From 8786fec0148a41409874cad133123da227d93751 Mon Sep 17 00:00:00 2001
From: Avi Eisenberg <12200693+ikeboy@users.noreply.github.com>
Date: Fri, 9 Oct 2026 15:44:47 -0400
Subject: [PATCH] =?UTF-8?q?Conditional=20=CE=BA=20=3D=206.92144604250060e-?=
 =?UTF-8?q?4:=20served=20diagonal=20operations=20on=20PR200's=20bit=20word?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

At 373 partner-diagonal operations of PR200's bit word, the control register
is a pure copy of the passive source. These operations now read the passive
data register, the copies and their copy operations go, and those pairs'
partner mixes run right after the injections. Every PR200 frame, sink and
alias stays. PR205's banks and PR193's assembly then give
kappa = 692144604250060/10^18 (+1.088% over PR217).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 .github/workflows/served-diagonal-bit.yml     |   38 +
 research/served-diagonal-bit/NOTICE           |   28 +
 research/served-diagonal-bit/PROOF.md         |   99 +
 research/served-diagonal-bit/README.md        |   80 +
 research/served-diagonal-bit/SOURCE.json      |   35 +
 research/served-diagonal-bit/arithmetic.py    |  109 +
 research/served-diagonal-bit/audit.py         |   81 +
 research/served-diagonal-bit/banks.py         |  104 +
 .../served-diagonal-bit/bit/served_prove.py   |  104 +
 .../bit/served_terminal.py                    |  236 ++
 .../served-diagonal-bit/bit/served_word.py    |  386 +++
 research/served-diagonal-bit/certificate.json | 2084 +++++++++++++++++
 research/served-diagonal-bit/controls.py      |   35 +
 research/served-diagonal-bit/packing.py       |  145 ++
 research/served-diagonal-bit/patch.py         |  156 ++
 .../selected/served/kchron_p12.json           |    1 +
 .../selected/served/profile_p12.json          |    1 +
 .../selected/served/word_p12.json.gz          |  Bin 0 -> 729706 bytes
 research/served-diagonal-bit/verify.py        |  106 +
 19 files changed, 3828 insertions(+)
 create mode 100644 .github/workflows/served-diagonal-bit.yml
 create mode 100644 research/served-diagonal-bit/NOTICE
 create mode 100644 research/served-diagonal-bit/PROOF.md
 create mode 100644 research/served-diagonal-bit/README.md
 create mode 100644 research/served-diagonal-bit/SOURCE.json
 create mode 100644 research/served-diagonal-bit/arithmetic.py
 create mode 100644 research/served-diagonal-bit/audit.py
 create mode 100644 research/served-diagonal-bit/banks.py
 create mode 100644 research/served-diagonal-bit/bit/served_prove.py
 create mode 100644 research/served-diagonal-bit/bit/served_terminal.py
 create mode 100644 research/served-diagonal-bit/bit/served_word.py
 create mode 100644 research/served-diagonal-bit/certificate.json
 create mode 100644 research/served-diagonal-bit/controls.py
 create mode 100644 research/served-diagonal-bit/packing.py
 create mode 100644 research/served-diagonal-bit/patch.py
 create mode 100644 research/served-diagonal-bit/selected/served/kchron_p12.json
 create mode 100644 research/served-diagonal-bit/selected/served/profile_p12.json
 create mode 100644 research/served-diagonal-bit/selected/served/word_p12.json.gz
 create mode 100644 research/served-diagonal-bit/verify.py

diff --git a/.github/workflows/served-diagonal-bit.yml b/.github/workflows/served-diagonal-bit.yml
new file mode 100644
index 0000000000..2b200e1f4d
--- /dev/null
+++ b/.github/workflows/served-diagonal-bit.yml
@@ -0,0 +1,38 @@
+name: Verify served diagonal bit supplier
+on:
+  pull_request:
+    paths:
+      - 'research/served-diagonal-bit/**'
+      - 'research/source-assisted-v4/**'
+      - 'research/source-assisted/**'
+      - 'scripts/paired_cube_assembly.py'
+      - '.github/workflows/served-diagonal-bit.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  full:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 45
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          repository: CrocSwap/integer-mult-bounds
+          ref: a1175449f34d39ff933d9d8ab23ced1f32b290ec
+          path: .dependencies/pr200
+          persist-credentials: false
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          repository: CrocSwap/integer-mult-bounds
+          ref: 187e1010ac8b259af8e9b5166f68b64bc27b4b47
+          path: .dependencies/pr193
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: '3.13'
+      - run: python -m pip install -r .dependencies/pr193/research/source-assisted/requirements-round13.txt
+      - run: python -B research/served-diagonal-bit/verify.py --complex-root .dependencies/pr193 --bit-root .dependencies/pr200 --full
+      - run: git diff --exit-code
diff --git a/research/served-diagonal-bit/NOTICE b/research/served-diagonal-bit/NOTICE
new file mode 100644
index 0000000000..d500a9e280
--- /dev/null
+++ b/research/served-diagonal-bit/NOTICE
@@ -0,0 +1,28 @@
+Served diagonal bit supplier. Apache-2.0.
+Prepared by Avi Eisenberg (ikeboy) with Anthropic Claude assistance.
+
+New here: the served diagonal operation (patch.py), its forked word and terminal
+checks (bit/served_word.py, bit/served_terminal.py, bit/served_prove.py) and the
+argument in PROOF.md.
+
+Reused, with credit:
+- Chafik Boukhalfa, PR200 at a1175449f34d39ff933d9d8ab23ced1f32b290ec: the
+  fixed-coordinate/face-diagonal bit word that patch.py starts from, its frames,
+  partner mixes, 34 terminal sinks, prime witnesses, paid-moment certification
+  and package verifier. bit/served_word.py forks PR200's bit/word.py and
+  bit/base_word.py; bit/served_terminal.py forks PR200's bit/terminal.py;
+  bit/served_prove.py follows PR200's bit/prove.py and imports its certify().
+- Rohan Arun, PR205: the completed-bank packing on PR200's word. packing.py,
+  arithmetic.py, audit.py and verify.py adapt PR205's files to the served word.
+- Evan McKinney, PR197: completed-bank packing, exact gauge charts, nine-colour
+  bank incidence, routing bound, arithmetic, audit and endpoint controls.
+  banks.py and controls.py are byte-identical to PR205's copies of PR197's code.
+- Avi Eisenberg, PR193 at 187e1010ac8b259af8e9b5166f68b64bc27b4b47: the v4
+  source-assisted complex supplier and balanced assembly bridge; icekylinx for
+  the source-assisted method (PR184) and the paired-cube framework (PR144).
+- eumemic, PR168: the v4 exact integer backend that the forked checks load from
+  PR200's pinned references.
+- jamesyc, PR166: the terminal lemma behind the sinks.
+- PR185/187: the finite ordinary-leaf composition.
+- hcg890, PR217: the previous best completed claim, used as the comparison.
+Original notices remain in the pinned checkouts.
diff --git a/research/served-diagonal-bit/PROOF.md b/research/served-diagonal-bit/PROOF.md
new file mode 100644
index 0000000000..5662024d1b
--- /dev/null
+++ b/research/served-diagonal-bit/PROOF.md
@@ -0,0 +1,99 @@
+# Served diagonal operations on the PR200 bit word
+
+This package changes one thing in PR200's bit word. Then it applies PR205's completed banks (PR197's construction) and PR193's balanced assembly without change. This file states the change and why the word stays correct. Every argument not restated here is PR200's, PR205's or PR197's, with the same inherited interfaces.
+
+## 1. The partner mixes in PR200
+
+PR200's word has `v = 1760` source lines, `h = 24` and `m = 72`. Each source `s` has a data register. The register holds `x_s` after the injection. The 1,760 sources form 880 partner pairs. Each pair has a carrier `c` and a passive `d`, with orthogonal labels. For each pair the word:
+
+- adds `x_d` into the carrier data register at the 2-dim mix frame, so it holds `x_c + x_d`;
+- delivers `x_c + x_d` to the pair's receivers at the cap frame;
+- subtracts `x_d` again at the end.
+
+So the passive data register always holds `x_d`. Only carrier registers change. The carrier chain is `line → mix → cap → full`. The passive chain is `line → mix → full`, with children `[1, 22]`.
+
+## 2. The served operation
+
+PR200 also forms the same sum `x_c + x_d` in auxiliary registers. Operation `i = (a, b, n)` adds register `b` into register `a`, and node `n` is the partner diagonal with `args[n] = {c, d}`. `patch.py` finds the operations where all of these hold:
+
+1. before `i`, register `a` holds exactly `x_c`, and register `b` holds exactly `x_d`;
+2. `b` is not a root, gauge, source or alias register;
+3. `b` has exactly two operations: one copy operation `j` that writes the source node `d` into it, and then `i`;
+4. the mix frame of the pair is inside the frame `F_i` of operation `i` (exact containment in PR200's own frame algebra).
+
+There are 373 such operations. All of them are in phase one, and every `F_i` has dimension 3. For each one, `patch.py`:
+
+- deletes register `b` and its copy operation `j`;
+- makes operation `i` read `x_d` from the passive data register: `ops[i] = [a, -1-d, n]`, with `served = [i, d, F_i]`;
+- moves the partner mix of that pair to the start of the word, right after the injections (`early = true` in the schedule);
+- extends the passive chain to `line → mix → F_i → full`, with children `[1, 1, 21]`.
+
+Nothing else changes. Operations, roles and read positions are renumbered compactly. `verify.py --full` runs `patch.py` again on PR200's frozen word and compares its output with the frozen files.
+
+## 3. Why the word is still correct
+
+**Values.** Before operation `i`, register `a` holds `x_c`. The passive data register holds `x_d` at all times. So `a` receives `x_c + x_d`, the same value as before. The checker simulates every register content and checks the operands of every served operation against the node's arguments.
+
+**Early mix.** After the injections, the word reads a carrier data register only at the deliveries and at the final subtraction. Both come after the mix in both schedules. Thus the early mix changes no value that the word reads.
+
+**Dirty registers.** The deleted register `b` takes its adjoint response with it. A served operation reads a data register, not a dirty auxiliary register, so it adds no dirty response.
+
+**Formal check.** `bit/served_prove.py` runs all `2v + 16,775 = 20,295` formal columns in F2 and over the integers. All target columns equal the defining decoder. All source and dirty columns return to their start values. No column is sampled.
+
+**Frames.** Each `F_i` is nondegenerate and contains the passive line. The passive chain `line ⊂ mix ⊂ F_i ⊂ full` is nested, and every other chain keeps PR200's check. The exact integer backend is eumemic's PR168 v4 backend, loaded from PR200's pinned references. The served word uses 24,401 frames. Each one is a PR200 frame with its PR200 prime witness, so every Gram inverse and projector stays valid at every prime `q > 2^80`, as in PR200. No new frame comes in.
+
+**Controls.** The checker rejects each of these changes:
+
+- PR200's three word controls (omitted compensation, missing partner, stale read);
+- a served operation that reads the carrier instead of the passive register;
+- a zero operation frame;
+- a served passive chain without its served stop;
+- a served pair whose mix is not early.
+
+## 4. Terminal sinks
+
+PR200's 34 PR166 terminal sinks apply unchanged. `bit/served_terminal.py` is PR200's `bit/terminal.py` with three edits:
+
+- a served operation is not a register-to-register gate, so it has no control use;
+- the gate replay adds the passive data register for a served operation;
+- the replay applies early mixes after the injections and late mixes at delivery.
+
+The retained scalar bill does not grow (delta −158). The three terminal controls are rejected.
+
+## 5. Ledger
+
+| Per copy | PR200 | Served |
+|---|---:|---:|
+| Logical auxiliary roles | 18,908 | 18,535 |
+| Physical chains (after 1,760 aliases and 34 sinks) | 17,114 | 16,741 |
+| Stock `W` | 20,634 | 20,261 |
+| Deficit `72W − mass` | 1,936 | 1,936 |
+| Coarse bit saving | 6.77774e-4 | 6.86716e-4 |
+
+The deficit stays at 1,936, so the telescoping identity holds with the same loss.
+
+## 6. Banks
+
+PR205's packing applies with new counts. There are three copies, 2,200 rank-20 gauges (220 distinct frames, the same charts as PR205) and 14,541 other physical chains:
+
+```
+6·3300 = 9·2200,      2·3300 + 3·41423 = 9·(16741 − 2200).
+```
+
+Thus `W = 3·2·1760 + 44,723 = 55,283` and the deficit is `5,808 = 3·1,936`. The largest child is 22. The chain/bank multigraph gets a proper 9-edge-colouring, and an independent check rejects a duplicated colour.
+
+## 7. Arithmetic
+
+`arithmetic.py` and `audit.py` are PR205's, with the served word's numbers. The paid moment includes the 10^-16 rare-class fallback. Two independent moment engines exclude the next 10^-18 grid point. Three finite ordinary-leaf levels start from the served word's completed ordinary supplier. PR193's complex supplier does not bind. The unchanged 47-constraint balanced assembly certifies κ, and the next 10^-18 κ point is rejected. `certificate.json` holds every value.
+
+## 8. Limits
+
+The finite checks establish the served word, the sinks, the charts, the banks, the moments, the leaf recurrence and the assembly arithmetic. These remain inherited assumptions, as in PR200, PR205 and PR197:
+
+- the completed-core contract;
+- the general Clifford interface;
+- uniform weighted compilation;
+- restored rows;
+- fixed-tape transfer.
+
+PR193's disclosed limits on the complex side also remain.
diff --git a/research/served-diagonal-bit/README.md b/research/served-diagonal-bit/README.md
new file mode 100644
index 0000000000..cd4b381cfe
--- /dev/null
+++ b/research/served-diagonal-bit/README.md
@@ -0,0 +1,80 @@
+# Served diagonal operations on PR200's bit word
+
+Under the retained multiplication interfaces, this finite witness certifies
+
+$$
+T(n)=O\left(n(\log n)^{1-\kappa}\right),\qquad
+\kappa=\frac{692144604250060}{10^{18}}=0.000692144604250060 .
+$$
+
+That is **+1.088%** over PR217 (`684696826673891/10^18`, the best completed claim) and **+1.330%** over PR205 (`683061299399923/10^18`).
+
+| Construction | Bit coarse saving | Conditional kappa |
+|---|---:|---:|
+| PR205: PR200 word, packed | 6.83528e-4 | 0.000683061299399923 |
+| PR217: butterflies and optimized frames, packed | 6.85166e-4 | 0.000684696826673891 |
+| Served word, unpacked | 6.86716e-4 | 0.000685800818606951 |
+| **Served word, packed** | **6.92624e-4** | **0.000692144604250060** |
+
+## What is new
+
+PR200's bit word mixes each partner pair on its data registers: the carrier register gets `x_c + x_d`, and the passive register keeps `x_d`. The same word also builds `x_c + x_d` again in auxiliary registers. At 373 of these operations, the control register is a pure copy of `x_d`, made by one copy operation and used once.
+
+This package reads `x_d` straight from the passive data register at those 373 operations. It then deletes the 373 copies and their copy operations. To keep the passive register's frame chain nested, the pair's partner mix moves to right after the injections. The passive chain gets one extra 3-dim stop: `line → mix → F_i → full`.
+
+| Per copy | PR200 | Served |
+|---|---:|---:|
+| Logical auxiliary roles | 18,908 | 18,535 |
+| Physical chains | 17,114 | 16,741 |
+| Stock `W` | 20,634 | 20,261 |
+| Deficit | 1,936 | 1,936 |
+| Coarse bit saving | 6.77774e-4 | 6.86716e-4 (+1.32%) |
+
+Every frame stays one of PR200's witnessed frames. The 34 terminal sinks, the 1,760 aliases, the gauges and every other operation are PR200's.
+
+**Checks.** `bit/served_prove.py` checks the served word completely, in the same way as PR200's `bit/prove.py`:
+
+- all 20,295 formal columns in F2 (identity) and over the integers (defining decoder), with no sampling;
+- exact frame geometry with PR200's PR168 v4 integer backend, including each served frame and the new passive chains;
+- PR200's 34 terminal sinks through a forked terminal compiler, with the scalar bill retained;
+- PR200's paid-moment certification, imported unchanged;
+- seven adverse word controls and three terminal controls, all rejected.
+
+**Banks and arithmetic.** PR205's completed banks (PR197's construction) then apply with new counts: 3,300 small banks and 41,423 large banks over three copies, so `W = 55,283` and the deficit is `5,808`. Three finite ordinary-leaf levels and PR193's unchanged 47-constraint assembly give κ. The bit branch binds; the complex supplier (`700918443859411/10^18`) has slack.
+
+`PROOF.md` gives the argument.
+
+## Verify
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds a1175449f34d39ff933d9d8ab23ced1f32b290ec
+git worktree add --detach ../served-bit-pr200 a1175449f34d39ff933d9d8ab23ced1f32b290ec
+git fetch https://github.com/CrocSwap/integer-mult-bounds 187e1010ac8b259af8e9b5166f68b64bc27b4b47
+git worktree add --detach ../served-complex-pr193 187e1010ac8b259af8e9b5166f68b64bc27b4b47
+python3 -m pip install -r ../served-complex-pr193/research/source-assisted/requirements-round13.txt
+python3 -B research/served-diagonal-bit/verify.py --complex-root ../served-complex-pr193 --bit-root ../served-bit-pr200 --full
+```
+
+`--full` takes about five minutes on Linux. It runs:
+
+1. PR193's and PR200's unchanged package verifiers;
+2. `patch.py`, which derives the served word again from PR200's frozen word and must match the frozen files;
+3. `bit/served_prove.py`, the complete check of the served word and its sinks;
+4. PR205's charts, banks and colouring on the served word;
+5. the arithmetic, the independent audit and the bank endpoint controls.
+
+Without `--full`, the saved receipts are used, and only the pins and the arithmetic run. The terminal compiler needs Linux (`resource`).
+
+## Scope and credit
+
+This is a conditional finite construction and composition. It is not an unconditional multiplication theorem or a speedup claim. The all-size compiler, analytic, precision, restored-row and fixed-tape hypotheses are inherited exactly as in PR200, PR205 and PR197.
+
+The served operation is new. Credit for everything it builds on goes to:
+
+- Chafik Boukhalfa (PR200) for the bit word, its sinks, witnesses and verifier, which the served checks fork;
+- Rohan Arun (PR205) and Evan McKinney (PR197) for the completed banks and their code;
+- PR193 for the complex supplier, and icekylinx for the source-assisted method and the paired-cube framework;
+- eumemic (PR168), jamesyc (PR166) and PR185/187 for the backend, the terminal lemma and the leaf composition;
+- hcg890 (PR217) for the previous best claim.
+
+Prepared by Avi Eisenberg with Anthropic Claude assistance. Apache-2.0.
diff --git a/research/served-diagonal-bit/SOURCE.json b/research/served-diagonal-bit/SOURCE.json
new file mode 100644
index 0000000000..42ec8e7210
--- /dev/null
+++ b/research/served-diagonal-bit/SOURCE.json
@@ -0,0 +1,35 @@
+{
+  "bit_commit": "a1175449f34d39ff933d9d8ab23ced1f32b290ec",
+  "bit_files": {
+    "research/paired-cube-diagonal-bit-168/arithmetic/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b",
+    "research/paired-cube-diagonal-bit-168/bit/base_word.py": "9fe3a81b7561d2b09c086f63fac4626e88a32369ef8bc5579c94878de1218a89",
+    "research/paired-cube-diagonal-bit-168/bit/prime-witnesses.json.gz": "612f0b91c7689b0cebcacb28278579aa2c88801df640798d7a119f11eca836c3",
+    "research/paired-cube-diagonal-bit-168/bit/prove.py": "c4a7f6ea79d2b9bbdace7c1e99bd4c068967d90fcab5bddc4ce37b5055cbf0cc",
+    "research/paired-cube-diagonal-bit-168/bit/word.py": "85822e9cca5b1b2335c3704a3df2f3c6ef01e42d8328daacb33701d30cee80ab",
+    "research/paired-cube-diagonal-bit-168/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py": "4d7c86cd999a1519e0dfb6dcf33a8f26e442a353c3665a0f06881216a260fbf3",
+    "research/paired-cube-diagonal-bit-168/selected/bit/frames_p12.json": "aec2f09df5b42165a353a9233d9c8549bf091167915f6b044689c4bfb189d406",
+    "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/sinks.json": "c00ff70c564829d4b97740f92796fc6ce14fbcd5ca519663828650552b80249d",
+    "research/paired-cube-diagonal-bit-168/selected/bit/word_p12.json": "0728ed1c7320430a87709b1034485cbabefec85d532b48897f74136cf3954218"
+  },
+  "bit_manifest_sha256": "015abe3342d08d08a9c4a764f103cafc1be1fe7f23d7a72471bd87412c57c2df",
+  "comparison": {
+    "pr205": "Rohan Arun, PR200 word with PR197 banks, kappa = 683061299399923/10^18",
+    "pr217": "paid XOR butterflies with cascade-optimized frames, kappa = 684696826673891/10^18"
+  },
+  "complex_commit": "187e1010ac8b259af8e9b5166f68b64bc27b4b47",
+  "complex_files": {
+    "research/source-assisted-v4/SOURCE.json": "99024e5c8296ad03b6e499c3c4e1e9e879bf6a5954d8558cc39abd557edf79d6",
+    "research/source-assisted-v4/certificate.json": "d84406d2fcc6990deba2b135509e6d86600e57123d88f9b21f7b7240e1aeb513",
+    "research/source-assisted/global/FINITE_BRIDGE.txt": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46",
+    "scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "served_files": {
+    "selected/served/kchron_p12.json": "8542463c58b25c97e10a7e80c5504e4517cc6acf439ce8c549741b8456f0ad76",
+    "selected/served/profile_p12.json": "428ab934b5f71093eba46b9fc341c5edda6354bdb48144e8496804587e8e5b3e",
+    "selected/served/word_p12.json.gz": "8d21c91a96d72cbe12b94e18ffc2d7c88c5958aee2199c94631723b420051b5d"
+  }
+}
diff --git a/research/served-diagonal-bit/arithmetic.py b/research/served-diagonal-bit/arithmetic.py
new file mode 100644
index 0000000000..b8abc1ae26
--- /dev/null
+++ b/research/served-diagonal-bit/arithmetic.py
@@ -0,0 +1,109 @@
+"""Exact paid moments, finite ordinary-leaf composition and the balanced assembly.
+
+PR205's arithmetic.py (Rohan Arun; adapted from PR197's, Evan McKinney; PR185/187 finite bootstrap, PR193
+balanced bridge inherited). The bit supplier is the served word (served_prove.py's record) instead of PR200's
+certificate; the comparison constants are PR205's and PR217's kappa. Apache-2.0.
+"""
+from fractions import Fraction as Q
+from pathlib import Path
+import importlib.util, json
+
+BIT_PACKAGE = 'research/paired-cube-diagonal-bit-168'
+PR205_KAPPA = Q(683061299399923, 10 ** 18)   # PR205: PR200 bit word with PR197's banks, PR193 complex
+PR217_KAPPA = Q(684696826673891, 10 ** 18)   # PR217: paid XOR butterflies with cascade-optimized frames
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m)
+    return m
+
+
+def build(ROOT, BIT, physical, served):
+    """served: the record printed by bit/served_prove.py (its terminal profile and paid-moment certificate)."""
+    im = load('interval_moment', BIT / BIT_PACKAGE / 'arithmetic/interval_moment.py')
+    assembly = load('frontier_assembly', ROOT / 'scripts/paired_cube_assembly.py')
+    p = physical
+    c191 = json.loads((ROOT / 'research/source-assisted-v4/certificate.json').read_text())
+    b200 = served
+
+    def profile(m, W, H, delta):
+        H = {int(r): int(n) for r, n in H.items()}
+        return dict(m=m, W=W, child_multiplicities=H, N=delta, L=0, total_rank=sum(r * n for r, n in H.items()), maxchild=max(H))
+    cp = c191['complex_profile']; cp = profile(cp['m'], cp['W_per_vertex'], cp['child_histogram'], cp['deficit_per_vertex'])
+    bp = b200['profile']
+    unpacked = profile(bp['m'], bp['W_per_vertex'], bp['child_histogram'], bp['deficit_per_vertex'])
+    assert unpacked['total_rank'] == bp['rank_per_vertex'] and unpacked['maxchild'] == bp['maxchild'] == 60
+    packed = profile(72, p['W'], p['child_histogram'], p['deficit'])
+
+    def paid(row, a, bit):
+        result = im.moment(row, a)
+        if bit:
+            l, u = im.log_interval(Q(row['m'])); e, f = im.exp_interval(a * l, a * u)
+            w = Q(1, 10 ** 16) * Q(32 * row['m'] * sum(row['child_multiplicities'].values()), row['W'])
+            result.update(lower=result['lower'] + w * e, upper=result['upper'] + w * f)
+        return result
+
+    def certify(row, bit):
+        den = 10 ** 18; lo = 0; hi = den // 100
+        assert paid(row, Q(lo, den), bit)['upper'] < 1 < paid(row, Q(hi, den), bit)['lower']
+        while hi - lo > 1:
+            mid = (lo + hi) // 2; v = paid(row, Q(mid, den), bit)
+            if v['upper'] < 1: lo = mid
+            elif v['lower'] > 1: hi = mid
+            else: raise AssertionError('Interval inconclusive')
+        a = Q(lo, den); b = Q(hi, den)
+        return dict(saving=a, accepted=paid(row, a, bit), next_excluded=paid(row, b, bit))
+
+    complex_cert = certify(cp, False)
+    original = certify(unpacked, True); new = certify(packed, True)
+    assert original['saving'] == Q(b200['coarse']['coarse_saving'])
+    assert new['saving'] > original['saving']
+    assert paid(packed, original['saving'], True)['upper'] < paid(unpacked, original['saving'], True)['lower']
+    # Finite-depth ordinary supplier composition, as in PR185/187/197, from PR200's completed ordinary supplier.
+    old = Q(b200['coarse']['ordinary_saving']); coarse = new['saving']; chain = [old]
+    for _ in range(3):
+        a = (1 - coarse) * coarse + coarse * chain[-1]
+        assert chain[-1] < a < coarse < 1 - a
+        chain.append(a)
+    assert 0 < p['conservative_selector_calls'] < 2 ** 40
+    # Additional chart/router calls use the inherited completed ordinary selector; their exponent is at most the
+    # atom exponent coarse, which is below 1 - ordinary.
+    assert coarse < 1 - chain[-1]
+    bridge = c191['assembly']['finite_bridge']; bridge['rows']['degree_gap'] = Q(bridge['rows']['degree_gap'])
+    beta = eta = Q(1, 10 ** 24); weak = Q(1, 10 ** 30); den = 10 ** 18
+
+    def assemble(bit_saving):
+        b = complex_cert['saving']; a = min(bit_saving, (1 - beta) * b - weak)
+        q = a * (1 - 2 * eta); bound = (1 - eta) * q / (1 + q); z = bound * den
+        k = Q((z.numerator - 1) // z.denominator, den)
+        out = assembly.assembly(a, b, bridge, k, eta=eta, beta=beta)
+        assert len(out['strict_constraints']) == 47 and len(out['margins']) == 7
+        try: assembly.assembly(a, b, bridge, k + Q(1, den), eta=eta, beta=beta)
+        except AssertionError: pass
+        else: raise AssertionError('Next final grid accepted')
+        constraints = out.pop('strict_constraints')
+        out['strict_constraint_count'] = len(constraints)
+        out['minimum_constraint'] = min(constraints.values())
+        return dict(kappa=k, assembly=out, binding='complex' if a == (1 - beta) * b - weak else 'bit')
+    before = assemble(old); after = assemble(chain[-1])
+    del before['assembly']
+    assert before['kappa'] < after['kappa'] and after['binding'] == 'bit'
+    assert after['kappa'] > PR205_KAPPA and after['kappa'] > PR217_KAPPA
+    controls = []
+    bad = dict(packed, total_rank=packed['total_rank'] + 1)
+    try: paid(bad, coarse, True)
+    except ValueError: controls.append('changed rank mass')
+    else: raise AssertionError('Corrupt mass accepted')
+
+    return dict(scope='Conditional composition; physical and finite bridge proof dependencies are separate',
+                source_commits=dict(complex='187e1010ac8b259af8e9b5166f68b64bc27b4b47', bit='a1175449f34d39ff933d9d8ab23ced1f32b290ec'),
+                bit_word='served word: PR200 terminal word with 373 served diagonal operations (selected/served)',
+                complex_profile=cp, unpacked_profile=unpacked, packed_profile=packed, complex=complex_cert,
+                bit_before=original, bit_after=new, bit_coarse_relative_gain=new['saving'] / original['saving'] - 1,
+                stock_relative_reduction=1 - Q(p['W'], 3 * unpacked['W']), ordinary_chain=chain,
+                extra_selector_calls=p['conservative_selector_calls'], selector_toll_gap=1 - chain[-1] - coarse,
+                comparison_pr205_kappa=PR205_KAPPA, comparison_pr217_kappa=PR217_KAPPA,
+                before_packing=before, after_packing=after,
+                kappa_gain_from_packing=after['kappa'] - before['kappa'],
+                relative_gain_over_pr205=after['kappa'] / PR205_KAPPA - 1,
+                relative_gain_over_pr217=after['kappa'] / PR217_KAPPA - 1, controls=controls)
diff --git a/research/served-diagonal-bit/audit.py b/research/served-diagonal-bit/audit.py
new file mode 100644
index 0000000000..f20204a184
--- /dev/null
+++ b/research/served-diagonal-bit/audit.py
@@ -0,0 +1,81 @@
+"""Independent exact moment and finite-leaf audit; no optimizer imports.
+
+PR205's audit.py (Rohan Arun; PR197's, Evan McKinney, Apache-2.0) with the served-word inventory constants."""
+from fractions import Fraction as Q
+from functools import lru_cache
+from math import factorial
+ROUND=2**192
+
+def lower(value):
+    return Q((value * ROUND).numerator // (value * ROUND).denominator, ROUND)
+
+def upper(value):
+    x = value * ROUND
+    return Q(-((-x.numerator) // x.denominator), ROUND)
+
+@lru_cache(None)
+def logarithm(x):
+    """Independent base-two reduction, 64 atanh terms and geometric remainder."""
+    assert x >= 1
+    power = 0
+    while x >= 2:
+        x /= 2
+        power += 1
+    def small(y):
+        z = (y - 1) / (y + 1)
+        s = 2 * sum((z**(2*j+1) / (2*j+1) for j in range(64)), Q(0))
+        return s, s + 2*z**129 / (129*(1-z*z))
+    l, u = small(x)
+    l2, u2 = small(Q(2))
+    return lower(l + power*l2), upper(u + power*u2)
+
+def exponential(l, u):
+    assert 0 <= l <= u < Q(1, 4)
+    def polynomial(x):
+        return sum((x**j / factorial(j) for j in range(17)), Q(0))
+    tail = u**17 / (factorial(17)*(1-u/18))
+    return lower(polynomial(l)), upper(polynomial(u) + tail)
+
+
+def moment(row,a,bit):
+    m,W=row['m'],row['W'];H={int(r):n for r,n in row['child_multiplicities'].items()}
+    assert sum(r*n for r,n in H.items())==row['total_rank']==m*W-row['N']
+    lo=hi=Q(0)
+    for r,n in H.items():
+        l,u=logarithm(Q(m,r));e,f=exponential(a*l,a*u)
+        lo+=Q(r*n,m*W)*e;hi+=Q(r*n,m*W)*f
+    if bit:
+        l,u=logarithm(Q(m));e,f=exponential(a*l,a*u)
+        weight=Q(32*m*sum(H.values()),10**16*W)
+        lo+=weight*e;hi+=weight*f
+    return lo,hi
+
+
+def run(record,original):
+    original=dict(original,child_multiplicities={int(r):n for r,n in original['child_multiplicities'].items()})
+    intervals={}
+    for name,row,bit in (('complex',record['complex_profile'],False),('bit_before',original,True),('bit_after',record['packed_profile'],True)):
+        a=Q(record[name]['saving']);lo,hi=moment(row,a,bit);next_lo,next_hi=moment(row,a+Q(1,10**18),bit)
+        assert hi<1<next_lo
+        intervals[name]=dict(accepted_lower=lo,accepted_upper=hi,next_lower=next_lo,next_upper=next_hi)
+    H={int(r):3*n for r,n in original['child_multiplicities'].items()}
+    assert H.pop(60)==6600
+    packed=record['packed_profile']
+    assert H=={int(r):n for r,n in packed['child_multiplicities'].items()}
+    assert packed['W']==3*2*1760+3300+(9*(16741-2200)-2*3300)//3==55283
+    assert 3*original['W']==60783
+    assert packed['N']==3*original['N']==5808
+    c=Q(record['bit_after']['saving']);chain=list(map(Q,record['ordinary_chain']))
+    assert len(chain)==4
+    for j,a in enumerate(chain[1:],1):
+        assert a==(1-c)*c+c*chain[j-1]==c-c**j*(c-chain[0])
+        assert chain[j-1]<a<c<1-a
+    b=Q(record['complex']['saving']);beta=eta=Q(1,10**24)
+    for name,saving in (('before_packing',chain[0]),('after_packing',chain[-1])):
+        a=min(saving,(1-beta)*b-Q(1,10**30));q=a*(1-2*eta);ceiling=(1-eta)*q/(1+q)
+        k=Q(record[name]['kappa'])
+        assert k<ceiling<=k+Q(1,10**18)
+        assert a==saving<b
+    assert Q(record['after_packing']['kappa'])>Q(record['comparison_pr205_kappa'])==Q(683061299399923,10**18)
+    assert Q(record['after_packing']['kappa'])>Q(record['comparison_pr217_kappa'])==Q(684696826673891,10**18)
+    return dict(status='PASS',moment_intervals=intervals,finite_leaf_levels=3,adjacent_final_grids_checked=2)
diff --git a/research/served-diagonal-bit/banks.py b/research/served-diagonal-bit/banks.py
new file mode 100644
index 0000000000..6505ebd37e
--- /dev/null
+++ b/research/served-diagonal-bit/banks.py
@@ -0,0 +1,104 @@
+"""PR197 chart inversion and bank colouring helpers (byte-identical extract of packing.py up to build()).
+
+Apache-2.0. Prepared with substantial OpenAI Codex assistance.
+"""
+from array import array
+from collections import Counter
+from fractions import Fraction as Q
+from math import gcd
+from pathlib import Path
+import hashlib,json,sys
+
+def inverse_integer(a):
+    """Fraction-free Gauss-Jordan; return integral C,d with a C = d I."""
+    n=len(a)
+    m=[list(row)+[int(i==j) for j in range(n)] for i,row in enumerate(a)]
+    previous=1
+    factors=[]
+    for k in range(n):
+        pivot=next((i for i in range(k,n) if m[i][k]),None)
+        if pivot is None:
+            raise ValueError('Singular basis')
+        m[k],m[pivot]=m[pivot],m[k]
+        if pivot != k:factors.append(('swap',k,pivot,1,1))
+        p=m[k][k]
+        if p != previous:
+            ratio=Q(previous,p)
+            factors.append(('scale',k,k,ratio.numerator,ratio.denominator))
+        for i in range(n):
+            if i==k:continue
+            u=m[i][k]
+            if u:
+                ratio=Q(-u,previous)
+                factors.append(('add',i,k,ratio.numerator,ratio.denominator))
+            for j in range(2*n):
+                if j==k:continue
+                value=p*m[i][j]-u*m[k][j]
+                assert value % previous==0
+                m[i][j]=value//previous
+            m[i][k]=0
+        previous=p
+    d=m[0][0]
+    assert d and all(m[i][j]==d*int(i==j) for i in range(n) for j in range(n))
+    c=[row[n:] for row in m]
+    common=abs(d)
+    for row in c:
+        for x in row:common=gcd(common,x)
+    d//=common
+    c=[[x//common for x in row] for row in c]
+    if d<0:d=-d;c=[[-x for x in row] for row in c]
+    return c,d,factors
+
+def color_incidence(left,right,nleft,nright,colors):
+    """Incremental two-color swaps; parallel edges are identified separately."""
+    assert len(left)==len(right)
+    full=(1<<colors)-1
+    lf=[full]*nleft;rf=[full]*nright
+    lc=[array('i',[-1])*colors for _ in range(nleft)]
+    rc=[{} for _ in range(nright)]
+    labels=array('i',[-1])*len(left)
+    swaps=longest=0
+    def remove(e):
+        u,v,c=left[e],right[e],labels[e]
+        assert lc[u][c]==e and rc[v][c]==e
+        lc[u][c]=-1;del rc[v][c]
+        lf[u]|=1<<c;rf[v]|=1<<c
+    def add(e,c):
+        u,v=left[e],right[e]
+        assert lf[u]&(1<<c) and rf[v]&(1<<c)
+        labels[e]=c;lc[u][c]=e;rc[v][c]=e
+        lf[u]&=~(1<<c);rf[v]&=~(1<<c)
+    for e,(u,v) in enumerate(zip(left,right)):
+        common=lf[u]&rf[v]
+        if common:
+            add(e,(common&-common).bit_length()-1)
+            continue
+        assert lf[u] and rf[v]
+        a=(lf[u]&-lf[u]).bit_length()-1
+        b=(rf[v]&-rf[v]).bit_length()-1
+        path=[];r=u
+        while True:
+            edge=lc[r][b]
+            if edge<0:break
+            path.append(edge);bank=right[edge]
+            assert bank!=v
+            edge=rc[bank].get(a,-1)
+            if edge<0:break
+            path.append(edge);r=left[edge]
+        changes=[(edge,b if labels[edge]==a else a) for edge in path]
+        for edge,_ in changes:remove(edge)
+        for edge,c in changes:add(edge,c)
+        add(e,b)
+        swaps+=1;longest=max(longest,len(path))
+    return labels,{'swaps':swaps,'longest_swapped_path':longest}
+
+def check_coloring(left,right,labels,nleft,nright,colors,full_left=False):
+    assert len(left)==len(right)==len(labels)
+    lm=[0]*nleft;rm=[0]*nright
+    for u,v,c in zip(left,right,labels):
+        assert 0<=u<nleft and 0<=v<nright and 0<=c<colors
+        bit=1<<c
+        assert not lm[u]&bit and not rm[v]&bit
+        lm[u]|=bit;rm[v]|=bit
+    if full_left:assert all(mask==(1<<colors)-1 for mask in lm)
+
diff --git a/research/served-diagonal-bit/bit/served_prove.py b/research/served-diagonal-bit/bit/served_prove.py
new file mode 100644
index 0000000000..fd7cc367d5
--- /dev/null
+++ b/research/served-diagonal-bit/bit/served_prove.py
@@ -0,0 +1,104 @@
+#!/usr/bin/env python3
+"""Complete check of the served bit word, its 34 terminal sinks and its paid moment.
+
+Counterpart of PR200's bit/prove.py: same formal columns (F2 identity and the integer defining decoder), the
+same adverse controls plus one for the served operations, PR200's terminal-sink compiler (served fork), PR200's
+paid-moment certification (imported unchanged) and PR200's prime witnesses (every frame used here is one of
+PR200's witnessed frames; no new frame is introduced). Prints one JSON record. Usage:
+
+    python3 served_prove.py PR200_PACKAGE_DIR SERVED_DIR
+"""
+from fractions import Fraction as Q
+from pathlib import Path
+import contextlib, gzip, importlib.util, json, sys
+
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+sys.dont_write_bytecode = True
+from served_word import Candidate, need
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    m = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(m)
+    return m
+
+
+def used_frames(word):
+    used = set(word.opframe) | set(word.w['source_frame']) | set(word.w['root_frame']) | {word.w['full_frame']}
+    used.update(z['frame'] for z in word.w['gauges'])
+    for e in word.k['entries']:
+        used.update((e['mix_frame'], e['deliver_frame']))
+        used.update(e['passive_chain'])
+    return used
+
+
+def prove(pr200, served):
+    pr200, served = Path(pr200), Path(served)
+    pr200_prove = load('pr200_prove', pr200 / 'bit/prove.py')     # certify() and js() are used unchanged
+    word = Candidate(pr200, served); word.exact_frames(); row = word.row()
+    need(row['reused_registers'] == len(word.pairs), 'physical aliases counted')
+    formal = [word.formal(r) for r in (2, 0)]
+    controls = []
+    for tamper in ('omit_compensation', 'missing_partner', 'stale', 'served_from_carrier'):
+        try:
+            word.formal(2, tamper)
+        except ValueError:
+            controls.append(tamper)
+        else:
+            raise ValueError('Adverse word control accepted: ' + tamper)
+    i = word.changed_frames[0]; old = word.opframe[i]; word.opframe[i] = word.register([])
+    try:
+        word.exact_frames()
+    except ValueError:
+        controls.append('zero_operation_frame')
+    else:
+        raise ValueError('Zero frame accepted')
+    word.opframe[i] = old
+    # a served passive chain that skips its served frame must fail the chain checks
+    e = next(e for e in word.k['entries'] if e.get('early'))
+    saved = e['passive_chain']; e['passive_chain'] = [saved[0], saved[1], saved[3]]
+    try:
+        word.C.chains()
+    except ValueError:
+        controls.append('served_passive_chain_without_stop')
+    else:
+        raise ValueError('Served chain without its stop accepted')
+    e['passive_chain'] = saved
+    e['early'] = False
+    try:
+        word.C.chains()
+    except ValueError:
+        controls.append('served_pair_without_early_mix')
+    else:
+        raise ValueError('Served pair without early mix accepted')
+    e['early'] = True
+    terminal_module = load('served_terminal', HERE / 'served_terminal.py')
+    selection = json.loads((pr200 / 'selected/bit/sinks.json').read_text())
+    with contextlib.redirect_stdout(sys.stderr):
+        terminal = terminal_module.prove(word, selection)
+    terminal.pop('seconds'); terminal.pop('maxrss')
+    unsunk = row; row = terminal['profile']
+    row['child_histogram'] = {int(k): n for k, n in row['child_histogram'].items()}
+    need(row['terminal_sinks'] == len(selection) and terminal['scalar_addition_delta'] <= 0, 'terminal sink count and retained scalar bill')
+    need(row['W_per_vertex'] == unsunk['W_per_vertex'] - len(selection) and row['R'] == unsunk['R'] - len(selection), 'terminal removals reduce stock by the sink count')
+    coarse = pr200_prove.certify(row)
+    witnesses = json.loads(gzip.decompress((pr200 / 'bit/prime-witnesses.json.gz').read_bytes()))
+    witnessed = {f for rec in witnesses['frame_witnesses'] for f in rec['frame_ids']}
+    used = used_frames(word)
+    need(used <= witnessed, 'every used frame carries a PR200 prime witness')
+    return pr200_prove.js(dict(status='PASS', profile=row, unsunk_profile=unsunk, terminal=terminal, formal=formal,
+                               coarse=coarse, word_controls=controls, served_operations=len(word.served),
+                               used_frames=len(used), used_frames_witnessed_by_pr200=True,
+                               scope='Complete F2 identity, integer defining decoder, exact physical frame geometry; '
+                                     'retained weighted-compiler contracts.'))
+
+
+def main():
+    need(not sys.flags.optimize, 'assertions enabled')
+    print(json.dumps(prove(sys.argv[1], sys.argv[2]), sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/served-diagonal-bit/bit/served_terminal.py b/research/served-diagonal-bit/bit/served_terminal.py
new file mode 100644
index 0000000000..baee93f2bd
--- /dev/null
+++ b/research/served-diagonal-bit/bit/served_terminal.py
@@ -0,0 +1,236 @@
+"""Exact terminal-target compiler on the served physical bit word.
+
+Fork of PR200's bit/terminal.py (Chafik Boukhalfa, Apache-2.0; James Chang's PR166 substitution) with served
+operations: a served gate adds the passive source data register into its destination, and a served pair's
+partner XOR runs right after the injections. Every check of the original is kept.
+
+James Chang's PR166 terminal substitution, specialized and independently
+verified by Chafik Boukhalfa with OpenAI Codex assistance. All inherited
+word, frame, gauge, reuse and partner-pair credits remain in the adapter.
+No source producer is executed. The original adjoint includes deleted roots.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from hashlib import sha256
+import argparse,importlib.util,json,time,math,sys,gc,resource,signal
+
+def need(x,msg):
+ if not x:raise AssertionError(msg)
+def compact(c):return {str(k):v for k,v in sorted(c.items()) if v}
+
+def prove(word,selection):
+ t0=time.monotonic();C=word.C;h,v,R=word.h,word.v,word.R;ops=word.ops
+ baseline=word.row();phase=set(word.phase1);order=word.phase1+word.rest;position={i:j for j,i in enumerate(word.rest)}
+ sources=set(word.source.values());aliasroles=set(word.donor)|set(word.donor.values());writes=defaultdict(list);uses=defaultdict(list);rootids=defaultdict(list)
+ for i,(a,b,n) in enumerate(ops):
+  writes[a].append(i)
+  if b>=0:uses[b].append(i)
+ for j,s in enumerate(word.w['rootroles']):rootids[s].append(j)
+ at=defaultdict(list)
+ for s in word.order:at[word.readtime[s]].append(s)
+ first=[len(word.rest)+1]*v
+ for s in word.order:
+  for target in word.gauge[s]['targets']:first[target]=min(first[target],word.readtime[s])
+ chosen=[];seen=set();targets=set()
+ for entry in selection:
+  j,pivot=entry['root'],entry['pivot'];need(type(j) is int and 0<=j<len(word.g['roots']),'root index')
+  r=word.g['roots'][j];s=word.w['rootroles'][j];U=word.w['root_frame'][j]
+  need(j not in seen and r['kind']=='side','distinct side roots');seen.add(j)
+  need(s not in sources|aliasroles|set(word.gauge),'zero-gauge independent scratch root')
+  need(rootids[s]==[j] and not uses[s] and writes[s],'one terminal root with writes and no retained consumers')
+  need(all(i not in phase for i in writes[s]),'root untouched in center phase')
+  need(all(C.sub(word.opframe[i],U) for i in writes[s]),'all writes within root cap')
+  need(type(pivot) is int and pivot in r['targets'],'pivot target')
+  need(first[pivot]>max(position[i] for i in writes[s]),'pivot untouched by compensation before post')
+  need(not targets.intersection(r['targets']),'simultaneous disjoint target groups');targets.update(r['targets'])
+  path=[word.opframe[i] for i in writes[s]]+[U,word.w['full_frame']];prev=None;prefix=[]
+  for f in path:
+   need(prev is None or C.sub(prev,f),'deleted root trajectory nested')
+   d=C.dimf[f]-(0 if prev is None else C.dimf[prev])
+   if d:prefix.append(d)
+   prev=f
+  need(sum(prefix)==h,'complete deleted root path')
+  chosen.append(dict(root=j,role=s,targets=r['targets'],pivot=pivot,root_frame=U,root_rank=C.dimf[U],writes=writes[s],deleted_path=prefix))
+ removed={e['role'] for e in chosen};deletedroots={e['root'] for e in chosen};bywrite={i:e for e in chosen for i in e['writes']};after={e['writes'][-1]:e for e in chosen}
+ need(all(a not in removed and b not in removed for i,(a,b,n) in enumerate(ops) if i not in bywrite),'removed roles only occur in their own writes')
+ # Complete modified target chronology, including every retained partner delivery.
+ Y=Counter();current=[None]*v;events=0
+ def move(t,f):
+  nonlocal events
+  prev=current[t];need(prev is None or C.sub(prev,f),'new target chain nesting')
+  need(all(word.module.dot(C.cov[t],b)==0 for b in C.B[f]),'target movement stays inside cap')
+  d=C.dimf[f]-(0 if prev is None else C.dimf[prev]);need(d>=0,'target rank monotonicity')
+  if d:Y[d]+=1
+  current[t]=f;events+=1
+ for j,i in enumerate(word.rest):
+  for s in at[j]:
+   for t in word.gauge[s]['targets']:move(t,word.gauge[s]['frame'])
+  if i in bywrite:move(bywrite[i]['pivot'],word.opframe[i])
+  if i in after:
+   for t in after[i]['targets']:move(t,after[i]['root_frame'])
+ for s in at[len(word.rest)]:
+  for t in word.gauge[s]['targets']:move(t,word.gauge[s]['frame'])
+ deliveries=defaultdict(list)
+ for e in word.k['entries']:deliveries[e['deliver_after_root']].append(e)
+ for j,r in enumerate(word.g['roots']):
+  if r['kind']=='side' and j not in deletedroots:
+   for t in r['targets']:move(t,word.w['root_frame'][j])
+  for e in deliveries[j]:
+   for t in e['receivers']:move(t,e['deliver_frame'])
+ for t,f in enumerate(current):
+  need(f is not None and C.dimf[f]<=h-1,'final target cap')
+  gap=h-1-C.dimf[f]
+  if gap:Y[gap]+=1
+ need(sum(r*n for r,n in Y.items())==v*(h-1),'full target rank mass')
+ local=Counter({int(r):n for r,n in baseline['physical_internal_histogram'].items()})
+ for e in chosen:local.subtract(e['deleted_path'])
+ need(all(n>=0 for n in local.values()),'positive remaining local ledger')
+ _,_,source,_=word.C.chains();child=Counter()
+ for part in (local,Y,source):
+  for r,n in part.items():
+   if r and n:child[r]+=3*n
+ for s,z in word.gauge.items():
+  if s not in word.donor:child[3*z['dim']]+=1
+ child[2]+=2*v;physical_R=baseline['R']-len(chosen);W=2*v+physical_R;rank=sum(r*n for r,n in child.items())
+ need(W*3*h-rank==baseline['deficit_per_vertex'],'terminal rank deficit unchanged')
+ delta=Counter(child);delta.subtract({int(r):n for r,n in baseline['child_histogram'].items()});expected=Counter()
+ for e in chosen:expected[e['root_rank']]-=3;expected[h-e['root_rank']]-=3
+ need(compact(delta)==compact(expected),'independent complete ledger agrees with exact terminal cancellation')
+ # Literal local sandwich, with arbitrary target values and non-pivot corrections.
+ for e in chosen:
+  ts=e['targets'];p=ts.index(e['pivot']);n=len(ts);k=len(e['writes']);N=2*n+k
+  initial=[[int(a==b) for b in range(N)] for a in range(n)];state=[r[:] for r in initial];program=[]
+  def apply(event,direction=1):
+   kind,a,b,c=event;c*=direction
+   if kind=='shear':state[a]=[x+c*y for x,y in zip(state[a],state[b])]
+   else:state[a][b]+=c
+  for a in range(n):
+   if a!=p:program.append(('shear',a,p,-1))
+  program.extend(('basis',p,n+j,1) for j in range(k))
+  program.extend(('basis',a,n+k+a,1) for a in range(n) if a!=p)
+  for a in range(n):
+   if a!=p:program.append(('shear',a,p,1))
+  for event in program:apply(event)
+  for a in range(n):
+   want=initial[a][:]
+   for j in range(k):want[n+j]+=1
+   if a!=p:want[n+k+a]+=1
+   need(state[a]==want,'integer arbitrary-target sandwich')
+  for event in reversed(program):apply(event,-1)
+  need(state==initial,'literal inverse of integer sandwich')
+ # Full original integer adjoint, including the removed root responses.
+ adj=word.adjoint()
+ def without_deleted():
+  out=[{} for _ in range(R)]
+  for j,(r,s) in enumerate(zip(word.g['roots'],word.w['rootroles'])):
+   if j not in deletedroots:
+    for t in r['targets']:out[s][t]=out[s].get(t,0)+1
+  for a,b,n in reversed(ops):
+   if b<0:continue
+   for t,c in out[a].items():out[b][t]=out[b].get(t,0)+c
+  return out
+ badadj=None;live=sorted(set(word.phys.values())-removed);index={r:2*v+i for i,r in enumerate(live)};columns=2*v+len(live)
+ need(len(live)==physical_R,'terminal physical inventory')
+ def execute(mode,direction=1,bits=None,mutation=None):
+  nonlocal badadj
+  major=mode=='bound';binary=mode=='F2'
+  unit=(lambda i:1) if major else (lambda i:1<<i) if binary else (lambda i:1<<(bits*i))
+  def add(x,c,y):return x+abs(c)*y if major else x^y if binary and c&1 else x if binary else x+c*y
+  X0=[unit(i) for i in range(v)];Y0=[unit(v+i) for i in range(v)];Z0={r:unit(index[r]) for r in live}
+  x=X0[:];y=Y0[:];z=Z0.copy();done=[];top=1
+  def track(value):
+   nonlocal top
+   if major:top=max(top,value)
+   return value
+  responses=adj
+  if mutation=='omit-ancestor-response':
+   if badadj is None:badadj=without_deleted()
+   responses=badadj
+  def read(s):
+   value=z[word.phys[s]]
+   for t,c in responses[s].items():y[t]=track(add(y[t],-direction*c,value))
+  def gate(i,sign):
+   a,b,n=ops[i]
+   if i in word.served:z[word.phys[a]]=track(add(z[word.phys[a]],sign,x[word.served[i][0]]));return
+   a,b=word.phys[a],word.phys[b];z[a]=track(add(z[a],sign,z[b]))
+  for s in range(R):
+   if s not in word.gauge and s not in removed:read(s)
+  for n,s in word.source.items():z[word.phys[s]]=track(add(z[word.phys[s]],1,x[n]))
+  for e in word.k['entries']:
+   if e.get('early'):x[e['carrier']]=track(add(x[e['carrier']],1,x[e['passive']]))
+  for i in word.phase1:gate(i,1);done.append(i)
+  for r,s in zip(word.g['roots'],word.w['rootroles']):
+   if r['kind']=='center':
+    for t in r['targets']:y[t]=track(add(y[t],direction,z[word.phys[s]]))
+  for e in chosen:
+   if mutation=='omit-pre-target' and e is chosen[0]:continue
+   for t in e['targets']:
+    if t!=e['pivot']:y[t]=track(add(y[t],-1,y[e['pivot']]))
+  omitted=False
+  for j,i in enumerate(word.rest):
+   for s in at[j]:read(s)
+   if i in bywrite:
+    e=bywrite[i];a,b,n=ops[i]
+    if mutation=='omit-write' and not omitted:omitted=True
+    else:y[e['pivot']]=track(add(y[e['pivot']],direction,z[word.phys[b]]))
+   else:gate(i,1);done.append(i)
+   if i in after:
+    e=after[i]
+    for t in e['targets']:
+     if t!=e['pivot']:y[t]=track(add(y[t],1,y[e['pivot']]))
+  for s in at[len(word.rest)]:read(s)
+  for j,(r,s) in enumerate(zip(word.g['roots'],word.w['rootroles'])):
+   if r['kind']=='side' and j not in deletedroots:
+    for t in r['targets']:y[t]=track(add(y[t],direction,z[word.phys[s]]))
+   for e in deliveries[j]:
+    a,b=e['carrier'],e['passive']
+    if not e.get('early'):x[a]=track(add(x[a],1,x[b]))
+    for t in e['receivers']:y[t]=track(add(y[t],direction,x[a]))
+  for e in word.k['entries']:
+   a,b=e['carrier'],e['passive'];x[a]=track(add(x[a],-1,x[b]))
+  need(done==[i for i in order if i not in bywrite],'exact retained forward operation list')
+  for i in reversed(done):gate(i,-1)
+  for n,s in word.source.items():z[word.phys[s]]=track(add(z[word.phys[s]],-1,x[n]))
+  if binary:want=[Y0[t]^X0[t] for t in range(v)]
+  else:
+   # Independent defining integer decoder from source-disjoint graph supports.
+   # It includes all original roots and every original partner delivery.
+   want=Y0[:];cache={}
+   for r in word.g['roots']:
+    n=r['node']
+    if n not in cache:
+     mask=C.sup[n];value=0
+     while mask:
+      bit=mask&-mask;mask-=bit;value=add(value,1,X0[bit.bit_length()-1])
+     cache[n]=value
+    for t in r['targets']:want[t]=add(want[t],direction,cache[n])
+   for e in word.k['entries']:
+    value=add(X0[e['carrier']],1,X0[e['passive']])
+    for t in e['receivers']:want[t]=add(want[t],direction,value)
+  if major:return max(top,max(a+b for a,b in zip(y,want)),max(z[r]+Z0[r] for r in live),max(a+b for a,b in zip(x,X0)))
+  need(y==want,'all output columns equal the independent defining decoder')
+  need(z==Z0 and x==X0,'all dirty and source columns restored')
+  return dict(mode=mode,direction=direction,formal_columns=columns,source_columns=v,target_columns=v,dirty_columns=len(live),all_outputs=True,all_sources_and_dirty_restored=True,partner_mix_unmix_at_original_anchors=True,retained_cleanup_literal_reverse=True)
+ bound=execute('bound');bits=8*((bound.bit_length()+2+7)//8);need((1<<bits)>2*bound,'injective integer residual digit bound')
+ print('bound',bound,'bits',bits,'columns',columns,flush=True)
+ formal=[execute('F2')];gc.collect();formal.append(execute('Z',1,bits));gc.collect();formal.append(execute('Z',-1,bits));gc.collect()
+ controls={}
+ for mutation in ['omit-ancestor-response','omit-pre-target','omit-write']:
+  try:execute('F2',mutation=mutation)
+  except AssertionError:controls[mutation]='REJECTED'
+  else:raise AssertionError('accepted mutation '+mutation)
+ original_hist={int(r):n for r,n in baseline['child_histogram'].items()}
+ profile=dict(baseline,R=physical_R,terminal_sinks=len(chosen),active_virtual_R=R-len(chosen),scalar_role_reserve=R,W_per_vertex=W,rank_per_vertex=rank,child_histogram=compact(child),physical_internal_histogram=compact(local),physical_target_histogram=compact(Y))
+ return dict(status='PASS complete terminal bit word, exact geometry/ledger/F2/integer columns',profile=profile,baseline_profile=baseline,selected=chosen,target_events=events,child_delta=compact(delta),formal=formal,integer_residual_bound=bound,packed_digit_bits=bits,base_exceeds_twice_bound=True,controls=controls,literal_sandwich_inverse=True,all_original_adjoint_responses_retained=True,original_partner_delivery_anchors_retained=True,new_frames_added=0,scalar_addition_delta=-sum(len(e['writes'])+2 for e in chosen),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.',foreign_producer_replays=0,seconds=time.monotonic()-t0,maxrss=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)
+
+if __name__=='__main__':
+ if sys.flags.optimize:raise SystemExit('run without -O')
+ p=argparse.ArgumentParser();p.add_argument('--adapter',type=Path,required=True);p.add_argument('--selection',type=Path,required=True);p.add_argument('--out',type=Path,required=True);a=p.parse_args()
+ resource.setrlimit(resource.RLIMIT_CPU,(180,180));signal.alarm(180)
+ spec=importlib.util.spec_from_file_location('checked_bit_adapter',a.adapter);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);w=m.Candidate();w.exact_frames()
+ pins={str(p):sha256(p.read_bytes()).hexdigest() for p in [Path(__file__),a.adapter,a.adapter.with_name('base_word.py'),Path(w.module.__file__),a.selection,*w.input_paths]}
+ a.out.with_suffix('.inputs.json').write_text(json.dumps(pins,sort_keys=True,indent=2)+'\n')
+ data=json.loads(a.selection.read_text());selected=data['selected'] if isinstance(data,dict) else data
+ result=prove(w,selected)
+ for path,digest in pins.items():need(sha256(Path(path).read_bytes()).hexdigest()==digest,'source changed during proof: '+path)
+ result['input_pins']=pins;a.out.write_text(json.dumps(result,sort_keys=True,indent=2)+'\n');print(json.dumps({k:result[k] for k in ['status','seconds','integer_residual_bound','packed_digit_bits','controls','maxrss']}),flush=True)
diff --git a/research/served-diagonal-bit/bit/served_word.py b/research/served-diagonal-bit/bit/served_word.py
new file mode 100644
index 0000000000..6b8acf35d6
--- /dev/null
+++ b/research/served-diagonal-bit/bit/served_word.py
@@ -0,0 +1,386 @@
+"""Formal admission of the served physical bit word.
+
+Fork of PR200's bit/word.py and bit/base_word.py (Chafik Boukhalfa, Apache-2.0; built on eumemic's PR168 v4
+exact integer backend) with one new operation kind. A served operation ops[i] = [a, -1-d, n] adds the passive
+source data register x_d into the auxiliary register a at frame op_frame[i]; that partner pair's XOR
+x_c += x_d runs right after the injections ('early'), so its passive chain is line -> mix -> op_frame[i] -> full.
+Everything else is PR200's check, unchanged: phase-one closure, register contents, gauges, compensated pairs,
+physical chains, target chronology, partner chains, the paid ledger and the complete F2 and integer columns.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import gzip, importlib.util, json, sys
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+
+def module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    m = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(m)
+    return m
+
+
+def read(p):
+    raw = p.read_bytes()
+    return json.loads(gzip.decompress(raw) if p.suffix == '.gz' else raw)
+
+
+class Candidate:
+    def __init__(self, pr200_package, served_dir):
+        pr200_package, served_dir = Path(pr200_package), Path(served_dir)
+        SOURCE = pr200_package / 'references/pr168-v4'
+        self.module = backend = module('exact_integer_backend', SOURCE / 'research/paired-cube-bit/check_paired_cube_bit.py')
+        C = backend.Checker.__new__(backend.Checker); self.C = C; C.mut = None
+        B = pr200_package / 'selected/bit'
+        self.input_paths = [B / 'graph_p12.json', served_dir / 'profile_p12.json', served_dir / 'word_p12.json.gz',
+                            B / 'frames_p12.json.gz', served_dir / 'kchron_p12.json']
+        C.g, C.prof, C.w, C.fr, C.k = map(read, self.input_paths)
+        C.h = C.g['h']; C.v = C.g['v']; C.frames()
+        self.h, self.v, self.R = C.h, C.v, C.prof['R']; self.w, self.g, self.k = C.w, C.g, C.k
+        self.ops = self.w['ops']; self.nf = {int(n): f for n, f in self.w['node_frame'].items()}
+        self.served = {i: (d, f) for i, d, f in self.w['served']}
+        need(all(self.ops[i][1] == -1 - d for i, (d, f) in self.served.items()), 'served operations carry the passive marker')
+        need(all(b >= 0 for i, (a, b, n) in enumerate(self.ops) if i not in self.served), 'only served operations read data registers')
+        need(all(self.w['op_frame'][i] == f for i, (d, f) in self.served.items()), 'served frame is the operation frame')
+        self.source = {int(n): s for n, s in self.w['sources'].items()}; self.gauge = {z['role']: z for z in self.w['gauges']}
+        need(len(self.gauge) == len(self.w['gauges']), 'unique gauge roles')
+        self.original_opframe = tuple(self.nf[n] for a, b, n in self.ops); self.opframe = self.w['op_frame'][:]
+        need(len(self.opframe) == len(self.ops), 'complete operation frame vector')
+        self.changed_frames = [i for i, (a, b) in enumerate(zip(self.original_opframe, self.opframe)) if a != b]
+        self.phase1 = sorted(self.w['phase1']); phase = set(self.phase1)
+        self.rest = [i for i in range(len(self.ops)) if i not in phase]; order = self.phase1 + self.rest
+        self.position = {i: p for p, i in enumerate(order)}; pos = {i: p for p, i in enumerate(self.rest)}
+        self.order = [z['role'] for z in reversed(self.w['gauges'])]
+        self.role_ops = defaultdict(list)
+        for i in order:
+            for s in self.ops[i][:2]:
+                if s >= 0:
+                    self.role_ops[s].append(i)
+        need(all(xs == sorted(xs) for xs in self.role_ops.values()), 'execution order preserves every role chronology')
+        need(all(s in self.role_ops or s in set(self.w['rootroles']) for s in range(self.R)), 'every role is used')
+        self.first = {s: pos.get(xs[0], -1) for s, xs in self.role_ops.items()}
+        self.last = {s: pos.get(xs[-1], -1) for s, xs in self.role_ops.items()}
+        self.endframe = {s: self.opframe[xs[-1]] for s, xs in self.role_ops.items()}
+        self.rootroles = set(self.w['rootroles']); self.rootkind = {s: r['kind'] for s, r in zip(self.w['rootroles'], self.g['roots'])}
+        need(len(self.rootroles) == len(self.w['rootroles']), 'unique root roles')
+        reads = {int(s): p for s, p in self.w['reads'].items()}
+        need(set(reads) <= set(self.gauge), 'only gauges have explicit reads')
+        self.readtime = {s: reads.get(s, len(self.phase1)) - len(self.phase1) for s in self.order}
+        need(all(0 <= self.readtime[s] <= self.first[s] for s in self.order), 'all gauge reads after centre phase and before first use')
+        self.pairs = [[b, a] for a, b in self.w['pairs']]; self.donor = dict(self.pairs)
+        need(len(self.donor) == len(self.pairs) == len(set(self.donor.values())), 'one-to-one aliases')
+        need(not set(self.donor) & set(self.donor.values()), 'disjoint donor recipient sets')
+        for b, d in self.pairs:
+            need(d not in self.gauge and d not in self.rootroles and b in self.gauge, 'ungauged non-root donor and gauged recipient')
+            need(self.last[d] < self.readtime[b], 'donor dead before recipient read')
+        self.phys = {s: self.donor.get(s, s) for s in range(self.R)}
+        need(len(set(self.phys.values())) == self.R - len(self.pairs), 'physical slot count')
+        need(all(self.phys[a] != self.phys[b] for i, (a, b, n) in enumerate(self.ops) if i not in self.served), 'distinct physical gate ports')
+        C.chains = self.base_chains
+
+    # ---------------------------------------------------------------- PR200 base_word.py, served-aware
+    def exact_frames(self):
+        C = self.C
+        C.decoder(); C.geometry()
+        for i in self.changed_frames:
+            f = self.opframe[i]; x = self.ops[i][2]; bits = C.sup[x]
+            need(C.nondeg(f), 'replacement operation frame nondegenerate')
+            while bits:
+                low = bits & -bits; s = low.bit_length() - 1; bits -= low
+                need(C.in_frame(C.chi[s], f), 'value span in replacement operation frame')
+        for b, d in self.pairs:
+            need(C.sub(self.endframe[d], self.gauge[b]['frame']), 'exact Q donor-to-birth containment')
+            need(C.nondeg(self.endframe[d]) and C.nondeg(self.gauge[b]['frame']), 'handoff endpoints nondegenerate')
+        for i, (d, f) in self.served.items():
+            need(C.nondeg(f) and C.in_frame(C.chi[d], f), 'served passive line inside the served frame')
+
+    def register(self, rows):
+        C = self.C
+        B, _ = self.module.reduce_rows(rows, self.h)
+        B = tuple(sorted(map(tuple, B), key=lambda r: next(i for i, x in enumerate(r) if x)))
+        if not hasattr(self, 'frame_ids'):
+            self.frame_ids = {}
+        if B in self.frame_ids:
+            return self.frame_ids[B]
+        f = max(C.B) + 1; A, _ = self.module.kernel(B, C.h)
+        C.B[f], C.A[f], C.dimf[f] = B, A, len(B); self.frame_ids[B] = f
+        return f
+
+    def base_chains(self):
+        """Phase/gauge/source contracts; the served passive chains carry their extra stop."""
+        C, w, h, v = self.C, self.w, self.h, self.v
+        order = self.phase1 + self.rest
+        roleprev = {}; pred = []
+        for i, (a, b, n) in enumerate(self.ops):
+            pa = roleprev.get(a, -1); pb = roleprev.get(b, -1) if b >= 0 else -1
+            pred.append((pa, pb)); roleprev[a] = i
+            if b >= 0:
+                roleprev[b] = i
+        pending = [roleprev[s] for s in self.rootroles if self.rootkind[s] == 'center' and s in roleprev]; closure = set()
+        while pending:
+            i = pending.pop()
+            if i not in closure:
+                closure.add(i); pending.extend(j for j in pred[i] if j >= 0)
+        need(closure == set(self.phase1), 'phase one is exactly centre closure')
+        content = [0] * self.R
+        for n, s in self.source.items():
+            content[s] = 1 << n
+        for i in order:
+            a, b, n = self.ops[i]; args = self.g['args'][n]
+            if i in self.served:
+                d = self.served[i][0]
+                need(content[a] and args is not None and {content[a], 1 << d} == {C.sup[t] for t in args}, 'served addition operands')
+                content[a] |= 1 << d
+                continue
+            if content[a]:
+                need(args is not None and {content[a], content[b]} == {C.sup[t] for t in args}, 'actual addition operands')
+            else:
+                need(content[b] == C.sup[n], 'actual copied node value')
+            content[a] |= content[b]
+        co = [set() for _ in range(self.R)]
+        for r, s in zip(self.g['roots'], w['rootroles']):
+            co[s].update(r['targets'])
+        for i in reversed(order):
+            a, b, n = self.ops[i]
+            if b >= 0:
+                co[b].update(co[a])
+        touched = {s for i in self.phase1 for s in self.ops[i][:2] if s >= 0}
+        for s, z in self.gauge.items():
+            need(s not in self.source.values() and s not in touched, 'gauge untouched in phase one and source injection')
+            need(set(z['targets']) == co[s] and C.dimf[z['frame']] == z['dim'] > 0, 'gauge dimension and complete response support')
+        served_by_passive = {d: f for i, (d, f) in self.served.items()}
+        need(len(served_by_passive) == len(self.served), 'one served operation per passive source')
+        src = Counter(); members = Counter(); labels = list(map(set, self.g['labels']))
+        for e in self.k['entries']:
+            c, d, f, cap = e['carrier'], e['passive'], e['mix_frame'], e['deliver_frame']
+            need(len(labels[c] & labels[d]) == 1, 'orthogonal partner pair')
+            need(C.dimf[f] == 2 and C.in_frame(C.chi[c], f) and C.in_frame(C.chi[d], f), 'partner mix span')
+            need(C.sub(f, cap) and all(self.module.dot(C.cov[t], u) == 0 for t in e['receivers'] for u in C.B[cap]), 'partner mix delivery cap')
+            need(e['carrier_chain'] == [w['source_frame'][c], f, cap, w['full_frame']], 'exact carrier chain')
+            if d in served_by_passive:
+                need(e.get('early') is True, 'served pair mixes right after injection')
+                need(e['passive_chain'] == [w['source_frame'][d], f, served_by_passive[d], w['full_frame']], 'served passive chain')
+            else:
+                need(not e.get('early'), 'unserved pair keeps its delivery-time mix')
+                need(e['passive_chain'] == [w['source_frame'][d], f, w['full_frame']], 'exact passive chain')
+            root = self.g['roots'][e['deliver_after_root']]
+            need(root['kind'] == 'side' and sorted(e['receivers']) == sorted(root['targets']), 'partner delivery at own receiver root')
+            for chain in (e['carrier_chain'], e['passive_chain']):
+                for a, b in zip(chain, chain[1:]):
+                    need(C.sub(a, b), 'nested source chronology'); src[C.dimf[b] - C.dimf[a]] += 1
+            members[c] += 1; members[d] += 1
+        need(all(members[s] == 1 for s in range(v)), 'every source in one partner pair')
+        need(set(served_by_passive) <= {e['passive'] for e in self.k['entries']}, 'served sources are passive partners')
+        return Counter(), Counter(), src, self.R
+
+    def row(self):
+        C, h, v = self.C, self.h, self.v
+        _, baseline_Y, src, _ = C.chains()
+        seq = defaultdict(list)
+        for i, (a, b, x) in enumerate(self.ops):
+            seq[a].append(self.opframe[i])
+            if b >= 0:
+                seq[b].append(self.opframe[i])
+        for j, s in enumerate(self.w['rootroles']):
+            seq[s].append(self.w['root_frame'][j])
+        start = {b: self.w['source_frame'][x] for x, b in self.source.items()}
+        start.update({b: z['frame'] for b, z in self.gauge.items()})
+        recipient = {d: b for b, d in self.pairs}
+        H = Counter()
+        for s in range(self.R):
+            if s in self.donor:
+                continue
+            chain = list(seq[s])
+            if s in recipient:
+                b = recipient[s]; chain += [self.gauge[b]['frame']] + seq[b]
+            chain.append(self.w['full_frame'])
+            prev = start.get(s); dp = 0 if prev is None else C.dimf[prev]
+            if s in self.source.values():
+                H[1] += 1
+            for f in chain:
+                need(prev is None or C.sub(prev, f), 'physical role chain nested')
+                d = C.dimf[f]
+                if d > dp:
+                    H[d - dp] += 1
+                prev, dp = f, d
+        for j, r in enumerate(self.g['roots']):
+            if r['kind'] == 'center':
+                H[C.dimf[self.w['root_frame'][j]]] += 1
+        Y = Counter(); current = [None] * v
+
+        def readt(t, f):
+            old = current[t]; d = 0 if old is None else C.dimf[old]
+            need(old is None or C.sub(old, f), 'actual target frame chronology')
+            if C.dimf[f] > d:
+                Y[C.dimf[f] - d] += 1
+            current[t] = f
+        for b in sorted(self.order, key=lambda b: self.readtime[b]):
+            for t in self.gauge[b]['targets']:
+                readt(t, self.gauge[b]['frame'])
+        deliveries = defaultdict(list)
+        for e in self.k['entries']:
+            deliveries[e['deliver_after_root']].append(e)
+        for j, r in enumerate(self.g['roots']):
+            if r['kind'] != 'center':
+                for t in r['targets']:
+                    readt(t, self.w['root_frame'][j])
+            for e in deliveries[j]:
+                for t in e['receivers']:
+                    readt(t, e['deliver_frame'])
+        for t, f in enumerate(current):
+            need(f is not None and all(self.module.dot(C.cov[t], b) == 0 for b in C.B[f]), 'final target cap')
+            gap = h - 1 - C.dimf[f]
+            if gap:
+                Y[gap] += 1
+        need(sum(r * n for r, n in Y.items()) == v * (h - 1), 'target rank mass')
+        hist = Counter()
+        for part in (H, Y, src):
+            for r, n in part.items():
+                if r and n:
+                    hist[r] += 3 * n
+        for b, z in self.gauge.items():
+            if b not in self.donor:
+                hist[3 * z['dim']] += 1
+        hist[2] += 2 * v
+        hist = {r: n for r, n in sorted(hist.items()) if n}
+        need(all(0 < r < 3 * h and n > 0 for r, n in hist.items()), 'positive proper child bins')
+        R = self.R - len(self.pairs); W = 2 * v + R; mass = sum(r * n for r, n in hist.items()); m = 3 * h
+        need(W * m - mass == C.prof['deficit_per_vertex'], 'reuse preserves telescoping deficit')
+        return dict(h=h, v=v, R=R, virtual_R=self.R, reused_registers=len(self.pairs), W_per_vertex=W, m=m,
+                    loss=C.prof['loss'], rank_per_vertex=mass, deficit_per_vertex=W * m - mass,
+                    child_histogram=hist, maxchild=max(hist), selected_roles=len(self.gauge) - len(self.pairs),
+                    selected_rank_histogram=dict(Counter(z['dim'] for b, z in self.gauge.items() if b not in self.donor)),
+                    changed_operation_frames=len(self.changed_frames), served_operations=len(self.served),
+                    frames_not_contained_in_original=sum(not C.sub(self.opframe[i], self.original_opframe[i]) for i in self.changed_frames),
+                    physical_target_histogram=dict(Y), physical_internal_histogram=dict(H),
+                    source_data_histogram=dict(src), foreign_producer_replays=0)
+
+    def adjoint(self):
+        """Dirty-register responses; a data register is not a dirty auxiliary, so served operations add none."""
+        adj = [dict() for _ in range(self.R)]
+        for r, s in zip(self.g['roots'], self.w['rootroles']):
+            for t in r['targets']:
+                adj[s][t] = adj[s].get(t, 0) + 1
+        for a, b, _ in reversed(self.ops):
+            if b < 0:
+                continue
+            for t, c in adj[a].items():
+                adj[b][t] = adj[b].get(t, 0) + c
+        return adj
+
+    def formal(self, ring, tamper=None):
+        """All source, target and dirty-register columns; no random sampling."""
+        v, phys = self.v, self.phys
+        regs = sorted(set(phys.values())); index = {r: 2 * v + j for j, r in enumerate(regs)}
+        if ring == 2:
+            unit = lambda i: 1 << i
+
+            def accum(dst, val, c):
+                return dst ^ val if c & 1 else dst
+        else:
+            unit = lambda i: {i: 1}
+
+            def accum(dst, val, c):
+                out = dict(dst)
+                for i, z in val.items():
+                    k = out.get(i, 0) + c * z
+                    if k:
+                        out[i] = k
+                    else:
+                        out.pop(i, None)
+                return out
+        x = [unit(s) for s in range(v)]; y = [unit(v + t) for t in range(v)]
+        a = {r: unit(index[r]) for r in regs}
+        adj = self.adjoint()
+        at = defaultdict(list)
+        for b in self.order:
+            at[self.readtime[b]].append(b)
+        done = []
+        stale_used = False
+
+        def read(b):
+            nonlocal stale_used
+            if tamper == 'omit_compensation' and b == self.order[0]:
+                return
+            value = a[phys[b]]
+            if tamper == 'stale' and b in self.donor and not stale_used:
+                value = unit(index[phys[b]]); stale_used = True
+            for t, c in adj[b].items():
+                y[t] = accum(y[t], value, -c)
+
+        def op(i, sign):
+            b, d, _ = self.ops[i]
+            if i in self.served:
+                p = self.served[i][0]
+                if tamper == 'served_from_carrier':
+                    p = next(e['carrier'] for e in self.k['entries'] if e['passive'] == p)
+                a[phys[b]] = accum(a[phys[b]], x[p], sign)
+            else:
+                a[phys[b]] = accum(a[phys[b]], a[phys[d]], sign)
+        for b in range(self.R):
+            if b not in self.gauge:
+                read(b)
+        for s, b in self.source.items():
+            a[phys[b]] = accum(a[phys[b]], x[s], 1)
+        for e in self.k['entries']:
+            if e.get('early') and tamper != 'late_served_mix':
+                x[e['carrier']] = accum(x[e['carrier']], x[e['passive']], 1)
+        for i in self.phase1:
+            op(i, 1); done.append(i)
+        for r, b in zip(self.g['roots'], self.w['rootroles']):
+            if r['kind'] == 'center':
+                for t in r['targets']:
+                    y[t] = accum(y[t], a[phys[b]], 1)
+        for j, i in enumerate(self.rest):
+            for b in at[j]:
+                read(b)
+            op(i, 1); done.append(i)
+        for b in at[len(self.rest)]:
+            read(b)
+        deliveries = defaultdict(list)
+        for e in self.k['entries']:
+            deliveries[e['deliver_after_root']].append(e)
+        broken = False
+        for j, (r, b) in enumerate(zip(self.g['roots'], self.w['rootroles'])):
+            if r['kind'] != 'center':
+                for t in r['targets']:
+                    y[t] = accum(y[t], a[phys[b]], 1)
+            for e in deliveries[j]:
+                c, d = e['carrier'], e['passive']
+                if not e.get('early') or tamper == 'late_served_mix':
+                    x[c] = accum(x[c], x[d], 1)
+                for t in e['receivers']:
+                    if tamper == 'missing_partner' and not broken:
+                        broken = True; continue
+                    y[t] = accum(y[t], x[c], 1)
+        for e in self.k['entries']:
+            x[e['carrier']] = accum(x[e['carrier']], x[e['passive']], -1)
+        for i in reversed(done):
+            op(i, -1)
+        for s, b in self.source.items():
+            a[phys[b]] = accum(a[phys[b]], x[s], -1)
+        need(all(a[r] == unit(index[r]) for r in regs), 'all dirty register columns restored')
+        need(all(x[s] == unit(s) for s in range(v)), 'all source columns restored')
+        if ring == 2:
+            want = [accum(unit(v + t), unit(t), 1) for t in range(v)]
+        else:
+            support = [{s: 1} for s in range(v)]
+            for aa, bb in self.g['args'][v:]:
+                support.append(accum(support[aa], support[bb], 1))
+            want = [unit(v + t) for t in range(v)]
+            for r in self.g['roots']:
+                for t in r['targets']:
+                    want[t] = accum(want[t], support[r['node']], 1)
+            for e in self.k['entries']:
+                for t in e['receivers']:
+                    want[t] = accum(want[t], unit(e['carrier']), 1)
+                    want[t] = accum(want[t], unit(e['passive']), 1)
+        need(y == want, 'all target columns equal defining decoder')
+        return dict(ring=str(ring), formal_variables=2 * v + len(regs),
+                    target_contract='F2 identity' if ring == 2 else 'integer defining decoder',
+                    identity=ring == 2, defining_decoder=True, all_dirty_and_source_columns_restored=True,
+                    served_operations=len(self.served))
diff --git a/research/served-diagonal-bit/certificate.json b/research/served-diagonal-bit/certificate.json
new file mode 100644
index 0000000000..2a0596e683
--- /dev/null
+++ b/research/served-diagonal-bit/certificate.json
@@ -0,0 +1,2084 @@
+{
+  "arithmetic": {
+    "after_packing": {
+      "assembly": {
+        "absorption_gap": "47916996423941817584536139642579287944193398784679205605438902950313556604535761451479043573020529536050799004007190390173/77405060643580954767609614251034024326988850885024976472140454090775754236834369522779043752950749183654653189609827000000000000000000000000",
+        "margins": {
+          "Gaussian_arithmetic": "85720792105765251937805396593795342227393806425711321400399556390321753958519095992379228966961859477922324331970249250816345346810390173/123848097029729527628175382801654438923182161416039962355424726545241206778934991236446470004721198693847445103375723200000000000000000000000",
+          "balanced_prefix": "53575495066103282461176751034024326988850885024976472140454090775754236834369522779043752950749183654653189609827/77405060643580954767609614251034024326988850885024976472140454090775754236834369522779043752950749183654653189609827",
+          "bulk_exposure": "10822250003352863057142100353372920757473993059245954118213241284688474332450880027849407473/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "compact_phase_layer": "53575495066103282461099345973380746034083275410725438116127101924869211857897382324952977196512349285130410566074049250816345346810390173/77405060643580954767609614251034024326988850885024976472140454090775754236834369522779043752950749183654653189609827000000000000000000000000",
+          "coordinate_movement": "10822250003352863057142100353372920757473993059245954118213241284688474332450880027849407473/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "dimension": "77351485148514851485148437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/77405060643580954767609614251034024326988850885024976472140454090775754236834369522779043752950749183654653189609827",
+          "scalar_work": "428603960528826259689336603211551034956039470585560743099305737355148869698484041778259247851756634867702737834863049250816345346810390173/619240485148647638140876914008272194615910807080199811777123632726206033894674956182232350023605993469237225516878616000000000000000000000000"
+        },
+        "minimum_constraint": "10822250003352863057142100353372920757473993059245954118213241284688474332450880027849407473/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "minimum_margin": "53575495066103282461099345973380746034083275410725438116127101924869211857897382324952977196512349285130410566074049250816345346810390173/77405060643580954767609614251034024326988850885024976472140454090775754236834369522779043752950749183654653189609827000000000000000000000000",
+        "parameters": {
+          "C0": {
+            "base": 2,
+            "exponent": 210000
+          },
+          "C1": 1,
+          "a_bit": "10822250003352863057142100353372920757473993059245954118213241284688474332450880027849407473/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "a_complex": "700918443859411/1000000000000000000",
+          "alpha_squared_power": "107150990132206564922276097007405073022934160435701910256581192700623448692266905103996730147261532939783600175901049250816345346810390173/154810121287161909535219228502068048653977701770049952944280908181551508473668739045558087505901498367309306379219654000000000000000000000000",
+          "beta": "1/1000000000000000000000000",
+          "c": "5411125001676431528572992479436457025873939387522623686185863168351177920271321800683419048025667549119972150592527/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "delta": "1/8000000000000000000000000",
+          "epsilon": "77351485148514851485148437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/77405060643580954767609614251034024326988850885024976472140454090775754236834369522779043752950749183654653189609827",
+          "eta": "1/1000000000000000000000000",
+          "kappa": "34607230212503/50000000000000000",
+          "lambda_": "15614177749996647136942857910468877082595389064082854399254707516189304584913503238185391877215474332450880027849407473/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "lambda_prime": "7807088874998323568471428960645563542974126060612477376313814136831648822079728678199316580951974332450880027849407473/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "q": "5411125001676431528571039354436457025873939387522623686185863168351177920271321800683419048025667549119972150592527/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "sigma": "999299081556140589/1000000000000000000",
+          "tau": "15614177749996647136942857899646627079242526006940754045881786758715311525667549119972150592527/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+        },
+        "recurrence": {
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+          "leaf": "999299081556140589000000000700918443859411/1000000000000000000000000000000000000000000",
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+        },
+        "strict_constraint_count": 47
+      },
+      "binding": "bit",
+      "kappa": "34607230212503/50000000000000000"
+    },
+    "before_packing": {
+      "binding": "bit",
+      "kappa": "685800818606951/1000000000000000000"
+    },
+    "bit_after": {
+      "accepted": {
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+        "saving": "346312000108347/500000000000000000",
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+      },
+      "saving": "346312000108347/500000000000000000"
+    },
+    "bit_before": {
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+        "saving": "85839543004729/125000000000000000",
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+      },
+      "saving": "85839543004729/125000000000000000"
+    },
+    "bit_coarse_relative_gain": "2953828089431/343358172018916",
+    "bit_word": "served word: PR200 terminal word with 373 served diagonal operations (selected/served)",
+    "comparison_pr205_kappa": "683061299399923/1000000000000000000",
+    "comparison_pr217_kappa": "684696826673891/1000000000000000000",
+    "complex": {
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+      },
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+      },
+      "saving": "700918443859411/1000000000000000000"
+    },
+    "complex_profile": {
+      "L": 0,
+      "N": 1320,
+      "W": 12052,
+      "child_multiplicities": {
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+        "10": 2790,
+        "11": 1062,
+        "12": 3591,
+        "13": 381,
+        "14": 2226,
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+        "8": 4593,
+        "9": 1287
+      },
+      "m": 66,
+      "maxchild": 20,
+      "total_rank": 794112
+    },
+    "controls": [
+      "changed rank mass"
+    ],
+    "extra_selector_calls": 5251508388,
+    "kappa_gain_from_packing": "6343785643109/1000000000000000000",
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+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1656,
+          "role": 13811,
+          "root": 6210,
+          "root_frame": 29744,
+          "root_rank": 21,
+          "targets": [
+            1656,
+            1657,
+            1658,
+            1659
+          ],
+          "writes": [
+            24759,
+            29055,
+            32218
+          ]
+        },
+        {
+          "deleted_path": [
+            19,
+            2,
+            3
+          ],
+          "pivot": 1688,
+          "role": 14395,
+          "root": 6330,
+          "root_frame": 29832,
+          "root_rank": 21,
+          "targets": [
+            1688,
+            1689,
+            1690,
+            1691
+          ],
+          "writes": [
+            29212,
+            32589
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1704,
+          "role": 13829,
+          "root": 6390,
+          "root_frame": 29876,
+          "root_rank": 21,
+          "targets": [
+            1704,
+            1705,
+            1706,
+            1707
+          ],
+          "writes": [
+            24873,
+            29219,
+            32532
+          ]
+        },
+        {
+          "deleted_path": [
+            14,
+            5,
+            2,
+            3
+          ],
+          "pivot": 1728,
+          "role": 13847,
+          "root": 6480,
+          "root_frame": 29942,
+          "root_rank": 21,
+          "targets": [
+            1728,
+            1729,
+            1730,
+            1731
+          ],
+          "writes": [
+            24987,
+            29383,
+            32854
+          ]
+        }
+      ],
+      "status": "PASS complete terminal bit word, exact geometry/ledger/F2/integer columns",
+      "target_events": 16810
+    },
+    "unsunk_profile": {
+      "R": 16775,
+      "W_per_vertex": 20295,
+      "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": 57535,
+        "20": 5280,
+        "21": 15120,
+        "22": 5553,
+        "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": 35391,
+        "10": 674,
+        "11": 404,
+        "12": 1354,
+        "13": 542,
+        "14": 1224,
+        "15": 288,
+        "16": 996,
+        "17": 452,
+        "18": 538,
+        "19": 216,
+        "2": 17125,
+        "21": 3787,
+        "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": 1459304,
+      "reused_registers": 1760,
+      "selected_rank_histogram": {
+        "20": 2200
+      },
+      "selected_roles": 2200,
+      "served_operations": 373,
+      "source_data_histogram": {
+        "1": 2133,
+        "2": 880,
+        "20": 880,
+        "21": 373,
+        "22": 507
+      },
+      "v": 1760,
+      "virtual_R": 18535
+    },
+    "used_frames": 24401,
+    "used_frames_witnessed_by_pr200": true,
+    "word_controls": [
+      "omit_compensation",
+      "missing_partner",
+      "stale",
+      "served_from_carrier",
+      "zero_operation_frame",
+      "served_passive_chain_without_stop",
+      "served_pair_without_early_mix"
+    ]
+  }
+}
diff --git a/research/served-diagonal-bit/controls.py b/research/served-diagonal-bit/controls.py
new file mode 100644
index 0000000000..5123541528
--- /dev/null
+++ b/research/served-diagonal-bit/controls.py
@@ -0,0 +1,35 @@
+"""Independent weighted completed-bank endpoint checks on arbitrary formal data."""
+from math import gcd
+
+
+def run():
+    m=72;cases=0;rejected=[]
+    patterns=([4]*6+[24]*2,[24]*3)
+    def apply(parts,modulus,reverse=False,repeat_first=False):
+        rows=[{i:1} for i in range(2*m)]
+        intervals=[];offset=0
+        for width in parts:intervals.append(range(offset,offset+width));offset+=width
+        if repeat_first:intervals.append(intervals[0])
+        if reverse:intervals.reverse()
+        for interval in intervals:
+            for i in interval:
+                weight=(1,2,4)[i%3];assert gcd(weight,modulus)==1
+                a,b=rows[i],rows[2*m-1-i]
+                rows[i]={j:weight*x%modulus for j,x in b.items()}
+                rows[2*m-1-i]={j:pow(weight,-1,modulus)*x%modulus for j,x in a.items()}
+        return rows
+    def expected(modulus):
+        return [{2*m-1-i:(1,2,4)[i%3]} for i in range(m)]+[
+            {m-1-i:pow((1,2,4)[(m-1-i)%3],-1,modulus)} for i in range(m)]
+    for modulus in (9,25,125):
+        for pattern in patterns:
+            for reverse in (False,True):
+                assert apply(pattern,modulus,reverse)==expected(modulus)
+                cases+=1
+        try:assert apply(patterns[0],modulus,repeat_first=True)==expected(modulus)
+        except AssertionError:rejected.append('repeated block mod '+str(modulus))
+        else:raise AssertionError('Repeated block accepted')
+        try:assert apply(patterns[0][:-1],modulus)==expected(modulus)
+        except AssertionError:rejected.append('omitted block mod '+str(modulus))
+        else:raise AssertionError('Omitted block accepted')
+    return dict(formal_columns_per_case=2*m,weighted_partition_cases=cases,rejected=rejected)
diff --git a/research/served-diagonal-bit/packing.py b/research/served-diagonal-bit/packing.py
new file mode 100644
index 0000000000..a60c472ee8
--- /dev/null
+++ b/research/served-diagonal-bit/packing.py
@@ -0,0 +1,145 @@
+"""Exact gauge charts and completed-residual bank allocation on the served bit word.
+
+PR205's packing.py (Rohan Arun; chart, colouring and inventory method from PR197, Evan McKinney, Apache-2.0),
+applied to the served word (PR200's terminal-modified word with 373 served diagonal operations) instead of
+PR200's word. Only the word file, its role count and the derived totals change. Apache-2.0.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from math import gcd
+from pathlib import Path
+import gzip, hashlib, json, sys
+if hasattr(sys, "set_int_max_str_digits"): sys.set_int_max_str_digits(0)
+
+HERE = Path(__file__).resolve().parent
+PACKAGE = 'research/paired-cube-diagonal-bit-168'
+sys.path.insert(0, str(HERE))
+from banks import inverse_integer, color_incidence, check_coloring   # PR197's helpers, byte-identical
+
+
+def kernel_basis(A, n):
+    """Integer basis of {x in Q^n : A x = 0}, by exact RREF."""
+    M = [[Q(x) for x in row] for row in A]; piv = []; r = 0
+    for c in range(n):
+        p = next((i for i in range(r, len(M)) if M[i][c]), None)
+        if p is None: continue
+        M[r], M[p] = M[p], M[r]; inv = 1 / M[r][c]; M[r] = [x * inv for x in M[r]]
+        for i in range(len(M)):
+            if i != r and M[i][c]: f = M[i][c]; M[i] = [x - f * y for x, y in zip(M[i], M[r])]
+        piv.append(c); r += 1
+        if r == len(M): break
+    free = [c for c in range(n) if c not in piv]; out = []
+    for fcol in free:
+        v = [Q(0)] * n; v[fcol] = Q(1)
+        for i, pc in enumerate(piv): v[pc] = -M[i][fcol]
+        den = 1
+        for x in v: den = den * x.denominator // gcd(den, x.denominator)
+        iv = [int(x * den) for x in v]; g = 0
+        for x in iv: g = gcd(g, abs(x))
+        out.append([x // g for x in iv])
+    return out
+
+
+def build(BIT, SERVED, profile):
+    """BIT: pinned PR200 checkout; SERVED: the served word directory; profile: served_prove's terminal profile."""
+    pkg = BIT / PACKAGE
+    word = json.loads(gzip.decompress((SERVED / 'word_p12.json.gz').read_bytes()))
+    frames = json.loads((pkg / 'selected/bit/frames_p12.json').read_text())['frames']
+    sinks = json.loads((pkg / 'selected/bit/sinks.json').read_text())
+    word_sha = hashlib.sha256((SERVED / 'word_p12.json.gz').read_bytes()).hexdigest()
+    h = 24
+    R = 1 + max(max(o[0], o[1]) for o in word['ops'])
+    assert R == profile['virtual_R'] == profile['scalar_role_reserve'] == 18908 - 373 == 18535
+    assert len(word['served']) == profile['served_operations'] == 373
+    donors = {a for a, b in word['pairs']}; recipients = {b for a, b in word['pairs']}
+    gauges = {z['role']: z for z in word['gauges']}
+    assert len(donors) == len(recipients) == len(word['pairs']) == profile['reused_registers'] == 1760
+    assert not donors & recipients and not donors & gauges.keys() and recipients <= gauges.keys()
+    sink_roles = {word['rootroles'][z['root']] for z in sinks}
+    assert len(sink_roles) == len(sinks) == profile['terminal_sinks'] == 34
+    assert not sink_roles & (donors | recipients | gauges.keys())
+    physical = sorted(set(range(R)) - recipients - sink_roles); ren = {r: i for i, r in enumerate(physical)}
+    assert len(physical) == profile['R'] == 16741
+    selected = set(gauges) - recipients
+    assert len(selected) == 2200 and {gauges[r]['dim'] for r in selected} == {20}
+    assert {gauges[r]['dim'] for r in recipients} == {21}
+    assert profile['selected_rank_histogram'] == {'20': 2200}
+    # Interior rank-21 recipient starts are paid splices, not entrance residuals.
+    inventory = Counter(gauges[r]['frame'] for r in selected)
+    digest = hashlib.sha256(); maxops = maxnum = maxden = 0
+    for f, count in sorted(inventory.items()):
+        rec = frames[str(f)]; A = rec['a']
+        assert rec['dim'] == 20 and len(A) == 4
+        source = kernel_basis(A, h)
+        assert len(source) == 20 and all(sum(x * y for x, y in zip(a, s)) == 0 for a in A for s in source)
+        residual = []
+        for a in A:
+            row = [15 * x - sum(a) for x in a]; d = gcd(*row); residual.append([x // d for x in row])
+        # G-orthogonality for G = 9I - J (the bit Gram I - J/9, scaled by 9)
+        assert all(9 * sum(x * y for x, y in zip(a, b)) - sum(a) * sum(b) == 0 for a in residual for b in source)
+        B = list(map(list, zip(*(residual + source))))
+        C, d, ops = inverse_integer(B)
+        for left, right in ((B, C), (C, B)):
+            assert all(sum(x * y for x, y in zip(row, col)) == d * int(i == j)
+                       for i, row in enumerate(left) for j, col in enumerate(zip(*right)))
+        replay = [list(map(Q, row)) for row in B]
+        for op, i, j, num, den in ops:
+            if op == 'swap': replay[i], replay[j] = replay[j], replay[i]
+            elif op == 'scale': replay[i] = [Q(num, den) * x for x in replay[i]]
+            else:
+                assert op == 'add'; replay[i] = [x + Q(num, den) * y for x, y in zip(replay[i], replay[j])]
+        assert all(x == int(i == j) for i, row in enumerate(replay) for j, x in enumerate(row))
+        maxops = max(maxops, len(ops)); maxnum = max(maxnum, max(abs(op[3]) for op in ops))
+        maxden = max(maxden, d, max(op[4] for op in ops))
+        digest.update(json.dumps([f, count, B, C, d, ops], separators=(',', ':')).encode())
+    assert max(maxnum, maxden) < 2 ** 80
+    families = {4: sorted(selected), 24: sorted(set(physical) - selected)}
+    degree = 9; copies = 3; small = degree * len(selected) // 6
+    assert 6 * small == degree * len(selected)
+    large = (degree * len(families[24]) - 2 * small) // 3
+    assert 3 * large + 2 * small == degree * len(families[24])
+    left = []; right = []; offsets = []; counts = Counter(); bank = 0
+    for pattern, n in (({4: 6, 24: 2}, small), ({24: 3}, large)):
+        for _ in range(n):
+            offset = 0
+            for rank, mult in sorted(pattern.items()):
+                for _ in range(mult):
+                    role = families[rank][counts[rank] // degree]
+                    left.append(ren[role]); right.append(bank); offsets.append(offset); counts[rank] += 1; offset += rank
+            assert offset == 72
+            bank += 1
+    assert all(counts[r] == degree * len(rs) for r, rs in families.items())
+    labels, stats = color_incidence(left, right, len(physical), bank, degree)
+    check_coloring(left, right, labels, len(physical), bank, degree, full_left=True)
+    first = {}; rejected = False
+    for e, r in enumerate(left):
+        if r not in first: first[r] = e; continue
+        old = labels[e]; labels[e] = labels[first[r]]
+        try: check_coloring(left, right, labels, len(physical), bank, degree, full_left=True)
+        except AssertionError: rejected = True
+        finally: labels[e] = old
+        break
+    assert rejected
+    incidence = hashlib.sha256()
+    for r, b, c, o in zip(left, right, labels, offsets): incidence.update(f'{r},{b},{c},{o}\n'.encode())
+    H = Counter({int(r): copies * n for r, n in profile['child_histogram'].items()})
+    assert H.pop(60) == copies * len(selected)
+    assert not any(r > 22 for r in H)
+    W = 2 * profile['v'] * copies + bank; mass = sum(r * n for r, n in H.items())
+    assert 72 * W - mass == copies * profile['deficit_per_vertex'] == 5808
+    K = 18 * ((W - 1) + len(physical) * 72 * (maxops + 71))
+    return dict(status='PASS exact actual-chain chart and incidence checks', source_package=PACKAGE,
+                served_word='selected/served/word_p12.json.gz',
+                word_sha256=word_sha, physical_roles=len(physical), interior_splices=len(recipients),
+                terminal_sinks=len(sink_roles), gauge_roles=len(selected), distinct_gauges=len(inventory), copies=copies,
+                banks=bank, patterns=[dict(rank4=6, rank24=2, count=small), dict(rank4=0, rank24=3, count=large)],
+                incidences=len(left), W=W, m=72, rank_mass=mass, deficit=5808, maxchild=max(H),
+                child_histogram=dict(sorted(H.items())), chart_sha256=digest.hexdigest(),
+                incidence_sha256=incidence.hexdigest(), max_chart_factors=maxops, max_num=maxnum, max_den=maxden,
+                conservative_selector_calls=K, color_stats=stats, conflicting_assignment_rejected=rejected)
+
+
+if __name__ == '__main__':
+    import time; t = time.time()
+    r = build(Path(sys.argv[1]), Path(sys.argv[2]), json.loads(Path(sys.argv[3]).read_text())['profile'])
+    print(json.dumps({k: v for k, v in r.items() if k != 'child_histogram'}, indent=1), time.time() - t)
diff --git a/research/served-diagonal-bit/patch.py b/research/served-diagonal-bit/patch.py
new file mode 100644
index 0000000000..e08a838adb
--- /dev/null
+++ b/research/served-diagonal-bit/patch.py
@@ -0,0 +1,156 @@
+#!/usr/bin/env python3
+"""Derive the served bit word from PR200's frozen physical bit word (deterministic; standard library only).
+
+A partner pair (carrier c, passive d) is mixed on its two source data registers at its 2-dim mix frame.
+PR200's word also forms the same sum x_c + x_d in auxiliary registers: operation i = (a, b, n) with node n the
+partner diagonal. When the destination a holds x_c and the control b is a pure copy of x_d (created by one copy
+operation and used only at i), this patch
+
+  * deletes b and its copy operation;
+  * reads x_d at operation i from the passive data register instead of from b;
+  * moves that pair's partner XOR to the start of the word (right after the injections), so the passive
+    register's chain line -> mix -> F_i -> full stays ascending, where F_i is operation i's frame.
+
+Every other operation, frame, gauge, pair, read, root and terminal sink is kept. Roles and operations are
+renumbered compactly; read positions follow the removed operations. Usage:
+
+    python3 patch.py PR200_PACKAGE_DIR OUT_DIR
+"""
+import gzip, json, sys
+from collections import defaultdict
+from pathlib import Path
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def dumps(obj):
+    return json.dumps(obj, sort_keys=True, separators=(',', ':')) + '\n'
+
+
+def exact_subset(pkg):
+    """PR200's own exact frame algebra (its retained PR168 v4 integer backend): sub(f, g) is f inside g."""
+    sys.path.insert(0, str(pkg / 'bit'))
+    import word as pr200_word
+    cand = pr200_word.Candidate()
+    return cand.C.sub
+
+
+def patch(pkg):
+    sel = pkg / 'selected/bit'
+    g = read(sel / 'graph_p12.json')
+    w = read(sel / 'word_p12.json')
+    k = read(sel / 'kchron_p12.json')
+    prof = read(sel / 'profile_p12.json')
+    sub = exact_subset(pkg)
+    v, args, ops = g['v'], g['args'], w['ops']
+    R = prof['R']
+    phase = set(w['phase1'])
+    order = sorted(phase) + [i for i in range(len(ops)) if i not in phase]
+    role_ops = defaultdict(list)
+    for i in order:
+        a, b, n = ops[i]
+        role_ops[a].append(i)
+        role_ops[b].append(i)
+    sources = {int(x): s for x, s in w['sources'].items()}
+    content = defaultdict(int)
+    for x, s in sources.items():
+        content[s] = 1 << x
+    before = {}
+    for i in order:
+        a, b, n = ops[i]
+        before[i] = (content[a], content[b])
+        content[a] |= content[b]
+    special = set(w['rootroles']) | {z['role'] for z in w['gauges']} | set(sources.values())
+    special |= {x for p in w['pairs'] for x in p}
+    entry = {}
+    for e in k['entries']:
+        entry[frozenset((e['carrier'], e['passive']))] = e
+    served, dead_roles, dead_ops = {}, set(), set()
+    for i, (a, b, n) in enumerate(ops):
+        pair = args[n]
+        if pair is None or len(pair) != 2 or not all(x < v for x in pair) or frozenset(pair) not in entry:
+            continue
+        e = entry[frozenset(pair)]
+        c, d = e['carrier'], e['passive']
+        ca, cb = before[i]
+        if ca != 1 << c or cb != 1 << d or b in special:
+            continue
+        if len(role_ops[b]) != 2 or role_ops[b][1] != i:
+            continue
+        j = role_ops[b][0]
+        ja, jb, jn = ops[j]
+        if ja != b or args[jn] is not None or jn != d:
+            continue
+        if not sub(e['mix_frame'], w['op_frame'][i]):
+            continue
+        served[i] = dict(passive=d, carrier=c, frame=w['op_frame'][i])
+        dead_roles.add(b)
+        dead_ops.add(j)
+    # compact renumbering of roles and operations
+    keep_roles = [s for s in range(R) if s not in dead_roles]
+    rmap = {s: t for t, s in enumerate(keep_roles)}
+    keep_ops = [i for i in range(len(ops)) if i not in dead_ops]
+    omap = {i: t for t, i in enumerate(keep_ops)}
+    new_ops = []
+    for i in keep_ops:
+        a, b, n = ops[i]
+        if i in served:
+            new_ops.append([rmap[a], -1 - served[i]['passive'], n])     # negative control: passive data register
+        else:
+            new_ops.append([rmap[a], rmap[b], n])
+    # execution positions: reads count positions in phase1 + rest order
+    old_pos = {i: p for p, i in enumerate(order)}
+    kept_before = []
+    count = 0
+    for i in order:
+        kept_before.append(count)
+        if i not in dead_ops:
+            count += 1
+    kept_before.append(count)
+    nw = dict(w)
+    nw['ops'] = new_ops
+    nw['op_frame'] = [w['op_frame'][i] for i in keep_ops]
+    nw['phase1'] = sorted(omap[i] for i in w['phase1'] if i not in dead_ops)
+    nw['sources'] = {x: rmap[s] for x, s in w['sources'].items()}
+    nw['rootroles'] = [rmap[s] for s in w['rootroles']]
+    nw['gauges'] = [dict(z, role=rmap[z['role']]) for z in w['gauges']]
+    nw['pairs'] = [[rmap[a], rmap[b]] for a, b in w['pairs']]
+    nw['reads'] = {str(rmap[int(s)]): kept_before[p] for s, p in w['reads'].items()}
+    nw['served'] = sorted([omap[i], z['passive'], z['frame']] for i, z in served.items())
+    nw['served_schedule'] = ('served operation [i, d, F]: ops[i] = [a, -1-d, n] adds the passive source data register '
+                             'x_d into a at frame F (op_frame[i]); that pair\'s partner XOR runs right after the '
+                             'injections (kchron early), and the passive chain is line -> mix -> F -> full')
+    nk = dict(k)
+    nk['entries'] = []
+    by_passive = {z['passive']: z for z in served.values()}
+    for e in k['entries']:
+        e = dict(e)
+        z = by_passive.get(e['passive'])
+        if z is not None:
+            e['early'] = True
+            line, mix, full = e['passive_chain']
+            e['passive_chain'] = [line, mix, z['frame'], full]
+            e['passive_ranks'] = None   # recomputed by the verifier from the exact frames
+        nk['entries'].append(e)
+    nprof = dict(prof)
+    nprof['R'] = R - len(dead_roles)
+    nprof['served_note'] = 'R counts logical roles after deleting the served pure-copy controls'
+    return dict(word=nw, kchron=nk, profile=nprof, served=len(served), deleted_roles=len(dead_roles),
+                deleted_ops=len(dead_ops))
+
+
+def main():
+    pkg, out = Path(sys.argv[1]), Path(sys.argv[2])
+    out.mkdir(parents=True, exist_ok=True)
+    r = patch(pkg)
+    (out / 'word_p12.json.gz').write_bytes(gzip.compress(dumps(r['word']).encode(), mtime=0))
+    (out / 'kchron_p12.json').write_bytes(dumps(r['kchron']).encode())
+    (out / 'profile_p12.json').write_bytes(dumps(r['profile']).encode())
+    print(json.dumps(dict(served=r['served'], deleted_roles=r['deleted_roles'], deleted_ops=r['deleted_ops'])))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/served-diagonal-bit/selected/served/kchron_p12.json b/research/served-diagonal-bit/selected/served/kchron_p12.json
new file mode 100644
index 0000000000..ec5760fc11
--- /dev/null
+++ b/research/served-diagonal-bit/selected/served/kchron_p12.json
@@ -0,0 +1 @@
+{"conventions":{"frame_ids":"frame id = id of the canonical annihilator; record \"a\" lists integer annihilator rows (frame = common kernel), record \"b\" lists integer basis rows; id 0 (empty \"a\") is the full space Q^h","gram":"G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested for G","nodes":"zero-based graph nodes; nodes < v are the source leaves (port index)","ops":"[dest, control, node]: dest ^= control at the frame of node (copies: dest is the fresh role)","target_covector":"3*chi_T - 1 (target cap = {u : (3 chi_T - 1).u = 0} = H0-orthogonal complement of 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diff --git a/research/served-diagonal-bit/verify.py b/research/served-diagonal-bit/verify.py
new file mode 100644
index 0000000000..49e5c9d270
--- /dev/null
+++ b/research/served-diagonal-bit/verify.py
@@ -0,0 +1,106 @@
+#!/usr/bin/env python3
+"""Verify the served diagonal bit supplier, packed with PR205's banks, against PR193's complex supplier.
+
+PR205's verify.py (Rohan Arun; adapted from PR197's, Evan McKinney, Apache-2.0) with two added steps:
+patch.py re-derives the served word from PR200's frozen word, and bit/served_prove.py checks the served word
+completely (F2 identity, integer decoder, exact frames, chains, terminal sinks and paid moment).
+"""
+from pathlib import Path
+import argparse, gzip, hashlib, json, os, subprocess, sys, tempfile
+if sys.flags.optimize: raise SystemExit('Assertions required')
+sys.set_int_max_str_digits(0)
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import packing, arithmetic, audit, controls
+from fractions import Fraction as Q
+
+BIT_PACKAGE = 'research/paired-cube-diagonal-bit-168'
+SERVED = HERE / 'selected/served'
+SERVED_FILES = ('word_p12.json.gz', 'kchron_p12.json', 'profile_p12.json')
+
+
+def serial(value):
+    if isinstance(value, Q): return str(value)
+    if isinstance(value, dict): return {str(k): serial(v) for k, v in value.items()}
+    if isinstance(value, (list, tuple)): return [serial(v) for v in value]
+    return value
+
+
+def run(root, script, *args):
+    subprocess.run([sys.executable, '-B', str(root / script), *args], cwd=root, check=True,
+                   env=dict(os.environ, PYTHONDONTWRITEBYTECODE='1'))
+
+
+def capture(script, *args):
+    """Run one of this package's scripts and parse the JSON record on its last stdout line."""
+    out = subprocess.run([sys.executable, '-B', str(script), *args], check=True, capture_output=True, text=True,
+                         env=dict(os.environ, PYTHONDONTWRITEBYTECODE='1')).stdout
+    return json.loads(out.strip().splitlines()[-1])
+
+
+def rederive(bit):
+    """patch.py must reproduce the frozen served word, schedule and profile from PR200's frozen word.
+
+    The gzip container is compared after decompression: its deflate bytes depend on the zlib build."""
+    with tempfile.TemporaryDirectory() as tmp:
+        stats = capture(HERE / 'patch.py', str(bit / BIT_PACKAGE), tmp)
+        for name in SERVED_FILES:
+            new, old = (Path(tmp) / name).read_bytes(), (SERVED / name).read_bytes()
+            if name.endswith('.gz'): new, old = gzip.decompress(new), gzip.decompress(old)
+            assert new == old, ('patch.py does not reproduce the frozen file', name)
+    assert stats == dict(served=373, deleted_roles=373, deleted_ops=373), stats
+    return dict(stats, reproduced=list(SERVED_FILES))
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--complex-root', type=Path, required=True, help='Checkout of the pinned PR193 commit')
+    parser.add_argument('--bit-root', type=Path, required=True, help='Checkout of the pinned PR200 commit')
+    parser.add_argument('--full', action='store_true',
+                        help='Run both inherited verifiers, re-derive and prove the served word, then rebuild charts and banks')
+    parser.add_argument('--write', action='store_true', help='Regenerate certificate; requires --full')
+    args = parser.parse_args(); assert not args.write or args.full
+    ROOT = args.complex_root.resolve()
+    source = json.loads((HERE / 'SOURCE.json').read_text())
+    head = subprocess.check_output(['git', '-C', str(ROOT), 'rev-parse', 'HEAD'], text=True).strip()
+    assert head == source['complex_commit'], 'Wrong complex checkout commit'
+    for name, expected in source['complex_files'].items():
+        assert hashlib.sha256((ROOT / name).read_bytes()).hexdigest() == expected, ('Changed source', name)
+    inherited = json.loads((ROOT / 'research/source-assisted-v4/SOURCE.json').read_text())
+    for name, expected in inherited['files'].items():
+        assert hashlib.sha256((ROOT / name).read_bytes()).hexdigest() == expected, ('Changed complex dependency', name)
+    bit = args.bit_root.resolve()
+    head = subprocess.check_output(['git', '-C', str(bit), 'rev-parse', 'HEAD'], text=True).strip()
+    assert head == source['bit_commit'], 'Wrong bit checkout commit'
+    manifest_path = bit / BIT_PACKAGE / 'SOURCE.json'
+    assert hashlib.sha256(manifest_path.read_bytes()).hexdigest() == source['bit_manifest_sha256']
+    manifest = json.loads(manifest_path.read_text())
+    for name, expected in manifest['files'].items():
+        assert hashlib.sha256((bit / name).read_bytes()).hexdigest() == expected, ('Changed bit dependency', name)
+    for name, expected in source['bit_files'].items():
+        assert hashlib.sha256((bit / name).read_bytes()).hexdigest() == expected, ('Changed bit word', name)
+    for name, expected in source['served_files'].items():
+        assert hashlib.sha256((HERE / name).read_bytes()).hexdigest() == expected, ('Changed served file', name)
+    if args.full:
+        run(ROOT, 'research/source-assisted-v4/verify.py')
+        run(bit, BIT_PACKAGE + '/verify.py')
+        derivation = rederive(bit)
+        served = capture(HERE / 'bit/served_prove.py', str(bit / BIT_PACKAGE), str(SERVED))
+        physical = packing.build(bit, SERVED, served['profile'])
+    else:
+        frozen = json.loads((HERE / 'certificate.json').read_text())
+        derivation, served, physical = frozen['derivation'], frozen['served'], frozen['physical']
+    assert served['status'] == 'PASS' and served['served_operations'] == 373
+    result = arithmetic.build(ROOT, bit, physical, served)
+    independent = audit.run(result, result['unpacked_profile'])
+    record = dict(derivation=derivation, served=served, physical=physical, arithmetic=result, independent=independent,
+                  bank_controls=controls.run(), pinned_bit_files=len(manifest['files']))
+    out = serial(record)
+    if args.write: (HERE / 'certificate.json').write_bytes((json.dumps(out, indent=2, sort_keys=True) + '\n').encode())
+    else: assert out == json.loads((HERE / 'certificate.json').read_text()), 'Certificate differs'
+    print('PASS served word (re-derived and fully checked), exact charts and banks, two moment engines, '
+          'finite leaf composition, 47 constraints and seven margins')
+    print('conditional kappa = ' + out['arithmetic']['after_packing']['kappa'])
+
+
+if __name__ == '__main__': main()