diff --git a/.github/workflows/depth-coarse.yml b/.github/workflows/depth-coarse.yml
new file mode 100644
index 0000000000..f87ca190b9
--- /dev/null
+++ b/.github/workflows/depth-coarse.yml
@@ -0,0 +1,52 @@
+name: Verify depth-coarse family
+
+on:
+  push:
+  pull_request:
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  selected:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 20
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.13', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Regenerate selected words and verify exact certificate
+        run: python3 research/depth-coarse/verify.py --regenerate
+      - name: Independently verify the root and finite-family ceiling
+        run: python3 research/depth-coarse/independent.py
+      - name: Check mathematical and adversarial controls
+        run: python3 -m unittest discover -s tests -p test_depth_coarse.py -v
+      - name: Require unchanged source and certificates
+        run: git diff --exit-code
+
+  family:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 20
+    strategy:
+      fail-fast: false
+      matrix:
+        choice: [ccc, ccr, crc, crr, rcc, rcr, rrc, rrr]
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: '3.13'
+      - name: Regenerate and replay both axes for this family member
+        run: python3 research/depth-coarse/verify.py --menu-choice ${{ matrix.choice }}
+      - name: Require unchanged source and certificates
+        run: git diff --exit-code
diff --git a/research/depth-coarse/.gitattributes b/research/depth-coarse/.gitattributes
new file mode 100644
index 0000000000..e847ceb71b
--- /dev/null
+++ b/research/depth-coarse/.gitattributes
@@ -0,0 +1,4 @@
+# Preserve byte-exact contributor snapshots and source manifests.
+vendor/** -text
+# Bind the selected archives as bytes; regeneration checks canonical raw words.
+*.gz -text
diff --git a/research/depth-coarse/PROOF-BARRIER.md b/research/depth-coarse/PROOF-BARRIER.md
new file mode 100644
index 0000000000..e8346c0166
--- /dev/null
+++ b/research/depth-coarse/PROOF-BARRIER.md
@@ -0,0 +1,142 @@
+# Optimal scalar recursion power within the frozen depth-coarse family
+
+This companion concerns the finite family of 64 complete interchange profiles
+obtained by choosing one word in `{c,r}^3` for each of the two axes, h=23 and
+h=25. Those letters select row/column regrouping at the **first three internal
+weighted-exclusion construction levels**, uniformly across the axis's common
+points; deeper levels use columns. This happens before a fixed word is compiled.
+It is not arbitrary internal per-node row/column assignment, nor a change to
+unit completion or carry exchange. The letters do not represent choices made
+at recursion depths of a growing-width interchange invocation. The latter
+choices are the subject of the theorem below.
+
+The scalar regrouping comes from eumemic's PR69; the anchored split and paid
+compiler come from PR71 and its credited predecessors. This companion proves
+a mathematical limitation of adaptive selection among the supplied complete
+profiles. It does not claim a record multiplication bound, worldwide novelty,
+an unconditional all-size theorem, or optimality over other circuits.
+
+## Fixed profiles and exact selection
+
+For profile j let m=575, W_j be its total physical role divisor, and n_{j,t}
+its **complete** positive child multiplicity, including all endpoint copies,
+exterior banks, data corners, physical growth and actual axis-profile children.
+Every child width satisfies 1<=t<=529<m. An invocation of width e>=m produces
+children with width t floor(e/m), each at relative logical volume 1/W_j.
+Define
+
+    M_j(alpha) = sum_t (n_{j,t}/W_j)(t/m)^alpha.
+
+These n/W coefficients are relative-volume weights, not probabilities.
+In this family M_j(0)>1 and M_j(1)=1-1846900/(575 W_j)<1. Each M_j is strictly
+decreasing and has one root alpha_j in (0,1). Write
+
+    alpha_* = min_j alpha_j,       a_* = 1-alpha_*.
+
+The independent arithmetic receipt checks the selected `rcr`/`rrr` profile
+below one at its accepted rational saving a, its next saving grid point above
+one, and every one of the other 63 profiles above one at a by **lower**
+moment bounds. Thus the selected profile has the unique smallest alpha_j.
+This certifies the strongest scalar characteristic within this frozen family;
+it does not follow merely from comparing W or rank mass.
+
+## A floor-exact adaptive barrier
+
+Assume the inherited complete interchange interfaces for all profiles. Consider
+any finite charged recursive tree which chooses one of them at each node,
+according to width, depth, orientation, role, previous choices or a random
+choice. Each occurrence retains its own relative volume; nonrecursive charges
+are nonnegative. At any elementary leaf assume work at least c_0 V e for one
+fixed c_0>0. A fixed bounded-width elementary implementation meets this
+condition after choosing its fixed constant c_0.
+
+**Theorem.** Every such complete-tree accounting has work at least
+
+    [c_0/(1+D)^alpha_*] V(e+D)^alpha_*,    D=13225/2.
+
+Consequently adaptive profile switching cannot improve the scalar recursion
+power beyond the best standalone root in this family.
+
+**Proof.** More generally take D=max_{j,t} tm_j/(m_j-t) for any finite menu.
+Here t<=529 and m=575, so D=529*575/(575-529)=13225/2 suffices. For every
+legal recursive width,
+
+    t floor(e/m)+D >= (t/m)(e+D),
+
+because floor(e/m)>=e/m-1 and D(1-t/m)>=t. Since alpha_* is positive and
+M_j(alpha_*)>=M_j(alpha_j)=1,
+
+    sum_t (n_{j,t}/W_j)[t floor(e/m)+D]^alpha_*
+       >= (e+D)^alpha_* M_j(alpha_*) >= (e+D)^alpha_*.
+
+The function e/(e+D)^alpha_* increases on e>0, so for e>=1,
+
+    e >= (e+D)^alpha_* /(1+D)^alpha_*.
+
+This supplies the elementary-leaf lower charge. Every recursive child has
+strictly smaller positive integer width. Strong induction, multiplying each
+child charge by its actual V/W_j and summing its multiplicity, proves the
+bound. Node overhead only adds work. The proof is pointwise for each realized
+tree, so randomized selection does not evade it. QED.
+
+This is a bound on the explicit recursive work functional. An upper recurrence
+by itself never implies a lower bound on an arbitrary machine's actual runtime.
+An algorithm sharing computations between child occurrences, exploiting a
+stronger restricted child contract, choosing unbounded input-dependent new
+networks, or changing the leaf cost model is outside the theorem.
+
+## Sharpness of this scalar power
+
+For the selected profile alone, the unshifted potential V e^alpha_* does not
+increase at a recursive expansion: floors only decrease child widths and its
+characteristic equals one. Therefore total elementary-leaf volume is at most
+V e^alpha_*, since every positive leaf width is at least one. Let
+B_0=sum_t n_t/W>1. Summing volume identities over the whole selected tree gives
+
+    leaf volume = root volume + (B_0-1) total internal-node volume.
+
+Hence the total internal volume is O(V e^alpha_*). Elementary leaves have
+width below the fixed m and cost O(their volume). If the nonrecursive charge
+of a node is O(its volume times a common polylogarithmic factor), the selected
+tree has work O(V e^alpha_* times that factor). Separate setup and tape costs
+remain separately charged. Under these hypotheses the optimal scalar power
+for this complete-profile family is exactly alpha_*.
+
+Finite tensor compositions have characteristic equal to the product of their
+constituent characteristics, so every factor is at least one at alpha_*.
+Expanding any such macro into its complete tree gives the same obstruction.
+The result does not extend to new unbounded network families.
+
+## Typed recursion and the balanced assembly ceiling
+
+Merely adding orientation tags cannot improve the root if every type has this
+same complete child histogram. Its nonnegative matrix characteristic then has
+constant row sum M(alpha), so its spectral radius is exactly M(alpha), by the
+all-ones eigenvector and the ordinary sup norm. A genuine multitype improvement
+needs independently proved cheaper child-operation contracts, with a positive
+vector v satisfying A(alpha)v<v; the existing generic contract does not supply
+that improvement automatically.
+
+The inherited balanced assembly requires kappa<min(1-epsilon,epsilon q) and
+q<a_b. Balancing the two expressions at epsilon=1/(1+q) gives the existing
+strict scoped ceiling kappa<a_b/(1+a_b). Substituting the independently bounded
+selected root therefore bounds the complete remaining analytic/parameter
+headroom for this finite family. The receipt supplies the exact numerical
+enclosure; this ceiling is inherited and is not claimed as a new assembly.
+
+For the frozen selected profile the independently enclosed saving root is
+strictly between 0.0000516459365535807612 and 0.0000516459365535807613. Thus this
+family's unchanged balanced assembly has strict ceiling
+
+    kappa < 516459365535807613/10000516459365535807613.
+
+Its published finite witness is kappa=5164326938841/100000000000000000.
+The entire remaining analytic/parameter headroom within these hypotheses is
+less than 1.565e-16 in absolute saving. This says nothing about a stronger
+construction outside the frozen 64-profile family.
+
+The all-size residual compiler, row/remainder handling, finite-alphabet tape
+simulation, analytic transfer, routing, address primes, setup, precision and
+exact-recovery contracts remain explicit hypotheses. Finite word/profile replay
+and the rational comparisons establish their respective finite layers, not
+these complete all-size theorem dependencies.
diff --git a/research/depth-coarse/PROOF.md b/research/depth-coarse/PROOF.md
new file mode 100644
index 0000000000..f087496342
--- /dev/null
+++ b/research/depth-coarse/PROOF.md
@@ -0,0 +1,65 @@
+# Local algebra and inherited proof boundary
+
+Let Gi,Gj be disjoint groups of vertices, each of size 1 or 2. Every edge value
+e(a,b) has support disjoint from all other edge values in this coarse sum.
+The coarse edge is
+
+    Cij = sum_{a in Gi, b in Gj} e(a,b).
+
+It can be emitted as either
+
+    sum_{b in Gj} (sum_{a in Gi} e(a,b))       [columns]
+    sum_{a in Gi} (sum_{b in Gj} e(a,b))       [rows].
+
+Both are finite distributive regroupings of precisely the same partition.
+Every nontrivial addition has disjoint support; singleton/empty summands are
+handled by the inherited total routine. Each intermediate core and cover is
+computed from its actual support. The resulting common-point exclusion graph
+therefore retains its weighted total and all single/pair exclusion identities.
+
+The row/column choice is fixed at each internal weighted-exclusion construction
+level before compilation. There are eight choices at levels 0–2; deeper levels
+use columns. This is a
+finite grammar, not a data-dependent runtime choice. The PR71 grouping vector
+[1,1,2], singleton/pair partition and strict contraction are unchanged, so its
+weighted induction and termination proof apply to either regrouping. The
+global-pair anchor remains a permutation of points other than each common point.
+
+Reassociation can share nodes with the existing strip DAG and can alter
+carrier matching/retirement. Thus fewer scalar additions do not prove fewer
+physical roles or a better exponent. The selected word is recompiled in full,
+with every paid XOR, frame raise, source, copy, endpoint and dirty-state cleanup.
+No actual price is replaced by the discovery heuristic. The full paid profile
+is constructed as in PR71: data and endpoint copies, replicated actual axis
+profiles, exteriors and data growth. It satisfies
+
+    W = 2N + 2300 R23 + 1771 R25,
+    sum_t t n_t = 575 W - 1846900,
+    0 < t <= 529 < 575.
+
+The normalized characteristic is
+
+    M(a) = sum_t n_t t/(575 W) exp(a log(575/t)).
+
+Inherited independent rational logarithm/Taylor bounds prove a strict accepted
+upper moment and strict rejected lower moment at adjacent saving grid points.
+The complete frozen PR #71 and #75 profiles are also lower-bounded above 1 at
+the selected saving; comparing width alone is insufficient. The inherited
+balanced assembly is rerun for all 47 strict inequalities, seven margins and
+the adjacent kappa-grid rejection, retaining backoff 10^-12 and the unchanged
+complex saving 717/10^7.
+
+The literal verifier explicitly reconstructs the entire ordered scatter list
+from the exact output inventory and compares it with the word. Canceling extra
+scatter operations therefore cannot pass merely because their net scalar map
+is zero. This binding follows PR64's verification precedent. All port/role
+indices are range-checked before inherited replay, so negative Python indices
+cannot masquerade as legitimate source/dirty roles. Every input, target and
+dirty basis coordinate is replayed in both orientations, and actual frame
+transitions and exact fixed-basis/CRT profiles are regenerated.
+
+These are finite algebra, word and arithmetic claims. The ambient framed lift,
+all-size row/remainder compiler, scalar overhead, tape/routing simulation,
+prime/setup/recovery and analytic multiplication transfer remain inherited
+dependencies. This local proof does not remove those hypotheses or establish
+global optimality of the finite search.
diff --git a/research/depth-coarse/README.md b/research/depth-coarse/README.md
new file mode 100644
index 0000000000..c74d81c5f5
--- /dev/null
+++ b/research/depth-coarse/README.md
@@ -0,0 +1,79 @@
+# Exact depth-coarse family and adaptive recursion barrier
+
+[The finite-family adaptive barrier](PROOF-BARRIER.md) proves that switching
+among these 64 complete profiles cannot improve their best scalar recursion
+power under the stated leaf-work and complete-tree accounting assumptions.
+It includes exact root and balanced-assembly headroom bounds; it is a scoped
+family theorem, not a lower bound for arbitrary multiplication machines.
+[The local construction proof](PROOF.md) gives the disjoint-support grammar
+and finite validity argument. An independent checker imports no package
+arithmetic and rederives the complete profile, exact root, all 47 constraints,
+seven margins and 63 competitor exclusions.
+
+Concurrent [PR #79](https://github.com/CrocSwap/integer-mult-bounds/pull/79),
+at `9a58e62cf9e8954a4dde3c9b1372d733c276a6d1`, reports the stronger conditional
+κ = 5.1745625472866e-5 using a per-cell grammar, unit completion and carry
+exchanges outside this family's frozen compiler.
+[PR #80](https://github.com/CrocSwap/integer-mult-bounds/pull/80), at
+`a9ed157ff106fd35557b5896197f66a1272f7f13`, reports κ = 5.1778825456819e-5.
+These are submitted comparison values; this package establishes a bounded
+family result and makes no priority or strongest-known-bound claim.
+
+This adds a finite conditional witness by composing eumemic's PR69 coarse-column
+factorization with Chafik Boukhalfa's PR71 anchored split/next-use compiler.
+The depth grammar allows row factoring independently at the first three
+internal weighted-exclusion construction levels, with columns below them.
+All eight words at each axis have been physically checked; all 64 complete
+profile combinations are compared exactly. The selected h=23 word is `rcr`
+and h=25 word is `rrr`, in construction-level order.
+
+The selected witness gives exact kappa
+`5164326938841/10^17 = 5.164326938841e-5`. Its role counts are
+27,309 / 35,798 and physical width is 134,355,558. Complete PR #71 and #75 profiles are
+excluded at the new bit saving, using immutable comparison certificates.
+See `certificate.json` for the accepted complete moment, all 47 assembly
+inequalities, seven margins, next-grid rejection and arithmetic cutoffs.
+Every other 63 finite-menu profile is strictly excluded at the selected saving.
+
+From the repository root:
+
+```
+python3 research/depth-coarse/verify.py
+python3 research/depth-coarse/verify.py --regenerate
+python3 research/depth-coarse/verify.py --arithmetic-only
+python3 research/depth-coarse/verify.py --menu-choice ccc
+python3 research/depth-coarse/menu.py
+python3 research/depth-coarse/independent.py
+python3 -m unittest discover -s tests -p test_depth_coarse.py -v
+```
+
+Default verification independently binds every literal scatter port and exact
+terminal inventory, replays every source/target/arbitrary dirty basis in both
+orientations, reconstructs frame transitions, regenerates actual fixed-I+J/CRT
+profiles and checks exact arithmetic. `--regenerate` additionally recompiles
+the selected DAG/matching/reclamation word and compares decompressed bytes.
+`CXX` can select a working C++17 compiler, as in inherited checks. Temporary
+files and logs are outside scientific certificates.
+`--menu-choice` regenerates both axes of any one menu word and compares their
+canonical word hashes, full dirty/frame receipts and actual CRT profiles with
+the frozen menu. The 16 recipe/profile receipts and hashes are shipped without
+duplicating all 16 large words. The default arithmetic path verifies all 64
+exact moment brackets, assemblies and strict nonwinner exclusions.
+
+This package changes no root headline, notice, Makefile or historical witness.
+It remains conditional on the inherited all-size framed-word/residual compiler,
+finite-alphabet tape, analytic, routing, prime selection, precision and recovery
+contracts. Arithmetic cutoffs are not a complete operational threshold. No
+global optimum, unconditional theorem or practical speedup is asserted.
+
+Prepared for Joseph Demarest with substantial OpenAI Codex assistance. Original
+code is retained byte-for-byte with source hashes and contributor notices in
+`vendor/`; root Apache-2.0 terms apply. PR69 supplies uniform column factoring;
+PR71 supplies split/anchor/next-use composition; Rohan Arun PR65/67 supplies
+schedules/profile costs/directed arithmetic; Dominik Scholz PR68 supplies live
+controls; Rohan Garg PR59 supplies split operation; eumemic PR57 supplies joint
+reversible compilation; Avi Eisenberg PR62 supplies interval/core-aware graph.
+rfu08 PR64 supplies explicit literal-scatter verification precedent. Earlier
+community, OpenAI and Harvey–van der Hoeven attribution remains in retained
+notices. The contribution is the independently verified depth factoring
+family, its exact optimum, and its scoped adaptive-recursion barrier.
diff --git a/research/depth-coarse/SOURCE.json b/research/depth-coarse/SOURCE.json
new file mode 100644
index 0000000000..09baebead0
--- /dev/null
+++ b/research/depth-coarse/SOURCE.json
@@ -0,0 +1,71 @@
+{
+  "files": {
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+    "research/depth-coarse/menu/rrc-25.json": "93a1b9409acf54f32eb747d1af6dfea21249695c40160e73834040beb20160e7",
+    "research/depth-coarse/menu/rrr-23.json": "6ce040e399d69cf83e00e7c3202790a832162dc85a0d444f08ca05c6a9e9fcb3",
+    "research/depth-coarse/menu/rrr-25.json": "2c7309dc9067a37cc4758152439265f871268da1c19c4e8ed9ed015127520c48",
+    "research/depth-coarse/mutation-controls.json": "63926bf765cebf02e2fda50df9aa932dfa81fb14243ab8c04f55719c77019d1a",
+    "research/depth-coarse/selection.json": "c4a1f257940a17fb7326d23c6ab280e6ec3e105b1e9966f3c040cc2c47be3a5a",
+    "research/depth-coarse/vendor/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "research/depth-coarse/vendor/PR71-NOTICE": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0",
+    "research/depth-coarse/vendor/SOURCE.json": "fdb1547ab98026799925311841b012c7aea4cfc60e5057e3ed59f6d9c75fc162",
+    "research/depth-coarse/vendor/pr65-audit.py": "aa297fffcdaa133f5dee17d97fac72aa5ba2cf943da5a8a5e3f4d62f6f0a7f79",
+    "research/depth-coarse/vendor/pr65-refine.py": "e0488c919e76850313ff93d7da704a7fcc14a316eee2cac81e2b8dff9c145b5d",
+    "research/depth-coarse/vendor/pr65-schedule.py": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352",
+    "research/depth-coarse/vendor/pr67-profile-oracle.cpp": "d1f6b650de9fb5842b412595369271d9eeb6f54045c76c0fb5cad29854955c35",
+    "research/depth-coarse/vendor/pr69-balanced-coarse.py": "bd8169bf9f5df185a8aa4aec22234b4fd483000a1cecc78b71bf32e479af1499",
+    "research/depth-coarse/vendor/pr71-engine.py": "58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70",
+    "research/depth-coarse/vendor/pr71-split-graph.py": "9d4ee7179f880f9576e81c7ad3a5290fe61380a7531d559ef3cf0939bb30089c",
+    "research/depth-coarse/verify.py": "ec278e5c8aa370b51a87faddc0b1c718e51d891cca1df8b0b3f83e954fe41c67",
+    "research/depth-coarse/word-23.json.gz": "b02021edbbf700b6d196abb06d35b867d114976f43316f2e0dd6426eb565a1a1",
+    "research/depth-coarse/word-25.json.gz": "7f606351b6407bf0df9f8b4e70494119d29842300f8547f2c53a2a867e980ed3",
+    "research/pair-assembly/pair_graph.py": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420",
+    "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0",
+    "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0",
+    "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3",
+    "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669",
+    "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc",
+    "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7",
+    "scripts/partial_swap/shared.py": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34",
+    "tests/test_depth_coarse.py": "de625a5b6a874b1354b8499021cf4bbf68db8773bf25756fcecc3ac355792141"
+  },
+  "main_base": "56b66d58297deca1d7dd130247d720e960f77a37",
+  "scope": "Finite depth-family words/profiles/menu certificate and scoped adaptive-recursion barrier; inherited data/complex/all-size dependencies remain"
+}
diff --git a/research/depth-coarse/axis-23.json b/research/depth-coarse/axis-23.json
new file mode 100644
index 0000000000..bb27551f75
--- /dev/null
+++ b/research/depth-coarse/axis-23.json
@@ -0,0 +1,197 @@
+{
+  "compiled": {
+    "all_physical_frame_inclusions": true,
+    "baseline_pr48_roles": 36432,
+    "baseline_pr65_roles": 27918,
+    "complete_dirty_basis_both_orientations": true,
+    "dirty_basis_vectors": 30851,
+    "elementary_xors": 161727,
+    "graph_configuration": {
+      "anchor": true,
+      "groups": [
+        1,
+        1,
+        2
+      ],
+      "schedule": "cover-core"
+    },
+    "h": 23,
+    "histogram": {
+      "0": 324842,
+      "1": 58280,
+      "2": 80771,
+      "3": 9989,
+      "4": 14545,
+      "5": 6421,
+      "6": 1923,
+      "7": 721,
+      "8": 1271,
+      "9": 527,
+      "10": 513,
+      "11": 100,
+      "12": 672,
+      "13": 223,
+      "14": 1872,
+      "15": 310,
+      "16": 420,
+      "17": 490,
+      "18": 3409,
+      "19": 6539,
+      "21": 373,
+      "22": 23
+    },
+    "mode": {
+      "matching": true,
+      "reclaim": true
+    },
+    "paid_clones": 0,
+    "pending_cost_uses_next_use_frame": true,
+    "pending_live_controls": true,
+    "rank_mass": 628613,
+    "reclamation_order": "all eligible retired ranks, exact integer profile cost, XOR count, slot ID",
+    "roles": 27309,
+    "scalar": {
+      "additions": 67460,
+      "all_additions_disjoint": true,
+      "all_partial_outputs_exact": true,
+      "circuit_sha256": "44c3db4820dd42286c4f2b7df29e49c4287bffe2d226551d136b80e937245d45",
+      "every_node_has_common_point": true,
+      "h": 23,
+      "inputs": 1771,
+      "merged_additions": 11937,
+      "partial_outputs": 5336,
+      "roles": 72796
+    },
+    "source_pr65_head": "49e84f939d15b618b50714eb039cabf97c74256a",
+    "source_pr67_head": "b3745601e947a94316bf25c2c6263d93c06e3364",
+    "source_pr68_head": "734c58e225e9d2254570c3b50296ed96943f62ea",
+    "stats": {
+      "augmentations": 12,
+      "clearing_xors": 3627,
+      "live_anchor_candidates": 73141,
+      "live_anchor_xors": 69,
+      "matched": 41730,
+      "multi_node_regions": 8694,
+      "reclaimed": 2101,
+      "regions": 59801
+    }
+  },
+  "gzip_sha256": "b02021edbbf700b6d196abb06d35b867d114976f43316f2e0dd6426eb565a1a1",
+  "profile": {
+    "R": 27309,
+    "blocks": [
+      0,
+      357598,
+      20698,
+      8085,
+      5448,
+      4187,
+      3760,
+      3190,
+      2534,
+      2049,
+      1710,
+      1474,
+      959,
+      839,
+      533,
+      461,
+      230,
+      177,
+      49,
+      46,
+      0,
+      23,
+      0,
+      0
+    ],
+    "crt_disagreements": 0,
+    "crt_matrices": 5526,
+    "distinct_matrices": 38457,
+    "field_prime": 2305843009213693951,
+    "frames": 59803,
+    "h": 23,
+    "loss": 506,
+    "rank_sum": 628613,
+    "v": 1771
+  },
+  "replay": {
+    "elementary_xors": 161727,
+    "full_basis_vectors": 30851,
+    "h": 23,
+    "histogram": {
+      "0": 173814,
+      "1": 58280,
+      "2": 80771,
+      "3": 9989,
+      "4": 14545,
+      "5": 6421,
+      "6": 1923,
+      "7": 721,
+      "8": 1271,
+      "9": 527,
+      "10": 513,
+      "11": 100,
+      "12": 672,
+      "13": 223,
+      "14": 1872,
+      "15": 310,
+      "16": 420,
+      "17": 490,
+      "18": 3409,
+      "19": 6539,
+      "21": 373,
+      "22": 23
+    },
+    "output_roles": 5336,
+    "rank_mass": 628613,
+    "roles": 27309,
+    "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS",
+    "word_length": 671702
+  },
+  "source": {
+    "after": "            def coarse_sum(i, j):\n                orientation = COARSE_CHOICES[level] if level < len(COARSE_CHOICES) else 'c'\n                if orientation == 'r':\n                    parts = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]\n                else:\n                    parts = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]\n                return self.total(parts)\n            coarse = {(i,j):coarse_sum(i,j) for i,j in combinations(range(ng),2)}",
+    "attribution": "PR69/eumemic column reassociation generalized to deterministic depth row/column choices on PR71/Chafik Boukhalfa split+anchor+cost/live; predecessor notices retained",
+    "before": "            coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]])\n                      for i, j in combinations(range(ng), 2)}",
+    "choices": "rcr",
+    "pr71_head": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "producer_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420",
+    "replacement_sha256": "0a8e61c8a06aecba2fdd706db4e31616c7cdf0852bed136b1e96b5d499016d9c"
+  },
+  "transitions": {
+    "R": 27309,
+    "copied_centers": 23,
+    "distinct_transitions": 152174,
+    "frames": 59803,
+    "h": 23,
+    "rank_histogram_with_side_growth_split_into_singletons": {
+      "1": 68906,
+      "2": 75458,
+      "3": 9989,
+      "4": 14545,
+      "5": 6421,
+      "6": 1923,
+      "7": 721,
+      "8": 1271,
+      "9": 527,
+      "10": 513,
+      "11": 100,
+      "12": 672,
+      "13": 223,
+      "14": 1872,
+      "15": 310,
+      "16": 420,
+      "17": 490,
+      "18": 3409,
+      "19": 6539,
+      "21": 373,
+      "22": 23
+    },
+    "rank_mass": 628613,
+    "singles": 15939,
+    "transition_events_equal_independent_xor_word_reconstruction": true,
+    "v": 1771,
+    "word_sha256": "fbae9a09e66521f5e1268fabb0f645db5988383283aa31cb0e4cd6ad51cb4497"
+  },
+  "word_sha256": "fbae9a09e66521f5e1268fabb0f645db5988383283aa31cb0e4cd6ad51cb4497"
+}
diff --git a/research/depth-coarse/axis-25.json b/research/depth-coarse/axis-25.json
new file mode 100644
index 0000000000..f176f13f95
--- /dev/null
+++ b/research/depth-coarse/axis-25.json
@@ -0,0 +1,205 @@
+{
+  "compiled": {
+    "all_physical_frame_inclusions": true,
+    "baseline_pr48_roles": 48329,
+    "baseline_pr65_roles": 36586,
+    "complete_dirty_basis_both_orientations": true,
+    "dirty_basis_vectors": 40398,
+    "elementary_xors": 226902,
+    "graph_configuration": {
+      "anchor": true,
+      "groups": [
+        1,
+        1,
+        2
+      ],
+      "schedule": "reverse-node"
+    },
+    "h": 25,
+    "histogram": {
+      "0": 454838,
+      "1": 77059,
+      "2": 117586,
+      "3": 13449,
+      "4": 18691,
+      "5": 8490,
+      "6": 3343,
+      "7": 1046,
+      "8": 1304,
+      "9": 749,
+      "10": 844,
+      "11": 27,
+      "12": 760,
+      "13": 73,
+      "14": 683,
+      "15": 199,
+      "16": 2178,
+      "17": 642,
+      "18": 621,
+      "19": 933,
+      "20": 4465,
+      "21": 8339,
+      "23": 442,
+      "24": 25
+    },
+    "mode": {
+      "matching": true,
+      "reclaim": true
+    },
+    "paid_clones": 0,
+    "pending_cost_uses_next_use_frame": true,
+    "pending_live_controls": true,
+    "rank_mass": 895550,
+    "reclamation_order": "all eligible retired ranks, exact integer profile cost, XOR count, slot ID",
+    "roles": 35798,
+    "scalar": {
+      "additions": 94993,
+      "all_additions_disjoint": true,
+      "all_partial_outputs_exact": true,
+      "circuit_sha256": "a5ac28e00abb036ab4f513bb775a92e977aa62da8ce2c1fa8abb5723d6b5324f",
+      "every_node_has_common_point": true,
+      "h": 25,
+      "inputs": 2300,
+      "merged_additions": 17168,
+      "partial_outputs": 6925,
+      "roles": 101918
+    },
+    "source_pr65_head": "49e84f939d15b618b50714eb039cabf97c74256a",
+    "source_pr67_head": "b3745601e947a94316bf25c2c6263d93c06e3364",
+    "source_pr68_head": "734c58e225e9d2254570c3b50296ed96943f62ea",
+    "stats": {
+      "augmentations": 16,
+      "clearing_xors": 5819,
+      "live_anchor_candidates": 100460,
+      "live_anchor_xors": 148,
+      "matched": 60971,
+      "multi_node_regions": 11575,
+      "reclaimed": 3149,
+      "regions": 84843
+    }
+  },
+  "gzip_sha256": "7f606351b6407bf0df9f8b4e70494119d29842300f8547f2c53a2a867e980ed3",
+  "profile": {
+    "R": 35798,
+    "blocks": [
+      0,
+      494065,
+      27473,
+      10551,
+      7862,
+      5542,
+      4948,
+      4073,
+      3738,
+      2963,
+      2422,
+      1995,
+      1771,
+      1405,
+      1109,
+      861,
+      546,
+      459,
+      247,
+      164,
+      46,
+      59,
+      0,
+      25,
+      0,
+      0
+    ],
+    "crt_disagreements": 0,
+    "crt_matrices": 7500,
+    "distinct_matrices": 51649,
+    "field_prime": 2305843009213693951,
+    "frames": 84845,
+    "h": 25,
+    "loss": 600,
+    "rank_sum": 895550,
+    "v": 2300
+  },
+  "replay": {
+    "elementary_xors": 226902,
+    "full_basis_vectors": 40398,
+    "h": 25,
+    "histogram": {
+      "0": 243804,
+      "1": 77059,
+      "2": 117586,
+      "3": 13449,
+      "4": 18691,
+      "5": 8490,
+      "6": 3343,
+      "7": 1046,
+      "8": 1304,
+      "9": 749,
+      "10": 844,
+      "11": 27,
+      "12": 760,
+      "13": 73,
+      "14": 683,
+      "15": 199,
+      "16": 2178,
+      "17": 642,
+      "18": 621,
+      "19": 933,
+      "20": 4465,
+      "21": 8339,
+      "23": 442,
+      "24": 25
+    },
+    "output_roles": 6925,
+    "rank_mass": 895550,
+    "roles": 35798,
+    "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS",
+    "word_length": 939808
+  },
+  "source": {
+    "after": "            def coarse_sum(i, j):\n                orientation = COARSE_CHOICES[level] if level < len(COARSE_CHOICES) else 'c'\n                if orientation == 'r':\n                    parts = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]\n                else:\n                    parts = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]\n                return self.total(parts)\n            coarse = {(i,j):coarse_sum(i,j) for i,j in combinations(range(ng),2)}",
+    "attribution": "PR69/eumemic column reassociation generalized to deterministic depth row/column choices on PR71/Chafik Boukhalfa split+anchor+cost/live; predecessor notices retained",
+    "before": "            coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]])\n                      for i, j in combinations(range(ng), 2)}",
+    "choices": "rrr",
+    "pr71_head": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "producer_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420",
+    "replacement_sha256": "0a8e61c8a06aecba2fdd706db4e31616c7cdf0852bed136b1e96b5d499016d9c"
+  },
+  "transitions": {
+    "R": 35798,
+    "copied_centers": 25,
+    "distinct_transitions": 212455,
+    "frames": 84845,
+    "h": 25,
+    "rank_histogram_with_side_growth_split_into_singletons": {
+      "1": 90859,
+      "2": 110686,
+      "3": 13449,
+      "4": 18691,
+      "5": 8490,
+      "6": 3343,
+      "7": 1046,
+      "8": 1304,
+      "9": 749,
+      "10": 844,
+      "11": 27,
+      "12": 760,
+      "13": 73,
+      "14": 683,
+      "15": 199,
+      "16": 2178,
+      "17": 642,
+      "18": 621,
+      "19": 933,
+      "20": 4465,
+      "21": 8339,
+      "23": 442,
+      "24": 25
+    },
+    "rank_mass": 895550,
+    "singles": 20700,
+    "transition_events_equal_independent_xor_word_reconstruction": true,
+    "v": 2300,
+    "word_sha256": "ab46b13e45d076c2104d0bf64a1db79886b643add11685edfde719650fb316f1"
+  },
+  "word_sha256": "ab46b13e45d076c2104d0bf64a1db79886b643add11685edfde719650fb316f1"
+}
diff --git a/research/depth-coarse/bindings.py b/research/depth-coarse/bindings.py
new file mode 100644
index 0000000000..f6364f57dc
--- /dev/null
+++ b/research/depth-coarse/bindings.py
@@ -0,0 +1,113 @@
+"""Pinned dependency adapters; mathematical/compiler bodies remain unchanged.
+
+PR71 Chafik Boukhalfa: split/anchor/next-use composition; PR65/67 Rohan Arun:
+schedule, directed arithmetic and profile cost; PR68 Dominik Scholz: live
+controls; PR69 eumemic: coarse columns. Earlier notices are in vendor/.
+Prepared with substantial OpenAI Codex assistance, Apache-2.0.
+"""
+import sys
+if sys.flags.optimize:raise ValueError('Assertions must remain enabled')
+sys.dont_write_bytecode=True
+from pathlib import Path
+import ast,hashlib,json,types,subprocess,tempfile,shlex,os
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+VENDOR=HERE/'vendor'
+_previous_import_path=list(sys.path)
+sys.path.insert(0,str(ROOT/'scripts/experiments'))
+INHERITED=ROOT/'references/frame-compiler/pr48'
+alias_paths={'partial_swap.paired':'scripts/partial_swap/paired.py',
+             'partial_swap.shared':'scripts/partial_swap/shared.py',
+             'exclusion_circuit':'scripts/exclusion_circuit.py'}
+def check_aliases():
+    manifest=json.loads((INHERITED/'SOURCE.json').read_text())['files']
+    for name,relative in alias_paths.items():
+        expected=manifest[relative]
+        assert hashlib.sha256((ROOT/relative).read_bytes()).hexdigest()==expected,'Changed root library: '+relative
+        if name in sys.modules:
+            module=sys.modules[name]
+            assert hashlib.sha256(Path(module.__file__).read_bytes()).hexdigest()==expected,'Unexpected imported library: '+name
+check_aliases()
+
+def checked_source(name):
+    pins=json.loads((VENDOR/'SOURCE.json').read_text())
+    raw=(VENDOR/name).read_bytes()
+    assert hashlib.sha256(raw).hexdigest()==pins[name]['sha256'],name
+    return raw.decode()
+
+def original_definition(name,function):
+    source=checked_source(name);tree=ast.parse(source)
+    node=next(x for x in tree.body if isinstance(x,ast.FunctionDef) and x.name==function)
+    return '\n'.join(source.splitlines()[node.lineno-1:node.end_lineno])+'\n'
+
+import binary_frame_math as arithmetic
+refine=types.ModuleType('balanced_split_refine');refine.__file__=str(VENDOR/'pr65-refine.py')
+refine.INJECTED_ROOT=ROOT
+source=checked_source('pr65-refine.py')
+needle='ROOT = Path(__file__).resolve().parents[3]';assert source.count(needle)==1
+exec(compile(source.replace(needle,'ROOT = INJECTED_ROOT'),refine.__file__,'exec'),refine.__dict__)
+previous=sys.modules.get('refine');sys.modules['refine']=refine
+try:
+    audit=types.ModuleType('balanced_split_audit');audit.__file__=str(VENDOR/'pr65-audit.py')
+    exec(compile(checked_source('pr65-audit.py'),audit.__file__,'exec'),audit.__dict__)
+finally:
+    if previous is None:sys.modules.pop('refine',None)
+    else:sys.modules['refine']=previous
+
+compiler=types.ModuleType('balanced_split_engine');compiler.__file__=str(VENDOR/'pr71-engine.py')
+compiler.INJECTED_REFERENCE=ROOT/'references/frame-compiler/pr48'
+source=checked_source('pr71-engine.py')
+needle="ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48'"
+assert source.count(needle)==1
+exec(compile(source.replace(needle,'ROOT=INJECTED_REFERENCE'),compiler.__file__,'exec'),compiler.__dict__)
+
+pair=types.ModuleType('balanced_split_original_pair');pair.__file__=str(ROOT/'research/pair-assembly/pair_graph.py')
+raw=Path(pair.__file__).read_bytes()
+assert hashlib.sha256(raw).hexdigest()=='3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420'
+exec(compile(raw,pair.__file__,'exec'),pair.__dict__)
+check_aliases()
+definitions={}
+exec(original_definition('pr71-split-graph.py','split_class'),definitions)
+exec(original_definition('pr65-schedule.py','reordered_build'),definitions)
+split_class=definitions['split_class'];reordered_build=definitions['reordered_build']
+producer=types.SimpleNamespace(_graph=pair)
+
+def graph(h):
+    assert h in (23,25)
+    module=producer._graph;original=module.circuit_class;original_points=module.alternating_points
+    try:
+        module.circuit_class=lambda dimension:split_class(original(dimension),[1,1,2])
+        def anchored_points(dimension,common):
+            points=original_points(dimension,common)
+            pairs=[(a,a+1) for a in range(0,dimension-1,2) if common not in (a,a+1)]
+            chosen=min(pairs)
+            result=list(chosen)+[x for x in points if x not in chosen]
+            assert sorted(result)==[x for x in range(dimension) if x!=common]
+            return result
+        module.alternating_points=anchored_points
+        return module.graph(h)
+    finally:module.circuit_class=original;module.alternating_points=original_points
+producer.graph=graph
+
+def compile_axis(h):
+    compiler.graph=graph
+    original_build=compiler.build
+    compiler.build=reordered_build(original_build,'cover-core' if h==23 else 'reverse-node')
+    compiler.PENDING_COST=True
+    try:
+        with tempfile.TemporaryDirectory(prefix='balanced-split-') as directory:
+            work=Path(directory);oracle=work/'oracle'
+            subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(VENDOR/'pr67-profile-oracle.cpp'),'-o',str(oracle)],check=True)
+            compiler.oracles=[];compiler.ORACLE_EXE=str(oracle);compiler.ORACLE_INPUT=str(work/'oracle-input.bin')
+            try:result,word=compiler.compile_(h,matching=True,reclaim=True,dirty=True)
+            finally:
+                for process in compiler.oracles:
+                    process.stdin.close();assert process.wait(timeout=10)==0
+    finally:compiler.build=original_build
+    result.pop('seconds',None)
+    result['scalar']=graph(h).verify()
+    return result,word
+
+# Imported definitions retain their private module globals. Deferred math
+# import is already bound in sys.modules; do not leak reference search paths.
+sys.path[:]=_previous_import_path
diff --git a/research/depth-coarse/certificate.json b/research/depth-coarse/certificate.json
new file mode 100644
index 0000000000..00b78e22fc
--- /dev/null
+++ b/research/depth-coarse/certificate.json
@@ -0,0 +1,811 @@
+{
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+    "eventual_bounds": {
+      "additional_eventual_conditions": [
+        "BHP prime threshold and distinct-prime packing",
+        "Fixed rational basis, eligible common prime and native table setup",
+        "Catalogue/descriptor domination, logarithm absorption, exact recovery"
+      ],
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+  "scope": "All-size transfer, tape, routing, primes, recovery and analytic hypotheses remain inherited; full repository checks not run",
+  "status": "PASS selected finite words, dirty replay, literal frame reconstruction, CRT profiles and exact arithmetic only",
+  "total_rank": 77252598950
+}
diff --git a/research/depth-coarse/comparisons/pr71.json b/research/depth-coarse/comparisons/pr71.json
new file mode 100644
index 0000000000..28e4da0b52
--- /dev/null
+++ b/research/depth-coarse/comparisons/pr71.json
@@ -0,0 +1,1547 @@
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+      "scope": "Preserved original split-pair operation and attribution. These files document the adapted grouping operation; they are not imported by this producer. Actual imported source closure is PR65 plus shared PR48."
+    }
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+  "status": "Finite conditional physical witness and exact balanced assembly; inherited transfer hypotheses remain assumed"
+}
diff --git a/research/depth-coarse/comparisons/pr75.json b/research/depth-coarse/comparisons/pr75.json
new file mode 100644
index 0000000000..c38f5f5406
--- /dev/null
+++ b/research/depth-coarse/comparisons/pr75.json
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+      "replay": {
+        "elementary_xors": 162131,
+        "full_basis_vectors": 30997,
+        "h": 23,
+        "histogram": {
+          "0": 175323,
+          "1": 58563,
+          "10": 542,
+          "11": 88,
+          "12": 674,
+          "13": 253,
+          "14": 1927,
+          "15": 436,
+          "16": 440,
+          "17": 484,
+          "18": 3417,
+          "19": 6882,
+          "2": 78910,
+          "21": 171,
+          "22": 23,
+          "3": 10224,
+          "4": 15387,
+          "5": 6447,
+          "6": 1604,
+          "7": 729,
+          "8": 1230,
+          "9": 406
+        },
+        "output_roles": 5336,
+        "rank_mass": 631971,
+        "roles": 27455,
+        "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS",
+        "word_length": 673318
+      },
+      "reused_verified_receipt_sha256": "e74332c962139aff37d68032b1d79c25285b9b6ee8ba112baeb5978fd81e947f",
+      "status": "PASS fresh full input/dirty basis both orientations, independent literal frame path, exact fixed profiles",
+      "word_sha256": "624dfd880b174dae9a6e87ced46ac8550dc36b4441754cf7b884b12b6782e6fe"
+    },
+    {
+      "elapsed_seconds": 22.671999999991385,
+      "gzip_sha256": "aa67a24ccd38597fece6f267ad48b98676fef0f2755ea917481fc7d355d35097",
+      "prepared": {
+        "R": 36015,
+        "copied_centers": 25,
+        "distinct_transitions": 212580,
+        "frames": 84845,
+        "h": 25,
+        "rank_histogram_with_side_growth_split_into_singletons": {
+          "1": 91025,
+          "10": 790,
+          "11": 42,
+          "12": 750,
+          "13": 148,
+          "14": 681,
+          "15": 168,
+          "16": 2266,
+          "17": 684,
+          "18": 566,
+          "19": 828,
+          "2": 108045,
+          "20": 4480,
+          "21": 8901,
+          "23": 280,
+          "24": 25,
+          "3": 13560,
+          "4": 19874,
+          "5": 8381,
+          "6": 2965,
+          "7": 1128,
+          "8": 1440,
+          "9": 652
+        },
+        "rank_mass": 900975,
+        "singles": 20700,
+        "transition_events_equal_independent_xor_word_reconstruction": true,
+        "v": 2300,
+        "word_sha256": "0920e11cb3a52ed892a834f97fcb6af96d34e44190e6d67e11b94f6b7be2ffde"
+      },
+      "profile": {
+        "R": 36015,
+        "blocks": [
+          0,
+          492613,
+          27862,
+          10468,
+          7884,
+          5690,
+          5028,
+          4101,
+          3812,
+          3047,
+          2491,
+          2047,
+          1818,
+          1443,
+          1153,
+          898,
+          569,
+          469,
+          271,
+          163,
+          47,
+          13,
+          0,
+          25,
+          0,
+          0
+        ],
+        "crt_disagreements": 0,
+        "crt_matrices": 7445,
+        "distinct_matrices": 52071,
+        "field_prime": 2305843009213693951,
+        "frames": 84845,
+        "h": 25,
+        "loss": 600,
+        "rank_sum": 900975,
+        "v": 2300
+      },
+      "replay": {
+        "elementary_xors": 225726,
+        "full_basis_vectors": 40615,
+        "h": 25,
+        "histogram": {
+          "0": 242838,
+          "1": 77225,
+          "10": 790,
+          "11": 42,
+          "12": 750,
+          "13": 148,
+          "14": 681,
+          "15": 168,
+          "16": 2266,
+          "17": 684,
+          "18": 566,
+          "19": 828,
+          "2": 114945,
+          "20": 4480,
+          "21": 8901,
+          "23": 280,
+          "24": 25,
+          "3": 13560,
+          "4": 19874,
+          "5": 8381,
+          "6": 2965,
+          "7": 1128,
+          "8": 1440,
+          "9": 652
+        },
+        "output_roles": 6925,
+        "rank_mass": 900975,
+        "roles": 36015,
+        "status": "independent serialized word, exact frames, full input and dirty basis both orientations PASS",
+        "word_length": 935104
+      },
+      "status": "PASS fresh full input/dirty basis both orientations, independent literal frame path, exact fixed profiles",
+      "word_sha256": "0920e11cb3a52ed892a834f97fcb6af96d34e44190e6d67e11b94f6b7be2ffde"
+    }
+  ],
+  "kappa": "257077122735047/5000000000000000000",
+  "scope": "Fresh changed-word/full-basis/frame/profile/CRT and rational arithmetic validation. Unchanged 4,073,300-pair data geometry and its recovered rational cases inherited from PR71; all-size analytic log/exp enclosure, compiler/frame transfer, finite-alphabet tape, routing, prime-selection/recovery and eventual setup arguments remain conditional.",
+  "source": {
+    "attribution": "PR71 Chafik Boukhalfa; PR68 live anchors Dominik Scholz; PR67 profile cost Rohan Arun; PR62 graph Avi Eisenberg; PR57 compiler eumemic; inherited source notices remain.",
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "files": {
+      "certificates/split-pair-compiler.json": "6561fab8609e8aa3a291a8197cd8b834b0881ee0b9a5b991926c2c93c4d5f884",
+      "certificates/split-pair-kappa.json": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e",
+      "references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py": "4d27575dcad2b45a281a34054d311409ecd954f373c0c3a62c29bcc843f06a86",
+      "references/frame-compiler/pr48/research/copied-fixed/certificate.json": "33b3373c04e18a7f4cee33ba68da6ed71934acc3e0179cca6197696be4befa22",
+      "references/frame-compiler/pr48/scripts/partial_swap/binary_io.hpp": "7e143eb75bb342ac8f0c82a60005e7c35c9ec827de479bf6fb773151f3af5fa1",
+      "scripts/experiments/binary_frame_math.py": "1f96e8aafc8ae89f8eeec5d03800131d93d58e01bf8a7fca8feb03702d1740d0",
+      "scripts/experiments/binary_frame_profile_prepare.py": "8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3",
+      "scripts/experiments/binary_frame_profiles.cpp": "8e2e391d3ee57cbb1372c68e4aa031e1b861321536eabd642ada54e12e678669",
+      "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc",
+      "scripts/experiments/split_pair_engine.py": "58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70",
+      "scripts/experiments/split_pair_graph.py": "9d4ee7179f880f9576e81c7ad3a5290fe61380a7531d559ef3cf0939bb30089c"
+    },
+    "native_certificate": "certificates/split-pair-kappa.json",
+    "verification_adapter_files": {
+      "batch_axes.py": "cba8d8d2ce2babf4e9ff512af4e07df9a2574a15c4b1748e437a83977aa3359e",
+      "check_guards.py": "e3fc1be56f80de10c6c5e6dea2713ec42e95cae4f2d5e0fe57846672dd58e44e",
+      "export_weighted_case.py": "51357229ef731f15b0cb8f5d96dc1a82668fdbeca31e3ad0f491430584193586",
+      "screen_axes.py": "bf06809c44e26883fcc93aa2dbf98fdf1951742b83ded161e725a84b3d616f98",
+      "verify_words.py": "1f5b87f98a7b59c35b71f9453deab7861cf805070198ede310cebda535d88f9b"
+    }
+  },
+  "status": "PASS exact characteristic upper enclosure, all 47 strict constraints and seven margins",
+  "verifier_sha256": "1f5b87f98a7b59c35b71f9453deab7861cf805070198ede310cebda535d88f9b"
+}
diff --git a/research/depth-coarse/construction.py b/research/depth-coarse/construction.py
new file mode 100644
index 0000000000..eff7c3b7db
--- /dev/null
+++ b/research/depth-coarse/construction.py
@@ -0,0 +1,137 @@
+"""Scratch PR69 coarse-column + PR71 split/anchor/live-cost composition.
+
+All inherited files remain byte-identical. PR69/eumemic supplies the exact
+coarse-column reassociation. PR71/Chafik Boukhalfa and its named predecessors
+supply split grouping, global pair anchors, schedules and compiler. This new
+composition experiment is prepared with OpenAI Codex assistance. No all-size
+theorem or global optimization claim. See audit report for source boundaries.
+"""
+import sys
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+sys.dont_write_bytecode = True
+from pathlib import Path
+ROOT = Path(__file__).resolve().parents[2]
+sys.path.insert(0, str(ROOT/'scripts/experiments'))
+import argparse, gzip, hashlib, json, subprocess, types, os, shlex
+from collections import Counter
+from fractions import Fraction as Q
+from math import comb
+from bindings import producer, compile_axis
+from binary_frame_replay import replay
+from binary_frame_profile_prepare import prepare
+import binary_frame_math as arithmetic
+from bindings import refine, audit
+
+BEFORE = '''            coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]])
+                      for i, j in combinations(range(ng), 2)}'''
+AFTER = '''            def coarse_sum(i, j):
+                columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]
+                return self.total(columns)
+            coarse = {(i,j):coarse_sum(i,j) for i,j in combinations(range(ng),2)}'''
+
+def activate(choices='ccc'):
+    original = producer._graph
+    path = Path(original.__file__)
+    raw = path.read_bytes()
+    assert hashlib.sha256(raw).hexdigest() == '3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420'
+    source = raw.decode()
+    assert source.count(BEFORE) == 1
+    module = types.ModuleType('balanced_split_private_pair_graph')
+    module.__file__ = str(path)
+    replacement = '''            def coarse_sum(i, j):
+                orientation = COARSE_CHOICES[level] if level < len(COARSE_CHOICES) else 'c'
+                if orientation == 'r':
+                    parts = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]
+                else:
+                    parts = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]
+                return self.total(parts)
+            coarse = {(i,j):coarse_sum(i,j) for i,j in combinations(range(ng),2)}'''
+    assert len(choices)==3 and set(choices)<=set('cr')
+    module.COARSE_CHOICES = choices
+    exec(compile(source.replace(BEFORE, replacement), str(path)+':depth-coarse-factoring', 'exec'), module.__dict__)
+    producer._graph = module
+    return dict(pr71_head='1bef94fd40a746452548c84a4a8f8834670a3113',
+                producer_sha256=hashlib.sha256(raw).hexdigest(),
+                replacement_sha256=hashlib.sha256(replacement.encode()).hexdigest(),choices=choices,
+                before=BEFORE, after=replacement, attribution='PR69/eumemic column reassociation generalized to deterministic depth row/column choices on PR71/Chafik Boukhalfa split+anchor+cost/live; predecessor notices retained')
+
+def axis(h, out, pins):
+    compiled, word = compile_axis(h)
+    path = out/f'word-{h}.json.gz'
+    raw = (json.dumps(word, separators=(',', ':'))+'\n').encode()
+    path.write_bytes(gzip.compress(raw, mtime=0))
+    receipt = replay(path)
+    binfile = out/f'transitions-{h}.bin'
+    prepared = prepare(path, binfile)
+    profiler = out/f'profiles-{h}'
+    if not profiler.exists():
+        subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(profiler)], check=True)
+    subprocess.run([str(profiler),str(binfile)], check=True)
+    profile = json.loads(Path(str(binfile)+'.profiles.json').read_text())
+    assert profile['crt_disagreements'] == 0
+    assert profile['R'] == compiled['roles'] == receipt['roles'] == prepared['R']
+    assert sum(t*n for t,n in enumerate(profile['blocks'])) == h*profile['R']+h*(h-1)
+    result = dict(source=pins, compiled=compiled, replay=receipt, transitions=prepared, profile=profile,
+                  word_sha256=hashlib.sha256(raw).hexdigest(),gzip_sha256=hashlib.sha256(path.read_bytes()).hexdigest())
+    (out/f'axis-{h}.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+    print('PASS AXIS',h,'PHYSICAL ROLES',profile['R'],'CRT',profile['crt_matrices'],flush=True)
+
+def compose(out,require_improvement=True):
+    axes = [json.loads((out/f'axis-{h}.json').read_text()) for h in (23,25)]
+    m,N = 575,comb(23,3)*comb(25,3)
+    W=2*N+sum((N//x['profile']['v'])*x['profile']['R'] for x in axes)
+    rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N})
+    for x in axes:
+        p=x['profile'];h=p['h'];rep=N//p['v'];bank=rep*p['R']
+        assert p['blocks'][0]==p['blocks'][h]==0
+        rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n})
+        rows.update({h:bank,m-2*h:bank})
+        rows.update({1:2*N,h-2:2*N})
+    mass=sum(t*n for t,n in rows.items())
+    assert mass==m*W-1846900 and max(rows)==529
+    d=10**18;lo,hi=1,refine.floor_scaled(Q(717,10**7),d)
+    while lo+1<hi:
+        mid=(lo+hi)//2;r=refine.exact_moment(m,W,rows,Q(mid,d))
+        if r['upper']<1:lo=mid
+        elif r['lower']>1:hi=mid
+        else:raise ValueError('Inconclusive exact enclosure')
+    saving=Q(lo,d);accepted=refine.exact_moment(m,W,rows,saving);rejected=refine.exact_moment(m,W,rows,Q(hi,d))
+    assert accepted['upper']<1<rejected['lower']
+    independent=audit.independent_moment(dict(m=m,W=W,child_multiplicities=dict(rows)),saving,arithmetic.js(accepted['terms']))
+    independent_rejected=audit.independent_moment(dict(m=m,W=W,child_multiplicities=dict(rows)),Q(hi,d),arithmetic.js(rejected['terms']))
+    assert independent[1]<1<independent_rejected[0]
+    old=json.loads((Path(__file__).resolve().parent/'comparisons/pr71.json').read_text())
+    bridge=old['finite_bridge'];bridge['bit']['W']=W
+    assert W.bit_length()==bridge['bit']['wire_bits']
+    assembly=refine.assemble(bridge,saving,Q(1,10**12),d)
+    oldrows={int(t):n for t,n in old['bit']['child_multiplicities'].items()}
+    oldlower=refine.exact_moment(m,old['bit']['W'],oldrows,saving)['lower']
+    if require_improvement:
+        assert oldlower>1 and assembly['kappa']>Q(old['kappa'])
+    result=dict(status='PASS selected finite words, dirty replay, literal frame reconstruction, CRT profiles and exact arithmetic only',
+        W=W,total_rank=mass,deficit=m*W-mass,roles={str(x['profile']['h']):x['profile']['R'] for x in axes},
+        bit_saving=saving,kappa=assembly['kappa'],child_multiplicities=dict(rows),accepted=accepted,rejected=rejected,
+        independent_accepted=independent,independent_rejected=independent_rejected,
+        exactness=[arithmetic.exactness(h) for h in (23,25)],
+        assembly=assembly,old_pr71_lower_at_new_saving=oldlower,
+        old_pr71_kappa=Q(old['kappa']),gain=assembly['kappa']-Q(old['kappa']),relative_gain=assembly['kappa']/Q(old['kappa'])-1,
+        scope='All-size transfer, tape, routing, primes, recovery and analytic hypotheses remain inherited; full repository checks not run')
+    (out/'certificate.json').write_text(json.dumps(arithmetic.js(result),indent=2,sort_keys=True)+'\n')
+    print('RESULT',json.dumps(arithmetic.js({k:result[k] for k in ('W','roles','bit_saving','kappa','gain','relative_gain','old_pr71_lower_at_new_saving')})),flush=True)
+
+def check_axis(h,out):
+    selected=json.loads((out/f'axis-{h}.json').read_text())
+    path=out/f'word-{h}.json.gz';packed=path.read_bytes()
+    assert hashlib.sha256(packed).hexdigest()==selected['gzip_sha256']
+    assert hashlib.sha256(gzip.decompress(packed)).hexdigest()==selected['word_sha256']
+    assert json.loads(json.dumps(replay(path)))==selected['replay']
+    target=out/f'check-transitions-{h}.bin'
+    prepared=prepare(path,target)
+    assert json.loads(json.dumps(prepared))==selected['transitions']
+    profiler=out/f'profiles-{h}'
+    if not profiler.exists():profiler=out/'profiles'
+    subprocess.run([str(profiler),str(target)],check=True)
+    profile=json.loads(Path(str(target)+'.profiles.json').read_text())
+    assert profile==selected['profile']
+    print('PASS independently rechecked axis',h,'roles',profile['R'],'CRT',profile['crt_matrices'],flush=True)
diff --git a/research/depth-coarse/independent-receipt.json b/research/depth-coarse/independent-receipt.json
new file mode 100644
index 0000000000..7fc2f0069d
--- /dev/null
+++ b/research/depth-coarse/independent-receipt.json
@@ -0,0 +1,592 @@
+{
+  "status": "PASS independent exact selected-profile mathematical audit",
+  "scope": "Finite grammar lemma reviewed, complete profile reconstructed, independent rational root and 47 margins; all-size transfer conditional; no physical replay in this checker",
+  "source_hashes": {
+    "research/depth-coarse/selection.json": "c4a1f257940a17fb7326d23c6ab280e6ec3e105b1e9966f3c040cc2c47be3a5a",
+    "research/depth-coarse/certificate.json": "922b3fa81d0161d7777230909b95e18678033e507c8f652f09cf5b81e25a130d",
+    "research/depth-coarse/menu-ledger.json": "34dfa71b67ca266f1ead4f2ef200d54c67ae5ffaba1b811f9027f440b908eefc",
+    "research/depth-coarse/axis-23.json": "001f6566d6cbe0955bc5877fe6748d8874eb53c857b08223b5adb1009c02e14c",
+    "research/depth-coarse/axis-25.json": "2c7309dc9067a37cc4758152439265f871268da1c19c4e8ed9ed015127520c48",
+    "research/depth-coarse/comparisons/pr71.json": "0fcb53fa374273efab6370953c966e8fa065dbfdba43691843a4788cb2cda42e",
+    "research/depth-coarse/comparisons/pr75.json": "34e6f208dc02458cac9fd68a13f47c3437190468dfabba9874b8a04182475113",
+    "research/depth-coarse/menu/ccc-23.json": "bd8ee31ead172060dd2aab7c0f4291032096f3148d6a93411852a213fa3ba526",
+    "research/depth-coarse/menu/ccc-25.json": "159453a3429c0589761e824fb25d4120ce78779c7435923e0195ad89480159b9",
+    "research/depth-coarse/menu/ccr-25.json": "84b4efaf12d6bf8cce0e032a20e1aa34c562d33a3be29373b6525d66eafc2141",
+    "research/depth-coarse/menu/crc-25.json": "2bc43a8305e43b24eaf42438ead2c89e24f2466e94695a8535c17852f6e2d78a",
+    "research/depth-coarse/menu/crr-25.json": "e8703dd1deab94104e46ef9e81ab12ce4c9c46355a9224c75c3ad1107aef0bc4",
+    "research/depth-coarse/menu/rcc-25.json": "2773ed9ad6f7b45e673d287c232436b2b94686b9ba87ab95522c3f0fd65b6554",
+    "research/depth-coarse/menu/rcr-25.json": "88a55402ae6e972e1761ee340b6ac3dd0fe58586022410ba50e165e7d9bdf043",
+    "research/depth-coarse/menu/rrc-25.json": "93a1b9409acf54f32eb747d1af6dfea21249695c40160e73834040beb20160e7",
+    "research/depth-coarse/menu/rrr-25.json": "2c7309dc9067a37cc4758152439265f871268da1c19c4e8ed9ed015127520c48",
+    "research/depth-coarse/menu/ccr-23.json": "056691d478d11a61dcad82635215904510e2ed197064dad827a7a1c494fd435f",
+    "research/depth-coarse/menu/crc-23.json": "ef68d05a0822c6ba60dfcc7c0d85177bb66daae4e8bbe73b86b8168bf04aa9db",
+    "research/depth-coarse/menu/crr-23.json": "d5414a0163f2462c234dc7b928de26615c1bb329a03a15d6aa18ded84deae791",
+    "research/depth-coarse/menu/rcc-23.json": "8f23fdb04df9e6d91ba3420bff980e074ac20a30b4df93ea4a6a564fa93c136f",
+    "research/depth-coarse/menu/rcr-23.json": "001f6566d6cbe0955bc5877fe6748d8874eb53c857b08223b5adb1009c02e14c",
+    "research/depth-coarse/menu/rrc-23.json": "c11281b3710c4bcba9d980e2fc4b7e45bc8053099ba131827762b74e5c3061ed",
+    "research/depth-coarse/menu/rrr-23.json": "6ce040e399d69cf83e00e7c3202790a832162dc85a0d444f08ca05c6a9e9fcb3"
+  },
+  "selection": {
+    "23": "rcr",
+    "25": "rrr"
+  },
+  "W": 134355558,
+  "total_rank": 77252598950,
+  "bit_saving": "2582296827679/50000000000000000",
+  "root_interval": [
+    "129114841383951903/2500000000000000000000",
+    "516459365535807613/10000000000000000000000"
+  ],
+  "accepted_interval": [
+    "99999999999999999964756498615507677557568962788521/100000000000000000000000000000000000000000000000000",
+    "49999999999999999982378249307753838778784481394261/50000000000000000000000000000000000000000000000000"
+  ],
+  "rejected_interval": [
+    "100000000000000000011050772098446702379936319173027/100000000000000000000000000000000000000000000000000",
+    "25000000000000000002762693024611675594984079793257/25000000000000000000000000000000000000000000000000"
+  ],
+  "kappa": "5164326938841/100000000000000000",
+  "balanced_family_ceiling_upper": "516459365535807613/10000516459365535807613",
+  "remaining_parameter_headroom_upper": "156507997614183006803467/1000051645936553580761300000000000000000",
+  "comparisons_lower_at_selected": {
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+      "lower": "100000001193344105352118549710402066767603970439109/100000000000000000000000000000000000000000000000000",
+      "upper": "10000000119334410535211854971040206676760397043911/10000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrc",
+      "h25": "rcr",
+      "W": 134401558,
+      "lower": "25000000175933382853544907000461005379165020423163/25000000000000000000000000000000000000000000000000",
+      "upper": "100000000703733531414179628001844021516660081692653/100000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrc",
+      "h25": "rrc",
+      "W": 134436978,
+      "lower": "5000000058413883126629753315626797223972473748859/5000000000000000000000000000000000000000000000000",
+      "upper": "100000001168277662532595066312535944479449474977181/100000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrc",
+      "h25": "rrr",
+      "W": 134401558,
+      "lower": "20000000136634857225133394620552063836494330187053/20000000000000000000000000000000000000000000000000",
+      "upper": "50000000341587143062833486551380159591235825467633/50000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "ccc",
+      "W": 134612882,
+      "lower": "12500000462919367153436956667127570341224853874567/12500000000000000000000000000000000000000000000000",
+      "upper": "100000003703354937227495653337020562729798830996537/100000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "ccr",
+      "W": 134563294,
+      "lower": "20000000602812940942021050568743888169059022790647/20000000000000000000000000000000000000000000000000",
+      "upper": "25000000753516176177526313210929860211323778488309/25000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "crc",
+      "W": 134612882,
+      "lower": "100000003679856635005329164318701122615250708977849/100000000000000000000000000000000000000000000000000",
+      "upper": "2000000073597132700106583286374022452305014179557/2000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "crr",
+      "W": 134563294,
+      "lower": "100000002996440996748087748332005986032302921775469/100000000000000000000000000000000000000000000000000",
+      "upper": "10000000299644099674808774833200598603230292177547/10000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "rcc",
+      "W": 134396820,
+      "lower": "10000000055424346667822465511609736842420915264927/10000000000000000000000000000000000000000000000000",
+      "upper": "100000000554243466678224655116097368424209152649271/100000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "rcr",
+      "W": 134357858,
+      "lower": "100000000064288315788447902048246238237106772920999/100000000000000000000000000000000000000000000000000",
+      "upper": "100000000064288315788447902048246238237106772921/100000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "rrc",
+      "W": 134393278,
+      "lower": "100000000529152029319812135107344057442096878615289/100000000000000000000000000000000000000000000000000",
+      "upper": "10000000052915202931981213510734405744209687861529/10000000000000000000000000000000000000000000000000"
+    },
+    {
+      "h23": "rrr",
+      "h25": "rrr",
+      "W": 134357858,
+      "lower": "100000000043722383589080297355164703950342825259911/100000000000000000000000000000000000000000000000000",
+      "upper": "12500000005465297948635037169395587993792853157489/12500000000000000000000000000000000000000000000000"
+    }
+  ],
+  "residual_proof_obligations": [
+    "Source/word closure and physical replay verified in separate checker.",
+    "Ambient framed lift, all-size residual/row/remainder compiler and fixed-tape simulation inherited.",
+    "Analytic/routing/prime/setup/precision/recovery multiplication interfaces inherited.",
+    "Not global optimality, unconditional multiplication theorem or measured runtime gain."
+  ]
+}
diff --git a/research/depth-coarse/independent.py b/research/depth-coarse/independent.py
new file mode 100644
index 0000000000..1129fce037
--- /dev/null
+++ b/research/depth-coarse/independent.py
@@ -0,0 +1,198 @@
+"""Independent selected grammar-profile/root/47-margin audit; no package imports."""
+import sys
+if sys.flags.optimize:
+    raise ValueError("Assertions must remain enabled")
+sys.dont_write_bytecode = True
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+from math import comb,factorial
+from hashlib import sha256
+import json,itertools,argparse
+
+SCALE=10**50
+def outward(q,up=False):
+    q*=SCALE
+    return F(-(-q.numerator//q.denominator) if up else q.numerator//q.denominator,SCALE)
+def small_log(x):
+    z=(x-1)/(x+1)
+    low=2*sum((z**(2*k+1)/F(2*k+1) for k in range(64)),F())
+    return low,low+2*z**129/(129*(1-z*z))
+LN2=small_log(F(2))
+def log_bounds(x):
+    assert x>=1
+    k=0
+    while x>2:x/=2;k+=1
+    lo,hi=small_log(x)
+    return outward(lo+k*LN2[0]),outward(hi+k*LN2[1],True)
+def exp_bounds(x):
+    assert 0<=x<1
+    low=sum((x**k/F(factorial(k)) for k in range(14)),F())
+    return low,low+x**14/F(factorial(14))/(1-x/15)
+def bracket(p):
+    denominator=10**22;low,high=1,10**18
+    assert p['moment'](F(low,denominator))[1]<1<p['moment'](F(high,denominator))[0]
+    while high-low>1:
+        mid=(high+low)//2;l,h=p['moment'](F(mid,denominator))
+        if h<1:low=mid
+        elif l>1:high=mid
+        else:raise ArithmeticError('Enclosure inconclusive')
+    return F(low,denominator),F(high,denominator)
+def string_data(x):
+    if isinstance(x,F):return str(x)
+    if isinstance(x,dict):return {str(k):string_data(v) for k,v in x.items()}
+    if isinstance(x,(list,tuple)):return [string_data(v) for v in x]
+    return x
+
+PACKAGE=Path(__file__).resolve().parents[2]
+BASE=Path(__file__).resolve().parent
+PINNED={}
+
+def read(path):
+    raw=path.read_bytes();PINNED[path.relative_to(PACKAGE).as_posix()]=sha256(raw).hexdigest()
+    return json.loads(raw)
+
+def make_profile(axes):
+    m,N=575,comb(23,3)*comb(25,3)
+    rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N})
+    W=2*N
+    for h,x in zip((23,25),axes):
+        p=x['profile'];R=p['R'];v=comb(h,3)
+        assert p['h']==h and p['v']==v and R==x['compiled']['roles']==x['replay']['roles']
+        assert p['crt_disagreements']==0 and p['blocks'][0]==p['blocks'][h]==0
+        assert len(p['blocks'])==h+1 and all(type(n)is int and n>=0 for n in p['blocks'])
+        assert sum(t*n for t,n in enumerate(p['blocks']))==h*R+h*(h-1)
+        rep=N//v;bank=rep*R;W+=bank
+        rows.update({t:rep*n for t,n in enumerate(p['blocks']) if t and n})
+        rows.update({h:bank,m-2*h:bank})
+        rows.update({1:2*N,h-2:2*N})
+    mass=sum(t*n for t,n in rows.items())
+    L=sum((N//comb(h,3))*h*(h-1) for h in (23,25))
+    assert mass==m*W-N+L==m*W-1846900 and max(rows)==529
+    logs={t:log_bounds(F(m,t)) for t in rows}
+    def moment(a):
+        lo,hi=F(),F()
+        for t,n in rows.items():
+            l,h=logs[t];weight=F(t*n,m*W)
+            lo+=weight*exp_bounds(a*l)[0];hi+=weight*exp_bounds(a*h)[1]
+        return outward(lo),outward(hi,True)
+    return dict(m=m,W=W,rows=rows,mass=mass,moment=moment)
+
+def half(m,r):
+    n=1
+    while m**n<=2*r**n:n+=1
+    return n
+
+def independent_assembly(cert,bridge):
+    recorded=cert['assembly']['assembly'];p=recorded['parameters']
+    a,b,h,beta,kappa=map(F,(cert['bit_saving'],'717/10000000','1/1000000000000','1/20',cert['kappa']))
+    tau,sigma=1-a,1-b;q=a*(1-2*h);lp=1-q;c=q+h/4;eps=(1-h)/(1+q)
+    lam=(tau+lp)/2;G=eps*q;r=(G+1-eps)/2;delta=h/8
+    phase=bridge['complex'];mc,Wc,s,scalar=(phase[k] for k in ('m','W','s','scalar_group_upper'))
+    E=64*(Wc+mc+scalar+1)**3;B=s+E;C0=32*mc*B*B
+    literal=2*scalar*Wc**2+8*s+4*Wc+4+32*mc
+    semantic=dict(E=E,B=B,C0=C0,C1=1,literal_charge=literal,strict_literal_gap=E-literal,
+                  induction_gap=2*B*(mc-phase['maxchild'])-(s+E))
+    assert all(F(bridge['semantic'][k])==v for k,v in semantic.items())
+    assert E>literal and semantic['induction_gap']>=0 and C0>2*B+18
+    bit=bridge['bit'];bit=dict(bit,W=cert['W'])
+    coeff=0
+    for data in (bit,phase):
+        degree=half(data['m'],data['maxchild']);bits=data['W'].bit_length()
+        assert data['halving_degree']==degree and data['wire_bits']==bits
+        coeff+=degree*bits
+    stock=bridge['rows'];gap=stock['degree']-F(51,25)*coeff
+    assert coeff==stock['coefficient'] and gap==F(stock['degree_gap']) and gap>0
+    assert stock['suffix_slope']==4*stock['degree']
+    internal=tau+(1-beta)*max(sigma-tau,F());leaf=sigma+beta*(1-sigma)
+    margins=dict(g1=1-eps,g2=a,g3=G,g4=a,g5=min(1-eps-delta,r-delta),g6=1-eps-delta,g7=eps)
+    slacks=dict(a_positive=a,a_below_b=b-a,b_below_one_over32=F(1,32)-b,
+       beta_positive=beta,beta_below_one=1-beta,phase_leaf_above_bit=(1-beta)*b-a,
+       q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,c_positive=c,
+       c_below_one=1-c,q_below_reservations=c-q,lambda_above_tau=lam-tau,
+       lambda_above_sigma=lam-sigma,lambda_above_internal=lam-internal,
+       lambda_prime_above_lambda=lp-lam,compact_leaf=lp-leaf,
+       compact_reservations=lp-(1-c),lambda_prime_below_one=q,
+       epsilon_positive=eps,epsilon_below_one=1-eps,guard_width=1-eps,
+       K_geometry=1-eps*(1+c),K_dominates_log=eps*c,record_suffix=1-eps,
+       phase_local=1-eps-delta,phase_boundary=r-delta,gamma_sublinear=1-eps-r,
+       cell_above_band=eps-(1-r)/2,prime_interval_packing=1-eps,alpha_positive=r,
+       alpha_below_one=1-r,alpha_below_one_fourth=F(1,4)-r,
+       delta_positive=delta,delta_below_one_eighth=F(1,8)-delta,
+       short_record_fallback=eps-a,small_field_exposure=1-eps-G,
+       artificial_boundary=8-eps+r-delta-G,literal_scalar_guard=E-literal,row_product_gap=gap)
+    slacks.update({name+'_above_kappa':value-kappa for name,value in margins.items()})
+    params=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,beta=beta,h=h,q=q,c=c,
+       epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r,delta=delta,
+       C0=C0,C1=1,kappa=kappa)
+    assert len(slacks)==47 and all(value>0 for value in slacks.values())
+    assert {k:F(v) for k,v in recorded['constraints'].items()}==slacks
+    assert {k:F(v) for k,v in recorded['parameters'].items()}==params
+    assert {k:F(v) for k,v in recorded['margins'].items()}==margins
+    assert min(margins.values())==G and G-kappa==F(recorded['absorption_gap'])
+    assert 1-eps-G==h and 1-eps-r==h/2 and 1-eps*(1+c)==h-eps*h/4
+    assert G<=kappa+F(1,10**18) # next kappa grid genuinely fails g3.
+    return dict(parameters=params,constraints=slacks,margins=margins,absorption_gap=G-kappa,
+                next_kappa_rejected_by_g3=True,semantic_and_product_stock_recomputed=True)
+
+def main():
+    global PACKAGE,BASE
+    cli=argparse.ArgumentParser()
+    cli.add_argument('--package-root',type=Path,default=PACKAGE)
+    cli.add_argument('--output',type=Path,help='Intentionally write a new independent receipt; default checks retained receipt')
+    args=cli.parse_args();PACKAGE=args.package_root.resolve();BASE=PACKAGE/'research/depth-coarse'
+    selection=read(BASE/'selection.json');cert=read(BASE/'certificate.json')
+    ledger=read(BASE/'menu-ledger.json')
+    assert ledger['selected']==selection and len(ledger['results'])==64
+    axes=[read(BASE/f'axis-{h}.json') for h in (23,25)]
+    for h,x in zip((23,25),axes):assert x['source']['choices']==selection[str(h)]
+    p=make_profile(axes)
+    assert p['W']==cert['W'] and p['mass']==cert['total_rank']
+    assert p['rows']=={int(t):n for t,n in cert['child_multiplicities'].items()}
+    a=F(cert['bit_saving']);next_a=a+F(1,10**18)
+    accepted=p['moment'](a);rejected=p['moment'](next_a)
+    assert accepted[1]<1<rejected[0]
+    root_interval=bracket(p)
+    old=read(BASE/'comparisons/pr71.json');old75=read(BASE/'comparisons/pr75.json')
+    assembly=independent_assembly(cert,old['finite_bridge'])
+    exclusions={}
+    for name,oldcert in (('pr71',old),('pr75',old75)):
+        bit=oldcert['bit'];total=F()
+        for t,n in bit['child_multiplicities'].items():
+            t=int(t);l,_=log_bounds(F(bit['m'],t))
+            total+=F(t*n,bit['m']*bit['W'])*exp_bounds(a*l)[0]
+        assert total>1 and F(cert['kappa'])>F(oldcert['kappa'])
+        exclusions[name]=outward(total)
+    menu_result=[]
+    choices=[''.join(x) for x in itertools.product('cr',repeat=3)]
+    for c23,c25 in itertools.product(choices,repeat=2):
+        menu_axes=[read(BASE/f'menu/{c}-{h}.json') for h,c in ((23,c23),(25,c25))]
+        trial=make_profile(menu_axes)
+        lo,hi=trial['moment'](a)
+        if (c23,c25)==(selection['23'],selection['25']):
+            assert trial['W']==p['W'] and trial['rows']==p['rows'] and hi<1
+        else:assert lo>1
+        menu_result.append(dict(h23=c23,h25=c25,W=trial['W'],lower=lo,upper=hi))
+    # Reject changing input bytes while the audit was running.
+    for rel,digest in PINNED.items():assert sha256((PACKAGE/rel).read_bytes()).hexdigest()==digest
+    ceiling=root_interval[1]/(1+root_interval[1])
+    assert 0<ceiling-F(cert['kappa'])<F(1565,10**19)
+    result=dict(status='PASS independent exact selected-profile mathematical audit',
+        scope='Finite grammar lemma reviewed, complete profile reconstructed, independent rational root and 47 margins; all-size transfer conditional; no physical replay in this checker',
+        source_hashes=PINNED,selection=selection,W=p['W'],total_rank=p['mass'],bit_saving=a,
+        root_interval=list(root_interval),accepted_interval=list(accepted),rejected_interval=list(rejected),kappa=F(cert['kappa']),
+        balanced_family_ceiling_upper=ceiling,remaining_parameter_headroom_upper=ceiling-F(cert['kappa']),
+        comparisons_lower_at_selected=exclusions,assembly=assembly,menu_64_at_selected=menu_result,
+        residual_proof_obligations=['Source/word closure and physical replay verified in separate checker.',
+            'Ambient framed lift, all-size residual/row/remainder compiler and fixed-tape simulation inherited.',
+            'Analytic/routing/prime/setup/precision/recovery multiplication interfaces inherited.',
+            'Not global optimality, unconditional multiplication theorem or measured runtime gain.'])
+    result=string_data(result)
+    if args.output is not None:
+        args.output.write_text(json.dumps(result,indent=2)+'\n')
+    else:
+        assert result==json.loads((BASE/'independent-receipt.json').read_text()), 'Independent receipt changed'
+    print('PASS complete rank/list, independent exact root, 47 constraints, seven margins, PR71/75 exclusions and 64-profile separation')
+    print('Selection',selection,'W',p['W'],'kappa',cert['kappa'])
+
+if __name__=='__main__':main()
diff --git a/research/depth-coarse/menu-ledger.json b/research/depth-coarse/menu-ledger.json
new file mode 100644
index 0000000000..89bd364629
--- /dev/null
+++ b/research/depth-coarse/menu-ledger.json
@@ -0,0 +1,742 @@
+{
+  "choices": [
+    "ccc",
+    "ccr",
+    "crc",
+    "crr",
+    "rcc",
+    "rcr",
+    "rrc",
+    "rrr"
+  ],
+  "grid_denominator": 1000000000000000000,
+  "profile_source_hashes": {
+    "menu/ccc-23.json": "bd8ee31ead172060dd2aab7c0f4291032096f3148d6a93411852a213fa3ba526",
+    "menu/ccc-25.json": "159453a3429c0589761e824fb25d4120ce78779c7435923e0195ad89480159b9",
+    "menu/ccr-23.json": "056691d478d11a61dcad82635215904510e2ed197064dad827a7a1c494fd435f",
+    "menu/ccr-25.json": "84b4efaf12d6bf8cce0e032a20e1aa34c562d33a3be29373b6525d66eafc2141",
+    "menu/crc-23.json": "ef68d05a0822c6ba60dfcc7c0d85177bb66daae4e8bbe73b86b8168bf04aa9db",
+    "menu/crc-25.json": "2bc43a8305e43b24eaf42438ead2c89e24f2466e94695a8535c17852f6e2d78a",
+    "menu/crr-23.json": "d5414a0163f2462c234dc7b928de26615c1bb329a03a15d6aa18ded84deae791",
+    "menu/crr-25.json": "e8703dd1deab94104e46ef9e81ab12ce4c9c46355a9224c75c3ad1107aef0bc4",
+    "menu/rcc-23.json": "8f23fdb04df9e6d91ba3420bff980e074ac20a30b4df93ea4a6a564fa93c136f",
+    "menu/rcc-25.json": "2773ed9ad6f7b45e673d287c232436b2b94686b9ba87ab95522c3f0fd65b6554",
+    "menu/rcr-23.json": "001f6566d6cbe0955bc5877fe6748d8874eb53c857b08223b5adb1009c02e14c",
+    "menu/rcr-25.json": "88a55402ae6e972e1761ee340b6ac3dd0fe58586022410ba50e165e7d9bdf043",
+    "menu/rrc-23.json": "c11281b3710c4bcba9d980e2fc4b7e45bc8053099ba131827762b74e5c3061ed",
+    "menu/rrc-25.json": "93a1b9409acf54f32eb747d1af6dfea21249695c40160e73834040beb20160e7",
+    "menu/rrr-23.json": "6ce040e399d69cf83e00e7c3202790a832162dc85a0d444f08ca05c6a9e9fcb3",
+    "menu/rrr-25.json": "2c7309dc9067a37cc4758152439265f871268da1c19c4e8ed9ed015127520c48"
+  },
+  "results": [
+    {
+      "W": 134355558,
+      "accepted_upper": "5598148249999999998027016544005317463146907305881/5598148250000000000000000000000000000000000000000",
+      "bit_saving": "2582296827679/50000000000000000",
+      "h23": "rcr",
+      "h25": "rrr",
+      "kappa": "5164326938841/100000000000000000",
+      "lower_at_selected_saving": "33588889499999999988162099264031903044045791315273/33588889500000000000000000000000000000000000000000",
+      "next_bit_saving": "51645936553581/1000000000000000000",
+      "rejected_lower": "8397222375000000000927957907261023361002319063703/8397222375000000000000000000000000000000000000000"
+    },
+    {
+      "W": 134355558,
+      "accepted_upper": "16794444749999999999485573461384306636700748478083/16794444750000000000000000000000000000000000000000",
+      "bit_saving": "12911373076563/250000000000000000",
+      "h23": "rcr",
+      "h25": "rcr",
+      "kappa": "25821412593483/500000000000000000",
+      "lower_at_selected_saving": "365096625075086809601769022466465858253742577867/365096625000000000000000000000000000000000000000",
+      "next_bit_saving": "51645492306253/1000000000000000000",
+      "rejected_lower": "1399537062500000000605042210478109123295628042109/1399537062500000000000000000000000000000000000000"
+    },
+    {
+      "W": 134357858,
+      "accepted_upper": "6717892899999999998712167122163397256695446131757/6717892900000000000000000000000000000000000000000",
+      "bit_saving": "51644992109933/1000000000000000000",
+      "h23": "rrr",
+      "h25": "rrr",
+      "kappa": "12910581260577/250000000000000000",
+      "lower_at_selected_saving": "33589464514686114514207952356607486515140962651973/33589464500000000000000000000000000000000000000000",
+      "next_bit_saving": "25822496054967/500000000000000000",
+      "rejected_lower": "1343578580000000000364434092884502276718815510459/1343578580000000000000000000000000000000000000000"
+    },
+    {
+      "W": 134357858,
+      "accepted_upper": "33589464499999999985543356862192738830474227881097/33589464500000000000000000000000000000000000000000",
+      "bit_saving": "51644547878853/1000000000000000000",
+      "h23": "rrr",
+      "h25": "rcr",
+      "kappa": "51641880857109/1000000000000000000",
+      "lower_at_selected_saving": "2099341532599631313088037697468152651902468031279/2099341531250000000000000000000000000000000000000",
+      "next_bit_saving": "25822273939427/500000000000000000",
+      "rejected_lower": "6717892900000000000218701467436229732301677534101/6717892900000000000000000000000000000000000000000"
+    },
+    {
+      "W": 134378558,
+      "accepted_upper": "33594639499999999989167102703275804114621147428069/33594639500000000000000000000000000000000000000000",
+      "bit_saving": "51640364642223/1000000000000000000",
+      "h23": "ccr",
+      "h25": "rrr",
+      "kappa": "51637698052511/1000000000000000000",
+      "lower_at_selected_saving": "33594639586651078050437104516423732547426632642573/33594639500000000000000000000000000000000000000000",
+      "next_bit_saving": "3227522790139/62500000000000000",
+      "rejected_lower": "33594639500000000004718512546763778218838956134379/33594639500000000000000000000000000000000000000000"
+    },
+    {
+      "W": 134378558,
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+    },
+    {
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+      "bit_saving": "6443336446151/125000000000000000",
+      "h23": "crc",
+      "h25": "crc",
+      "kappa": "51544034644597/1000000000000000000",
+      "lower_at_selected_saving": "3367047204620408805460581809606464721393796366507/3367047050000000000000000000000000000000000000000",
+      "next_bit_saving": "51546691569209/1000000000000000000",
+      "rejected_lower": "33670470500000000012749711439849278487043236361299/33670470500000000000000000000000000000000000000000"
+    },
+    {
+      "W": 134681882,
+      "accepted_upper": "673409409999999999933012186420357159945828164443/673409410000000000000000000000000000000000000000",
+      "bit_saving": "515461849693/10000000000000000",
+      "h23": "crc",
+      "h25": "ccc",
+      "kappa": "3221470506057/62500000000000000",
+      "lower_at_selected_saving": "33670472054112023515187906522507973790042182284223/33670470500000000000000000000000000000000000000000",
+      "next_bit_saving": "51546184969301/1000000000000000000",
+      "rejected_lower": "3367047050000000001223042927135683899656798499403/3367047050000000000000000000000000000000000000000"
+    }
+  ],
+  "scope": "Exact maximum among 64 frozen whole-profile choices at 1e18 grid; every nonselected profile strictly rejected at selected saving; no broader optimum claimed",
+  "selected": {
+    "23": "rcr",
+    "25": "rrr"
+  }
+}
diff --git a/research/depth-coarse/menu.py b/research/depth-coarse/menu.py
new file mode 100644
index 0000000000..83621537a7
--- /dev/null
+++ b/research/depth-coarse/menu.py
@@ -0,0 +1,75 @@
+"""Exact 8x8 finite profile-menu comparison; no unrestricted optimum claim."""
+import argparse,hashlib,itertools,json,contextlib,io,tempfile
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+from math import comb
+from bindings import refine,arithmetic
+HERE=Path(__file__).resolve().parent
+CHOICES=[''.join(x) for x in itertools.product('cr',repeat=3)]
+
+def profile(a,b):
+    axes=[json.loads((HERE/f'menu/{c}-{h}.json').read_text()) for h,c in ((23,a),(25,b))]
+    N=comb(23,3)*comb(25,3);W=2*N+sum(N//x['profile']['v']*x['profile']['R'] for x in axes)
+    rows=Counter({1:19*N,21:2*N,17:2*N,481:2*N})
+    for x in axes:
+        p=x['profile'];h=p['h'];rep=N//p['v'];bank=rep*p['R']
+        assert p['crt_disagreements']==0 and p['blocks'][0]==p['blocks'][h]==0
+        assert sum(t*n for t,n in enumerate(p['blocks']))==h*p['R']+h*(h-1)
+        rows.update({t:n*rep for t,n in enumerate(p['blocks']) if t and n})
+        rows.update({h:bank,575-2*h:bank});rows.update({1:2*N,h-2:2*N})
+    assert sum(t*n for t,n in rows.items())==575*W-1846900
+    return W,rows
+
+def build():
+    d=10**18;results=[]
+    bridge=json.loads((HERE/'comparisons/pr71.json').read_text())['finite_bridge']
+    for a,b in itertools.product(CHOICES,repeat=2):
+        W,rows=profile(a,b);lo,hi=1,refine.floor_scaled(Q(717,10**7),d)
+        while lo+1<hi:
+            mid=(lo+hi)//2;r=refine.exact_moment(575,W,rows,Q(mid,d))
+            if r['upper']<1:lo=mid
+            elif r['lower']>1:hi=mid
+            else:raise ArithmeticError('Inconclusive exact menu enclosure')
+        saving=Q(lo,d);lower=refine.exact_moment(575,W,rows,Q(hi,d))['lower'];upper=refine.exact_moment(575,W,rows,saving)['upper']
+        assert upper<1<lower
+        bridge['bit']['W']=W;assembled=refine.assemble(bridge,saving,Q(1,10**12),d)
+        results.append(dict(h23=a,h25=b,W=W,bit_saving=saving,next_bit_saving=Q(hi,d),accepted_upper=upper,rejected_lower=lower,kappa=assembled['kappa']))
+        print('SCREEN',a,b,str(assembled['kappa']),flush=True)
+    results.sort(key=lambda x:(x['kappa'],x['bit_saving']),reverse=True)
+    best=results[0]
+    for row in results:
+        W,children=profile(row['h23'],row['h25'])
+        row['lower_at_selected_saving']=refine.exact_moment(575,W,children,best['bit_saving'])['lower']
+        if row is not best:assert row['lower_at_selected_saving']>1,'Menu winner not strictly separated'
+    paths=sorted((HERE/'menu').glob('*.json'))
+    return arithmetic.js(dict(scope='Exact maximum among 64 frozen whole-profile choices at 1e18 grid; every nonselected profile strictly rejected at selected saving; no broader optimum claimed',
+        choices=CHOICES,selected={'23':best['h23'],'25':best['h25']},grid_denominator=d,
+        profile_source_hashes={str(p.relative_to(HERE)):hashlib.sha256(p.read_bytes()).hexdigest() for p in paths},results=results))
+
+def check():
+    ledger=json.loads((HERE/'menu-ledger.json').read_text());rows=ledger['results'];d=ledger['grid_denominator']
+    assert d==10**18 and ledger['choices']==CHOICES
+    assert len(rows)==64 and {(x['h23'],x['h25']) for x in rows}==set(itertools.product(CHOICES,repeat=2))
+    for name,digest in ledger['profile_source_hashes'].items():
+        assert hashlib.sha256((HERE/name).read_bytes()).hexdigest()==digest
+    chosen=next(x for x in rows if (x['h23'],x['h25'])==(ledger['selected']['23'],ledger['selected']['25']))
+    bridge=json.loads((HERE/'comparisons/pr71.json').read_text())['finite_bridge']
+    for row in rows:
+        W,children=profile(row['h23'],row['h25']);assert W==row['W']
+        a=Q(row['bit_saving']);n=Q(row['next_bit_saving']);assert n==a+Q(1,d)
+        upper=refine.exact_moment(575,W,children,a)['upper'];lower=refine.exact_moment(575,W,children,n)['lower']
+        assert upper==Q(row['accepted_upper']) and lower==Q(row['rejected_lower']) and upper<1<lower
+        bridge['bit']['W']=W;assembled=refine.assemble(bridge,a,Q(1,10**12),d)
+        assert assembled['kappa']==Q(row['kappa']) and Q(row['kappa'])<=Q(chosen['kappa'])
+        strict=refine.exact_moment(575,W,children,Q(chosen['bit_saving']))['lower']
+        assert strict==Q(row['lower_at_selected_saving'])
+        if row is not chosen:assert strict>1
+    return ledger
+
+if __name__=='__main__':
+    p=argparse.ArgumentParser();p.add_argument('--record',action='store_true');a=p.parse_args();result=build() if a.record else check()
+    path=HERE/'menu-ledger.json'
+    if a.record:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+    else:assert result==json.loads(path.read_text()),'Menu ledger changed'
+    print('PASS 64 exact combinations; selected '+str(result['selected']),flush=True)
diff --git a/research/depth-coarse/menu/ccc-23.json b/research/depth-coarse/menu/ccc-23.json
new file mode 100644
index 0000000000..6df77d5a1c
--- /dev/null
+++ b/research/depth-coarse/menu/ccc-23.json
@@ -0,0 +1,195 @@
+{
+  "compiled": {
+    "all_physical_frame_inclusions": true,
+    "baseline_pr48_roles": 36432,
+    "baseline_pr65_roles": 27918,
+    "complete_dirty_basis_both_orientations": true,
+    "dirty_basis_vectors": 30880,
+    "elementary_xors": 161763,
+    "graph_configuration": {
+      "anchor": true,
+      "groups": [
+        1,
+        1,
+        2
+      ],
+      "schedule": "cover-core"
+    },
+    "h": 23,
+    "histogram": {
+      "0": 324996,
+      "1": 58279,
+      "2": 80746,
+      "3": 9986,
+      "4": 14480,
+      "5": 6448,
+      "6": 1969,
+      "7": 717,
+      "8": 1214,
+      "9": 521,
+      "10": 528,
+      "11": 102,
+      "12": 663,
+      "13": 198,
+      "14": 1900,
+      "15": 305,
+      "16": 438,
+      "17": 538,
+      "18": 3409,
+      "19": 6478,
+      "21": 426,
+      "22": 23
+    },
+    "mode": {
+      "matching": true,
+      "reclaim": true
+    },
+    "paid_clones": 0,
+    "pending_cost_uses_next_use_frame": true,
+    "pending_live_controls": true,
+    "rank_mass": 629280,
+    "reclamation_order": "all eligible retired ranks, exact integer profile cost, XOR count, slot ID",
+    "roles": 27338,
+    "scalar": {
+      "additions": 67460,
+      "all_additions_disjoint": true,
+      "all_partial_outputs_exact": true,
+      "circuit_sha256": "53763e256dd7343a2b000b3226e6230e6cf7a9dfa80e094a02e6ded16e266003",
+      "every_node_has_common_point": true,
+      "h": 23,
+      "inputs": 1771,
+      "merged_additions": 11937,
+      "partial_outputs": 5336,
+      "roles": 72796
+    },
+    "source_pr65_head": "49e84f939d15b618b50714eb039cabf97c74256a",
+    "source_pr67_head": "b3745601e947a94316bf25c2c6263d93c06e3364",
+    "source_pr68_head": "734c58e225e9d2254570c3b50296ed96943f62ea",
+    "stats": {
+      "clearing_xors": 3543,
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index 0000000000..5bb62e34f8
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index 0000000000..a43d55e63d
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index 0000000000..82425a2298
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new file mode 100644
index 0000000000..042f0a456b
--- /dev/null
+++ b/research/depth-coarse/menu/crc-23.json
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new file mode 100644
index 0000000000..be07584238
--- /dev/null
+++ b/research/depth-coarse/menu/crc-25.json
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new file mode 100644
index 0000000000..c47adba37c
--- /dev/null
+++ b/research/depth-coarse/menu/crr-23.json
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index 0000000000..435aadac90
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index 0000000000..a0589d40d5
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index 0000000000..6ce5547900
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index 0000000000..25a541e1f7
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new file mode 100644
index 0000000000..3443001118
--- /dev/null
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index 0000000000..498c4780a8
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index 0000000000..f176f13f95
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+  },
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+    "after": "            def coarse_sum(i, j):\n                orientation = COARSE_CHOICES[level] if level < len(COARSE_CHOICES) else 'c'\n                if orientation == 'r':\n                    parts = [self.total([e(a,b) for b in groups[j]]) for a in groups[i]]\n                else:\n                    parts = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]\n                return self.total(parts)\n            coarse = {(i,j):coarse_sum(i,j) for i,j in combinations(range(ng),2)}",
+    "attribution": "PR69/eumemic column reassociation generalized to deterministic depth row/column choices on PR71/Chafik Boukhalfa split+anchor+cost/live; predecessor notices retained",
+    "before": "            coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]])\n                      for i, j in combinations(range(ng), 2)}",
+    "choices": "rrr",
+    "pr71_head": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "producer_sha256": "3d47e89d2649c90800a276bdd0480131def50e0bdf92c122a19494b55bf17420",
+    "replacement_sha256": "0a8e61c8a06aecba2fdd706db4e31616c7cdf0852bed136b1e96b5d499016d9c"
+  },
+  "transitions": {
+    "R": 35798,
+    "copied_centers": 25,
+    "distinct_transitions": 212455,
+    "frames": 84845,
+    "h": 25,
+    "rank_histogram_with_side_growth_split_into_singletons": {
+      "1": 90859,
+      "2": 110686,
+      "3": 13449,
+      "4": 18691,
+      "5": 8490,
+      "6": 3343,
+      "7": 1046,
+      "8": 1304,
+      "9": 749,
+      "10": 844,
+      "11": 27,
+      "12": 760,
+      "13": 73,
+      "14": 683,
+      "15": 199,
+      "16": 2178,
+      "17": 642,
+      "18": 621,
+      "19": 933,
+      "20": 4465,
+      "21": 8339,
+      "23": 442,
+      "24": 25
+    },
+    "rank_mass": 895550,
+    "singles": 20700,
+    "transition_events_equal_independent_xor_word_reconstruction": true,
+    "v": 2300,
+    "word_sha256": "ab46b13e45d076c2104d0bf64a1db79886b643add11685edfde719650fb316f1"
+  },
+  "word_sha256": "ab46b13e45d076c2104d0bf64a1db79886b643add11685edfde719650fb316f1"
+}
diff --git a/research/depth-coarse/mutation-controls.json b/research/depth-coarse/mutation-controls.json
new file mode 100644
index 0000000000..599ac770cb
--- /dev/null
+++ b/research/depth-coarse/mutation-controls.json
@@ -0,0 +1,14 @@
+{
+  "omitted_xor": {
+    "rejected": true,
+    "exception": "AssertionError"
+  },
+  "understated_roles": {
+    "rejected": true,
+    "exception": "IndexError"
+  },
+  "omitted_transition": {
+    "rejected": true,
+    "exception": "AssertionError"
+  }
+}
diff --git a/research/depth-coarse/selection.json b/research/depth-coarse/selection.json
new file mode 100644
index 0000000000..e0e361b6df
--- /dev/null
+++ b/research/depth-coarse/selection.json
@@ -0,0 +1,4 @@
+{
+  "23": "rcr",
+  "25": "rrr"
+}
diff --git a/research/depth-coarse/vendor/LICENSE b/research/depth-coarse/vendor/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/depth-coarse/vendor/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
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+   5. Submission of Contributions. Unless You explicitly state otherwise,
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+   6. Trademarks. This License does not grant permission to use the trade
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+      Contributor provides its Contributions) on an "AS IS" BASIS,
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
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diff --git a/research/depth-coarse/vendor/PR71-NOTICE b/research/depth-coarse/vendor/PR71-NOTICE
new file mode 100644
index 0000000000..8adab44ba3
--- /dev/null
+++ b/research/depth-coarse/vendor/PR71-NOTICE
@@ -0,0 +1,324 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Aligned split-pair composition (2026-10-08)
+------------------------------------------
+Avi Eisenberg: PR62 interval strips and core-aware pair assembly. Dominik
+Scholz with OpenAI assistance: PR63 ranked-frame composition and PR68 pending
+live-carrier controls. Rohan Arun with OpenAI assistance: PR65 region schedules
+and refined exact arithmetic, and PR67 all-rank profile-cost selection and
+its profile oracle. Rohan Garg / rohangar1
+with substantial OpenAI Codex assistance: PR59 split-pair operation. Eumemic
+with substantial OpenAI Codex assistance: PR57 joint reversible compiler and
+independent physical-word/profile checks. Chafik Boukhalfa with OpenAI Codex
+assistance: PR60 ranked reclamation and this selected [1,1,2] split vector,
+aligned common-point permutation, next-use profile score, composition and
+certification package.
+The complete PR65 baseline words, profiles and arithmetic, plus 43 original
+source/provenance files, are preserved under references/frame-compiler/pr65.
+The original PR59 split operation and notices are separately preserved.
+PR67's compiler/oracle and baseline profile, and PR68's compiler/driver/proof,
+retain their original bytes, licenses and notices in their own archives.
+All previous notices and mathematical dependencies remain applicable.
diff --git a/research/depth-coarse/vendor/SOURCE.json b/research/depth-coarse/vendor/SOURCE.json
new file mode 100644
index 0000000000..538ea00753
--- /dev/null
+++ b/research/depth-coarse/vendor/SOURCE.json
@@ -0,0 +1,56 @@
+{
+  "pr71-engine.py": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "scripts/experiments/split_pair_engine.py",
+    "sha256": "58f13f82ce1bb7f2b5549e17628bc6034e5e05cb24db2acb9a91c24820872f70"
+  },
+  "pr71-split-graph.py": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "scripts/experiments/split_pair_graph.py",
+    "sha256": "9d4ee7179f880f9576e81c7ad3a5290fe61380a7531d559ef3cf0939bb30089c"
+  },
+  "pr65-schedule.py": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "references/frame-compiler/pr65/research/reordered-rank-pair/verify.py",
+    "sha256": "e84ed21dad24f9b8c429441caae49c13ccae883be2f04e696993cfe665b57352"
+  },
+  "pr65-refine.py": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/refine.py",
+    "sha256": "e0488c919e76850313ff93d7da704a7fcc14a316eee2cac81e2b8dff9c145b5d"
+  },
+  "pr65-audit.py": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "references/frame-compiler/pr65/research/reordered-rank-pair/arithmetic/audit.py",
+    "sha256": "aa297fffcdaa133f5dee17d97fac72aa5ba2cf943da5a8a5e3f4d62f6f0a7f79"
+  },
+  "pr67-profile-oracle.cpp": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "references/frame-compiler/pr67/research/slot-cost-rank-pair/profile_oracle.cpp",
+    "sha256": "d1f6b650de9fb5842b412595369271d9eeb6f54045c76c0fb5cad29854955c35"
+  },
+  "pr69-balanced-coarse.py": {
+    "pr": 69,
+    "commit": "91aa1f17e6e3fc063241686a41a34ddd0dc24c50",
+    "path": "scripts/experiments/balanced_coarse_compiler.py",
+    "sha256": "bd8169bf9f5df185a8aa4aec22234b4fd483000a1cecc78b71bf32e479af1499"
+  },
+  "PR71-NOTICE": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "NOTICE",
+    "sha256": "1e0702aa665673508fa91169163c5785d680637fff636fda01f36e3b127c3ee0"
+  },
+  "LICENSE": {
+    "pr": 71,
+    "commit": "1bef94fd40a746452548c84a4a8f8834670a3113",
+    "path": "LICENSE",
+    "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+  }
+}
diff --git a/research/depth-coarse/vendor/pr65-audit.py b/research/depth-coarse/vendor/pr65-audit.py
new file mode 100644
index 0000000000..7d9949e676
--- /dev/null
+++ b/research/depth-coarse/vendor/pr65-audit.py
@@ -0,0 +1,120 @@
+#!/usr/bin/env python3
+"""Independent exact enclosure, assembly and negative-control verification."""
+import sys
+sys.dont_write_bytecode = True
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+import refine
+
+ROOT = refine.ROOT
+HERE = Path(__file__).resolve().parent
+
+
+def log_interval(x):
+    """Atanh expansion with independent 3/2 reduction and 60 exact terms."""
+    assert x >= 1
+    k = 0
+    while x > Q(3, 2):
+        x /= Q(3, 2)
+        k += 1
+    def small(y):
+        z = (y-1)/(y+1)
+        power, total = z, Q()
+        for j in range(60):
+            total += power/Q(2*j+1)
+            power *= z*z
+        return 2*total, 2*total+2*power/(121*(1-z*z))
+    lo, hi = small(x)
+    blo, bhi = small(Q(3, 2))
+    return lo+k*blo, hi+k*bhi
+
+
+def independent_moment(profile, saving, recorded_terms):
+    low, high = Q(), Q()
+    rows = {int(t): n for t, n in profile['child_multiplicities'].items()}
+    for t, n in sorted(rows.items()):
+        lo, hi = log_interval(Q(profile['m'], t))
+        recorded = recorded_terms[str(t)]
+        assert Q(recorded['log_lower']) <= lo <= hi <= Q(recorded['log_upper'])
+        u, v = lo*saving, hi*saving
+        assert 0 < u <= v < Q(1, 1000)
+        # Directed rounding of input logs bounds rational denominator sizes.
+        u = Q(refine.floor_scaled(u, 10**40), 10**40)
+        v = Q(refine.ceiling_scaled(v, 10**40), 10**40)
+        tlo, thi = Q(1), Q(1)
+        elo, ehi = Q(1), Q(1)
+        for j in range(1, 13):
+            tlo, thi = tlo*u/j, thi*v/j
+            elo, ehi = elo+tlo, ehi+thi
+        # First omitted term is degree13; subsequent ratios <1/2.
+        ehi += 2*thi*v/13
+        weight = Q(t*n, profile['m']*profile['W'])
+        low += weight*Q(refine.floor_scaled(elo, 10**40), 10**40)
+        high += weight*Q(refine.ceiling_scaled(ehi, 10**40), 10**40)
+    return low, high
+
+
+def audit(certificate):
+    profile_path = ROOT/certificate['profile_path']
+    assert sha256(profile_path.read_bytes()).hexdigest() == certificate['profile_sha256']
+    for name, digest in certificate['source_sha256'].items():
+        assert sha256((ROOT/name).read_bytes()).hexdigest() == digest, name
+    source = json.loads(profile_path.read_text())
+    p = source['bit']
+    assert sum(int(t)*n for t, n in p['child_multiplicities'].items()) == p['total_rank']
+    accepted = independent_moment(p, Q(certificate['bit_saving']), certificate['accepted_moment']['terms'])
+    rejected = independent_moment(p, Q(certificate['next_bit_saving']), certificate['accepted_moment']['terms'])
+    assert accepted[1] < 1 < rejected[0]
+    controls = {}
+    for name, variant in [('preferred', certificate['preferred']), ('coarse_grid_control', certificate['coarse_grid_control'])]:
+        params = variant['assembly']['parameters']
+        result = refine.balanced.assembly(source['finite_bridge'], Q(params['a_bit']), Q(params['kappa']), h=Q(params['h']))
+        assert refine.arithmetic.js(result) == variant['assembly']
+        assert len(result['constraints']) == 47 and len(result['margins']) == 7
+        assert all(v > 0 for v in result['constraints'].values())
+        for label, kwargs in [('next_grid', dict(kappa=Q(variant['next_kappa']))),
+                              ('zero_backoff', dict(h=Q())),
+                              ('original_prefix', dict(original_prefix=True)),
+                              ('old_guard', dict(old_guard=True)),
+                              ('old_exposures', dict(old_exposures=True))]:
+            call = dict(a_bit=Q(params['a_bit']), kappa=Q(params['kappa']), h=Q(params['h']))
+            call.update(kwargs)
+            try:
+                refine.balanced.assembly(source['finite_bridge'], **call)
+            except refine.balanced.InvalidAssembly as error:
+                controls[name+'/'+label] = str(error)
+            else:
+                raise AssertionError('Negative control accepted: '+name+'/'+label)
+    next_a = Q(certificate['next_bit_saving'])
+    best = Q(certificate['preferred']['kappa'])
+    cap = next_a/(1+next_a)
+    assert cap > best
+    return dict(status='PASS', independent_log_base='3/2', independent_log_terms=60,
+        independent_exp_degree=12, independent_tail='twice first omitted term',
+        independent_accepted_gap=1-accepted[1], independent_rejected_gap=rejected[0]-1,
+        variants_reassembled=2, constraints_each=47, margins_each=7, controls=controls,
+        fixed_profile_balanced_family_kappa_strict_upper=cap,
+        remaining_possible_parameter_gain_upper=cap-best)
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--certificate', type=Path, default=HERE/'certificate.json')
+    parser.add_argument('--receipt', type=Path, default=HERE/'audit-receipt.json')
+    parser.add_argument('--record', action='store_true')
+    args = parser.parse_args()
+    result = refine.arithmetic.js(audit(json.loads(args.certificate.read_text())))
+    if args.record:
+        args.receipt.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    else:
+        assert result == json.loads(args.receipt.read_text()), 'Independent receipt changed'
+    print('PASS independent logarithm/exponential enclosures; 47 strict constraints; seven margins; ten assembly negative controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/depth-coarse/vendor/pr65-refine.py b/research/depth-coarse/vendor/pr65-refine.py
new file mode 100644
index 0000000000..399299089e
--- /dev/null
+++ b/research/depth-coarse/vendor/pr65-refine.py
@@ -0,0 +1,162 @@
+#!/usr/bin/env python3
+"""Exact arithmetic screen of the reordered rank-pair complete physical profile.
+
+Uses PR63's paid profile, inherited PR48 logarithm enclosures and balanced
+assembly (PR34 and successors). New directed Taylor bounds are documented in
+this file. Prepared with OpenAI assistance. Inherited licenses apply.
+Physical linkage is checked by the parent verifier; no full theorem or practical speedup claim is implied.
+"""
+import sys
+sys.dont_write_bytecode = True
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import importlib.util
+import json
+from math import factorial
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[3]
+sys.path.insert(0, str(ROOT/'scripts/experiments'))
+import binary_frame_math as arithmetic
+spec = importlib.util.spec_from_file_location('inherited_assembly', ROOT/'references/frame-compiler/pr48/research/copied-fixed/balanced_assembly.py')
+balanced = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(balanced)
+
+
+def floor_scaled(x, denominator):
+    return (x * denominator).numerator // (x * denominator).denominator
+
+
+def ceiling_scaled(x, denominator):
+    return -floor_scaled(-x, denominator)
+
+
+def exact_moment(m, width, rows, saving, degree=8, rounding=10**40):
+    """Bound sum n*t/(mW)*exp(saving*log(m/t)) entirely in Q.
+
+    At 0 <= u <= v < 1, S_d(u) is a lower bound for exp(u).
+    The tail at v has first term v^(d+1)/(d+1)!; successive ratios
+    are at most v/(d+2). Thus S_d(v)+first/(1-v/(d+2)) is upper.
+    Directed rounding per exp bound preserves both inequalities.
+    The inherited logarithm helper encloses log(m/t) rationally.
+    """
+    assert type(saving) is Q and 0 < saving < 1 and degree >= 1
+    lo, hi = Q(), Q()
+    terms = {}
+    for t, count in sorted(rows.items()):
+        assert type(t) is int and type(count) is int and 0 < t < m and count > 0
+        loglo, loghi = arithmetic.logs(Q(m, t))
+        u, v = saving*loglo, saving*loghi
+        assert 0 <= u <= v < 1
+        lower = sum((u**j / factorial(j) for j in range(degree+1)), Q())
+        upper = sum((v**j / factorial(j) for j in range(degree+1)), Q())
+        upper += v**(degree+1)/factorial(degree+1)/(1-v/Q(degree+2))
+        lower = Q(floor_scaled(lower, rounding), rounding)
+        upper = Q(ceiling_scaled(upper, rounding), rounding)
+        weight = Q(t*count, m*width)
+        lo += weight*lower
+        hi += weight*upper
+        terms[t] = dict(weight=weight, log_lower=loglo, log_upper=loghi,
+                        exp_lower=lower, exp_upper=upper)
+    return dict(saving=saving, lower=lo, upper=hi, strict_gap=1-hi,
+                degree=degree, rounding_denominator=rounding, terms=terms)
+
+
+def assemble(bridge, saving, h, denominator):
+    preliminary = balanced.assembly(bridge, saving, Q(1, denominator), h=h)
+    kappa = Q(ceiling_scaled(preliminary['minimum_margin'], denominator)-1, denominator)
+    accepted = balanced.assembly(bridge, saving, kappa, h=h)
+    assert len(accepted['constraints']) == 47 and len(accepted['margins']) == 7
+    assert all(v > 0 for v in accepted['constraints'].values())
+    assert all(v > kappa for v in accepted['margins'].values())
+    try:
+        balanced.assembly(bridge, saving, kappa+Q(1, denominator), h=h)
+    except balanced.InvalidAssembly as error:
+        rejected = str(error)
+    else:
+        raise AssertionError('Next kappa grid unexpectedly passes')
+    return dict(kappa=kappa, assembly=accepted,
+                next_kappa=kappa+Q(1, denominator), next_kappa_rejection=rejected,
+                eventual_bounds=balanced.cutoffs(bridge, accepted))
+
+
+def build_certificate(profile_path, denominator=10**18, h=Q(1, 10**12)):
+    profile_path = profile_path.resolve()
+    source = json.loads(profile_path.read_text())
+    profile = source['bit']
+    bridge = source['finite_bridge']
+    m, width = profile['m'], profile['W']
+    rows = {int(t): n for t, n in profile['child_multiplicities'].items()}
+    assert sum(t*n for t, n in rows.items()) == profile['total_rank']
+    assert bridge['bit']['W'] == width
+    low, high = 1, floor_scaled(Q(717, 10**7), denominator)
+    assert exact_moment(m, width, rows, Q(low, denominator))['upper'] < 1
+    assert exact_moment(m, width, rows, Q(high, denominator))['lower'] > 1
+    steps = 0
+    while low+1 < high:
+        mid = (low+high)//2
+        test = exact_moment(m, width, rows, Q(mid, denominator))
+        if test['upper'] < 1:
+            low = mid
+        elif test['lower'] > 1:
+            high = mid
+        else:
+            raise ArithmeticError('Rational bounds inconclusive: increase enclosure precision')
+        steps += 1
+    saving = Q(low, denominator)
+    accepted = exact_moment(m, width, rows, saving)
+    rejected = exact_moment(m, width, rows, Q(high, denominator))
+    assert accepted['upper'] < 1 < rejected['lower']
+    preferred = assemble(bridge, saving, h, denominator)
+    coarse_denom = 10**11
+    coarse_bit = Q(floor_scaled(saving, coarse_denom), coarse_denom)
+    assert exact_moment(m, width, rows, coarse_bit)['upper'] < 1
+    coarse = assemble(bridge, coarse_bit, h, coarse_denom)
+    inherited_coarse = arithmetic.moment(m, width, rows, coarse_bit)
+    inherited_next = arithmetic.moment(m, width, rows, coarse_bit+Q(1, coarse_denom))
+    assert inherited_coarse['upper'] < 1 < inherited_next['lower']
+    coarse['original_enclosure_control'] = dict(accepted_upper=inherited_coarse['upper'],
+        next_bit_lower=inherited_next['lower'])
+    # Same coarse grid/backoff as PR63 separates the structural gain from
+    # the additional precision refinement suggested by the PR61 precedent.
+    prior = Q(source['kappa'])
+    paths = (Path(__file__), Path(__file__).with_name('audit.py'),
+        ROOT/'scripts/experiments/binary_frame_math.py', Path(balanced.__file__))
+    return dict(status='Exact finite conditional screen; physical linkage checked by parent verifier',
+        profile_path=str(profile_path.relative_to(ROOT)),
+        profile_sha256=sha256(profile_path.read_bytes()).hexdigest(),
+        source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in paths},
+        grid_denominator=denominator, binary_search_steps=steps, bit_saving=saving,
+        next_bit_saving=Q(high, denominator), accepted_moment=accepted, rejected_moment=rejected,
+        preferred=preferred, coarse_grid_control=dict(bit_saving=coarse_bit, **coarse),
+        comparison=dict(pr63_kappa=prior, kappa=preferred['kappa'],
+            difference=preferred['kappa']-prior,
+            structural_gain_on_original_grid=coarse['kappa']-prior,
+            additional_precision_gain=preferred['kappa']-coarse['kappa']),
+        proof_limits=['The complete physical profile is supplied; independent word and CRT replay are parent-verifier responsibilities.',
+                     'The rational logarithm and exponential enclosure derivations are documented in README.md, not formally mechanized.',
+                     'All-size compiler, routing, recovery, prime-selection and fixed-tape transfer remain inherited.',
+                     'Neither global optimality nor measured practical speedup is claimed.'])
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--profile', type=Path, default=Path(__file__).resolve().parent.parent/'paired-candidate.json')
+    parser.add_argument('--certificate', type=Path, default=Path(__file__).with_name('certificate.json'))
+    parser.add_argument('--record', action='store_true', help='Regenerate certificate instead of comparing with recorded result')
+    args = parser.parse_args()
+    result = arithmetic.js(build_certificate(args.profile))
+    if args.record:
+        args.certificate.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    else:
+        assert result == json.loads(args.certificate.read_text()), 'Arithmetic certificate changed'
+    print(json.dumps(dict(status='PASS exact arithmetic', bit_saving=result['bit_saving'],
+        kappa=result['preferred']['kappa'], constraints=47, margins=7,
+        next_grid_controls='PASS', comparison=result['comparison']), indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/depth-coarse/vendor/pr65-schedule.py b/research/depth-coarse/vendor/pr65-schedule.py
new file mode 100644
index 0000000000..5ac300ecd0
--- /dev/null
+++ b/research/depth-coarse/vendor/pr65-schedule.py
@@ -0,0 +1,102 @@
+#!/usr/bin/env python3
+"""Replay, profile, or deterministically rebuild a reordered PR63 circuit.
+
+PR62 graph: Avi Eisenberg, assisted by Claude; PR60 compiler: Chafik
+Boukhalfa, derived from eumemic PR57, with OpenAI Codex assistance.
+Region scheduling experiment: Rohan Arun with OpenAI Codex assistance.
+Apache-2.0; inherited notices and mathematical dependencies remain applicable.
+"""
+import sys
+sys.dont_write_bytecode = True
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+import argparse, gzip, importlib.util, json, os, shlex, subprocess, tempfile
+from hashlib import sha256
+from pathlib import Path
+
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+EXP=ROOT/'scripts/experiments'
+sys.path[:0]=[str(EXP),str(ROOT/'scripts')]
+from binary_frame_replay import replay
+from binary_frame_profile_prepare import prepare
+import binary_frame_math as arithmetic
+
+def load(path,name):
+    spec=importlib.util.spec_from_file_location(name,path)
+    module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+    return module
+
+def sha(path):return sha256(path.read_bytes()).hexdigest()
+
+def reordered_build(original,mode):
+    def build(h):
+        parts=list(original(h))
+        c,blocks,uses,value_uses,owner,signal,order,contains=parts
+        if mode=='reverse-node':
+            key=lambda g:(blocks[g]['rank'],-min(blocks[g]['nodes']))
+        elif mode=='cover-core':
+            key=lambda g:(blocks[g]['rank'],blocks[g]['frame'][1],blocks[g]['frame'][0])
+        else:raise ValueError(mode)
+        parts[6]=sorted(range(len(blocks)),key=key)
+        position={g:i for i,g in enumerate(parts[6])}
+        for g,b in enumerate(blocks):
+            for x in b['inputs']:
+                assert position[owner[x]]<position[g], 'Non-topological region order'
+            for u,i in b['candidates']:
+                assert position[g]<position[uses[u][1]], 'Backward carrier candidate'
+        return tuple(parts)
+    return build
+
+def main():
+    p=argparse.ArgumentParser(description=__doc__)
+    p.add_argument('--rebuild',action='store_true',help='Recompile both words and compare to committed witnesses')
+    p.add_argument('--work-dir',type=Path,default=ROOT/'build/reordered-rank-pair')
+    a=p.parse_args()
+    records=json.loads((HERE/'frame-compiler.json').read_text())
+    for name,digest in records['source_sha256'].items():
+        assert sha(ROOT/name)==digest, 'Changed source: '+name
+    for name,digest in records['artifact_sha256'].items():
+        assert sha(HERE/name)==digest, 'Changed artifact: '+name
+    a.work_dir.mkdir(parents=True,exist_ok=True)
+    profiles=[]
+    with tempfile.TemporaryDirectory(prefix='verify-',dir=a.work_dir) as temporary:
+        work=Path(temporary)
+        if a.rebuild:
+            import rank_pair_compiler as compiler
+            compiler.graph=load(ROOT/'research/pair-assembly/pair_graph.py','pinned_pair_graph').graph
+            original=compiler.build
+            for h in (23,25):
+                compiler.build=reordered_build(original,records['axes'][str(h)]['schedule'])
+                result,word=compiler.compile_(h,matching=True,reclaim=True,dirty=True)
+                result.pop('seconds')
+                assert json.loads(json.dumps(result))==records['axes'][str(h)]['compiled']
+                raw=(json.dumps(word,separators=(',',':'))+'\n').encode()
+                assert sha256(raw).hexdigest()==records['axes'][str(h)]['word_sha256']
+                assert raw==gzip.decompress((HERE/f'frame-word-{h}.json.gz').read_bytes())
+                print(f'PASS deterministic rebuild h={h}',flush=True)
+        binary=work/'profiles'
+        env=dict(os.environ,TMPDIR=str(work))
+        subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(EXP/'binary_frame_profiles.cpp'),'-o',str(binary)],check=True,env=env)
+        for h in (23,25):
+            word=HERE/f'frame-word-{h}.json.gz'
+            receipt=replay(word)
+            assert json.loads(json.dumps(receipt))==records['axes'][str(h)]['replay']
+            transitions=work/f'word{h}.bin'
+            prepared=json.loads(json.dumps(prepare(word,transitions)))
+            assert prepared==json.loads((HERE/f'frame-transitions-{h}.json').read_text())
+            subprocess.run([str(binary),str(transitions)],check=True,env=env)
+            profile=json.loads(Path(str(transitions)+'.profiles.json').read_text())
+            assert profile==json.loads((HERE/f'frame-profiles-{h}.json').read_text())
+            profiles.append(profile)
+            print(f'PASS h={h}: complete dirty basis in both orientations, frame paths, fixed profiles',flush=True)
+        constructor=load(ROOT/'research/pair-assembly/frame/frame_verify.py','inherited_profile_constructor')
+        constructor.check_sources()
+        constructor.WIRES_S=2*4073300+sum(4073300//f['v']*f['R'] for f in profiles)
+        constructor.MASS_S=575*constructor.WIRES_S-1846900
+        actual=arithmetic.js(constructor.profile(profiles,records))
+        expected=json.loads((HERE/'paired-candidate.json').read_text())['bit']
+        assert json.loads(json.dumps(actual))==expected
+        print('PASS complete paid profile, literal rank identity and pinned artifacts',flush=True)
+
+if __name__=='__main__':main()
diff --git a/research/depth-coarse/vendor/pr67-profile-oracle.cpp b/research/depth-coarse/vendor/pr67-profile-oracle.cpp
new file mode 100644
index 0000000000..bed146cb88
--- /dev/null
+++ b/research/depth-coarse/vendor/pr67-profile-oracle.cpp
@@ -0,0 +1,90 @@
+// Optimal-matching variant of research/copied-fixed/profiles.cpp (PR #43, Chafik
+// Boukhalfa), itself adapted from Dominik Scholz PR35 and icekylinx PR32.
+// Change: with LINKS_IN=<file>, the carrier matching is read from a pinned file
+// instead of Hopcroft-Karp. Every pinned edge must lie in the same admissible
+// adjacency (causal order and frame inclusion); donors and uses are distinct.
+// This replay-only adaptation omits the discovery edge dumper. The original
+// optimizer and profiler are preserved in references/copied-fixed/pr44.
+// Replay-only adaptation prepared with OpenAI Codex assistance.
+// Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0.
+// Adapted at h=23,25; original PR35 by Dominik Scholz, PR32 by icekylinx.
+// Dimension adaptation at 45/47; extra primes for all source-growth cases.
+// Exact bounded-minor inequalities are checked by verify.py. Original credit below.
+// Copyright 2026 icekylinx. Apache-2.0; AI-assisted handoff integration.
+// Original round3_rankone_profiles.cpp. Requires GCC/Clang unsigned __int128.
+
+// Adapted input reader for complete serialized frame-compiler transitions.
+// Actual-word fixed-I+J profiling, adapted from PR48 profiles.cpp.
+// All projector, pivot and CRT formulas below are unchanged.
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <vector>
+#include <map>
+#include <unordered_map>
+#include <cmath>
+#include <iomanip>
+#include <cstdlib>
+using U=uint32_t;using V=uint64_t;
+#include "binary_io.hpp"
+int main(int argc,char**argv){
+assert(argc==2);std::ifstream f(argv[1],std::ios::binary);U hdr[6];read_array(f,hdr);
+U h=hdr[0],v=hdr[1],R=hdr[2],nf=hdr[3],nt=hdr[4];int64_t singles=hdr[5];assert(h==23||h==25);
+V sum,loss;f.read(reinterpret_cast<char*>(&sum),8);f.read(reinterpret_cast<char*>(&loss),8);
+struct Frame{V core,cover;U rank;};std::vector<Frame>frames;
+for(U i=0;i<nf;i++){Frame a;f.read(reinterpret_cast<char*>(&a.core),8);f.read(reinterpret_cast<char*>(&a.cover),8);f.read(reinterpret_cast<char*>(&a.rank),4);frames.push_back(a);}
+std::map<std::pair<U,U>,int64_t>transitions;
+for(U i=0;i<nt;i++){U a,b;int64_t count;f.read(reinterpret_cast<char*>(&a),4);f.read(reinterpret_cast<char*>(&b),4);f.read(reinterpret_cast<char*>(&count),8);transitions[{a,b}]=count;}
+assert(f);assert(sum==h*V(R)+loss);
+V p=2305843009213693951ULL;
+auto mul=[&](V a,V b)->V{return (__uint128_t)a*b%p;};
+auto power=[&](V a,V b)->V{V r=1;for(;b;b>>=1,a=mul(a,a))if(b&1)r=mul(r,a);return r;};
+auto sub=[&](V a,V b)->V{return (a+p-b)%p;};
+std::vector<std::vector<V>>matrix_cache(frames.size());
+auto matrix=[&](U id)->const std::vector<V>&{auto&A=matrix_cache[id];if(!A.empty())return A;A.assign(h*h,0);if(id==0)return A;if(id==1){for(U i=0;i<h;i++)A[i*h+i]=1;return A;}
+ auto f=frames[id];U c=popcount64(f.core);V out=f.cover&~f.core;U nn=popcount64(out);
+ if(c==3){V factor=power(6*(h+1),p-2);for(U i=0;i<h;i++)for(U j=0;j<h;j++){V wi=3+((f.core>>i)&1);V zj=((f.core>>j)&1)?3*(h+1)-10:p-10;A[i*h+j]=mul(mul(wi,zj),factor);}return A;}
+ assert(c==1||c==2);V s=3-c,d=s*s+(c-1)*nn,den=3*(h+1)*d,inv=power(den,p-2);
+ for(U i=0;i<h;i++)for(U j=0;j<h;j++){V oi=(out>>i)&1,oj=(out>>j)&1,wi=3+((f.core>>i)&1),zj=((f.core>>j)&1)?3*(h+1)-10:p-10;
+  V num=(mul(s*oi,zj)+3*(h+1)*s*wi*oj+mul(nn*wi,zj))%p;num=sub(num,3*(h+1)*(c-1)*oi*oj);A[i*h+j]=(V(i==j&&oi)+mul(num,inv))%p;
+ }return A;};
+
+std::vector<int64_t>blocks(h+1);blocks[1]=singles;V done=0,matrices=0,crt_matrices=0,crt_disagreements=0;U longest=0;std::map<U,V>correction_hist;
+U aa,bb;
+while(std::cin>>aa>>bb){
+ assert(aa<frames.size()&&bb<frames.size());
+ int64_t count=1;std::fill(blocks.begin(),blocks.end(),0);
+ U rr=frames[bb].rank-frames[aa].rank;
+ assert(frames[bb].rank>=frames[aa].rank);
+ if(rr<=2){blocks[1]=rr; for(U t=0;t<=h;t++)std::cout<<blocks[t]<<" ";std::cout<<"\n"<<std::flush;continue;}
+ if(aa==0&&bb==1){blocks[h]=1;for(U t=0;t<=h;t++)std::cout<<blocks[t]<<" ";std::cout<<"\n"<<std::flush;continue;}
+ if(aa>1&&bb>1){
+  assert(!(frames[bb].core&~frames[aa].core));
+  assert(!(frames[aa].cover&~frames[bb].cover));
+  U ca=popcount64(frames[aa].core),cb=popcount64(frames[bb].core);
+  assert(ca==3||frames[aa].core==frames[bb].core||(ca==2&&cb==1));
+ }
+ const auto&A=matrix(aa);const auto&B=matrix(bb);std::vector<V>M(h*h);for(U x=0;x<h*h;x++)M[x]=sub(B[x],A[x]);std::vector<std::pair<U,U>>pivots;
+ for(U i=0;i<h;i++){int j=h-1;while(j>=0&&!M[i*h+j])j--;if(j<0)continue;pivots.push_back({i,U(j)});V inv=power(M[i*h+j],p-2);for(U k=i+1;k<h;k++){V z=mul(M[k*h+j],inv);if(z)for(U col=0;col<=U(j);col++)M[k*h+col]=sub(M[k*h+col],mul(z,M[i*h+col]));}}
+ assert(pivots.size()==rr);
+// All minors have numerator bounded independently of matrix size, since the
+// matrix is a 0/1 diagonal mask plus a correction of rank at most four.
+// Source growth and core-two -> core-one use all three primes at these dimensions.
+if(aa>1&&bb>1&&(popcount64(frames[aa].core)==3||(popcount64(frames[aa].core)==2&&popcount64(frames[bb].core)==1))){
+ assert(h==23||h==25);crt_matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();std::vector<std::vector<std::pair<U,U>>> all{pivots};
+ for(V extra:{2147483647ULL,524287ULL}){p=extra;matrix_cache[aa].clear();matrix_cache[bb].clear();const auto&C=matrix(aa);const auto&D=matrix(bb);std::vector<V>Y(h*h);for(U z=0;z<h*h;z++)Y[z]=sub(D[z],C[z]);std::vector<std::pair<U,U>> pp;
+  for(U i=0;i<h;i++){int j=h-1;while(j>=0&&!Y[i*h+j])j--;if(j<0)continue;pp.push_back({i,U(j)});V inv=power(Y[i*h+j],p-2);for(U k=i+1;k<h;k++){V z=mul(Y[k*h+j],inv);if(z)for(U col=0;col<=U(j);col++)Y[k*h+col]=sub(Y[k*h+col],mul(z,Y[i*h+col]));}}
+  if(pp!=pivots)crt_disagreements++;all.push_back(std::move(pp));
+ }
+ p=2305843009213693951ULL;matrix_cache[aa].clear();matrix_cache[bb].clear();
+ std::vector<int> corner((h+1)*(h+1));for(U i=0;i<h;i++)for(U j=0;j<h;j++){int best=0;for(auto&pp:all){int rank=0;for(auto [row,col]:pp)rank+=row<=i&&col>=j;best=std::max(best,rank);}corner[(i+1)*(h+1)+j]=best;}
+ pivots.clear();for(U i=0;i<h;i++)for(U j=0;j<h;j++){int z=corner[(i+1)*(h+1)+j]-corner[i*(h+1)+j]-corner[(i+1)*(h+1)+j+1]+corner[i*(h+1)+j+1];assert(z==0||z==1);if(z)pivots.push_back({i,j});}assert(pivots.size()==rr);
+}
+U run=0;for(U j=0;j<pivots.size();j++){if(j&&pivots[j].first==pivots[j-1].first+1&&pivots[j].second==pivots[j-1].second+1)run++;else{if(run){blocks[run]+=count;longest=std::max(longest,run);}run=1;}}if(run){blocks[run]+=count;longest=std::max(longest,run);}matrices++;matrix_cache[aa].clear();matrix_cache[bb].clear();
+ for(U t=0;t<=h;t++)std::cout<<blocks[t]<<" ";
+ std::cout<<"\n"<<std::flush;
+}
+}
diff --git a/research/depth-coarse/vendor/pr69-balanced-coarse.py b/research/depth-coarse/vendor/pr69-balanced-coarse.py
new file mode 100644
index 0000000000..271b44d795
--- /dev/null
+++ b/research/depth-coarse/vendor/pr69-balanced-coarse.py
@@ -0,0 +1,93 @@
+#!/usr/bin/env python3
+"""Balance each four-edge coarse sum in PR62 into two column pair-star sums.
+
+Instead of a three-addition chain, use (e(a,b)+e(a2,b))+(e(a,b2)+e(a2,b2)).
+The existing interning shares pair-star sums with the strip computations.
+Only the coarse-edge construction changes. The full graph is checked and
+compiled, so all remaining copies and clearing operations remain charged.
+
+Base graph: Avi Eisenberg / ikeboy, with Anthropic Claude assistance (#62).
+Compiler: eumemic with OpenAI Codex assistance (#57). Rank priority: Chafik
+Boukhalfa with OpenAI Codex assistance (#60). Their unchanged composition
+is also published by Dominik Scholz with OpenAI Codex assistance (#63).
+This coarse-sum experiment was prepared with OpenAI Codex assistance.
+All inherited licenses and notices remain.
+"""
+import sys
+sys.dont_write_bytecode = True
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+import argparse
+import gzip
+from hashlib import sha256
+import inspect
+import json
+from pathlib import Path
+
+import binary_frame_compiler as compiler
+import ranked_interval_compiler as predecessor
+
+ROOT = Path(__file__).resolve().parents[2]
+PIN = ROOT / 'references/frame-compiler/balanced-coarse'
+BEFORE = '''            coarse = {(i, j): self.total([e(a, b) for a in groups[i] for b in groups[j]])
+                      for i, j in combinations(range(ng), 2)}'''
+AFTER = '''            def coarse_sum(i, j):
+                columns = [self.total([e(a,b) for a in groups[i]]) for b in groups[j]]
+                return self.total(columns)
+            coarse = {(i,j):coarse_sum(i,j) for i,j in combinations(range(ng),2)}'''
+
+
+def check_sources():
+    predecessor.check_sources()
+    manifest = json.loads((PIN / 'SOURCE.json').read_text())
+    for name, digest in manifest['files'].items():
+        assert sha256((PIN / name).read_bytes()).hexdigest() == digest, name
+    dependency = PIN / manifest['shared_dependency_manifest']
+    assert sha256(dependency.read_bytes()).hexdigest() == manifest['shared_dependency_manifest_sha256']
+    return manifest
+
+
+def graph(h):
+    assert h in (23, 25)
+    check_sources()
+    path = predecessor.PIN / 'research/pair-assembly/pair_graph.py'
+    source = path.read_text()
+    assert source.count(BEFORE) == 1
+    namespace = {'__file__': str(path), '__name__': 'balanced_coarse_pr62'}
+    exec(compile(source.replace(BEFORE, AFTER), str(path) + ':balanced_coarse', 'exec'), namespace)
+    result = namespace['graph'](h)
+    result.verify()
+    return result
+
+
+def compile_axis(h):
+    circuit = graph(h)
+    source = inspect.getsource(compiler.compile_)
+    before = 'for s in sorted(retired):'
+    after = "for s in sorted(retired, key=lambda s: (-blocks[frames[s]]['rank'], s)):"
+    assert source.count(before) == 1
+    namespace = dict(vars(compiler))
+    exec(compile(source.replace(before, after), __file__ + ':ranked_compile', 'exec'), namespace)
+    # build() is the original function and resolves graph in compiler's globals.
+    previous = compiler.graph
+    compiler.graph = lambda _: circuit
+    try:
+        result, word = namespace['compile_'](h, matching=True, reclaim=True, dirty=True)
+    finally:
+        compiler.graph = previous
+    result['scalar'] = circuit.verify()
+    result['baseline_pr62_stacked_roles'] = {23: 27918, 25: 36586}[h]
+    return result, word
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--h', type=int, choices=(23, 25), required=True)
+    parser.add_argument('--output', type=Path, required=True)
+    parser.add_argument('--word', type=Path, required=True)
+    args = parser.parse_args()
+    result, word = compile_axis(args.h)
+    raw = (json.dumps(word, separators=(',', ':')) + '\n').encode()
+    args.word.write_bytes(gzip.compress(raw, mtime=0))
+    args.output.write_text(json.dumps(result, indent=2) + '\n')
+    print(json.dumps(result), flush=True)
diff --git a/research/depth-coarse/vendor/pr71-engine.py b/research/depth-coarse/vendor/pr71-engine.py
new file mode 100644
index 0000000000..1290ef2eb8
--- /dev/null
+++ b/research/depth-coarse/vendor/pr71-engine.py
@@ -0,0 +1,275 @@
+# Composition of PR67 profile-cost reclamation and PR68 pending live controls.
+# Next-use transition scoring added by Chafik Boukhalfa with OpenAI Codex assistance.
+# All-rank profile-cost selection: Rohan Arun, with OpenAI Codex assistance.
+# Derived from Dominik Scholz PR63, Chafik Boukhalfa PR60, Avi Eisenberg PR62
+# and eumemic PR57. Apache-2.0; all inherited notices remain applicable.
+"""Exact-envelope block synthesis on the pinned PR48 scalar graph.
+Experimental finite compiler; no fixed-I+J profile or multiplication claim.
+"""
+# Derived from eumemic's PR57 compiler; original notices remain applicable.
+# Descending-rank reclamation priority: Chafik Boukhalfa, with OpenAI Codex assistance.
+import sys
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+sys.dont_write_bytecode=True
+from pathlib import Path
+ROOT=Path(__file__).resolve().parents[2]/'references/frame-compiler/pr48'
+from hashlib import sha256
+import json
+manifest=json.loads((ROOT/'SOURCE.json').read_text())
+for name,digest in manifest['files'].items():
+ assert sha256((ROOT/name).read_bytes()).hexdigest()==digest, 'Changed producer source: '+name
+sys.path[:0]=[str(ROOT/'scripts'),str(ROOT/'research/copied-fixed')]
+from changed_graph import graph
+from collections import defaultdict,Counter,deque
+import argparse,json,time,struct
+
+def independent(rows,vec):
+ for row in rows:
+  vec=min(vec,vec^row)
+ return bool(vec)
+def basis(rows):
+ out=[]
+ for vec in rows:
+  for row in out:vec=min(vec,vec^row)
+  if vec:out.append(vec)
+ return out
+
+def build(h):
+ c=graph(h);groups={};owner={};signal={};blocks=[]
+ for x in sorted(c.active):
+  key=(c.core[x],c.union[x])
+  if key not in groups:
+   groups[key]=len(blocks);blocks.append(dict(nodes=[],frame=key,inputs=set(),uses=[]))
+  g=groups[key];owner[x]=g;blocks[g]['nodes'].append(x)
+  signal[x]=(signal[c.args[x][0]]^signal[c.args[x][1]])if c.args[x]else 1<<(x-1)
+ for x in sorted(c.active):
+  for y in c.args[x]or():
+   if owner[y]!=owner[x]:blocks[owner[x]]['inputs'].add(y)
+ uses=[];value_uses=defaultdict(list)
+ for g,b in enumerate(blocks):
+  b['inputs']=sorted(b['inputs']);b['source']=not c.args[b['nodes'][0]]
+  for y in b['inputs']:
+   k=len(uses);uses.append((y,g,None));value_uses[y].append(k);blocks[owner[y]]['uses'].append(k)
+ for target,x in c.outputs.items():
+  k=len(uses);uses.append((x,owner[x],target));value_uses[x].append(k);blocks[owner[x]]['uses'].append(k)
+ for g,b in enumerate(blocks):
+  b['rank']=1 if b['source']else b['frame'][1].bit_count()-b['frame'][0].bit_count()
+ order=sorted(range(len(blocks)),key=lambda g:(blocks[g]['rank'],min(blocks[g]['nodes'])))
+ place={g:i for i,g in enumerate(order)}
+ def contained(a,b):return not(b[0]&~a[0])and not(a[1]&~b[1])
+ for g,b in enumerate(blocks):
+  coeff={y:1<<i for i,y in enumerate(b['inputs'])}
+  if b['source']:coeff[b['nodes'][0]]=1
+  for x in b['nodes']:
+   if c.args[x]:coeff[x]=coeff[c.args[x][0]]^coeff[c.args[x][1]]
+  b['coeff']=coeff;b['outvalues']=sorted({uses[u][0]for u in b['uses']})
+  b['outbasis']=basis(coeff[x]for x in b['outvalues']);b['candidates']=[];b['selected']=set()
+  if not b['source']:
+   for i,y in enumerate(b['inputs']):
+    if not independent(b['outbasis'],1<<i):continue
+    for u in value_uses[y]:
+     _,target,terminal=uses[u]
+     if place[g]<place[target]and contained(b['frame'],blocks[target]['frame']):
+      b['candidates'].append((u,i))
+ return c,blocks,uses,value_uses,owner,signal,order,contained
+
+def match(blocks,uses,enabled):
+ edges=[];byblock=[]
+ for g,b in enumerate(blocks):
+  row=[]
+  for u,i in b['candidates']:row.append(len(edges));edges.append((g,u,i))
+  byblock.append(row)
+ chosen=set();right={};stats=Counter()
+ def can(e,drop=None):
+  g,u,i=edges[e];selected=blocks[g]['selected']
+  rows=blocks[g]['outbasis']+[1<<edges[f][2]for f in selected if f!=drop]
+  return independent(basis(rows),1<<i)
+ if not enabled:return edges,chosen,right,stats
+ # Greedy first, then exact augmenting paths in linear/partition matroid intersection.
+ for e,(g,u,i)in enumerate(edges):
+  if u not in right and can(e):chosen.add(e);right[u]=e;blocks[g]['selected'].add(e)
+ while True:
+  prev={};queue=deque()
+  for e,(g,u,i)in enumerate(edges):
+   if e not in chosen and can(e):prev[e]=None;queue.append(e)
+  end=None
+  while queue:
+   e=queue.popleft();g,u,i=edges[e]
+   if u not in right:end=e;break
+   f=right[u];fg=edges[f][0]
+   if f in prev:continue
+   prev[f]=e
+   for z in byblock[fg]:
+    if z not in chosen and z not in prev and can(z,f):prev[z]=f;queue.append(z)
+  if end is None:break
+  path=[]
+  while end is not None:path.append(end);end=prev[end]
+  for e in path:
+   g,u,i=edges[e]
+   if e in chosen:chosen.remove(e);blocks[g]['selected'].remove(e);del right[u]
+  for e in path:
+   if e not in chosen and e not in path[1::2]:
+    g,u,i=edges[e];chosen.add(e);blocks[g]['selected'].add(e);assert u not in right;right[u]=e
+  stats['augmentations']+=1
+  if stats['augmentations']%100==0:print('augment',stats['augmentations'],len(chosen),flush=True,file=sys.stderr)
+ for g,b in enumerate(blocks):assert len(basis(b['outbasis']+[1<<edges[e][2]for e in b['selected']]))==len(b['outbasis'])+len(b['selected'])
+ return edges,chosen,right,stats
+
+def compile_(h,matching=True,reclaim=False,dirty=True):
+ t0=time.time();c,blocks,uses,value_uses,owner,signal,order,contains=build(h);v=len(c.inputs)
+ print('built',h,len(blocks),'regions',flush=True,file=sys.stderr)
+ edges,chosen,right,stats=match(blocks,uses,matching)
+ print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr)
+ slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();pending={};stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks)
+ def new(g):
+  s=len(slots);slots.append(0);frames.append(g);hist[blocks[g]['rank']]+=1;events.append((s,-1,g));return s
+ def raise_(s,g):
+  old=frames[s];assert contains(blocks[old]['frame'],blocks[g]['frame']);hist[blocks[g]['rank']-blocks[old]['rank']]+=1;frames[s]=g;events.append((s,old,g))
+ def xor(a,b,g):
+  assert a!=b;raise_(a,g);raise_(b,g);slots[a]^=slots[b];ops.append((a,b,g))
+ import subprocess,struct
+ from binary_frame_math import logs
+ # Integer midpoint enclosures give a reproducible discovery score.
+ # Every candidate is independently checked by the complete exact screen.
+ weights=[0]+[int(t*sum(logs(t))*10**30//2) for t in range(1,h+1)]
+ oracle_input=Path(ORACLE_INPUT)
+ with oracle_input.open('wb') as stream:
+  stream.write(struct.pack('<6I2Q',h,v,0,len(blocks)+2,0,0,h*(h-1),h*(h-1)))
+  stream.write(struct.pack('<2QI',0,0,0));stream.write(struct.pack('<2QI',0,0,h))
+  for b in blocks:stream.write(struct.pack('<2QI',*b['frame'],b['rank']))
+ oracle=subprocess.Popen([ORACLE_EXE,str(oracle_input)],stdin=subprocess.PIPE,stdout=subprocess.PIPE,text=True,bufsize=1)
+ oracles.append(oracle)
+ cache={}
+ def profile_entropy(a,b):
+  if (a,b) not in cache:
+   oracle.stdin.write(f'{a} {b}\n');oracle.stdin.flush()
+   answer=oracle.stdout.readline()
+   assert answer, 'profile oracle failed'
+   parts=list(map(int,answer.split()));assert len(parts)==h+1
+   cache[a,b]=sum(n*w for n,w in zip(parts,weights))
+  return cache[a,b]
+ def profile_cost(a,g):
+  old=frames[a]+2;target=g+2
+  endpoint=pending[a]+2 if PENDING_COST and a in pending else 1
+  return profile_entropy(old,endpoint)-profile_entropy(old,target)-profile_entropy(target,endpoint)
+ def acquire(g,anchors):
+  if reclaim:
+   bb={}
+   def ins(s):
+    row=slots[s];expr=1<<s
+    while row:
+     p=row.bit_length()-1
+     if p not in bb:bb[p]=(row,expr);return None
+     old,e=bb[p];row^=old;expr^=e
+    return expr
+   for s in anchors:ins(s)
+   for s,target in pending.items():
+    if contains(blocks[frames[s]]['frame'],blocks[g]['frame']) and contains(blocks[g]['frame'],blocks[target]['frame']):
+     ins(s);stats['live_anchor_candidates']+=1
+   best=None
+   # Inspect every eligible dependent candidate across all retired ranks.
+   # Rank the actual fixed-basis growth/cleanup profiles by an integer entropy score.
+   for s in sorted(retired,key=lambda s:(-blocks[frames[s]]['rank'],s)):
+    if not contains(blocks[frames[s]]['frame'],blocks[g]['frame']):continue
+    e=ins(s)
+    if e is None:continue
+    assert e>>s&1;e^=1<<s;aa=[]
+    while e:
+     bit=e&-e;aa.append(bit.bit_length()-1);e^=bit
+    cost=sum(profile_cost(a,g) for a in [s]+aa)
+    key=(cost,len(aa),s)
+    if best is None or key<best[0]:best=(key,s,aa)
+   if best is not None:
+    _,s,aa=best
+    for a in aa:
+     if a in pending:stats['live_anchor_xors']+=1
+     xor(s,a,g)
+    assert not slots[s];retired.remove(s);stats['reclaimed']+=1;stats['clearing_xors']+=len(aa);return s
+  return new(g)
+ for step,g in enumerate(order):
+  b=blocks[g];outuses=[u for u in b['uses']if u not in right];outvalues=sorted({uses[u][0]for u in outuses});assert outvalues==b['outvalues']
+  if b['source']:
+   x=b['nodes'][0];s=new(g);sources[x-1]=s;slots[s]=signal[x];value_slots={x:s};spare=[]
+  else:
+   ins=[assign[next(u for u in value_uses[y]if uses[u][1]==g and uses[u][2]is None)]for y in b['inputs']]
+   assert len(set(ins))==len(ins)
+   for s in ins:assert pending.pop(s)==g
+   for s,y in zip(ins,b['inputs']):assert slots[s]==signal[y];raise_(s,g)
+   # Independent desired output rows first, then preserved input signals,
+   # then standard-unit completion. Every row is a literal linear form
+   # on incoming physical roles, hence invertible on all dirty inputs.
+   rows=[];labels=[];echelon=[]
+   for x in outvalues:
+    r=b['coeff'][x]
+    if independent(echelon,r):rows.append(r);labels.append(('value',x));echelon=basis(rows)
+   output_rank=len(rows)
+   for e in sorted(b['selected']):
+    _,u,i=edges[e];r=1<<i;assert independent(echelon,r);rows.append(r);labels.append(('carry',u));echelon=basis(rows)
+   for i in range(len(ins)):
+    if independent(echelon,1<<i):rows.append(1<<i);labels.append(('retire',i));echelon=basis(rows)
+   assert len(rows)==len(ins)
+   rr=rows.copy();elim=[]
+   for i in range(len(ins)):
+    j=next(j for j in range(i,len(ins))if rr[j]>>i&1)
+    if j!=i:
+     # Synthesize swap as three XORs at the single common frame.
+     for a,z in ((i,j),(j,i),(i,j)):rr[a]^=rr[z];elim.append((a,z))
+    for j in range(len(ins)):
+     if j!=i and rr[j]>>i&1:rr[j]^=rr[i];elim.append((j,i))
+   assert rr==[1<<i for i in range(len(ins))]
+   for a,z in reversed(elim):xor(ins[a],ins[z],g)
+   value_slots={};spare=[]
+   for s,(kind,key)in zip(ins,labels):
+    if kind=='value':value_slots[key]=s;assert slots[s]==signal[key]
+    elif kind=='carry':assign[key]=s;pending[s]=uses[key][1];assert slots[s]==signal[uses[key][0]]
+    else:retired.add(s);spare.append(s)
+   # Express every dependent desired output in the new independent basis.
+   ob=list(value_slots);bb={}
+   for i,x in enumerate(ob):
+    r=b['coeff'][x];e=1<<i
+    while r:
+     p=r.bit_length()-1
+     if p not in bb:bb[p]=(r,e);break
+     old,ee=bb[p];r^=old;e^=ee
+   for x in outvalues:
+    if x in value_slots:continue
+    r=b['coeff'][x];e=0
+    while r:p=r.bit_length()-1;old,ee=bb[p];r^=old;e^=ee
+    s=acquire(g,list(value_slots.values()))
+    for i,y in enumerate(ob):
+     if e>>i&1:xor(s,value_slots[y],g)
+    assert slots[s]==signal[x];value_slots[x]=s
+  used=set()
+  for u in outuses:
+   x=uses[u][0];s=value_slots[x]
+   if x in used:
+    ss=acquire(g,list(value_slots.values()));xor(ss,s,g);s=ss
+   used.add(x);assert u not in assign;assign[u]=s;assert s not in pending;pending[s]=uses[u][1]
+  if step%5000==0:print('compile',h,step,len(slots),'reclaimed',stats['reclaimed'],'seconds',time.time()-t0,flush=True,file=sys.stderr)
+ output_slots=[];output_records=[];scatter=[0]*v;J=[]
+ for u,(x,g,target)in enumerate(uses):
+  if target is None:continue
+  s=assign[u];assert slots[s]==signal[x];raise_(s,g);output_slots.append(s)
+  common,triple=target;output_records.append((s,g,common,triple))
+  targets=[i for i,t in enumerate(c.inputs)if common in t]if len(triple)==1 else[c.inputs.index(triple)]
+  for i in targets:scatter[i]^=slots[s];J.append((v+i,2*v+s))
+  rank=blocks[g]['rank']
+  if len(triple)==1:hist[rank]+=1;hist[h-rank]+=1
+  else:hist[h-1-rank]+=1;hist[1]+=1
+ assert len(set(output_slots))==len(output_slots)
+ for s in retired:hist[h-blocks[frames[s]]['rank']]+=1
+ assert len(retired)+len(output_slots)==len(slots)
+ assert scatter==[1<<i for i in range(v)]
+ R=len(slots);mass=sum(k*v for k,v in hist.items());assert mass==h*R+h*(h-1),(mass,R)
+ if dirty:
+  initial=[1<<i for i in range(2*v+R)];M=[(2*v+a,2*v+b)for a,b,g in ops];V=[(2*v+s,i)for i,s in sources.items()];word=M+J+M[::-1]+V+M+J+M[::-1]+V
+  for dual in (False,True):
+   values=initial.copy()
+   for a,b in reversed(word)if dual else word:
+    if dual:a,b=b,a
+    values[a]^=values[b]
+   assert values[2*v:]==initial[2*v:]
+   if dual:assert values[:v]==[initial[i]^initial[v+i]for i in range(v)]and values[v:2*v]==initial[v:2*v]
+   else:assert values[v:2*v]==[initial[i]^initial[v+i]for i in range(v)]and values[:v]==initial[:v]
+ return dict(h=h,mode=dict(matching=matching,reclaim=reclaim),roles=R,baseline_pr48_roles={23:36432,25:48329}[h],histogram=dict(hist),rank_mass=mass,elementary_xors=len(ops),stats=dict(stats),dirty_basis_vectors=2*v+R,complete_dirty_basis_both_orientations=dirty,all_physical_frame_inclusions=True,seconds=time.time()-t0),dict(h=h,v=v,R=R,ops=ops,sources=sources,scatter=J,outputs=output_records,frames=[b['frame']for b in blocks],events=events)
diff --git a/research/depth-coarse/vendor/pr71-split-graph.py b/research/depth-coarse/vendor/pr71-split-graph.py
new file mode 100644
index 0000000000..acdf4d312d
--- /dev/null
+++ b/research/depth-coarse/vendor/pr71-split-graph.py
@@ -0,0 +1,122 @@
+"""Split-pair recursion on PR65's preserved interval/pair graph and schedules.
+
+PR62 interval strips/core-aware assembly: Avi Eisenberg. PR63 ranked-frame
+composition: Dominik Scholz. PR65 region order: Rohan Arun. The [1,1,2]
+group vector was selected by Chafik Boukhalfa with OpenAI Codex assistance,
+using the split-pair operation introduced in Rohan Garg's PR59. All original
+sources and notices remain unchanged in the pinned contributor archive.
+"""
+import sys
+if sys.flags.optimize:
+    raise ValueError('Assertions must remain enabled')
+sys.dont_write_bytecode = True
+
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[2]
+BASELINE = ROOT / 'references/frame-compiler/pr65'
+EXPECTED_CONFIGS = {
+    23: dict(groups=[1, 1, 2], schedule='cover-core', anchor=True),
+    25: dict(groups=[1, 1, 2], schedule='reverse-node', anchor=True),
+}
+
+
+def checked_manifest(directory):
+    manifest = json.loads((directory / 'SOURCE.json').read_text())
+    for name, digest in manifest['files'].items():
+        assert sha256((directory / name).read_bytes()).hexdigest() == digest, name
+    if 'shared_dependency_manifest' in manifest:
+        path = directory / manifest['shared_dependency_manifest']
+        assert sha256(path.read_bytes()).hexdigest() == manifest['shared_dependency_manifest_sha256']
+    return manifest
+
+
+def _load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def _private_modules():
+    checked_manifest(BASELINE)
+    inherited = ROOT / 'references/frame-compiler/pr48'
+    checked_manifest(inherited)
+    for name in ('scripts/partial_swap/paired.py', 'scripts/partial_swap/shared.py',
+                 'scripts/exclusion_circuit.py'):
+        assert (BASELINE / name).read_bytes() == (inherited / name).read_bytes()
+    previous_path = sys.path[:]
+    try:
+        sys.path.insert(0, str(inherited / 'scripts'))
+        graph = _load('split_pair_private_graph', BASELINE / 'research/pair-assembly/pair_graph.py')
+        schedule = _load('split_pair_private_schedule', BASELINE / 'research/reordered-rank-pair/verify.py')
+        # Imported aliases may preexist in a test process; verify their bytes.
+        for module_name, relative in (
+                ('partial_swap.paired', 'scripts/partial_swap/paired.py'),
+                ('partial_swap.shared', 'scripts/partial_swap/shared.py'),
+                ('exclusion_circuit', 'scripts/exclusion_circuit.py')):
+            assert Path(sys.modules[module_name].__file__).read_bytes() == (inherited / relative).read_bytes()
+        return graph, schedule
+    finally:
+        sys.path[:] = previous_path
+
+
+_graph, _schedule = _private_modules()
+
+
+def configuration(h):
+    if type(h) is not int or h not in EXPECTED_CONFIGS:
+        raise ValueError('Only the certified dimensions 23 and 25 are supported')
+    config = json.loads((ROOT / f'research/split-pair/config-{h}.json').read_text())
+    if (type(config) is not dict or config != EXPECTED_CONFIGS[h]
+            or any(type(choice) is not int for choice in config['groups'])
+            or type(config['anchor']) is not bool):
+        raise ValueError('The certified graph configuration changed')
+    return config
+
+
+def split_class(parent, choices):
+    class SplitPair(parent):
+        def grouping(self, points):
+            groups = super().grouping(points)
+            choice = choices[self._level] if self._level < len(choices) else 0
+            if len(points) > 3 and choice:
+                index = {1: 0, 2: (len(groups)-1)//2, 3: len(groups)-1}[choice]
+                if len(groups[index]) == 2:
+                    groups[index:index+1] = [[point] for point in groups[index]]
+            assert all(len(group) in (1, 2) for group in groups)
+            assert len(groups) < len(points)
+            assert sorted(point for group in groups for point in group) == sorted(points)
+            return groups
+    return SplitPair
+
+
+def graph(h):
+    config = configuration(h)
+    original = _graph.circuit_class
+    previous_points = _graph.alternating_points
+    try:
+        _graph.circuit_class = lambda dimension: split_class(original(dimension), config['groups'])
+        if config['anchor']:
+            def anchored_points(dimension, common):
+                points = previous_points(dimension, common)
+                pairs = [(a, a+1) for a in range(0, dimension-1, 2) if common not in (a, a+1)]
+                chosen = min(pairs)
+                result = list(chosen) + [x for x in points if x not in chosen]
+                assert sorted(result) == [x for x in range(dimension) if x != common]
+                return result
+            _graph.alternating_points = anchored_points
+        return _graph.graph(h)
+    finally:
+        _graph.circuit_class = original
+        _graph.alternating_points = previous_points
+
+
+def ordered_build(original, h):
+    mode = configuration(h)['schedule']
+    if mode == 'original':
+        return original
+    return _schedule.reordered_build(original, mode)
diff --git a/research/depth-coarse/verify.py b/research/depth-coarse/verify.py
new file mode 100644
index 0000000000..f26e473607
--- /dev/null
+++ b/research/depth-coarse/verify.py
@@ -0,0 +1,138 @@
+"""Independent literal-word/profile/exact certificate acceptance boundary.
+
+Explicit scatter binding follows the verification correction in rfu08 PR64.
+Substantial OpenAI Codex assistance. Retained all-size hypotheses remain.
+"""
+import sys
+if sys.flags.optimize:raise ValueError('Assertions must remain enabled')
+sys.dont_write_bytecode=True
+from pathlib import Path
+import argparse,gzip,hashlib,itertools,json,os,shlex,shutil,subprocess,tempfile
+from fractions import Fraction as Q
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+sys.path.insert(0,str(ROOT/'scripts/experiments'))
+from binary_frame_replay import replay
+from binary_frame_profile_prepare import prepare
+import binary_frame_math as arithmetic
+from bindings import refine,audit
+from construction import activate,compile_axis,compose
+
+def source_check():
+    source=json.loads((HERE/'SOURCE.json').read_text())
+    for name,digest in source['files'].items():
+        assert hashlib.sha256((ROOT/name).read_bytes()).hexdigest()==digest,'Source/artifact changed: '+name
+
+def literal_binding(word):
+    """Exact ports, terminals and every literal J; no cancelling gate exemption."""
+    d=json.loads(gzip.decompress(word.read_bytes()))
+    h,v,R=d['h'],d['v'],d['R']
+    assert type(h) is int and h in (23,25)
+    triples=list(itertools.combinations(range(h),3));assert type(v) is int and v==len(triples)
+    assert type(R) is int and R>0
+    valid=lambda n,limit:type(n) is int and 0<=n<limit
+    sources=d['sources'];assert type(sources) is dict and set(sources)=={str(i) for i in range(v)}
+    assert all(valid(s,R) for s in sources.values()) and len(set(sources.values()))==v
+    frames=d['frames'];assert len(frames)==len({tuple(f) for f in frames})
+    for a,b,g in d['ops']:
+        assert valid(a,R) and valid(b,R) and a!=b and valid(g,len(frames))
+    for s,a,b in d['events']:
+        assert valid(s,R) and type(a) is int and -1<=a<len(frames) and valid(b,len(frames))
+    expected=[];terminals=set();inventory=set();centers=set()
+    index={t:i for i,t in enumerate(triples)}
+    for s,g,common,triple in d['outputs']:
+        assert valid(s,R) and valid(g,len(frames)) and valid(common,h)
+        assert s not in terminals;terminals.add(s)
+        assert type(triple) is list and all(valid(x,h) for x in triple)
+        t=tuple(triple);assert t==tuple(sorted(set(t))) and common in t
+        if len(t)==1:
+            assert t==(common,) and common not in centers;centers.add(common)
+            targets=[i for i,t3 in enumerate(triples) if common in t3]
+        else:
+            assert len(t)==3 and t in index
+            targets=[index[t]]
+        assert (common,t) not in inventory;inventory.add((common,t))
+        expected.extend([[v+i,2*v+s] for i in targets])
+    assert centers==set(range(h)) and len(terminals)==h+3*v
+    complete={(c,(c,)) for c in range(h)}|{(c,t) for t in triples for c in t}
+    assert inventory==complete
+    assert d['scatter']==expected,'Literal scatter must equal complete ordered output incidence list'
+    return d
+
+def arithmetic_check(work):
+    for h in (23,25):shutil.copy2(HERE/f'axis-{h}.json',work/f'axis-{h}.json')
+    result=compose(work)
+    accepted=json.loads((work/'certificate.json').read_text())
+    expected=json.loads((HERE/'certificate.json').read_text())
+    assert accepted==expected,'Exact certificate changed'
+    selection=json.loads((HERE/'selection.json').read_text())
+    ledger=json.loads((HERE/'menu-ledger.json').read_text())
+    assert selection==ledger['selected']
+    import menu
+    assert menu.check()==ledger
+    for h in (23,25):
+        receipt=json.loads((HERE/f'axis-{h}.json').read_text())
+        assert receipt['source']['choices']==selection[str(h)]
+        assert receipt==json.loads((HERE/f"menu/{selection[str(h)]}-{h}.json").read_text())
+    p=accepted
+    for name in ('pr71','pr75'):
+        old=json.loads((HERE/f'comparisons/{name}.json').read_text())
+        oldrows={int(t):n for t,n in old['bit']['child_multiplicities'].items()}
+        lower=refine.exact_moment(old['bit']['m'],old['bit']['W'],oldrows,Q(p['bit_saving']))['lower']
+        assert lower>1 and Q(p['kappa'])>Q(old['kappa']),name+' complete profile not excluded'
+    return p
+
+def verify_menu_choice(choice):
+    source_check()
+    with tempfile.TemporaryDirectory(prefix='depth-coarse-menu-') as directory:
+        work=Path(directory);profiler=work/'profiles'
+        subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(profiler)],check=True)
+        for h in (23,25):
+            selected=json.loads((HERE/f'menu/{choice}-{h}.json').read_text())
+            activate(choice);_,generated=compile_axis(h)
+            raw=(json.dumps(generated,separators=(',',':'))+'\n').encode()
+            assert hashlib.sha256(raw).hexdigest()==selected['word_sha256'],'Menu word differs'
+            word=work/f'word-{h}.json.gz';word.write_bytes(gzip.compress(raw,mtime=0))
+            literal_binding(word)
+            assert json.loads(json.dumps(replay(word)))==selected['replay']
+            transitions=work/f'axis-{h}.bin'
+            assert json.loads(json.dumps(prepare(word,transitions)))==selected['transitions']
+            subprocess.run([str(profiler),str(transitions)],check=True)
+            assert json.loads(Path(str(transitions)+'.profiles.json').read_text())==selected['profile']
+            print('PASS regenerated full menu axis',choice,h,flush=True)
+
+def verify(regenerate=False,arithmetic_only=False):
+    source_check()
+    with tempfile.TemporaryDirectory(prefix='balanced-split-verify-') as directory:
+        work=Path(directory)
+        if not arithmetic_only:
+            profiler=work/'profiles'
+            subprocess.run([*shlex.split(os.environ.get('CXX','c++')),'-O3','-std=c++17','-I',str(ROOT/'references/frame-compiler/pr48/scripts/partial_swap'),str(ROOT/'scripts/experiments/binary_frame_profiles.cpp'),'-o',str(profiler)],check=True)
+            for h in (23,25):
+                word=HERE/f'word-{h}.json.gz';literal_binding(word)
+                selected=json.loads((HERE/f'axis-{h}.json').read_text())
+                raw=gzip.decompress(word.read_bytes())
+                assert hashlib.sha256(raw).hexdigest()==selected['word_sha256']
+                assert json.loads(json.dumps(replay(word)))==selected['replay']
+                transitions=work/f'axis-{h}.bin'
+                assert json.loads(json.dumps(prepare(word,transitions)))==selected['transitions']
+                subprocess.run([str(profiler),str(transitions)],check=True)
+                assert json.loads(Path(str(transitions)+'.profiles.json').read_text())==selected['profile']
+                if regenerate:
+                    selection=json.loads((HERE/'selection.json').read_text())
+                    activate(selection[str(h)])
+                    _,generated=compile_axis(h)
+                    generated_raw=(json.dumps(generated,separators=(',',':'))+'\n').encode()
+                    assert generated_raw==raw,'Regenerated word differs'
+                print('PASS literal scatter, all dirty/source/target basis, frames and CRT profiles h='+str(h),flush=True)
+        result=arithmetic_check(work)
+        print('PASS exact characteristic, complete PR71/75 exclusion, 47 strict constraints, 7 margins, next grids',flush=True)
+        return result
+
+if __name__=='__main__':
+    p=argparse.ArgumentParser();p.add_argument('--regenerate',action='store_true');p.add_argument('--arithmetic-only',action='store_true');p.add_argument('--menu-choice',choices=[''.join(x) for x in itertools.product('cr',repeat=3)]);a=p.parse_args()
+    if a.regenerate and a.arithmetic_only:p.error('Choose one mode')
+    if a.menu_choice:
+        if a.regenerate or a.arithmetic_only:p.error('Choose one mode')
+        verify_menu_choice(a.menu_choice)
+    else:verify(a.regenerate,a.arithmetic_only)
diff --git a/research/depth-coarse/word-23.json.gz b/research/depth-coarse/word-23.json.gz
new file mode 100644
index 0000000000..0d0d5b65ca
Binary files /dev/null and b/research/depth-coarse/word-23.json.gz differ
diff --git a/research/depth-coarse/word-25.json.gz b/research/depth-coarse/word-25.json.gz
new file mode 100644
index 0000000000..96ed424c4b
Binary files /dev/null and b/research/depth-coarse/word-25.json.gz differ
diff --git a/tests/test_depth_coarse.py b/tests/test_depth_coarse.py
new file mode 100644
index 0000000000..c458a312f4
--- /dev/null
+++ b/tests/test_depth_coarse.py
@@ -0,0 +1,72 @@
+"""Finite certificate and adversarial literal-port controls, no theorem claim."""
+import copy,gzip,importlib.util,json,pathlib,subprocess,sys,tempfile,unittest
+ROOT=pathlib.Path(__file__).resolve().parents[1]
+HERE=ROOT/'research/depth-coarse'
+sys.path.insert(0,str(HERE))
+spec=importlib.util.spec_from_file_location('balanced_split_verify',HERE/'verify.py')
+verify=importlib.util.module_from_spec(spec);spec.loader.exec_module(verify)
+
+class BalancedSplitControls(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.word=json.loads(gzip.decompress((HERE/'word-23.json.gz').read_bytes()))
+
+    def rejected(self,change):
+        word=copy.deepcopy(self.word);change(word)
+        with tempfile.TemporaryDirectory() as directory:
+            path=pathlib.Path(directory)/'word.json.gz'
+            path.write_bytes(gzip.compress(json.dumps(word).encode()))
+            with self.assertRaises(AssertionError):verify.literal_binding(path)
+
+    def test_complete_exact_certificate(self):
+        with tempfile.TemporaryDirectory() as directory:
+            verify.arithmetic_check(pathlib.Path(directory))
+
+    def test_source_manifest_excludes_runtime_caches(self):
+        manifest=json.loads((HERE/'SOURCE.json').read_text())['files']
+        for name in manifest:
+            path=pathlib.PurePosixPath(name)
+            self.assertFalse(path.is_absolute(),name)
+            self.assertNotIn('..',path.parts,name)
+            self.assertNotIn('__pycache__',path.parts,name)
+            self.assertNotIn(path.suffix,('.pyc','.pyo'),name)
+        verify.source_check()
+
+    def test_selected_literal_scatter(self):
+        for h in (23,25):verify.literal_binding(HERE/f'word-{h}.json.gz')
+
+    def test_canceling_uncharged_scatter_rejected(self):
+        def change(w):w['scatter']+=w['scatter'][:1]*2
+        self.rejected(change)
+
+    def test_self_scatter_rejected(self):
+        def change(w):w['scatter'].append([w['v'],w['v']])
+        self.rejected(change)
+
+    def test_dirty_source_coordinate_rejected(self):
+        def change(w):w['sources']['-1']=w['sources'].pop('0')
+        self.rejected(change)
+
+    def test_aliased_source_rejected(self):
+        def change(w):w['sources']['1']=w['sources']['0']
+        self.rejected(change)
+
+    def test_negative_xor_index_rejected(self):
+        def change(w):w['ops'][0][0]=-1
+        self.rejected(change)
+
+    def test_missing_terminal_rejected(self):
+        def change(w):w['outputs'].pop()
+        self.rejected(change)
+
+    def test_assertion_disabled_verifier_rejected(self):
+        result=subprocess.run([sys.executable,'-O',str(HERE/'verify.py'),'--arithmetic-only'],capture_output=True,text=True)
+        self.assertNotEqual(result.returncode,0)
+        self.assertIn('Assertions must remain enabled',result.stderr)
+
+    def test_assertion_disabled_independent_checker_rejected(self):
+        result=subprocess.run([sys.executable,'-O',str(HERE/'independent.py')],capture_output=True,text=True)
+        self.assertNotEqual(result.returncode,0)
+        self.assertIn('Assertions must remain enabled',result.stderr)
+
+if __name__=='__main__':unittest.main()