diff --git a/notes/wrapping-type-census-axis-L5-diamond-L4-20260908.md b/notes/wrapping-type-census-axis-L5-diamond-L4-20260908.md
new file mode 100644
index 00000000..2a904aef
--- /dev/null
+++ b/notes/wrapping-type-census-axis-L5-diamond-L4-20260908.md
@@ -0,0 +1,70 @@
+# #640 / #651 wrapping-type census: axis L=5 and diamond L=4
+
+CLI job on `XPk2PZ` hit `--max-turns 120` without a PR. The enumerations had already finished. Grok downloaded the artifacts, checked the Bernstein tripwire against PR #649, and records them here. No `docs/STATUS.md`. Tickets left open.
+
+Enumerator: `scripts/wrap_census.cpp`, instrumented from PR #649 `exact_matching_ladder_bruteforce.cpp` (kernels K1/K2). Labels as in `scripts/probe635_sector_decomposition.py`: `none / x / y / both-same / both-two`. Coarse 4×4 folds `both-two` into `both`.
+
+Machine: Huawei DevEnvC `XPk2PZ`, 14 threads, BLAS/OMP 1. Persistent dir `/workspace/wrapping-640-651/`.
+
+---
+
+## Axis L=5 (`N=25`, `2^25 = 33 554 432`)
+
+| | |
+|---|---|
+| configs visited | 33 554 432 |
+| wall | 2.209 s (K1; two kernels agree on collapsed D) |
+| tripwire | **PASS** vs `rungs.axis_L5.k1_counts` on PR #649 |
+| binomial row sums | \(\binom{25}{k}\) at every k |
+| 5×5 reconstructs collapsed D | yes |
+
+Support, all k:
+
+| black × white | count | D |
+|---|---:|---:|
+| none × both-same | 20 218 851 | −1 |
+| both-same × none | 3 685 661 | +1 |
+| x × x | 4 482 280 | 0 |
+| y × y | 4 482 280 | 0 |
+| both-same × both-same | 685 360 | 0 |
+| any cell with both-two | **0** | — |
+
+Coarse 4×4 is the same five Mertens–Ziff cells as L=3,4. No sixth cell. `dir0=dir1` at every k.
+
+**#651 verdict: A-continues.** `both-two` has zero mass at every k. `x`/`y` have mass and zero D (they pair). Degeneracy is not a small-L accident on the last independently checkable axis rung.
+
+---
+
+## Diamond L=4 (`N=32`, `2^32 = 4 294 967 296`)
+
+| | K1 | K2 |
+|---|---:|---:|
+| configs visited | 4 294 967 296 | 4 294 967 296 |
+| wall | 323.827 s | 75.363 s |
+| tripwire vs PR #649 `diamond_L4` | PASS | PASS |
+| 5×5 tables K1 vs K2 | **identical** | **identical** |
+
+Support, all k (both kernels):
+
+| black × white | count | D |
+|---|---:|---:|
+| none × both-same | 2 739 595 215 | −1 |
+| both-same × none | 408 426 325 | +1 |
+| x × x | 520 535 376 | 0 |
+| y × y | 520 535 376 | 0 |
+| both-same × both-same | 105 875 004 | 0 |
+| any cell with both-two | **0** | — |
+
+Same five-cell coarse 4×4. MZ-forbidden cells: none.
+
+**#651 on this geometry: A-continues**, same sentence.
+
+---
+
+## What this does not do
+
+- Does not prove degeneracy at every L.
+- Does not fund #636 by itself. Sector labels #636 would carry remain the degenerate both-same pair (black NN vs white NN+NNN).
+- Does not identify those finite-L sectors with Jacobsen’s transfer-matrix eigenvalues (#637 / remainder of #635).
+
+Artifacts: `results/wrapping-type-census/axis-L5.json`, `diamond-L4-k1.json`, `diamond-L4-k2.json`.
diff --git a/results/wrapping-type-census/axis-L5.json b/results/wrapping-type-census/axis-L5.json
new file mode 100644
index 00000000..51d053ed
--- /dev/null
+++ b/results/wrapping-type-census/axis-L5.json
@@ -0,0 +1,243 @@
+{
+ "geometry": "axis",
+ "L": 5,
+ "N": 25,
+ "physical_period": "5",
+ "threads": 14,
+ "configs_expect": 33554432,
+ "k1": {
+  "configs_visited": 33554432,
+  "wall_seconds": 2.209,
+  "collapsed_D_per_k": [-1,-25,-300,-2300,-12650,-53120,-176900,-478700,-1068575,-1982325,-3054280,-3863250,-3890950,-2905150,-1290250,128000,765475,709225,406900,168100,52610,12650,2300,300,25,1],
+  "joint_label_counts_per_k": [
+   [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,2300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,12650,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,53120,0,0,5,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,176900,0,0,100,0,0,0,0,0,100,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,478700,0,0,1000,0,0,0,0,0,1000,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,1068575,0,0,6500,0,0,0,0,0,6500,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,1982350,0,0,30300,0,0,0,0,0,30300,0,0,25,0,0,0,0,0,0,0,0,0],
+   [0,0,0,3054880,0,0,106185,0,0,0,0,0,106185,0,0,600,0,0,910,0,0,0,0,0,0],
+   [0,0,0,3869650,0,0,285725,0,0,0,0,0,285725,0,0,6400,0,0,9900,0,0,0,0,0,0],
+   [0,0,0,3931075,0,0,591150,0,0,0,0,0,591150,0,0,40125,0,0,46800,0,0,0,0,0,0],
+   [0,0,0,3067350,0,0,923875,0,0,0,0,0,923875,0,0,162200,0,0,123000,0,0,0,0,0,0],
+   [0,0,0,1723100,0,0,1054375,0,0,0,0,0,1054375,0,0,432850,0,0,192700,0,0,0,0,0,0],
+   [0,0,0,639850,0,0,840585,0,0,0,0,0,840585,0,0,767850,0,0,179890,0,0,0,0,0,0],
+   [0,0,0,141575,0,0,448500,0,0,0,0,0,448500,0,0,907050,0,0,97350,0,0,0,0,0,0],
+   [0,0,0,15900,0,0,155450,0,0,0,0,0,155450,0,0,725125,0,0,29650,0,0,0,0,0,0],
+   [0,0,0,550,0,0,33950,0,0,0,0,0,33950,0,0,407450,0,0,4800,0,0,0,0,0,0],
+   [0,0,0,0,0,0,4325,0,0,0,0,0,4325,0,0,168100,0,0,350,0,0,0,0,0,0],
+   [0,0,0,0,0,0,255,0,0,0,0,0,255,0,0,52610,0,0,10,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12650,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2300,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,300,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,25,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
+  "coarse_4x4_counts_per_k": [
+   [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,25,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,300,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,2300,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,12650,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,53120,0,5,0,0,0,0,5,0,0,0,0,0],
+   [0,0,0,176900,0,100,0,0,0,0,100,0,0,0,0,0],
+   [0,0,0,478700,0,1000,0,0,0,0,1000,0,0,0,0,0],
+   [0,0,0,1068575,0,6500,0,0,0,0,6500,0,0,0,0,0],
+   [0,0,0,1982350,0,30300,0,0,0,0,30300,0,25,0,0,0],
+   [0,0,0,3054880,0,106185,0,0,0,0,106185,0,600,0,0,910],
+   [0,0,0,3869650,0,285725,0,0,0,0,285725,0,6400,0,0,9900],
+   [0,0,0,3931075,0,591150,0,0,0,0,591150,0,40125,0,0,46800],
+   [0,0,0,3067350,0,923875,0,0,0,0,923875,0,162200,0,0,123000],
+   [0,0,0,1723100,0,1054375,0,0,0,0,1054375,0,432850,0,0,192700],
+   [0,0,0,639850,0,840585,0,0,0,0,840585,0,767850,0,0,179890],
+   [0,0,0,141575,0,448500,0,0,0,0,448500,0,907050,0,0,97350],
+   [0,0,0,15900,0,155450,0,0,0,0,155450,0,725125,0,0,29650],
+   [0,0,0,550,0,33950,0,0,0,0,33950,0,407450,0,0,4800],
+   [0,0,0,0,0,4325,0,0,0,0,4325,0,168100,0,0,350],
+   [0,0,0,0,0,255,0,0,0,0,255,0,52610,0,0,10],
+   [0,0,0,0,0,0,0,0,0,0,0,0,12650,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,2300,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,300,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,25,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]
+  ],
+  "D_positive_attribution_per_k": [
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,5,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,100,0,0,0,0,0,100,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,1000,0,0,0,0,0,1000,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,6500,0,0,0,0,0,6500,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,30300,0,0,0,0,0,30300,0,0,25,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,106185,0,0,0,0,0,106185,0,0,600,0,0,910,0,0,0,0,0,0],
+   [0,0,0,0,0,0,285725,0,0,0,0,0,285725,0,0,6400,0,0,9900,0,0,0,0,0,0],
+   [0,0,0,0,0,0,591150,0,0,0,0,0,591150,0,0,40125,0,0,46800,0,0,0,0,0,0],
+   [0,0,0,0,0,0,923875,0,0,0,0,0,923875,0,0,162200,0,0,123000,0,0,0,0,0,0],
+   [0,0,0,0,0,0,1054375,0,0,0,0,0,1054375,0,0,432850,0,0,192700,0,0,0,0,0,0],
+   [0,0,0,0,0,0,840585,0,0,0,0,0,840585,0,0,767850,0,0,179890,0,0,0,0,0,0],
+   [0,0,0,0,0,0,448500,0,0,0,0,0,448500,0,0,907050,0,0,97350,0,0,0,0,0,0],
+   [0,0,0,0,0,0,155450,0,0,0,0,0,155450,0,0,725125,0,0,29650,0,0,0,0,0,0],
+   [0,0,0,0,0,0,33950,0,0,0,0,0,33950,0,0,407450,0,0,4800,0,0,0,0,0,0],
+   [0,0,0,0,0,0,4325,0,0,0,0,0,4325,0,0,168100,0,0,350,0,0,0,0,0,0],
+   [0,0,0,0,0,0,255,0,0,0,0,0,255,0,0,52610,0,0,10,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12650,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2300,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,300,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,25,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
+  "D_negative_attribution_per_k": [
+   [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-2300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-12650,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-53120,0,0,-5,0,0,0,0,0,-5,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-176900,0,0,-100,0,0,0,0,0,-100,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-478700,0,0,-1000,0,0,0,0,0,-1000,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-1068575,0,0,-6500,0,0,0,0,0,-6500,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-1982350,0,0,-30300,0,0,0,0,0,-30300,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-3054880,0,0,-106185,0,0,0,0,0,-106185,0,0,0,0,0,-910,0,0,0,0,0,0],
+   [0,0,0,-3869650,0,0,-285725,0,0,0,0,0,-285725,0,0,0,0,0,-9900,0,0,0,0,0,0],
+   [0,0,0,-3931075,0,0,-591150,0,0,0,0,0,-591150,0,0,0,0,0,-46800,0,0,0,0,0,0],
+   [0,0,0,-3067350,0,0,-923875,0,0,0,0,0,-923875,0,0,0,0,0,-123000,0,0,0,0,0,0],
+   [0,0,0,-1723100,0,0,-1054375,0,0,0,0,0,-1054375,0,0,0,0,0,-192700,0,0,0,0,0,0],
+   [0,0,0,-639850,0,0,-840585,0,0,0,0,0,-840585,0,0,0,0,0,-179890,0,0,0,0,0,0],
+   [0,0,0,-141575,0,0,-448500,0,0,0,0,0,-448500,0,0,0,0,0,-97350,0,0,0,0,0,0],
+   [0,0,0,-15900,0,0,-155450,0,0,0,0,0,-155450,0,0,0,0,0,-29650,0,0,0,0,0,0],
+   [0,0,0,-550,0,0,-33950,0,0,0,0,0,-33950,0,0,0,0,0,-4800,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-4325,0,0,0,0,0,-4325,0,0,0,0,0,-350,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-255,0,0,0,0,0,-255,0,0,0,0,0,-10,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
+  ]
+ },
+ "k2": {
+  "configs_visited": 33554432,
+  "wall_seconds": 0.536,
+  "collapsed_D_per_k": [-1,-25,-300,-2300,-12650,-53120,-176900,-478700,-1068575,-1982325,-3054280,-3863250,-3890950,-2905150,-1290250,128000,765475,709225,406900,168100,52610,12650,2300,300,25,1],
+  "joint_label_counts_per_k": [
+   [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,2300,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,12650,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,53120,0,0,5,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,176900,0,0,100,0,0,0,0,0,100,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,478700,0,0,1000,0,0,0,0,0,1000,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,1068575,0,0,6500,0,0,0,0,0,6500,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,1982350,0,0,30300,0,0,0,0,0,30300,0,0,25,0,0,0,0,0,0,0,0,0],
+   [0,0,0,3054880,0,0,106185,0,0,0,0,0,106185,0,0,600,0,0,910,0,0,0,0,0,0],
+   [0,0,0,3869650,0,0,285725,0,0,0,0,0,285725,0,0,6400,0,0,9900,0,0,0,0,0,0],
+   [0,0,0,3931075,0,0,591150,0,0,0,0,0,591150,0,0,40125,0,0,46800,0,0,0,0,0,0],
+   [0,0,0,3067350,0,0,923875,0,0,0,0,0,923875,0,0,162200,0,0,123000,0,0,0,0,0,0],
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+  ],
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+   [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]
+  ],
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+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
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+   [0,0,0,0,0,0,-4325,0,0,0,0,0,-4325,0,0,0,0,0,-350,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-255,0,0,0,0,0,-255,0,0,0,0,0,-10,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
+  ]
+ }
+ ,"k1_k2_collapsed_agree": true
+}
diff --git a/results/wrapping-type-census/diamond-L4-k1.json b/results/wrapping-type-census/diamond-L4-k1.json
new file mode 100644
index 00000000..50a7abb2
--- /dev/null
+++ b/results/wrapping-type-census/diamond-L4-k1.json
@@ -0,0 +1,153 @@
+{
+ "geometry": "diamond",
+ "L": 4,
+ "N": 32,
+ "physical_period": "sqrt(2)*4",
+ "threads": 14,
+ "configs_expect": 4294967296,
+ "k1": {
+  "configs_visited": 4294967296,
+  "wall_seconds": 323.827,
+  "collapsed_D_per_k": [-1,-32,-496,-4960,-35960,-201376,-906192,-3365856,-10517732,-28036448,-64383504,-128169312,-221730472,-332706976,-429729648,-470311264,-423397330,-294981856,-133649680,-2692064,61769064,67601440,46308016,23815392,9756620,3263072,896432,200800,35944,4960,496,32,1],
+  "joint_label_counts_per_k": [
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+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
+  "coarse_4x4_counts_per_k": [
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+   [0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0],
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+   [0,0,0,430139712,0,19184832,0,0,0,0,19184832,0,410064,0,0,2516160],
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+   [0,0,0,319948992,0,99548800,0,0,0,0,99548800,0,24967136,0,0,21708992],
+   [0,0,0,184581168,0,105751456,0,0,0,0,105751456,0,50931488,0,0,24420032],
+   [0,0,0,79528832,0,85723936,0,0,0,0,85723936,0,76836768,0,0,19560128],
+   [0,0,0,24432232,0,52177384,0,0,0,0,52177384,0,86201296,0,0,10804544],
+   [0,0,0,5103360,0,23625792,0,0,0,0,23625792,0,72704800,0,0,3964736],
+   [0,0,0,687232,0,7955456,0,0,0,0,7955456,0,46995248,0,0,918848],
+   [0,0,0,55232,0,2000384,0,0,0,0,2000384,0,23870624,0,0,122176],
+   [0,0,0,2240,0,375004,0,0,0,0,375004,0,9758860,0,0,7192],
+   [0,0,0,32,0,51360,0,0,0,0,51360,0,3263104,0,0,0],
+   [0,0,0,0,0,4880,0,0,0,0,4880,0,896432,0,0,0],
+   [0,0,0,0,0,288,0,0,0,0,288,0,200800,0,0,0],
+   [0,0,0,0,0,8,0,0,0,0,8,0,35944,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,4960,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,496,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]
+  ],
+  "D_positive_attribution_per_k": [
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,280,0,0,0,0,0,280,0,0,0,0,0,8,0,0,0,0,0,0],
+   [0,0,0,0,0,0,6080,0,0,0,0,0,6080,0,0,0,0,0,192,0,0,0,0,0,0],
+   [0,0,0,0,0,0,63104,0,0,0,0,0,63104,0,0,0,0,0,2528,0,0,0,0,0,0],
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+   [0,0,0,0,0,0,1955800,0,0,0,0,0,1955800,0,0,2688,0,0,145392,0,0,0,0,0,0],
+   [0,0,0,0,0,0,6939136,0,0,0,0,0,6939136,0,0,45440,0,0,697472,0,0,0,0,0,0],
+   [0,0,0,0,0,0,19184832,0,0,0,0,0,19184832,0,0,410064,0,0,2516160,0,0,0,0,0,0],
+   [0,0,0,0,0,0,41955584,0,0,0,0,0,41955584,0,0,2319520,0,0,6861248,0,0,0,0,0,0],
+   [0,0,0,0,0,0,72799556,0,0,0,0,0,72799556,0,0,8980560,0,0,14122828,0,0,0,0,0,0],
+   [0,0,0,0,0,0,99548800,0,0,0,0,0,99548800,0,0,24967136,0,0,21708992,0,0,0,0,0,0],
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+   [0,0,0,0,0,0,85723936,0,0,0,0,0,85723936,0,0,76836768,0,0,19560128,0,0,0,0,0,0],
+   [0,0,0,0,0,0,52177384,0,0,0,0,0,52177384,0,0,86201296,0,0,10804544,0,0,0,0,0,0],
+   [0,0,0,0,0,0,23625792,0,0,0,0,0,23625792,0,0,72704800,0,0,3964736,0,0,0,0,0,0],
+   [0,0,0,0,0,0,7955456,0,0,0,0,0,7955456,0,0,46995248,0,0,918848,0,0,0,0,0,0],
+   [0,0,0,0,0,0,2000384,0,0,0,0,0,2000384,0,0,23870624,0,0,122176,0,0,0,0,0,0],
+   [0,0,0,0,0,0,375004,0,0,0,0,0,375004,0,0,9758860,0,0,7192,0,0,0,0,0,0],
+   [0,0,0,0,0,0,51360,0,0,0,0,0,51360,0,0,3263104,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,4880,0,0,0,0,0,4880,0,0,896432,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,288,0,0,0,0,0,288,0,0,200800,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,8,0,0,0,0,0,8,0,0,35944,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4960,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,496,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
+  "D_negative_attribution_per_k": [
+   [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-496,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-4960,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-35960,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-201376,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-906192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-3365856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-10517732,0,0,-280,0,0,0,0,0,-280,0,0,0,0,0,-8,0,0,0,0,0,0],
+   [0,0,0,-28036448,0,0,-6080,0,0,0,0,0,-6080,0,0,0,0,0,-192,0,0,0,0,0,0],
+   [0,0,0,-64383504,0,0,-63104,0,0,0,0,0,-63104,0,0,0,0,0,-2528,0,0,0,0,0,0],
+   [0,0,0,-128169376,0,0,-416256,0,0,0,0,0,-416256,0,0,0,0,0,-22528,0,0,0,0,0,0],
+   [0,0,0,-221733160,0,0,-1955800,0,0,0,0,0,-1955800,0,0,0,0,0,-145392,0,0,0,0,0,0],
+   [0,0,0,-332752416,0,0,-6939136,0,0,0,0,0,-6939136,0,0,0,0,0,-697472,0,0,0,0,0,0],
+   [0,0,0,-430139712,0,0,-19184832,0,0,0,0,0,-19184832,0,0,0,0,0,-2516160,0,0,0,0,0,0],
+   [0,0,0,-472630784,0,0,-41955584,0,0,0,0,0,-41955584,0,0,0,0,0,-6861248,0,0,0,0,0,0],
+   [0,0,0,-432377890,0,0,-72799556,0,0,0,0,0,-72799556,0,0,0,0,0,-14122828,0,0,0,0,0,0],
+   [0,0,0,-319948992,0,0,-99548800,0,0,0,0,0,-99548800,0,0,0,0,0,-21708992,0,0,0,0,0,0],
+   [0,0,0,-184581168,0,0,-105751456,0,0,0,0,0,-105751456,0,0,0,0,0,-24420032,0,0,0,0,0,0],
+   [0,0,0,-79528832,0,0,-85723936,0,0,0,0,0,-85723936,0,0,0,0,0,-19560128,0,0,0,0,0,0],
+   [0,0,0,-24432232,0,0,-52177384,0,0,0,0,0,-52177384,0,0,0,0,0,-10804544,0,0,0,0,0,0],
+   [0,0,0,-5103360,0,0,-23625792,0,0,0,0,0,-23625792,0,0,0,0,0,-3964736,0,0,0,0,0,0],
+   [0,0,0,-687232,0,0,-7955456,0,0,0,0,0,-7955456,0,0,0,0,0,-918848,0,0,0,0,0,0],
+   [0,0,0,-55232,0,0,-2000384,0,0,0,0,0,-2000384,0,0,0,0,0,-122176,0,0,0,0,0,0],
+   [0,0,0,-2240,0,0,-375004,0,0,0,0,0,-375004,0,0,0,0,0,-7192,0,0,0,0,0,0],
+   [0,0,0,-32,0,0,-51360,0,0,0,0,0,-51360,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-4880,0,0,0,0,0,-4880,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-288,0,0,0,0,0,-288,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-8,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
+  ]
+ }
+}
diff --git a/results/wrapping-type-census/diamond-L4-k2.json b/results/wrapping-type-census/diamond-L4-k2.json
new file mode 100644
index 00000000..e367cde9
--- /dev/null
+++ b/results/wrapping-type-census/diamond-L4-k2.json
@@ -0,0 +1,153 @@
+{
+ "geometry": "diamond",
+ "L": 4,
+ "N": 32,
+ "physical_period": "sqrt(2)*4",
+ "threads": 14,
+ "configs_expect": 4294967296,
+ "k2": {
+  "configs_visited": 4294967296,
+  "wall_seconds": 75.363,
+  "collapsed_D_per_k": [-1,-32,-496,-4960,-35960,-201376,-906192,-3365856,-10517732,-28036448,-64383504,-128169312,-221730472,-332706976,-429729648,-470311264,-423397330,-294981856,-133649680,-2692064,61769064,67601440,46308016,23815392,9756620,3263072,896432,200800,35944,4960,496,32,1],
+  "joint_label_counts_per_k": [
+   [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,496,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,4960,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,35960,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,201376,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,906192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,3365856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,10517732,0,0,280,0,0,0,0,0,280,0,0,0,0,0,8,0,0,0,0,0,0],
+   [0,0,0,28036448,0,0,6080,0,0,0,0,0,6080,0,0,0,0,0,192,0,0,0,0,0,0],
+   [0,0,0,64383504,0,0,63104,0,0,0,0,0,63104,0,0,0,0,0,2528,0,0,0,0,0,0],
+   [0,0,0,128169376,0,0,416256,0,0,0,0,0,416256,0,0,64,0,0,22528,0,0,0,0,0,0],
+   [0,0,0,221733160,0,0,1955800,0,0,0,0,0,1955800,0,0,2688,0,0,145392,0,0,0,0,0,0],
+   [0,0,0,332752416,0,0,6939136,0,0,0,0,0,6939136,0,0,45440,0,0,697472,0,0,0,0,0,0],
+   [0,0,0,430139712,0,0,19184832,0,0,0,0,0,19184832,0,0,410064,0,0,2516160,0,0,0,0,0,0],
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+   [0,0,0,432377890,0,0,72799556,0,0,0,0,0,72799556,0,0,8980560,0,0,14122828,0,0,0,0,0,0],
+   [0,0,0,319948992,0,0,99548800,0,0,0,0,0,99548800,0,0,24967136,0,0,21708992,0,0,0,0,0,0],
+   [0,0,0,184581168,0,0,105751456,0,0,0,0,0,105751456,0,0,50931488,0,0,24420032,0,0,0,0,0,0],
+   [0,0,0,79528832,0,0,85723936,0,0,0,0,0,85723936,0,0,76836768,0,0,19560128,0,0,0,0,0,0],
+   [0,0,0,24432232,0,0,52177384,0,0,0,0,0,52177384,0,0,86201296,0,0,10804544,0,0,0,0,0,0],
+   [0,0,0,5103360,0,0,23625792,0,0,0,0,0,23625792,0,0,72704800,0,0,3964736,0,0,0,0,0,0],
+   [0,0,0,687232,0,0,7955456,0,0,0,0,0,7955456,0,0,46995248,0,0,918848,0,0,0,0,0,0],
+   [0,0,0,55232,0,0,2000384,0,0,0,0,0,2000384,0,0,23870624,0,0,122176,0,0,0,0,0,0],
+   [0,0,0,2240,0,0,375004,0,0,0,0,0,375004,0,0,9758860,0,0,7192,0,0,0,0,0,0],
+   [0,0,0,32,0,0,51360,0,0,0,0,0,51360,0,0,3263104,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,4880,0,0,0,0,0,4880,0,0,896432,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,288,0,0,0,0,0,288,0,0,200800,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,8,0,0,0,0,0,8,0,0,35944,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4960,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,496,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
+  "coarse_4x4_counts_per_k": [
+   [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,496,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,4960,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,35960,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,201376,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,906192,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,3365856,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,10517732,0,280,0,0,0,0,280,0,0,0,0,8],
+   [0,0,0,28036448,0,6080,0,0,0,0,6080,0,0,0,0,192],
+   [0,0,0,64383504,0,63104,0,0,0,0,63104,0,0,0,0,2528],
+   [0,0,0,128169376,0,416256,0,0,0,0,416256,0,64,0,0,22528],
+   [0,0,0,221733160,0,1955800,0,0,0,0,1955800,0,2688,0,0,145392],
+   [0,0,0,332752416,0,6939136,0,0,0,0,6939136,0,45440,0,0,697472],
+   [0,0,0,430139712,0,19184832,0,0,0,0,19184832,0,410064,0,0,2516160],
+   [0,0,0,472630784,0,41955584,0,0,0,0,41955584,0,2319520,0,0,6861248],
+   [0,0,0,432377890,0,72799556,0,0,0,0,72799556,0,8980560,0,0,14122828],
+   [0,0,0,319948992,0,99548800,0,0,0,0,99548800,0,24967136,0,0,21708992],
+   [0,0,0,184581168,0,105751456,0,0,0,0,105751456,0,50931488,0,0,24420032],
+   [0,0,0,79528832,0,85723936,0,0,0,0,85723936,0,76836768,0,0,19560128],
+   [0,0,0,24432232,0,52177384,0,0,0,0,52177384,0,86201296,0,0,10804544],
+   [0,0,0,5103360,0,23625792,0,0,0,0,23625792,0,72704800,0,0,3964736],
+   [0,0,0,687232,0,7955456,0,0,0,0,7955456,0,46995248,0,0,918848],
+   [0,0,0,55232,0,2000384,0,0,0,0,2000384,0,23870624,0,0,122176],
+   [0,0,0,2240,0,375004,0,0,0,0,375004,0,9758860,0,0,7192],
+   [0,0,0,32,0,51360,0,0,0,0,51360,0,3263104,0,0,0],
+   [0,0,0,0,0,4880,0,0,0,0,4880,0,896432,0,0,0],
+   [0,0,0,0,0,288,0,0,0,0,288,0,200800,0,0,0],
+   [0,0,0,0,0,8,0,0,0,0,8,0,35944,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,4960,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,496,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]
+  ],
+  "D_positive_attribution_per_k": [
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,280,0,0,0,0,0,280,0,0,0,0,0,8,0,0,0,0,0,0],
+   [0,0,0,0,0,0,6080,0,0,0,0,0,6080,0,0,0,0,0,192,0,0,0,0,0,0],
+   [0,0,0,0,0,0,63104,0,0,0,0,0,63104,0,0,0,0,0,2528,0,0,0,0,0,0],
+   [0,0,0,0,0,0,416256,0,0,0,0,0,416256,0,0,64,0,0,22528,0,0,0,0,0,0],
+   [0,0,0,0,0,0,1955800,0,0,0,0,0,1955800,0,0,2688,0,0,145392,0,0,0,0,0,0],
+   [0,0,0,0,0,0,6939136,0,0,0,0,0,6939136,0,0,45440,0,0,697472,0,0,0,0,0,0],
+   [0,0,0,0,0,0,19184832,0,0,0,0,0,19184832,0,0,410064,0,0,2516160,0,0,0,0,0,0],
+   [0,0,0,0,0,0,41955584,0,0,0,0,0,41955584,0,0,2319520,0,0,6861248,0,0,0,0,0,0],
+   [0,0,0,0,0,0,72799556,0,0,0,0,0,72799556,0,0,8980560,0,0,14122828,0,0,0,0,0,0],
+   [0,0,0,0,0,0,99548800,0,0,0,0,0,99548800,0,0,24967136,0,0,21708992,0,0,0,0,0,0],
+   [0,0,0,0,0,0,105751456,0,0,0,0,0,105751456,0,0,50931488,0,0,24420032,0,0,0,0,0,0],
+   [0,0,0,0,0,0,85723936,0,0,0,0,0,85723936,0,0,76836768,0,0,19560128,0,0,0,0,0,0],
+   [0,0,0,0,0,0,52177384,0,0,0,0,0,52177384,0,0,86201296,0,0,10804544,0,0,0,0,0,0],
+   [0,0,0,0,0,0,23625792,0,0,0,0,0,23625792,0,0,72704800,0,0,3964736,0,0,0,0,0,0],
+   [0,0,0,0,0,0,7955456,0,0,0,0,0,7955456,0,0,46995248,0,0,918848,0,0,0,0,0,0],
+   [0,0,0,0,0,0,2000384,0,0,0,0,0,2000384,0,0,23870624,0,0,122176,0,0,0,0,0,0],
+   [0,0,0,0,0,0,375004,0,0,0,0,0,375004,0,0,9758860,0,0,7192,0,0,0,0,0,0],
+   [0,0,0,0,0,0,51360,0,0,0,0,0,51360,0,0,3263104,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,4880,0,0,0,0,0,4880,0,0,896432,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,288,0,0,0,0,0,288,0,0,200800,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,8,0,0,0,0,0,8,0,0,35944,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4960,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,496,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
+  ],
+  "D_negative_attribution_per_k": [
+   [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-496,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-4960,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-35960,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-201376,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-906192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-3365856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,-10517732,0,0,-280,0,0,0,0,0,-280,0,0,0,0,0,-8,0,0,0,0,0,0],
+   [0,0,0,-28036448,0,0,-6080,0,0,0,0,0,-6080,0,0,0,0,0,-192,0,0,0,0,0,0],
+   [0,0,0,-64383504,0,0,-63104,0,0,0,0,0,-63104,0,0,0,0,0,-2528,0,0,0,0,0,0],
+   [0,0,0,-128169376,0,0,-416256,0,0,0,0,0,-416256,0,0,0,0,0,-22528,0,0,0,0,0,0],
+   [0,0,0,-221733160,0,0,-1955800,0,0,0,0,0,-1955800,0,0,0,0,0,-145392,0,0,0,0,0,0],
+   [0,0,0,-332752416,0,0,-6939136,0,0,0,0,0,-6939136,0,0,0,0,0,-697472,0,0,0,0,0,0],
+   [0,0,0,-430139712,0,0,-19184832,0,0,0,0,0,-19184832,0,0,0,0,0,-2516160,0,0,0,0,0,0],
+   [0,0,0,-472630784,0,0,-41955584,0,0,0,0,0,-41955584,0,0,0,0,0,-6861248,0,0,0,0,0,0],
+   [0,0,0,-432377890,0,0,-72799556,0,0,0,0,0,-72799556,0,0,0,0,0,-14122828,0,0,0,0,0,0],
+   [0,0,0,-319948992,0,0,-99548800,0,0,0,0,0,-99548800,0,0,0,0,0,-21708992,0,0,0,0,0,0],
+   [0,0,0,-184581168,0,0,-105751456,0,0,0,0,0,-105751456,0,0,0,0,0,-24420032,0,0,0,0,0,0],
+   [0,0,0,-79528832,0,0,-85723936,0,0,0,0,0,-85723936,0,0,0,0,0,-19560128,0,0,0,0,0,0],
+   [0,0,0,-24432232,0,0,-52177384,0,0,0,0,0,-52177384,0,0,0,0,0,-10804544,0,0,0,0,0,0],
+   [0,0,0,-5103360,0,0,-23625792,0,0,0,0,0,-23625792,0,0,0,0,0,-3964736,0,0,0,0,0,0],
+   [0,0,0,-687232,0,0,-7955456,0,0,0,0,0,-7955456,0,0,0,0,0,-918848,0,0,0,0,0,0],
+   [0,0,0,-55232,0,0,-2000384,0,0,0,0,0,-2000384,0,0,0,0,0,-122176,0,0,0,0,0,0],
+   [0,0,0,-2240,0,0,-375004,0,0,0,0,0,-375004,0,0,0,0,0,-7192,0,0,0,0,0,0],
+   [0,0,0,-32,0,0,-51360,0,0,0,0,0,-51360,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-4880,0,0,0,0,0,-4880,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-288,0,0,0,0,0,-288,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,-8,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
+   [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
+  ]
+ }
+}
diff --git a/scripts/wrap_census.cpp b/scripts/wrap_census.cpp
new file mode 100644
index 00000000..7b87f9ed
--- /dev/null
+++ b/scripts/wrap_census.cpp
@@ -0,0 +1,697 @@
+// Wrapping-type census with #646 winding labels (issues #640, #651).
+//
+// Base: scripts/exact_matching_ladder_bruteforce.cpp from PR #649 (branch
+// exact-bernstein-ladder-639) — the two independent exact kernels K1/K2 that
+// reproduce the committed axis L=2..5, diamond L=2..4 Bernstein integers.
+// This file adds per-configuration wrap-type instrumentation ONLY; the DSU,
+// edge lists, enumeration order and D(C) semantics are untouched.
+//
+// Wrap labels (#646 semantics, scripts/probe635_sector_decomposition.py):
+//   wrap_homology() maintains per-cluster wrap_x / wrap_y flags from the raw
+//   displacement deltas.  Label of a color class:
+//     none       no cluster wraps in either direction
+//     x / y      some cluster wraps exactly one axis (up to sign)
+//     both-same  a single cluster wraps both axes
+//     both-two   wraps both axes but only via two distinct clusters
+//   The union path is identical to the base file's find/add_edge (same delta
+//   convention), so the label computation shares the displacement bookkeeping
+//   that D(C) uses.  For the merged-label path (K1 and K2 replay) we carry
+//   wrap_x / wrap_y per root instead of the single wrap_ bit.
+//
+// Outputs per geometry+kernel:
+//   - collapsed D per k: a_k = sum_{|C|=k} 1{black NN wraps} - 1{white NN+NNN
+//     wraps}.  This is the tripwire: must equal the committed Bernstein
+//     integers bit-for-bit.
+//   - #646 joint label tables: per k, 5x5 counts [black label][white label].
+//   - #640 coarse tables: per k, 4x4 counts [black hxv][white hxv] where each
+//     side is 0=none,1=x,2=y,3=both (h/v/both/neither from the issue text).
+//   - signed D attributed to (black label, white label) pairs: per k,
+//     contribution sums.  Verdict data for #651: D mass in labels other than
+//     (both-same, both-same) must be zero for A to continue.
+//
+// Build: g++ -O2 -std=c++17 -pthread -o wrap_census wrap_census.cpp
+// Usage: ./wrap_census --geometry axis|diamond --L N [--kernel k1|k2|both]
+//        [--threads T] [--split B] --out prefix.json
+//        [--labels k]  print the 5x5 joint table for occupation k
+
+#include <algorithm>
+#include <atomic>
+#include <chrono>
+#include <cstdio>
+#include <cstdlib>
+#include <cstring>
+#include <map>
+#include <memory>
+#include <string>
+#include <thread>
+#include <utility>
+#include <vector>
+
+namespace {
+
+struct Edge {
+  int i;
+  int j;
+  int dx;
+  int dy;
+};
+
+struct Geometry {
+  std::string name;
+  int L = 0;
+  int n = 0;
+  std::string physical_period;
+  std::vector<Edge> primal;    // black NN, both directions
+  std::vector<Edge> matching;  // white NN+NNN, both directions
+};
+
+int mod(int a, int p) {
+  int r = a % p;
+  return r < 0 ? r + p : r;
+}
+
+std::vector<Edge> make_edges(const std::vector<std::pair<int, int>>& coords,
+                             const std::map<std::pair<int, int>, int>& ids,
+                             int period,
+                             const std::vector<std::pair<int, int>>& vectors) {
+  std::vector<Edge> edges;
+  for (int i = 0; i < static_cast<int>(coords.size()); ++i) {
+    const int x = coords[i].first;
+    const int y = coords[i].second;
+    for (const auto& v : vectors) {
+      const int tx = mod(x + v.first, period);
+      const int ty = mod(y + v.second, period);
+      edges.push_back(Edge{i, ids.at({tx, ty}), v.first, v.second});
+    }
+  }
+  return edges;
+}
+
+Geometry axis_geometry(int L) {
+  Geometry g;
+  g.name = "axis";
+  g.L = L;
+  g.physical_period = std::to_string(L);
+  std::vector<std::pair<int, int>> coords;
+  coords.reserve(L * L);
+  for (int y = 0; y < L; ++y)
+    for (int x = 0; x < L; ++x) coords.emplace_back(x, y);
+  std::map<std::pair<int, int>, int> ids;
+  for (int i = 0; i < static_cast<int>(coords.size()); ++i) ids[coords[i]] = i;
+  g.n = static_cast<int>(coords.size());
+  g.primal = make_edges(coords, ids, L, {{1, 0}, {0, 1}});
+  g.matching = make_edges(coords, ids, L, {{1, 0}, {0, 1}, {1, 1}, {1, -1}});
+  return g;
+}
+
+Geometry diamond_geometry(int L) {
+  Geometry g;
+  g.name = "diamond";
+  g.L = L;
+  g.physical_period = "sqrt(2)*" + std::to_string(L);
+  const int period = 2 * L;
+  std::vector<std::pair<int, int>> coords;
+  for (int u = 0; u < period; ++u)
+    for (int v = 0; v < period; ++v)
+      if (mod(u - v, 2) == 0) coords.emplace_back(u, v);
+  std::map<std::pair<int, int>, int> ids;
+  for (int i = 0; i < static_cast<int>(coords.size()); ++i) ids[coords[i]] = i;
+  g.n = static_cast<int>(coords.size());
+  g.primal = make_edges(coords, ids, period, {{1, -1}, {1, 1}});
+  g.matching = make_edges(coords, ids, period, {{1, -1}, {1, 1}, {2, 0}, {0, 2}});
+  return g;
+}
+
+// ---------------------------------------------------------------------------
+// Labels: 0=none 1=x 2=y 3=both-same 4=both-two
+// ---------------------------------------------------------------------------
+// Joint per-k counters: [black label][white label], plus signed-D tables.
+struct Tables {
+  int n = 0;
+  // occurrence counts (regardless of D)
+  std::vector<long long> joint;          // 5*5 per k
+  std::vector<long long> coarse;         // 4*4 per k (#640: 0=none 1=x 2=y 3=both)
+  // signed D attribution
+  std::vector<long long> d_joint;        // +1 at (black label, white label) when db=1
+  std::vector<long long> d_joint_neg;    // -1 when dw=1
+  std::vector<long long> collapsed;      // per-k D
+  long long visited = 0;
+
+  void init(int nn) {
+    n = nn;
+    joint.assign((n + 1) * 25, 0);
+    coarse.assign((n + 1) * 16, 0);
+    d_joint.assign((n + 1) * 25, 0);
+    d_joint_neg.assign((n + 1) * 25, 0);
+    collapsed.assign(n + 1, 0);
+    visited = 0;
+  }
+
+  void record(int k, int lb, int lw, int db, int dw) {
+    joint[(size_t)k * 25 + lb * 5 + lw] += 1;
+    const int cb = (lb == 4 ? 3 : lb);  // coarse: both-two folds into both
+    const int cw = (lw == 4 ? 3 : lw);
+    coarse[(size_t)k * 16 + cb * 4 + cw] += 1;
+    if (db) d_joint[(size_t)k * 25 + lb * 5 + lw] += 1;
+    if (dw) d_joint_neg[(size_t)k * 25 + lb * 5 + lw] -= 1;
+    collapsed[k] += db - dw;
+  }
+
+  void merge(const Tables& o) {
+    for (size_t i = 0; i < joint.size(); ++i) joint[i] += o.joint[i];
+    for (size_t i = 0; i < coarse.size(); ++i) coarse[i] += o.coarse[i];
+    for (size_t i = 0; i < d_joint.size(); ++i) d_joint[i] += o.d_joint[i];
+    for (size_t i = 0; i < d_joint_neg.size(); ++i) d_joint_neg[i] += o.d_joint_neg[i];
+    for (size_t i = 0; i < collapsed.size(); ++i) collapsed[i] += o.collapsed[i];
+    visited += o.visited;
+  }
+
+  void add_collapsed_only(int k, int db, int dw) { collapsed[k] += db - dw; }
+};
+
+const char* LABEL_NAMES[5] = {"none", "x", "y", "both-same", "both-two"};
+
+// ---------------------------------------------------------------------------
+// K1: compressing union-find with x/y wrap flags (base WrapDsu + label split).
+// The find/add_edge delta convention is identical to the base file.
+// ---------------------------------------------------------------------------
+class LabelDsu {
+ public:
+  explicit LabelDsu(int n)
+      : n_(n), parent_(n), size_(n, 1), dx_(n, 0), dy_(n, 0), wx_(n, 0),
+        wy_(n, 0) {}
+
+  void reset() {
+    for (int i = 0; i < n_; ++i) {
+      parent_[i] = i;
+      size_[i] = 1;
+      dx_[i] = 0;
+      dy_[i] = 0;
+      wx_[i] = 0;
+      wy_[i] = 0;
+    }
+  }
+
+  int find(int x, int& dx, int& dy) {
+    if (parent_[x] == x) {
+      dx = 0;
+      dy = 0;
+      return x;
+    }
+    const int p = parent_[x];
+    int px = 0, py = 0;
+    const int root = find(p, px, py);
+    const int odx = dx_[x], ody = dy_[x];
+    parent_[x] = root;
+    dx_[x] = odx + px;
+    dy_[x] = ody + py;
+    dx = dx_[x];
+    dy = dy_[x];
+    return root;
+  }
+
+  void add_edge(int i, int j, int edge_dx, int edge_dy) {
+    int ix = 0, iy = 0, jx = 0, jy = 0;
+    const int ri = find(i, ix, iy);
+    const int rj = find(j, jx, jy);
+    const int rdx = ix + edge_dx - jx;
+    const int rdy = iy + edge_dy - jy;
+    if (ri == rj) {
+      if (rdx != 0) wx_[ri] = 1;
+      if (rdy != 0) wy_[ri] = 1;
+      return;
+    }
+    if (size_[ri] >= size_[rj]) {
+      parent_[rj] = ri;
+      dx_[rj] = rdx;
+      dy_[rj] = rdy;
+      size_[ri] += size_[rj];
+      wx_[ri] |= wx_[rj];
+      wy_[ri] |= wy_[rj];
+    } else {
+      parent_[ri] = rj;
+      dx_[ri] = -rdx;
+      dy_[ri] = -rdy;
+      size_[rj] += size_[ri];
+      wx_[rj] |= wx_[ri];
+      wy_[rj] |= wy_[ri];
+    }
+  }
+
+  // Label over all active vertices.  Returns (wraps_any, label).
+  std::pair<bool, int> label(const std::vector<char>& active) {
+    bool ax = false, ay = false, same = false;
+    for (int i = 0; i < n_; ++i) {
+      if (!active[i]) continue;
+      int dx = 0, dy = 0;
+      const int r = find(i, dx, dy);
+      if (wx_[r]) ax = true;
+      if (wy_[r]) ay = true;
+    }
+    if (ax && ay) {
+      for (int i = 0; i < n_; ++i) {
+        if (!active[i]) continue;
+        int dx = 0, dy = 0;
+        const int r = find(i, dx, dy);
+        if (wx_[r] && wy_[r]) {
+          same = true;
+          break;
+        }
+      }
+    }
+    const bool any = ax || ay;
+    int lab;
+    if (!ax && !ay) lab = 0;
+    else if (ax && !ay) lab = 1;
+    else if (ay && !ax) lab = 2;
+    else if (same) lab = 3;
+    else lab = 4;
+    return {any, lab};
+  }
+
+ private:
+  int n_;
+  std::vector<int> parent_, size_, dx_, dy_;
+  std::vector<char> wx_, wy_;
+};
+
+void kernel1_threaded(const Geometry& g, int threads, Tables& out,
+                      double& seconds) {
+  const int n = g.n;
+  out.init(n);
+  const unsigned long long total = 1ULL << n;
+  const unsigned long long chunk = (total + threads - 1) / threads;
+  std::vector<Tables> locals(threads);
+  auto t0 = std::chrono::steady_clock::now();
+  std::vector<std::thread> pool;
+  for (int t = 0; t < threads; ++t) {
+    pool.emplace_back([&, t]() {
+      const unsigned long long begin = t * chunk;
+      const unsigned long long end = std::min(total, begin + chunk);
+      locals[t].init(n);
+      if (begin >= end) return;
+      LabelDsu dsu(n);
+      std::vector<char> black(n), white(n);
+      Tables& local = locals[t];
+      for (unsigned long long mask = begin; mask < end; ++mask) {
+        for (int i = 0; i < n; ++i) {
+          const bool b = (mask >> i) & 1ULL;
+          black[i] = b ? 1 : 0;
+          white[i] = b ? 0 : 1;
+        }
+        const int k = __builtin_popcountll(mask);
+        dsu.reset();
+        for (const Edge& e : g.primal)
+          if (black[e.i] && black[e.j]) dsu.add_edge(e.i, e.j, e.dx, e.dy);
+        const auto bw = dsu.label(black);
+        dsu.reset();
+        for (const Edge& e : g.matching)
+          if (white[e.i] && white[e.j]) dsu.add_edge(e.i, e.j, e.dx, e.dy);
+        const auto ww = dsu.label(white);
+        local.record(k, bw.second, ww.second, bw.first ? 1 : 0, ww.first ? 1 : 0);
+      }
+      local.visited = end - begin;
+    });
+  }
+  for (auto& th : pool) th.join();
+  auto t1 = std::chrono::steady_clock::now();
+  seconds = std::chrono::duration<double>(t1 - t0).count();
+  for (int t = 0; t < threads; ++t) out.merge(locals[t]);
+}
+
+// ---------------------------------------------------------------------------
+// K2: journaled union-find (no path compression) + DFS, x/y wrap flags.
+// The journal/undo logic is identical to the base file; only the wrap flag is
+// split into wx_/wy_.
+// ---------------------------------------------------------------------------
+class JLabelDsu {
+ public:
+  explicit JLabelDsu(int n)
+      : n_(n), parent_(n), size_(n), dx_(n), dy_(n), wx_(n), wy_(n) {}
+
+  void reset() {
+    for (int i = 0; i < n_; ++i) {
+      parent_[i] = i;
+      size_[i] = 1;
+      dx_[i] = 0;
+      dy_[i] = 0;
+      wx_[i] = 0;
+      wy_[i] = 0;
+    }
+    journal_.clear();
+  }
+
+  int find(int x, int& dx, int& dy) const {
+    dx = 0;
+    dy = 0;
+    while (parent_[x] != x) {
+      dx += dx_[x];
+      dy += dy_[x];
+      x = parent_[x];
+    }
+    return x;
+  }
+
+  void add_edge(int i, int j, int edge_dx, int edge_dy) {
+    int ix = 0, iy = 0, jx = 0, jy = 0;
+    const int ri = find(i, ix, iy);
+    const int rj = find(j, jx, jy);
+    const int rdx = ix + edge_dx - jx;
+    const int rdy = iy + edge_dy - jy;
+    if (ri == rj) {
+      if (rdx != 0 && !wx_[ri]) {
+        journal_.push_back(Mut{2, ri, 0, 0, 0, 0});
+        wx_[ri] = 1;
+      }
+      if (rdy != 0 && !wy_[ri]) {
+        journal_.push_back(Mut{3, ri, 0, 0, 0, 0});
+        wy_[ri] = 1;
+      }
+      return;
+    }
+    if (size_[ri] >= size_[rj]) {
+      journal_.push_back(Mut{1, rj, ri, size_[ri], wx_[ri], wy_[ri]});
+      parent_[rj] = ri;
+      dx_[rj] = rdx;
+      dy_[rj] = rdy;
+      size_[ri] += size_[rj];
+      wx_[ri] |= wx_[rj];
+      wy_[ri] |= wy_[rj];
+    } else {
+      journal_.push_back(Mut{1, ri, rj, size_[rj], wx_[rj], wy_[rj]});
+      parent_[ri] = rj;
+      dx_[ri] = -rdx;
+      dy_[ri] = -rdy;
+      size_[rj] += size_[ri];
+      wx_[rj] |= wx_[ri];
+      wy_[rj] |= wy_[ri];
+    }
+  }
+
+  void undo_to(size_t mark) {
+    while (journal_.size() > mark) {
+      const Mut& m = journal_.back();
+      if (m.kind == 1) {
+        parent_[m.root] = m.root;
+        dx_[m.root] = 0;
+        dy_[m.root] = 0;
+        size_[m.newroot] = m.old_size_newroot;
+        wx_[m.newroot] = m.old_a;
+        wy_[m.newroot] = m.old_b;
+      } else if (m.kind == 2) {
+        wx_[m.root] = 0;
+      } else {
+        wy_[m.root] = 0;
+      }
+      journal_.pop_back();
+    }
+  }
+
+  size_t mark() const { return journal_.size(); }
+
+  // Label over all vertices (active == color != unassigned handled by caller:
+  // every vertex is colored at the leaf).
+  std::pair<bool, int> label(int n, const uint8_t* color, uint8_t active_val) {
+    bool ax = false, ay = false, same = false;
+    for (int i = 0; i < n; ++i) {
+      if (color[i] != active_val) continue;
+      int dx = 0, dy = 0;
+      const int r = find(i, dx, dy);
+      if (wx_[r]) ax = true;
+      if (wy_[r]) ay = true;
+    }
+    if (ax && ay) {
+      for (int i = 0; i < n; ++i) {
+        if (color[i] != active_val) continue;
+        int dx = 0, dy = 0;
+        const int r = find(i, dx, dy);
+        if (wx_[r] && wy_[r]) {
+          same = true;
+          break;
+        }
+      }
+    }
+    const bool any = ax || ay;
+    int lab;
+    if (!ax && !ay) lab = 0;
+    else if (ax && !ay) lab = 1;
+    else if (ay && !ax) lab = 2;
+    else if (same) lab = 3;
+    else lab = 4;
+    return {any, lab};
+  }
+
+ private:
+  struct Mut {
+    int kind;      // 1=merge, 2=wx set, 3=wy set
+    int root;      // child root (merge) or root whose flag was set
+    int newroot;   // merge: surviving root
+    int old_size_newroot;
+    char old_a;
+    char old_b;
+  };
+  int n_;
+  std::vector<int> parent_, size_, dx_, dy_;
+  std::vector<char> wx_, wy_;
+  std::vector<Mut> journal_;
+};
+
+struct AdjEntry {
+  int u;
+  int dx;
+  int dy;
+};
+
+std::vector<std::vector<AdjEntry>> build_adjacency(const std::vector<Edge>& edges,
+                                                   int n) {
+  std::vector<std::vector<AdjEntry>> adj(n);
+  // No dedup: identical to the base file (directed edges kept individually).
+  for (const Edge& e : edges) {
+    const int lo = std::min(e.i, e.j);
+    const int hi = std::max(e.i, e.j);
+    if (lo == hi) continue;
+    if (e.i == hi) adj[hi].push_back(AdjEntry{lo, e.dx, e.dy});
+    else adj[hi].push_back(AdjEntry{lo, -e.dx, -e.dy});
+  }
+  return adj;
+}
+
+struct K2Ctx {
+  JLabelDsu* black;
+  JLabelDsu* white;
+  const std::vector<std::vector<AdjEntry>>* adj_black;
+  const std::vector<std::vector<AdjEntry>>* adj_white;
+  uint8_t* color;
+  int n;
+  Tables* local;
+};
+
+void dfs(K2Ctx& ctx, int idx, int black_cnt) {
+  if (idx == ctx.n) {
+    const int k = black_cnt;
+    const auto bw = ctx.black->label(ctx.n, ctx.color, 1);
+    const auto ww = ctx.white->label(ctx.n, ctx.color, 0);
+    ctx.local->record(k, bw.second, ww.second, bw.first ? 1 : 0,
+                      ww.first ? 1 : 0);
+    return;
+  }
+  {
+    ctx.color[idx] = 0;
+    const size_t m = ctx.white->mark();
+    for (const AdjEntry& e : (*ctx.adj_white)[idx])
+      if (e.u < idx && ctx.color[e.u] == 0)
+        ctx.white->add_edge(idx, e.u, e.dx, e.dy);
+    dfs(ctx, idx + 1, black_cnt);
+    ctx.white->undo_to(m);
+  }
+  {
+    ctx.color[idx] = 1;
+    const size_t m = ctx.black->mark();
+    for (const AdjEntry& e : (*ctx.adj_black)[idx])
+      if (e.u < idx && ctx.color[e.u] == 1)
+        ctx.black->add_edge(idx, e.u, e.dx, e.dy);
+    dfs(ctx, idx + 1, black_cnt + 1);
+    ctx.black->undo_to(m);
+  }
+}
+
+void kernel2_threaded(const Geometry& g, int threads, int split, Tables& out,
+                      double& seconds) {
+  const int n = g.n;
+  out.init(n);
+  auto adj_black = std::make_shared<std::vector<std::vector<AdjEntry>>>(
+      build_adjacency(g.primal, n));
+  auto adj_white = std::make_shared<std::vector<std::vector<AdjEntry>>>(
+      build_adjacency(g.matching, n));
+  if (split <= 0 || split >= n) split = std::min(n, 12);
+  const int B = split;
+  const unsigned long long tasks = 1ULL << B;
+
+  std::vector<Tables> locals(threads);
+  std::atomic<unsigned long long> next_task{0};
+  auto t0 = std::chrono::steady_clock::now();
+  std::vector<std::thread> pool;
+  for (int t = 0; t < threads; ++t) {
+    pool.emplace_back([&, t]() {
+      JLabelDsu black(n), white(n);
+      std::vector<uint8_t> color(n, 0);
+      locals[t].init(n);
+      K2Ctx ctx{&black, &white, &*adj_black, &*adj_white, color.data(), n,
+                &locals[t]};
+      for (;;) {
+        const unsigned long long task = next_task.fetch_add(1);
+        if (task >= tasks) break;
+        black.reset();
+        white.reset();
+        std::fill(color.begin(), color.end(), 2);
+        int black_cnt = 0;
+        for (int v = 0; v < B; ++v) {
+          const int c = static_cast<int>((task >> v) & 1ULL);
+          color[v] = static_cast<uint8_t>(c);
+          if (c) ++black_cnt;
+          if (c == 1) {
+            for (const AdjEntry& e : (*adj_black)[v])
+              if (color[e.u] == 1) black.add_edge(v, e.u, e.dx, e.dy);
+          } else {
+            for (const AdjEntry& e : (*adj_white)[v])
+              if (color[e.u] == 0) white.add_edge(v, e.u, e.dx, e.dy);
+          }
+        }
+        dfs(ctx, B, black_cnt);
+      }
+      locals[t].visited = 1LL << (n - B);  // per task; merged below as tasks*2^(n-B)
+    });
+  }
+  for (auto& th : pool) th.join();
+  auto t1 = std::chrono::steady_clock::now();
+  seconds = std::chrono::duration<double>(t1 - t0).count();
+  out.init(n);
+  for (int t = 0; t < threads; ++t) out.merge(locals[t]);
+  out.visited = 1LL << n;
+}
+
+void dump_tables_json(FILE* f, const char* key, const std::vector<long long>& v,
+                      int n, int stride, const char** names, bool comma) {
+  std::fprintf(f, "  \"%s\": [\n", key);
+  for (int k = 0; k <= n; ++k) {
+    std::fprintf(f, "   [");
+    for (int a = 0; a < stride; ++a) {
+      for (int b = 0; b < stride; ++b) {
+        std::fprintf(f, "%lld%s", v[(size_t)k * stride * stride + a * stride + b],
+                     (a + 1 == stride && b + 1 == stride) ? "" : ",");
+      }
+    }
+    std::fprintf(f, "]%s\n", k == n ? "" : ",");
+  }
+  std::fprintf(f, "  ]%s\n", comma ? "," : "");
+}
+
+}  // namespace
+
+int main(int argc, char** argv) {
+  std::string geometry_name;
+  int L = 0;
+  std::string kernel = "both";
+  int threads = static_cast<int>(std::thread::hardware_concurrency());
+  int split = 0;
+  std::string out_path;
+  int labels_k = -1;
+
+  for (int i = 1; i < argc; ++i) {
+    auto need = [&]() -> const char* { return argv[++i]; };
+    if (!std::strcmp(argv[i], "--geometry")) geometry_name = need();
+    else if (!std::strcmp(argv[i], "--L")) L = std::atoi(need());
+    else if (!std::strcmp(argv[i], "--kernel")) kernel = need();
+    else if (!std::strcmp(argv[i], "--threads")) threads = std::atoi(need());
+    else if (!std::strcmp(argv[i], "--split")) split = std::atoi(need());
+    else if (!std::strcmp(argv[i], "--out")) out_path = need();
+    else if (!std::strcmp(argv[i], "--labels-k")) labels_k = std::atoi(need());
+    else {
+      std::fprintf(stderr, "unknown arg %s\n", argv[i]);
+      return 2;
+    }
+  }
+  if (geometry_name.empty() || L <= 0 || out_path.empty()) {
+    std::fprintf(stderr,
+                 "usage: wrap_census --geometry axis|diamond --L N --out f "
+                 "[--kernel k1|k2|both] [--threads T] [--split B] "
+                 "[--labels-k K]\n");
+    return 2;
+  }
+  if (threads <= 0) threads = 1;
+
+  Geometry g = geometry_name == "axis" ? axis_geometry(L) : diamond_geometry(L);
+  const int n = g.n;
+
+  FILE* f = std::fopen(out_path.c_str(), "w");
+  if (!f) {
+    std::fprintf(stderr, "cannot open %s\n", out_path.c_str());
+    return 3;
+  }
+  std::fprintf(f, "{\n");
+  std::fprintf(f, " \"geometry\": \"%s\",\n", g.name.c_str());
+  std::fprintf(f, " \"L\": %d,\n", g.L);
+  std::fprintf(f, " \"N\": %d,\n", n);
+  std::fprintf(f, " \"physical_period\": \"%s\",\n", g.physical_period.c_str());
+  std::fprintf(f, " \"threads\": %d,\n", threads);
+  std::fprintf(f, " \"configs_expect\": %lld,\n", 1LL << n);
+
+  auto run_kernel = [&](const char* kn, bool comma_after_kernel) {
+    Tables t;
+    double seconds = 0.0;
+    if (!std::strcmp(kn, "k1")) {
+      if (n > 40) {
+        std::fprintf(stderr, "K1 refuses N=%d > 40\n", n);
+        std::exit(3);
+      }
+      kernel1_threaded(g, threads, t, seconds);
+    } else {
+      kernel2_threaded(g, threads, split, t, seconds);
+    }
+    std::fprintf(f, " \"%s\": {\n", kn);
+    std::fprintf(f, "  \"configs_visited\": %lld,\n", t.visited);
+    std::fprintf(f, "  \"wall_seconds\": %.3f,\n", seconds);
+    std::fprintf(f, "  \"collapsed_D_per_k\": [");
+    for (int k = 0; k <= n; ++k)
+      std::fprintf(f, "%lld%s", t.collapsed[k], k == n ? "" : ",");
+    std::fprintf(f, "],\n");
+    dump_tables_json(f, "joint_label_counts_per_k", t.joint, n, 5, LABEL_NAMES, true);
+    dump_tables_json(f, "coarse_4x4_counts_per_k", t.coarse, n, 4, nullptr, true);
+    dump_tables_json(f, "D_positive_attribution_per_k", t.d_joint, n, 5, LABEL_NAMES, true);
+    dump_tables_json(f, "D_negative_attribution_per_k", t.d_joint_neg, n, 5, LABEL_NAMES, false);
+    std::fprintf(f, " }%s\n", comma_after_kernel ? "," : "");
+
+    // human-readable 5x5 for one k
+    if (labels_k >= 0 && labels_k <= n) {
+      std::printf("joint labels at k=%d (%s):\n", labels_k, kn);
+      for (int a = 0; a < 5; ++a) {
+        std::printf("  %-10s", LABEL_NAMES[a]);
+        for (int b = 0; b < 5; ++b)
+          std::printf(" %12lld",
+                      t.joint[(size_t)labels_k * 25 + a * 5 + b]);
+        std::printf("\n");
+      }
+      std::printf("  columns: none/x/y/both-same/both-two\n");
+    }
+    std::fflush(f);
+    return t;
+  };
+
+  Tables t1res, t2res;
+  bool have1 = false, have2 = false;
+  if (kernel == "k1" || kernel == "both") {
+    t1res = run_kernel("k1", kernel == "both");
+    have1 = true;
+  }
+  if (kernel == "k2" || kernel == "both") {
+    t2res = run_kernel("k2", false);
+    have2 = true;
+  }
+  if (have1 && have2) {
+    bool agree = t1res.collapsed == t2res.collapsed;
+    std::fprintf(f, " ,\"k1_k2_collapsed_agree\": %s\n", agree ? "true" : "false");
+  }
+  std::fprintf(f, "}\n");
+  std::fclose(f);
+  return 0;
+}