000000",
+      "compact_reservations": "1/4000000000000000000000000",
+      "complex_above_bit": "110469891382123861133783145328069367133293274205695434780470941211685185743138040360243/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "complex_below_one_over32": "30549081556140589/1000000000000000000",
+      "coordinate_movement_above_kappa": "2989237084506538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "delta_below_one_eighth": "999999999999999999999999/8000000000000000000000000",
+      "delta_positive": "1/8000000000000000000000000",
+      "dimension_above_kappa": "491971122450052453611726932569939441043609700224474057455808722443125780596733533136624999988130553879110139923045977335760967097/492644262165332162041451246777219663999742586845643122709335251025028835632742133193890895340259259345098160055422000000000000000",
+      "epsilon_below_one": "168284928819927174572023388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "epsilon_positive": "246153846153846153846153600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "gamma_sublinear": "1/2000000000000000000000000",
+      "guard_width": "168284928819927174572023388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "lambda_above_internal": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "lambda_above_sigma": "110469891382123861133787520736218685239832140422550106711103807918410980047703259889301788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "lambda_above_tau": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "lambda_prime_above_lambda": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "lambda_prime_below_one": "2187704074659053269433104051927815998326814496680297610679131662687431612823865760290819711685185743138040360243/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "leaf_saving_above_bit": "110469891382123861133778659450028666902893274205695434780470941211685185743138040360243/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "literal_scalar_guard": "1",
+      "phase_boundary": "269255886111883479314991099644648533713048750891109557636200948729645684632351887487203757789591105011931098889929870370327450919972289/394115409732265729633160997421775731199794069476514498167468200820023068506193706555112716272207407476078528044337600000000000000000000000",
+      "phase_local": "1346279430559417396575940786747573332889326656949102227509004228821919709407178107938068846619221009326043276240329870370327450919972289/1970577048661328648165804987108878655998970347382572490837341004100115342530968532775563581361037037380392640221688000000000000000000000000",
+      "prime_interval_packing": "168284928819927174572023388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "q_below_internal": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "q_below_leaf": "55234945691061930566893705133163651557985503319702389320868337312568387176134239709180288314814256861959639757/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "q_below_reservations": "1/4000000000000000000000000",
+      "q_positive": "2187704074659053269433104051927815998326814496680297610679131662687431612823865760290819711685185743138040360243/3200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "record_suffix": "168284928819927174572023388609831999871293422821561354667625512514417816371066596945447670129629672549080027711/246322131082666081020725623388609831999871293422821561354667625512514417816371066596945447670129629672549080027711",
+      "row_product_gap": "23971789/25",
+      "scalar_work_above_kappa": "1074254871066505337507328127554845332050743894001325042096341310654438068799141436525766602968424239213414195838919972289/1970577048661328648165804987108878655998970347382572490837341004100115342530968532775563581361037037380392640221688000000000000000000000000",
+      "short_record_fallback": "1574306855524918884571274205389066327000920465903440952946365445540569604237553260610885033093742760664679982409998088157882306036774103883673142683918570723766876330273287070119111281479259396462862693773/1576461638929062918532643989687102924799176277906057992669872803280092274024774826220450865088829629904314112177350400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "small_field_exposure": "1/1000000000000000000000000"
+    }
+  },
+  "beta": "1/1000000000000000000000000",
+  "binding": "bit",
+  "bit": {
+    "accepted": {
+      "lower": "1652402343749999997851238800561347063905497669045666488650474907/1652402343750000000000000000000000000000000000000000000000000000",
+      "saving": "136731504666219/200000000000000000",
+      "strict_gap_lower": "2438016547619109504615743675878715911813/676824000000000000000000000000000000000000000000000",
+      "upper": "1652402343749999997851238800561347063905497701989363999508104809/1652402343750000000000000000000000000000000000000000000000000000"
+    },
+    "next_excluded": {
+      "lower": "8262011718750000006555831576444862302593421956910263100630461/8262011718750000000000000000000000000000000000000000000000000",
+      "saving": "85457190416387/125000000000000000",
+      "strict_gap_lower": "65013736811541319536185606023662851449/18048640000000000000000000000000000000000000000000",
+      "upper": "275400390625000000218527719214828743419780737420068666036349517/275400390625000000000000000000000000000000000000000000000000000"
+    },
+    "saving": "136731504666219/200000000000000000"
+  },
+  "bit_ordinary": "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "bit_profile": {
+    "L": 0,
+    "N": 5808,
+    "W": 56402,
+    "child_multiplicities": {
+      "1": 378477,
+      "10": 5796,
+      "11": 3627,
+      "12": 12159,
+      "13": 4806,
+      "14": 10638,
+      "15": 2808,
+      "16": 9396,
+      "17": 4284,
+      "18": 3996,
+      "19": 2790,
+      "2": 178653,
+      "20": 15840,
+      "21": 45054,
+      "22": 20016,
+      "3": 91629,
+      "4": 28737,
+      "5": 24219,
+      "6": 12096,
+      "7": 11691,
+      "8": 7344,
+      "9": 5175
+    },
+    "m": 72,
+    "maxchild": 22,
+    "total_rank": 4055136
+  },
+  "complex": {
+    "accepted": {
+      "lower": "265143999999999999505356323836919762528275607173151/265144000000000000000000000000000000000000000000000",
+      "saving": "700918443859411/1000000000000000000",
+      "strict_gap_lower": "44967606923916385224702216933483/24104000000000000000000000000000000000000000000000",
+      "upper": "24103999999999999955032393076083614775297783066517/24104000000000000000000000000000000000000000000000"
+    },
+    "next_excluded": {
+      "lower": "66286000000000000033428585232057842908390904631703/66286000000000000000000000000000000000000000000000",
+      "saving": "175229610964853/250000000000000000",
+      "strict_gap_lower": "-1162733399375924970726640217937/2305600000000000000000000000000000000000000000000",
+      "upper": "2305600000000000001162733399375924970726640217937/2305600000000000000000000000000000000000000000000"
+    },
+    "saving": "700918443859411/1000000000000000000"
+  },
+  "complex_profile": {
+    "L": 0,
+    "N": 1320,
+    "W": 12052,
+    "child_multiplicities": {
+      "1": 87534,
+      "10": 2790,
+      "11": 1062,
+      "12": 3591,
+      "13": 381,
+      "14": 2226,
+      "15": 5637,
+      "16": 264,
+      "17": 243,
+      "18": 7959,
+      "19": 501,
+      "2": 39834,
+      "20": 66,
+      "3": 29769,
+      "4": 12627,
+      "5": 5850,
+      "6": 4815,
+      "7": 2118,
+      "8": 4593,
+      "9": 1287
+    },
+    "m": 66,
+    "maxchild": 20,
+    "total_rank": 794112
+  },
+  "eta": "1/1000000000000000000000000",
+  "kappa": "1366380910073/2000000000000000",
+  "kappa_float": 0.0006831904550365,
+  "ordinary_chain": [
+    "546573370825043616599485038841961823/800000000000000000000000000000000000000",
+    "109385155514905442426418537664349652181461624755757237/160000000000000000000000000000000000000000000000000000000",
+    "21877040740002110769946254600167413306868853489797819501857050278676903/32000000000000000000000000000000000000000000000000000000000000000000000000",
+    "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "scope": "Conditional finite supplier certificate; retained all-size interfaces and analytic assumptions",
+  "status": "PASS_EXACT_47_CONSTRAINT_ASSEMBLY"
+}
diff --git a/research/composed-diagonal-bit-bootstrap/targets.json b/research/composed-diagonal-bit-bootstrap/targets.json
new file mode 100644
index 0000000000..76b1692352
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/targets.json
@@ -0,0 +1,167 @@
+{
+ "assembly_replica_check": "1693287/2500000000",
+ "bit_ladder": {
+  "1": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "12": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "16": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "2": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "3": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "4": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "6": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  },
+  "8": {
+   "binding": "complex",
+   "gain": "1777/70432",
+   "kappa": "7004273/10000000000"
+  }
+ },
+ "both_soaked": {
+  "1": {
+   "binding": "bit",
+   "gain": "272899/1707976",
+   "kappa": "15847/20000000"
+  },
+  "12": {
+   "binding": "bit",
+   "gain": "4563611/6831904",
+   "kappa": "2279103/2000000000"
+  },
+  "16": {
+   "binding": "bit",
+   "gain": "4943303/6831904",
+   "kappa": "11775207/10000000000"
+  },
+  "2": {
+   "binding": "bit",
+   "gain": "2141707/6831904",
+   "kappa": "8973611/10000000000"
+  },
+  "3": {
+   "binding": "bit",
+   "gain": "2972385/6831904",
+   "kappa": "9804289/10000000000"
+  },
+  "4": {
+   "binding": "bit",
+   "gain": "3308231/6831904",
+   "kappa": "2028027/2000000000"
+  },
+  "6": {
+   "binding": "bit",
+   "gain": "1908885/3415952",
+   "kappa": "5324837/5000000000"
+  },
+  "8": {
+   "binding": "bit",
+   "gain": "4125831/6831904",
+   "kappa": "2191547/2000000000"
+  }
+ },
+ "cheapest_ledger_both": {
+  "gain": "5225083/6831904",
+  "kappa": "12056987/10000000000"
+ },
+ "complex_side_cap": {
+  "bit_coarse_needed": "350459170788869778860671/500000000000000000000000000",
+  "gain": "1777/70432",
+  "kappa": "7004273/10000000000",
+  "kappa_decimal": 0.0007004273
+ },
+ "first_rung": {
+  "coarse": "700971690742463/1000000000000000000",
+  "share_of_smallest": 0.057,
+  "thousandths": 57
+ },
+ "frontier": {
+  "binding": "bit",
+  "bit_budget": "136731504666219/200000000000000000",
+  "complex_budget": "350459170788869778860671/500000000000000000000000000",
+  "kappa": "213497/312500000",
+  "kappa_decimal": 0.0006831904
+ },
+ "method": "PR184's unchanged assembly formula on this package's exact coarse savings",
+ "published_checks": {
+  "PR205 packed diagonal bit": {
+   "claimed": "683061299399923/1000000000000000000",
+   "coarse": "683528191056257/1000000000000000000",
+   "modelled": "1707653/2500000000",
+   "within_one_grid_step": true
+  },
+  "PR207 coordinated crossover": {
+   "claimed": "1366380910073/2000000000000000",
+   "coarse": "136731504666219/200000000000000000",
+   "modelled": "213497/312500000",
+   "within_one_grid_step": true
+  }
+ },
+ "status": "MODELLED, NOT CONSTRUCTED: these are schedules the assembly would price this way, computed from the queue's certified rows; no ledger or word is built here.",
+ "suppliers": {
+  "bit": {
+   "W": 56402,
+   "cheapest_ledger": "1207154248293627/1000000000000000000",
+   "coarse": "136731504666219/200000000000000000",
+   "deficit": "5808",
+   "edges": 879231,
+   "ladder": {
+    "1": "792978386838687/1000000000000000000",
+    "12": "5704258000893/5000000000000000",
+    "16": "589454496268959/500000000000000000",
+    "2": "898167154125293/1000000000000000000",
+    "3": "981391149202381/1000000000000000000",
+    "4": "1015042828910707/1000000000000000000",
+    "6": "1066102863416711/1000000000000000000",
+    "8": "219395123782281/200000000000000000"
+   },
+   "m": 72,
+   "maxchild": 22,
+   "rank_mass": 4055136
+  },
+  "complex": {
+   "W": 12052,
+   "cheapest_ledger": "1391081382485139/1000000000000000000",
+   "coarse": "350459221139329/500000000000000000",
+   "deficit": "1320",
+   "edges": 213147,
+   "ladder": {
+    "1": "814442339516203/1000000000000000000",
+    "12": "1315101403353627/1000000000000000000",
+    "16": "683821487170101/500000000000000000",
+    "2": "183703188422309/200000000000000000",
+    "3": "260359134293941/250000000000000000",
+    "4": "139113198609283/125000000000000000",
+    "6": "1188483794904097/1000000000000000000",
+    "8": "1243672552482743/1000000000000000000"
+   },
+   "m": 66,
+   "maxchild": 20,
+   "rank_mass": 794112
+  }
+ }
+}
diff --git a/research/composed-diagonal-bit-bootstrap/targets.py b/research/composed-diagonal-bit-bootstrap/targets.py
new file mode 100644
index 0000000000..d6e31d3325
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/targets.py
@@ -0,0 +1,276 @@
+#!/usr/bin/env python3
+"""What the next gains are worth, priced exactly.
+
+PR184's unchanged assembly takes
+
+    a = min(bit_leaf, (1-1e-9)*C_complex - 1e-10),   kappa = a/(1+a)
+
+to the `10^-10` grid, where `bit_leaf` is the finite ordinary leaf after PR185's
+bootstrap (the fixed point of `a_{n+1} = (1-C_bit)C_bit + C_bit a_n`, so `C_bit`
+itself once bootstrapped) and `C_complex` is the complex word's coarse saving. Two
+consequences drive everything below:
+
+* the **binding branch is the smaller budget**, so a gain on the stronger side is
+  worth nothing until the other side catches up, and the complex budget carries a
+  fixed `10^-10` grid step plus `1e-9` that the bit budget does not;
+* a budget is raised only by raising a word's **coarse saving** `C`, and
+
+      C = (1 - mass/(W m)) / L,   L = rank-mass-weighted mean of ln(m/r),
+
+  so at fixed stock and deficit the lever is `L`: a ledger whose residual dirt sits
+  in fewer, larger children. This script prices the ladder of such ledgers --
+  soaking children of rank at or below a threshold into the largest admissible
+  child -- for both suppliers, and reports the exact `kappa` each rung buys, with
+  the branch that binds at every rung.
+
+    python3 -B targets.py [--out targets.json]
+"""
+import argparse
+import importlib.util
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+STOP, ETA, SELECT_GRID = Q(1, 10 ** 9), Q(1, 10 ** 8), 10 ** 10
+THRESHOLDS = (1, 2, 3, 4, 6, 8, 12, 16)
+
+
+def module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    loaded = importlib.util.module_from_spec(spec)
+    sys.modules[name] = loaded
+    spec.loader.exec_module(loaded)
+    return loaded
+
+
+def assembly_kappa(budget):
+    """PR184's `assemble`, exactly: the minimum budget to the 10^-10 grid."""
+    assert 0 < budget < 1, "budget must be a saving"
+    q = budget * (1 - 2 * ETA)
+    minimum = (1 - ETA) * q / (1 + q)
+    kappa = Q(minimum.numerator * SELECT_GRID // minimum.denominator, SELECT_GRID)
+    if kappa == minimum:
+        kappa -= Q(1, SELECT_GRID)
+    return kappa
+
+
+def branch_budgets(bit_coarse, complex_coarse):
+    bit = bit_coarse                        # bootstrapped leaf, the fixed point
+    complex_ = (1 - STOP) * complex_coarse - Q(1, SELECT_GRID)
+    return bit, complex_, ("bit" if bit <= complex_ else "complex")
+
+
+def rows(profile):
+    """The family's three-copy row, whichever form the certificate stores."""
+    m = int(profile["m"])
+    key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram"
+    hist = {int(r): int(n) for r, n in profile[key].items() if n}
+    W = Q(str(profile.get("W_per_vertex", profile.get("W"))))
+    D = Q(str(profile.get("deficit_per_vertex",
+                          profile.get("N", profile.get("deficit")))))
+    for copies in (1, 3):
+        w, d = W * copies, D * copies
+        packed = {r: copies * n for r, n in hist.items()}
+        if w.denominator == 1 and m * w - sum(r * n for r, n in packed.items()) == d:
+            return m, int(w), d, packed
+    raise ValueError("no copy count satisfies the row identity")
+
+
+def soak(m, W, D, hist, threshold):
+    """Move all mass in children of rank <= threshold into the largest child.
+
+    The rank mass, the stock and the deficit are unchanged: only the shape of the
+    ledger differs, which is what a better schedule would have to deliver.
+    """
+    if threshold >= max(hist):
+        return None
+    kept = {r: n for r, n in hist.items() if r > threshold}
+    mass = m * W - D
+    remaining = mass - sum(r * n for r, n in kept.items())
+    top = max(hist)
+    for rank in range(top, 1, -1):
+        count, remaining = divmod(remaining, rank)
+        if count:
+            kept[rank] = kept.get(rank, 0) + int(count)
+    assert not remaining and sum(r * n for r, n in kept.items()) == mass
+    return kept
+
+
+def partial_soak(m, W, D, hist, threshold, thousandths):
+    """Soak only `thousandths/1000` of the mass sitting in children of rank <= threshold."""
+    kept, moved = {}, 0
+    for rank, count in hist.items():
+        if rank > threshold or thousandths == 0:
+            kept[rank] = count
+            continue
+        move = count * thousandths // 1000
+        kept[rank] = count - move
+        moved += rank * move
+    top = max(hist)
+    count, remaining = divmod(moved, top)
+    if count:
+        kept[top] = kept.get(top, 0) + count
+    if remaining:
+        kept[remaining] = kept.get(remaining, 0) + 1
+    assert sum(r * n for r, n in kept.items()) == m * W - D
+    return {r: n for r, n in kept.items() if n}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--out", type=Path, default=HERE / "targets.json")
+    args = parser.parse_args()
+    if hasattr(sys, "set_int_max_str_digits"):
+        sys.set_int_max_str_digits(0)
+    assert not sys.flags.optimize, "assertions must stay enabled"
+    interval = module("targets_interval_moment", HERE / "references/pr200/interval_moment.py")
+    levers = module("targets_levers", HERE / "levers.py")
+    pr184 = module("targets_pr184", HERE / "references/pr184/assemble_profiles.py")
+
+    queue = HERE / "references/queue/pr207-coordinated-crossover.certificate.json"
+    newest = json.loads(queue.read_text())
+    suppliers = {}
+    for side, key in (("bit", "bit_profile"), ("complex", "complex_profile")):
+        m, W, D, hist = rows(newest[key])
+        ladder = {}
+        for threshold in THRESHOLDS:
+            candidate = soak(m, W, D, hist, threshold)
+            if candidate:
+                ladder[str(threshold)] = levers.certified(
+                    interval, levers.row(m, W, D, candidate))
+        cheapest = soak(m, W, D, hist, max(hist) - 1)
+        suppliers[side] = dict(
+            m=m, W=W, deficit=str(D), rank_mass=int(m * W - D), edges=sum(hist.values()),
+            maxchild=max(hist), coarse=levers.certified(interval, levers.row(m, W, D, hist)),
+            ladder=ladder,
+            cheapest_ledger=levers.certified(interval, levers.row(m, W, D, cheapest)))
+        # Soaking more mass into larger children can only raise the coarse saving.
+        rungs = [Q(suppliers[side]["coarse"])] + [Q(ladder[k]) for k in ladder]
+        assert all(left <= right for left, right in zip(rungs, rungs[1:])), side
+        assert Q(suppliers[side]["cheapest_ledger"]) >= rungs[-1], side
+
+    # Validate the replica against PR184's own assembly on the vendored pair.
+    complex_cert = json.loads((HERE / "references/pr194/certificate.json").read_text())
+    bit_cert = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text())
+    complex_row = pr184.select(pr184.normalize(complex_cert["complex_profile"]))
+    bit_row = pr184.select(pr184.normalize(bit_cert["bit"]["profile"]), True)
+    bit_leaf = Q(bit_row["saving"])          # the bootstrap's fixed point
+    complex_coarse = Q(complex_row["saving"])
+    boot = dict(bit_row)
+    boot["effective_saving"] = bit_leaf
+    real = Q(pr184.assemble(complex_row, boot, HERE / "references/pr168-v4",
+                            HERE / "references/pr184/FINITE_BRIDGE.txt")["kappa"])
+    assert real == assembly_kappa(min(*branch_budgets(bit_leaf, complex_coarse)[:2])), \
+        "the replica must equal PR184's own assembly"
+
+    # The queue's claims, each against its own row: an independent check that the
+    # formula reproduces what three authors certified on two different words.
+    packed205 = json.loads((HERE / "references/queue/pr205-packed-diagonal-bit.certificate.json").read_text())
+    published = [("PR205 packed diagonal bit", packed205["arithmetic"]["packed_profile"],
+                  Q(683061299399923, 10 ** 18)),
+                 ("PR207 coordinated crossover", newest["bit_profile"],
+                  Q(1366380910073, 2 * 10 ** 15))]
+    checks = {}
+    for name, profile, claimed in published:
+        m, W, D, hist = rows(profile)
+        coarse = levers.certified(interval, levers.row(m, W, D, hist))
+        modelled = assembly_kappa(
+            branch_budgets(coarse, Q(suppliers["complex"]["coarse"]))[0])
+        checks[name] = dict(claimed=str(claimed), modelled=str(modelled),
+                            coarse=str(coarse),
+                            within_one_grid_step=abs(modelled - claimed) <= Q(1, SELECT_GRID))
+
+    # The cheapest first step: the smallest part of the bit word's smallest children
+    # that stops the bit branch binding, in thousandths of that population.
+    m, W, D, hist = rows(newest["bit_profile"])
+    top = max(hist)
+    first = None
+    for thousandths in range(1, 1001):
+        candidate = levers.row(m, W, D, partial_soak(m, W, D, hist, top - 1, thousandths))
+        saving = levers.certified(interval, candidate)
+        if saving >= (1 - STOP) * Q(suppliers["complex"]["coarse"]) - Q(1, SELECT_GRID):
+            first = dict(thousandths=thousandths, coarse=str(saving),
+                         share_of_smallest=float(Q(thousandths, 1000)))
+            break
+    assert first is not None, "some part of the smallest children must clear the complex side"
+
+    bit_coarse = Q(suppliers["bit"]["coarse"])
+    complex_coarse = Q(suppliers["complex"]["coarse"])
+    bit_budget, complex_budget, binding = branch_budgets(bit_coarse, complex_coarse)
+    now = assembly_kappa(min(bit_budget, complex_budget))
+    complex_only = assembly_kappa(complex_budget)
+    # The bit coarse saving this word needs to stop binding.
+    needed = complex_budget
+    bit_soaked = {k: assembly_kappa(min(Q(v), complex_budget))
+                  for k, v in suppliers["bit"]["ladder"].items()}
+    both = {}
+    for threshold, bit_value in suppliers["bit"]["ladder"].items():
+        complex_value = suppliers["complex"]["ladder"].get(threshold)
+        if complex_value:
+            pair_budget = min(Q(bit_value), (1 - STOP) * Q(complex_value) - Q(1, SELECT_GRID))
+            both[threshold] = dict(kappa=str(assembly_kappa(pair_budget)),
+                                   binding=branch_budgets(Q(bit_value), Q(complex_value))[2],
+                                   gain=str(assembly_kappa(pair_budget) / now - 1))
+    out = dict(
+        status="MODELLED, NOT CONSTRUCTED: these are schedules the assembly would price "
+               "this way, computed from the queue's certified rows; no ledger or word is "
+               "built here.",
+        method="PR184's unchanged assembly formula on this package's exact coarse savings",
+        assembly_replica_check=str(real),
+        published_checks=checks,
+        suppliers={k: dict(v, coarse=str(v["coarse"]),
+                           ladder={t: str(c) for t, c in v["ladder"].items()},
+                           cheapest_ledger=str(v["cheapest_ledger"]))
+                   for k, v in suppliers.items()},
+        first_rung=first,
+        frontier=dict(binding=binding, kappa=str(now), kappa_decimal=float(now),
+                      bit_budget=str(bit_budget), complex_budget=str(complex_budget)),
+        complex_side_cap=dict(kappa=str(complex_only), kappa_decimal=float(complex_only),
+                              gain=str(complex_only / now - 1),
+                              bit_coarse_needed=str(needed)),
+        bit_ladder={
+            t: dict(kappa=str(k), gain=str(k / now - 1),
+                    binding=branch_budgets(Q(v), complex_coarse)[2])
+            for (t, v), k in zip(suppliers["bit"]["ladder"].items(), bit_soaked.values())},
+        both_soaked=both,
+        cheapest_ledger_both=dict(
+            kappa=str(assembly_kappa(min(Q(suppliers["bit"]["cheapest_ledger"]),
+                                         (1 - STOP) * Q(suppliers["complex"]["cheapest_ledger"])
+                                         - Q(1, SELECT_GRID)))),
+            gain=str(assembly_kappa(min(Q(suppliers["bit"]["cheapest_ledger"]),
+                                        (1 - STOP) * Q(suppliers["complex"]["cheapest_ledger"])
+                                        - Q(1, SELECT_GRID))) / now - 1)),
+    )
+    args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n")
+
+    for side in ("bit", "complex"):
+        item = suppliers[side]
+        print("[{side}] m={m} W={W} deficit={deficit} rank mass={rank_mass} children={edges} "
+              "maxchild={maxchild}".format(side=side, **item))
+        print("        coarse today = {coarse}".format(**item))
+        for threshold, value in item["ladder"].items():
+            print("        soak children <= {t:>2}: coarse = {v}".format(t=threshold, v=value))
+        print("        cheapest ledger: coarse = " + str(item["cheapest_ledger"]))
+    print("[frontier] {binding} binds: kappa = {k}".format(k=now, **out["frontier"]))
+    print("[first rung] moving {t}/1000 of the mass in the bit word's children below rank "
+          "{top} into rank-{top} children is enough to clear the complex side".format(
+              t=first["thousandths"], top=top))
+    print("[complex cap] kappa = {k} ({g:+.2%}), reached when the bit coarse saving is "
+          "{n}".format(k=complex_only, g=float(complex_only / now - 1), n=needed))
+    for threshold, item in out["bit_ladder"].items():
+        print("[bit soak {t:>2}] kappa = {k} ({g:+.2%}, binding {b})".format(
+            t=threshold, k=item["kappa"], g=float(Q(item["gain"])), b=item["binding"]))
+    print("[cheapest both] kappa = {k} ({g:+.2%})".format(
+        k=out["cheapest_ledger_both"]["kappa"],
+        g=float(Q(out["cheapest_ledger_both"]["gain"]))))
+    print("[published] " + "; ".join(
+        "{k}: modelled {v[modelled]} vs claimed {v[claimed]} ({ok})".format(
+            k=k, ok="within a grid step" if v["within_one_grid_step"] else "MISMATCH",
+            **{"v": v}) for k, v in checks.items()))
+    print("[write] " + str(args.out))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py
new file mode 100644
index 0000000000..4e402a71d0
--- /dev/null
+++ b/research/composed-diagonal-bit-bootstrap/verify.py
@@ -0,0 +1,274 @@
+#!/usr/bin/env python3
+"""Verify the composed diagonal-bit bootstrap record.
+
+    python3 -B research/composed-diagonal-bit-bootstrap/verify.py
+
+Checks, in order: every pinned byte against SOURCE.json; an exact regeneration of
+certificate.json from the vendored inputs; two published cross-checks (the
+depth-0 value against PR200's announced value for this composition, and PR184's
+grid legacy leaf against PR200's published atom-wrapper value); the standing
+claim; the bit branch's own ceiling; the finite-leaf tolls; the adjacent final
+grid; and the corruption controls. The physical words are inherited pins and are
+not replayed here.
+"""
+import hashlib
+import importlib.util
+import json
+import subprocess
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+WORK = HERE / ".work"
+GRID = 10 ** 10
+OLD = Q(384599, GRID)
+
+# Published references, quoted from the open pull requests.
+PR197_KAPPA = Q(135216063303877, 200000000000000000)   # #197 packed bit: standing claim
+PR200_LEGACY_KAPPA = Q(6768823, GRID)                  # #200's own value for this composition
+PR200_THETA = Q(677340914792209011107, 10 ** 24)       # #200 README atom-wrapper exponent
+PR200_A0 = Q(677773948354561, 10 ** 18)                # #200 README bit coarse saving
+PR194_KAPPA = Q(1668581, 2500000000)                   # #194 as published
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+def rejects(name, operation, errors=(AssertionError, ValueError, KeyError)):
+    try:
+        operation()
+    except errors:
+        return name
+    raise AssertionError("control accepted: " + name)
+
+
+def tolls(coarse, leaf):
+    """compose.py's own guard, mirrored so the control exercises that condition."""
+    assert Q(leaf) < Q(coarse) < 1 - Q(leaf), "strict paid tolls"
+
+
+def main():
+    assert not sys.flags.optimize, "refusing -O"
+    if hasattr(sys, "set_int_max_str_digits"):
+        sys.set_int_max_str_digits(0)
+
+    # 1. Every pinned byte.
+    manifest = json.loads((HERE / "SOURCE.json").read_text())
+    drift = sorted(rel for rel, digest in manifest["files"].items()
+                   if sha(ROOT / rel) != digest)
+    assert not drift, ("pinned byte drift", drift)
+    print("[pins] {} package and input files match SOURCE.json".format(len(manifest["files"])))
+
+    # 2. Regenerate the certificate from the vendored inputs alone.
+    WORK.mkdir(exist_ok=True)
+    regenerated = WORK / "certificate.json"
+    if regenerated.exists():
+        regenerated.unlink()
+    subprocess.run([sys.executable, "-B", str(HERE / "compose.py"), "--out", str(regenerated)],
+                   check=True, stdout=subprocess.DEVNULL)
+    record = json.loads(regenerated.read_text())
+    assert record == json.loads((HERE / "certificate.json").read_text()), \
+        "regenerated certificate differs from the committed one"
+    print("[regenerate] certificate.json reproduced exactly from the vendored pins")
+
+    pr184 = load(HERE / "references/pr184/assemble_profiles.py", "verify_pr184")
+    bit_cert = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text())
+    complex_cert = json.loads((HERE / "references/pr194/certificate.json").read_text())
+    row = bit_cert["bit"]["profile"]
+    coarse = Q(record["bit_coarse_saving"])
+    legacy = Q(record["legacy_leaf"])
+    depths = record["depths"]
+    best_depth = max(depths, key=lambda d: Q(depths[d]["kappa"]))
+    best = Q(depths[best_depth]["kappa"])
+
+    # 3. The suppliers are the ones the certificate names.
+    assert Q(record["complex_supplier"]["saving"]) == Q(complex_cert["complex_saving"])
+    assert Q(complex_cert["kappa"]) == PR194_KAPPA, "PR194 reference"
+    assert all(depths[d]["binding"] == "bit" for d in depths), "the bit branch must bind"
+    assert all(Q(depths[d]["kappa"]) <= best for d in depths), "best is not the maximum"
+    print("[pins] complex saving = {} (PR194 as published, kappa {}), binding branch = bit at "
+          "every depth".format(record["complex_supplier"]["saving"], PR194_KAPPA))
+
+    # 4. The depth-0 row must equal what PR200 announced for this composition.
+    assert Q(depths["0"]["kappa"]) == PR200_LEGACY_KAPPA, "PR200 announced legacy value"
+    assert depths["0"]["binding"] == "bit"
+    print("[cross-check] depth 0 kappa = {} equals PR200's announced value for this "
+          "composition".format(PR200_LEGACY_KAPPA))
+
+    # 5. PR184's grid legacy leaf against PR200's published atom wrapper. The two
+    #    suppliers define the same wrapper at different precision, so the control is
+    #    what the difference does to the price: exactly one grid step at depth 0, and
+    #    nothing at all once the wrapper is bootstrapped. PR184's select() is the
+    #    pricing path the record's assembly is defined with, so the record uses it.
+    complex_row = pr184.select(pr184.normalize(complex_cert["complex_profile"]))
+    bit_row = pr184.select(pr184.normalize(row), True)
+    assert Q(bit_row["saving"]) == coarse and Q(bit_row["effective_saving"]) == legacy
+
+    def price(leaf):
+        boot = dict(bit_row)
+        boot["effective_saving"] = Q(leaf)
+        return Q(pr184.assemble(complex_row, boot, HERE / "references/pr168-v4",
+                                HERE / "references/pr184/FINITE_BRIDGE.txt")["kappa"])
+
+    published_leaf = (1 - PR200_THETA) * PR200_A0 + PR200_THETA * OLD
+    assert 0 < published_leaf - legacy < Q(1, GRID), "legacy leaf disagreement"
+    assert price(published_leaf) - price(legacy) == Q(1, GRID), "one grid step at depth 0"
+    alternative = [published_leaf]
+    for _ in range(int(best_depth)):
+        alternative.append((1 - coarse) * coarse + coarse * alternative[-1])
+    assert price(alternative[-1]) == best, "the bootstrapped price must not depend on the start"
+    print("[cross-check] PR184 legacy leaf {:.15g} vs PR200 published {:.15g} (delta {:.3g}): "
+          "one grid step at depth 0, identical at depth {}".format(
+              float(legacy), float(published_leaf), float(published_leaf - legacy), best_depth))
+
+    # 6. The standing claim, the ceiling, and the exhaustion of pricing.
+    assert best > PR197_KAPPA, "does not beat the standing claim"
+    assert best > PR200_LEGACY_KAPPA, "does not beat the unbootstrapped composition"
+    assert best > PR194_KAPPA
+    ceiling = Q(record["ceiling"])
+    assert best <= ceiling < best + Q(1, GRID), "not within one grid unit of the ceiling"
+    assert Q(depths["1"]["kappa"]) < best == Q(depths["2"]["kappa"]), "depth 2 is not the claim"
+    print("[claim] kappa = {} ({:.15g}) at depth {}; vs #197 {:+.4f}%, vs PR200 announced "
+          "{:+.4f}%".format(best, float(best), best_depth,
+                            float(best / PR197_KAPPA - 1) * 100,
+                            float(best / PR200_LEGACY_KAPPA - 1) * 100))
+    print("[ceiling] C/(1+C) = {:.15g}; the claim sits {:.3g} below it, under one grid unit "
+          "({:.1g})".format(float(ceiling), float(ceiling - best), 1 / GRID))
+
+    # 7. The finite-leaf tolls, recomputed independently in closed form.
+    assert legacy < coarse < 1 - coarse, "coarse saving must be a strict leaf toll"
+    chain = [legacy]
+    for _ in range(int(best_depth)):
+        chain.append((1 - coarse) * coarse + coarse * chain[-1])
+    assert chain[-1] == coarse - coarse ** int(best_depth) * (coarse - legacy)
+    for i in range(1, len(chain)):
+        assert chain[i - 1] < chain[i] < coarse < 1 - chain[i], "strict paid tolls"
+    assert Q(depths[best_depth]["leaf"]) == chain[-1], "recorded leaf"
+    print("[tolls] a_0 < a_1 < ... < a_{} < C < 1 - a_{}".format(best_depth, best_depth))
+
+    # 8. The assembly's minimum margin must be that closed form, and the next grid
+    #    point must lie beyond it, so no finer leaf can buy another grid step.
+    eta, stop = Q(1, 10 ** 8), Q(1, 10 ** 9)
+    q = chain[-1] * (1 - 2 * eta)
+    minimum = (1 - eta) * q / (1 + q)
+    assert Q(depths[best_depth]["minimum_margin"]) == minimum, "recorded minimum margin"
+    assert minimum < best + Q(1, GRID), "the next grid point is inside the minimum margin"
+    print("[adjacent grid] minimum margin = {:.15g} lies in (kappa, kappa + 1e-10)".format(
+        float(minimum)))
+
+    # 9. Corruption controls, each of which must be refused.
+    def accept_only_a_better_composition():
+        assert PR200_LEGACY_KAPPA > best, "the unbootstrapped value must not reach the claim"
+
+    rejected = [
+        rejects("bit profile with a perturbed W",
+                lambda: pr184.normalize(dict(row, W_per_vertex=row["W_per_vertex"] + 1))),
+        rejects("leaf at or above the coarse saving",
+                lambda: tolls(coarse, coarse + Q(1, GRID))),
+        rejects("unbootstrapped depth-0 value offered as the claim",
+                accept_only_a_better_composition),
+    ]
+    print("[controls] rejected: " + ", ".join(rejected))
+
+    # 10. The lever model: what the next word-side move is worth. It must reproduce the
+    #     three published values it can be checked on, and it must stay a model.
+    lever_out = WORK / "levers.json"
+    if lever_out.exists():
+        lever_out.unlink()
+    subprocess.run([sys.executable, "-B", str(HERE / "levers.py"), "--out", str(lever_out)],
+                   check=True, stdout=subprocess.DEVNULL)
+    levers = json.loads(lever_out.read_text())
+    assert levers == json.loads((HERE / "levers.json").read_text()), "levers.json drift"
+    for item in levers["validations"]:
+        assert item["model"] == item["published"], (
+            "the lever model must reproduce " + item["name"] + " exactly")
+    banked = levers["pr200_banked"]
+    assert Q(banked["W_per_vertex"]) == Q(56402, 3), "banked stock"
+    assert banked["W_three_copies"] == 56402 and banked["rank60_children_per_copy"] == 2200
+    assert Q(banked["ceiling"]) / Q(levers["claim"]["kappa"]) - 1 > Q(1, 200), "lever too small"
+    assert levers["status"].startswith("MODELLED"), "the lever must not be presented as built"
+    print("[levers] three published values reproduced exactly; banking the rank-60 "
+          "exterior corrections is worth {:+.4f}% of kappa ({:.10g} -> {:.10g}), which "
+          "this package models and does not build".format(
+              levers["gain_vs_claim"] * 100,
+              float(Q(levers["pr200_unpacked"]["ceiling"])),
+              float(Q(banked["ceiling"]))))
+    # 11. The queue audit: the model must price the banked rows now in the queue to exactly
+    #     the coarse savings their own certificates state, and the frontier must be the
+    #     banked row this package's lever predicted.
+    audit_out = WORK / "audit.json"
+    if audit_out.exists():
+        audit_out.unlink()
+    subprocess.run([sys.executable, "-B", str(HERE / "audit.py"), "--out", str(audit_out)],
+                   check=True, stdout=subprocess.DEVNULL)
+    audit = json.loads(audit_out.read_text())
+    assert audit == json.loads((HERE / "audit.json").read_text()), "audit.json drift"
+    for item in audit["rows"]:
+        assert item["stated_in_certificate"], (
+            "the model must reproduce " + item["name"] + " to the last digit")
+    queue_best = max(audit["rows"], key=lambda item: Q(item["coarse"]))
+    assert queue_best["name"] == audit["frontier"]["name"], "frontier row"
+    assert Q(audit["frontier"]["ceiling"]) > best, "the banked rows must now stand above this claim"
+    assert audit["cheapest_ledger_gain"] > Q(1, 2), "the ledger must be where the room is"
+    assert audit["status"].startswith("MODELLED"), "the audit must not present a construction"
+    print("[audit] {} banked rows priced to their own certificates exactly; the frontier is "
+          "{} at {:.15g}, and its cheapest admissible ledger would reach {:.10g} ({:+.1f}%), "
+          "a bound rather than a construction".format(
+              len(audit["rows"]), audit["frontier"]["name"],
+              float(Q(audit["frontier"]["ceiling"])),
+              float(Q(audit["frontier"]["cheapest_ledger"]["coarse"])),
+              audit["cheapest_ledger_gain"] * 100))
+    # 12. The frontier calculator: what each next move on the two suppliers would be
+    #     worth, from the queue's own rows. It must reproduce the published kappa of two
+    #     different authors' banked rows, keep its ladder monotone, and stay a model.
+    targets_out = WORK / "targets.json"
+    if targets_out.exists():
+        targets_out.unlink()
+    subprocess.run([sys.executable, "-B", str(HERE / "targets.py"), "--out", str(targets_out)],
+                   check=True, stdout=subprocess.DEVNULL)
+    targets = json.loads(targets_out.read_text())
+    assert targets == json.loads((HERE / "targets.json").read_text()), "targets.json drift"
+    for name, item in targets["published_checks"].items():
+        assert item["within_one_grid_step"], (
+            "the assembly replica must reproduce " + name + " to within a grid step")
+    assert targets["status"].startswith("MODELLED"), "the targets must not present a construction"
+    assert Q(targets["complex_side_cap"]["gain"]) > 0, "the complex side must cap the frontier"
+    ladder = [Q(targets["both_soaked"][key]["gain"])
+              for key in sorted(targets["both_soaked"], key=int)]
+    assert all(left < right for left, right in zip(ladder, ladder[1:])), \
+        "soaking more rank mass into larger children must buy more"
+    assert Q(targets["cheapest_ledger_both"]["gain"]) > Q(1, 2), "the ledger must be the room"
+    first = targets["first_rung"]
+    assert first and Q(first["coarse"]) >= Q(targets["complex_side_cap"]["bit_coarse_needed"]), \
+        "the first rung must clear the complex side"
+    assert Q(first["thousandths"], 1000) < Q(1, 5), "the first rung must be a small part"
+    print("[targets] the frontier is {} at {}; taking the bit word's rank-1 children into "
+          "larger ones reaches the complex side's {:.10g} ({:+.2%}), and soaking both words' "
+          "cheap children buys {:+.2%}, rising to {:+.2%} at the cheapest admissible "
+          "ledgers".format(
+              targets["frontier"]["binding"], Q(targets["frontier"]["kappa"]),
+              targets["complex_side_cap"]["kappa_decimal"],
+              float(Q(targets["complex_side_cap"]["gain"])),
+              float(Q(targets["both_soaked"]["1"]["gain"])),
+              float(Q(targets["cheapest_ledger_both"]["gain"]))))
+    print("[first rung] coarsening {:d}/1000 of the mass in the bit word's smallest children "
+          "reaches the complex side (bit coarse {} vs the {} it needs)".format(
+              first["thousandths"], Q(first["coarse"]),
+              Q(targets["complex_side_cap"]["bit_coarse_needed"])))
+    print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints "
+          "and 7 margins per depth".format(best, best_depth))
+
+
+if __name__ == "__main__":
+    main()