diff --git a/research/complex-insert-slides-seed20/CLAIM.md b/research/complex-insert-slides-seed20/CLAIM.md
new file mode 100644
index 0000000000..acaa617f40
--- /dev/null
+++ b/research/complex-insert-slides-seed20/CLAIM.md
@@ -0,0 +1,65 @@
+# Sprint claim — agent-06
+
+No pinned sprint coordination issue exists in the repository (checked
+2026-10-13; the only open issue is #650), so the claim is recorded here.
+
+- **Track and seed:** 20–39 complex supplier; assignment seed 20 (fresh
+  OS-random draw, `RandomNumberGenerator`, 2026-10-13).
+- **Base commit:** `f567884aeb8851b6e794af1184119a3bfbe1e631`
+  (origin/main). Branch `research/agent-06-complex-seed20`.
+- **Object:** SW4's eight r2h compensation pre-reads on the pinned promoted
+  P6k4 complex word (content sha256 `0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073`),
+  the complex word of the selected frontier ancestry
+  (`research/complex-sw4-frame8`, PR741 checkpoint).
+- **Question:** SW4 inserts each compensating pre-read `add(t,h,-c)` at one
+  fixed position ("right after h's last existing pre-read"). Can any other
+  placement of those eight pre-reads inside their exactness window (anywhere
+  before the helper's copy gate, where `h = E_h`) lower the complex cost?
+- **Method:** deterministic complete enumeration of all single slides, all
+  pair slides, and all same-position tie-order swaps, up to positional
+  equivalence (positions between consecutive gates touching the moved target
+  or helper are identical). Every candidate is checked for the exact B-end
+  state (mod p) and by the inherited frame refit/profile checks, and priced by
+  the exact complex endpoint functional of the pinned moment engine.
+- **Expected deliverable:** a scoped negative result with exact coverage
+  counts, or a priced insertion schedule; in both cases a reproducible
+  package with controls.
+- **Expected finish:** 2026-10-13 (same session).
+
+## Candidates considered (three, per the sprint brief)
+
+1. **Chosen: insertion-slide census (this claim).** Named as uncovered by
+   #775's scope list ("alternative insertion positions"), untouched by #815
+   (frame-optimal for the *fixed* gate sequence) and #864 (frame reassignment
+   of a fixed program), and disjoint from #876 (full pair/triple read-set
+   exchanges) and seed 28's frame duals.
+2. **Tail/early-cleanup membership changes on the selected X4 complex word.**
+   Not chosen: every candidate needs a global owner/hosting repricing to
+   value honestly, which does not fit a bounded session.
+3. **Larger-group coupled partial read exchanges beyond #775's connected
+   triples.** Not chosen: #775 and #876 already cover the main mass of this
+   space and a second coverage sweep there would duplicate their method.
+
+## Result (2026-10-13)
+
+PR: https://github.com/CrocSwap/integer-mult-bounds/pull/910
+
+The complete census (1,432 configurations: 56 singles, 1,372 pairs, 4
+same-position tie-order swaps) finds **0 improving placements**: all 1,060
+legal configurations have exactly the pinned paid profile
+`{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`, so the complex endpoint is
+pinned at `0.0016634287545401745`; the 372 refused configurations are
+frame-cap violations and all 1,432 preserve the exact B-end state. Scoped
+negative result; the "alternative insertion positions" gap in #775's scope
+list is now covered for singles, pairs and tie orders. Reproduce with
+`python3 -B research/complex-insert-slides-seed20/verify.py`
+(`PASS_INSERT_SLIDES_SEED20 singles=56 pairs=1372 swaps=4 legal=1060 improving=0 best_root=0.001663428754540`).
+
+## Overlap statement
+
+Concurrent work acknowledged and not duplicated: #775 (coupled partial read
+exchanges on P6k4), #876 (full pair/triple exchanges; also the source of the
+byte-identical vendored input word, content-pinned by the SW4 recipe),
+#815 (LP/CP-SAT frame optimality of the fixed sequences), #864 (exact frame
+duals for the selected X4 word). This claim changes gate *positions*, which
+none of their scopes include.
diff --git a/research/complex-insert-slides-seed20/EVIDENCE.json b/research/complex-insert-slides-seed20/EVIDENCE.json
new file mode 100644
index 0000000000..b1cee18062
--- /dev/null
+++ b/research/complex-insert-slides-seed20/EVIDENCE.json
@@ -0,0 +1,49582 @@
+{
+ "composition_round": "vacuous: the best legal configuration is the pinned one",
+ "controls": {
+  "frame8_calibration_matches_selected_endpoint": true,
+  "frame8_calibration_root": 0.001663966829367475,
+  "out_of_window_observed": {
+   "exact": false,
+   "first_problem": null,
+   "legal": false,
+   "n_problems": 0,
+   "profile": {
+    "1": 2548,
+    "2": 342,
+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   },
+   "rank_mass": 5634,
+   "root": 0.0016634287545401745,
+   "slides": {
+    "2": 637
+   },
+   "swap_pairs": [],
+   "widths": {
+    "4": 80,
+    "5": 32,
+    "7": 54,
+    "8": 122,
+    "9": 216
+   },
+   "word_sha256": "11155ae65bdc172fae3054cf29237233edfae65501c597ea256c6fa7edcbd320"
+  },
+  "out_of_window_rejected": true,
+  "pinned_no_refit_problems": true,
+  "pinned_output_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+  "pinned_output_sha_matches_recipe": true,
+  "pinned_profile_matches_recipe": true,
+  "pinned_root": 0.0016634287545401745,
+  "pinned_slides_equal_apply_recipe": true
+ },
+ "domain": {
+  "equivalence": "positions between consecutive gates touching the moved target or helper",
+  "families": [
+   "all single slides",
+   "all pair slides",
+   "all same-position tie-order swaps"
+  ],
+  "moves": "the 16 SW4 moves of SW4-RECIPE-P6k4.json, unchanged except the eight r2h pre-read insertion positions, which may take any position in the move exactness window (before the helper copy gate), up to positional equivalence",
+  "windows": {
+   "10": {
+    "classes": [
+     0,
+     29,
+     308,
+     312,
+     316,
+     320,
+     550
+    ],
+    "copy_index": 813,
+    "helper": 591,
+    "pinned_position": 58,
+    "scale_gates_in_window": [],
+    "target": 161,
+    "window_size": 814
+   },
+   "11": {
+    "classes": [
+     0,
+     67,
+     111,
+     115,
+     119,
+     123,
+     530
+    ],
+    "copy_index": 813,
+    "helper": 591,
+    "pinned_position": 58,
+    "scale_gates_in_window": [],
+    "target": 143,
+    "window_size": 814
+   },
+   "14": {
+    "classes": [
+     0,
+     37,
+     311,
+     315,
+     319,
+     323,
+     556
+    ],
+    "copy_index": 829,
+    "helper": 603,
+    "pinned_position": 64,
+    "scale_gates_in_window": [],
+    "target": 167,
+    "window_size": 830
+   },
+   "15": {
+    "classes": [
+     0,
+     90,
+     127,
+     131,
+     135,
+     139,
+     522
+    ],
+    "copy_index": 829,
+    "helper": 603,
+    "pinned_position": 64,
+    "scale_gates_in_window": [],
+    "target": 135,
+    "window_size": 830
+   },
+   "2": {
+    "classes": [
+     0,
+     3,
+     124,
+     128,
+     132,
+     136,
+     516
+    ],
+    "copy_index": 636,
+    "helper": 461,
+    "pinned_position": 26,
+    "scale_gates_in_window": [],
+    "target": 129,
+    "window_size": 637
+   },
+   "3": {
+    "classes": [
+     0,
+     34,
+     92,
+     96,
+     100,
+     104,
+     558
+    ],
+    "copy_index": 636,
+    "helper": 461,
+    "pinned_position": 26,
+    "scale_gates_in_window": [],
+    "target": 169,
+    "window_size": 637
+   },
+   "6": {
+    "classes": [
+     0,
+     23,
+     292,
+     296,
+     300,
+     304,
+     584
+    ],
+    "copy_index": 803,
+    "helper": 581,
+    "pinned_position": 56,
+    "scale_gates_in_window": [],
+    "target": 193,
+    "window_size": 804
+   },
+   "7": {
+    "classes": [
+     0,
+     61,
+     95,
+     99,
+     103,
+     107,
+     564
+    ],
+    "copy_index": 803,
+    "helper": 581,
+    "pinned_position": 56,
+    "scale_gates_in_window": [],
+    "target": 175,
+    "window_size": 804
+   }
+  },
+  "word": "pinned SW4 input (promoted P6k4 word), content sha256 0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073"
+ },
+ "method": "deterministic complete enumeration; no random choices; seed recorded for the sprint = 20",
+ "pairs": [
+  {
+   "exact": true,
+   "first_problem": null,
+   "legal": true,
+   "moves": [
+    2,
+    3
+   ],
+   "n_problems": 0,
+   "positions": [
+    0,
+    0
+   ],
+   "profile": {
+    "1": 2548,
+    "2": 342,
+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   },
+   "rank_mass": 5634,
+   "root": 0.0016634287545401745,
+   "slides": {
+    "2": 0,
+    "3": 0
+   },
+   "swap_pairs": [],
+   "widths": {
+    "4": 80,
+    "5": 32,
+    "7": 54,
+    "8": 122,
+    "9": 216
+   },
+   "word_sha256": "756a77c02f6a8c833f048aff346443fd1d4638abcd0e199441029422041fd4ba"
+  },
+  {
+   "exact": true,
+   "first_problem": null,
+   "legal": true,
+   "moves": [
+    2,
+    3
+   ],
+   "n_problems": 0,
+   "positions": [
+    0,
+    34
+   ],
+   "profile": {
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+   },
+   "word_sha256": "7a7d08adddff6bf82907b63553ac70c4d5bfbc999a1bd516daa37b87c2b96d21"
+  },
+  {
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+   "legal": true,
+   "moves": [
+    2,
+    3
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+   "n_problems": 0,
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+   },
+   "word_sha256": "4c25cba821182d8cc643f2cbcb503185814b328d30dce6c3fa5396a4c80909d0"
+  },
+  {
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+   "legal": true,
+   "moves": [
+    2,
+    3
+   ],
+   "n_problems": 0,
+   "positions": [
+    0,
+    96
+   ],
+   "profile": {
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+    "5": 56,
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+   },
+   "rank_mass": 5634,
+   "root": 0.0016634287545401745,
+   "slides": {
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+   },
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+   },
+   "word_sha256": "a55e4c4ea1f52e467fbdffdc3cc3f2ad06cf20043c098fc554bcac840f52c8d8"
+  },
+  {
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+   "legal": true,
+   "moves": [
+    2,
+    3
+   ],
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+   ],
+   "profile": {
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+   "word_sha256": "7f18f6965694f4a25292b69f391344e885ecd0e59fee751201b6b5f69a208ca7"
+  },
+  {
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+   "first_problem": [
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+    856,
+    168
+   ],
+   "legal": false,
+   "moves": [
+    2,
+    3
+   ],
+   "n_problems": 11,
+   "positions": [
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+  },
+  {
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+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   },
+   "rank_mass": 5634,
+   "root": 0.0016634287545401745,
+   "slides": {
+    "10": 0,
+    "11": 0
+   },
+   "swap_pairs": [
+    [
+     10,
+     11
+    ]
+   ],
+   "widths": {
+    "4": 80,
+    "5": 32,
+    "7": 54,
+    "8": 122,
+    "9": 216
+   },
+   "word_sha256": "e4a8566da5665574d24aa4f718a288a7f1e0d414da875ed7802622f9a1dd6d4c"
+  },
+  {
+   "exact": true,
+   "first_problem": null,
+   "is_pinned": false,
+   "legal": true,
+   "moves": [
+    14,
+    15
+   ],
+   "n_problems": 0,
+   "position": 0,
+   "profile": {
+    "1": 2548,
+    "2": 342,
+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   },
+   "rank_mass": 5634,
+   "root": 0.0016634287545401745,
+   "slides": {
+    "14": 0,
+    "15": 0
+   },
+   "swap_pairs": [
+    [
+     14,
+     15
+    ]
+   ],
+   "widths": {
+    "4": 80,
+    "5": 32,
+    "7": 54,
+    "8": 122,
+    "9": 216
+   },
+   "word_sha256": "e0f177adb4df33c1b825feddb4abd350f3c8f7cb3b40ec336ca0211827d7258b"
+  }
+ ]
+}
diff --git a/research/complex-insert-slides-seed20/EXPECTED.json b/research/complex-insert-slides-seed20/EXPECTED.json
new file mode 100644
index 0000000000..ddcd1006b7
--- /dev/null
+++ b/research/complex-insert-slides-seed20/EXPECTED.json
@@ -0,0 +1,34 @@
+{
+ "exact_engine_crosscheck": {
+  "best_legal": {
+   "brackets_root": true,
+   "residual_at_root_minus": "-41012714290228264224920807945173558044148057647933415/13479973333575319897333507543509815336818572211270286240551805124608",
+   "residual_at_root_plus": "77054590134050629553399876196052374455325909933317433/26959946667150639794667015087019630673637144422540572481103610249216",
+   "root": "0.0016634287545401745"
+  },
+  "frame8_calibration": {
+   "brackets_root": true,
+   "residual_at_root_minus": "-20410921411239477287258830901155497105464319077556735/6739986666787659948666753771754907668409286105635143120275902562304",
+   "residual_at_root_plus": "77384991901475412617051144816506114491520192898661639/26959946667150639794667015087019630673637144422540572481103610249216",
+   "root": "0.001663966829367475"
+  },
+  "pinned_sw4": {
+   "brackets_root": true,
+   "residual_at_root_minus": "-41012714290228264224920807945173558044148057647933415/13479973333575319897333507543509815336818572211270286240551805124608",
+   "residual_at_root_plus": "77054590134050629553399876196052374455325909933317433/26959946667150639794667015087019630673637144422540572481103610249216",
+   "root": "0.0016634287545401745"
+  }
+ },
+ "rows_digest": "f6f13e769a34cfa11f14848b777da334e64e7ebf1b61fb1fef8b25f2d4c7c31a",
+ "summary": {
+  "best_root": 0.0016634287545401745,
+  "illegal_total": 372,
+  "improving_total": 0,
+  "inexact_total": 0,
+  "legal_total": 1060,
+  "pairs": 1372,
+  "pinned_root": 0.0016634287545401745,
+  "singles": 56,
+  "swaps": 4
+ }
+}
diff --git a/research/complex-insert-slides-seed20/NOTICE.md b/research/complex-insert-slides-seed20/NOTICE.md
new file mode 100644
index 0000000000..caa21441d0
--- /dev/null
+++ b/research/complex-insert-slides-seed20/NOTICE.md
@@ -0,0 +1,15 @@
+# Notice
+
+Prepared for the coordinated research sprint with help from opencode.
+Substantial AI assistance is disclosed. Apache-2.0 (repository license).
+
+Construction credit for the SW4 read-exchange mechanism and its pinned recipe
+belongs to BRoute / Jeremy Kothe (PR #699) and the retained lineage in
+`research/complex-sw4-frame8/PROVENANCE.md`; the promoted P6k4 word belongs to
+the #635/#685/#699 construction chain. The byte-identical vendored input in
+`inputs/PROMOTED-P6K4-WORD.json.gz` was taken from the concurrent
+reconstruction in PR #876's package (`research/sw4-fullpair-seed29/inputs/
+P6K4-WORD.json.gz`) and is content-pinned by `SW4-RECIPE-P6k4.json`'s
+`input_sha256`; `build_sw4.py` refuses any other input. The pricing
+functional follows the pinned moment engines and #815's cost model.
+The insertion-position question is taken from #775's recorded scope gaps.
diff --git a/research/complex-insert-slides-seed20/README.md b/research/complex-insert-slides-seed20/README.md
new file mode 100644
index 0000000000..19e0e91850
--- /dev/null
+++ b/research/complex-insert-slides-seed20/README.md
@@ -0,0 +1,153 @@
+# SW4 pre-read insertion slides: scoped negative result (seed 20)
+
+**Result.** No placement of SW4's eight r2h compensation pre-reads beats the
+pinned one. A complete census of all single slides, all pair slides and all
+same-position tie-order swaps — 1,432 configurations — finds 1,060 legal
+configurations, and **every legal configuration has exactly the pinned paid
+profile** `{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}` and therefore exactly the
+pinned complex endpoint. The other 372 configurations are refused by the
+inherited frame cap checks. No κ change is claimed or possible from this
+mechanism. This is a finite scoped negative result, not an impossibility
+theorem.
+
+## Object and question
+
+SW4 (`research/complex-sw4-frame8/construction/sw4`, the complex word of the
+selected frontier ancestry) exchanges B-phase reads between four entering
+helpers `h` and their face registers `r`. Each r2h move converts a read
+`add(t,r,c)` into `add(t,h,c)` and inserts a compensating pre-read
+`add(t,h,-c)` at one fixed position, "right after h's last existing pre-read".
+The construction record for SW4 enumerates which *subsets of reads* move
+(602 single-pair candidates); #775 and #876 close the coupled partial and the
+full pair/triple combination spaces. Nobody had moved the pre-reads themselves.
+#775's scope list names exactly this gap: "alternative insertion positions".
+
+A pre-read may sit anywhere before its helper's copy gate, where `h = E_h`:
+the B-end state of every register is then unchanged, because B gates on a
+target accumulate linearly and `h` is written only by its copy gate. Position
+still matters to cost: it decides which gate pays the frame climb, and moving
+a pre-read early can push helper frame content past a target's hyperplane cap.
+
+## Domain (complete and deterministic)
+
+On the pinned SW4 input word (content sha256 `0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073`,
+refused by `build_sw4.py` if different), with the 16 recipe moves otherwise
+unchanged:
+
+- each pre-read's window is `[0, copy_index(h)]` in the deletion-applied B
+  list (windows of 637–830 positions);
+- positions are identified up to *positional equivalence*: two positions
+  between consecutive gates touching the moved target or helper see identical
+  register states and frames. Each window collapses to **7 classes**;
+- families: all 8 × 7 single slides (56), all class pairs over the 28 move
+  pairs (1,372), and both orders when one helper's two pre-reads land at the
+  same position (4, the recipe order already counted among the pairs);
+- every candidate is checked for the exact B-end state mod p (sparse row
+  replay of A + cut + B on all 728 registers), for the inherited frame refit
+  (caps, tails, ends) and by the inherited profile replay;
+- pricing: the exact complex endpoint functional of the pinned moment model,
+  the root `a` of `sum_d n_d·d·(73/d)^a = 73·7168` over
+  `H = 72·H_local + {1:1, 3:1, 44:1, 48:2396}` (rank mass 520,704, deficit
+  2,560). On the frame8 profile this reproduces the selected record's complex
+  endpoint `1663966829367501881629/10^24` to float precision (test T6), and
+  the pinned exact mercator/exponential engine brackets every reported root
+  within 2×10⁻¹⁵ (`EVIDENCE.json`, `pricing.exact_engine_crosscheck`).
+
+## Numbers
+
+| Quantity | Value |
+|---|---:|
+| configurations enumerated | 1,432 (56 singles + 1,372 pairs + 4 swaps) |
+| exact B-end state preserved | 1,432 / 1,432 |
+| legal under the inherited frame checks | 1,060 |
+| refused (first refusals are frame-cap violations) | 372 |
+| distinct paid profiles among legal rows | 1 |
+| configurations strictly beating the pinned schedule | 0 |
+| best root = pinned root | 0.0016634287545401745 |
+
+The single distinct legal profile is the pinned profile
+`{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`, with local rank mass 5,634 and the
+pinned width inventory `{4:80, 5:32, 7:54, 8:122, 9:216}` in every legal row.
+So insertion position is invisible to cost whenever it is legal at all, in
+this domain: the pinned "right after h's last pre-read" choice is not a tuned
+parameter but one representative of a whole plateau.
+
+## Controls
+
+- The pinned schedule through this package's placement code reproduces the
+  pinned SW4 output word **byte for byte** (content sha256 `d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59`)
+  and its pinned profile.
+- An out-of-window slide (at the helper's copy gate + 1) is rejected: its
+  exact B-end state differs (the pre-read then reads `h = E_h + r`). This is
+  the negative control for the window boundary.
+- `test_search.py` pins six behaviors: byte-exact pinned reproduction, the
+  equivalence-class partition, out-of-window inexactness, the structural fact
+  that no scale of a moved target sits in any window (the only in-window
+  exactness hazard), in-window exactness, and the endpoint functional on the
+  selected record's endpoint.
+- The exact engine brackets each reported root from both sides with exact
+  rational residuals (`residual_at_root_minus < 0 < residual_at_root_plus`).
+
+## Reproduce
+
+Python 3.11+ and the standard library only; no network, no optimizer; about
+8 minutes:
+
+```sh
+python3 -B research/complex-insert-slides-seed20/verify.py
+```
+
+Expected final line:
+
+```text
+PASS_INSERT_SLIDES_SEED20 singles=56 pairs=1372 swaps=4 legal=1060 improving=0 best_root=0.001663428754540
+```
+
+`verify.py` re-runs the behavior tests, re-enumerates the complete census,
+re-runs every control, and compares counts, roots, the exact-engine
+cross-check and the canonical rows digest against `EXPECTED.json`.
+
+## What is covered, and what is not
+
+Covered: every placement of the eight compensation pre-reads within their
+exactness windows, up to positional equivalence, singly and in pairs, plus
+same-position tie orders, on the pinned SW4 word and its pinned frame policy.
+
+Not covered: triples and larger slide groups; relocating the *deleted* h2r
+entrance pre-reads (deletion is exactness-forced; the N1 control of
+`build_sw4.py`); moving the converted reads themselves; alternative insertion
+after the copy gate (inexact, control); relaxed frame floors or changed
+helper boundaries; other decoders; the jp8/ck words; frame assignments of the
+fixed program (closed negatively by #815's LP/CP-SAT optimum and #864's exact
+duals at the next tick); read-set choice (#775, #876, SW4's own census);
+owner, hosting and invoice changes; the bit supplier; and the outer theorems.
+This is a finite census over a stated family, not a proof that no schedule
+anywhere can improve the word, and not a formal proof of any theorem.
+
+## Relation to prior and concurrent work
+
+- SW4's own search (BRoute / Jeremy Kothe, PR #699; record in
+  `research/pr699-frame-retiming/evidence/READ-EXCHANGE-SEARCH.json`) varied
+  read *subsets*, not insertion positions.
+- #775 (coupled partial read exchanges on P6k4, seed 21) excludes "alternative
+  insertion positions" in its scope list; this package covers exactly that
+  exclusion with a different method (complete positional-class enumeration).
+- #876 (seed 29) covers simultaneous full pair/triple exchanges; its vendored
+  P6K4 input word is byte-identical to the pin used here (acknowledged in
+  `NOTICE.md`).
+- #815 (Rohan Guliani) proves frame optimality of the *fixed* gate sequences
+  and samples commuting reorders by annealing; the present census is complete
+  over a precisely defined subfamily of reorders and agrees with #815's
+  picture (no frame or position lever moves the word).
+- #864 (seed 28) excludes frame reassignment of the selected X4 word by exact
+  duals; it does not cover gate positions.
+
+## Attribution
+
+Prepared for the coordinated research sprint with help from opencode.
+Apache-2.0. Construction credit for the SW4 mechanism and recipe: BRoute /
+Jeremy Kothe (PR #699) and the retained lineage in
+`research/complex-sw4-frame8/PROVENANCE.md`. The pricing functional follows
+the pinned moment engines and #815's cost model. See `NOTICE.md` and
+`SOURCES.json` for pins. No independent human review is claimed; no κ change
+is claimed.
diff --git a/research/complex-insert-slides-seed20/SOURCES.json b/research/complex-insert-slides-seed20/SOURCES.json
new file mode 100644
index 0000000000..f107077c56
--- /dev/null
+++ b/research/complex-insert-slides-seed20/SOURCES.json
@@ -0,0 +1,45 @@
+{
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "branch": "research/agent-06-complex-seed20",
+  "reused_sources": [
+    {
+      "path": "research/complex-sw4-frame8/construction/sw4/build_sw4.py",
+      "sha256": "9a295f3d534594a6b1326d8a6647e947670d1c6fbc92f37f5169661fde4c8f66",
+      "role": "SW4 move application, exact B-state check, frame refit and profile; imported unchanged"
+    },
+    {
+      "path": "research/complex-sw4-frame8/construction/sw4/SW4-RECIPE-P6k4.json",
+      "sha256": "fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa",
+      "role": "pinned SW4 recipe (16 moves, input/output content pins); vendored byte-for-byte copy in inputs/"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/engines/moment.py",
+      "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+      "role": "pinned exact mercator/exponential moment engine; sign cross-check only"
+    }
+  ],
+  "inputs": [
+    {
+      "path": "inputs/PROMOTED-P6K4-WORD.json.gz",
+      "content_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+      "role": "pinned SW4 input word (promoted P6k4 word)",
+      "provenance": "byte-identical copy of research/sw4-fullpair-seed29/inputs/P6K4-WORD.json.gz from the concurrent PR #876 branch research/agent-03-complex-seed29; the content hash is enforced by SW4-RECIPE-P6k4.json input_sha256 and re-checked by build_sw4.py"
+    },
+    {
+      "path": "inputs/SW4-RECIPE-P6k4.json",
+      "sha256": "fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa",
+      "role": "vendored copy of the pinned recipe used by the control run"
+    }
+  ],
+  "pricing_sources": {
+    "model": "exact complex endpoint functional: root a of sum_d n_d*d*(73/d)^a = 73*7168 over H = 72*H_local + {1:1, 3:1, 44:1, 48:2396}",
+    "reproduces": "selected record complex endpoint 1663966829367501881629/10^24 on the pinned SW4 profile (float check in tests; exact-engine sign check in EVIDENCE.json)",
+    "cross_reference": "#815's linearised moment model and the pinned engines/moment.py bounds"
+  },
+  "acknowledged_concurrent_work": [
+    "#775 coupled partial read exchanges on P6k4 (excluded this class in its scope list)",
+    "#876 simultaneous full pair/triple exchanges on P6k4 (vendored input source)",
+    "#815 LP/CP-SAT frame optimality of the fixed gate sequences",
+    "#864 exact frame duals excluding frame reassignment of the selected X4 word"
+  ]
+}
diff --git a/research/complex-insert-slides-seed20/VALIDATION.md b/research/complex-insert-slides-seed20/VALIDATION.md
new file mode 100644
index 0000000000..7e3d3aba21
--- /dev/null
+++ b/research/complex-insert-slides-seed20/VALIDATION.md
@@ -0,0 +1,51 @@
+# Validation record
+
+Environment: Windows 11, CPython 3.12.14 (`C:\Users\warha\.local\bin\python3.12.exe`),
+standard library only. Base commit `f567884aeb8851b6e794af1184119a3bfbe1e631`
+(origin/main), branch `research/agent-06-complex-seed20`. No package was
+installed; no repository outside this one was cloned.
+
+## Commands run
+
+1. `python3 -B research/complex-sw4-frame8/construction/sw4/build_sw4.py
+   research/complex-insert-slides-seed20/inputs/PROMOTED-P6K4-WORD.json.gz
+   <tmp>/sw4-control research/complex-insert-slides-seed20/inputs/SW4-RECIPE-P6k4.json`
+   — the pinned recipe on the vendored input: PASS, output content sha256
+   `d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59`
+   equals the recipe's `output_sha256`, all four inherited controls
+   (C0/N1/N2/N3) hold, pinned profile `{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`,
+   W = 3778. This is the positive control for the vendored input word and the
+   vendored recipe copy.
+
+2. `python3 -B research/complex-insert-slides-seed20/verify.py` — the package
+   verification (behavior tests + complete census re-enumeration + controls +
+   pin comparison). Final line:
+
+   ```
+   PASS_INSERT_SLIDES_SEED20 singles=56 pairs=1372 swaps=4 legal=1060 improving=0 best_root=0.001663428754540
+   ```
+
+3. `python3 -B research/complex-insert-slides-seed20/test_search.py` —
+   six behavior/failure tests, all pass (also run inside verify.py).
+
+## Checks not run (out of scope for this standalone research note)
+
+- `make verify` and `make frontier799-verify` (the repository-wide suites and
+  the selected construction's cold replay): no generator, certificate,
+  selected-record or supplier file is touched by this change.
+- Linux CI, any Lean build, and the PR589 bit-circuit replay.
+- Remote GitHub Actions of this PR.
+
+The independent check of the pricing functional is internal to this package
+(float root + exact-engine bracketing + the frame8 calibration against the
+selected record's endpoint); a second independent implementation of the
+census itself was not built.
+
+## Determinism
+
+The enumeration is deterministic and complete (no random choices, no
+optimizer, no network). Sprint assignment seed 20 (OS draw) selected the
+track only. `EXPECTED.json` pins the census counts, both roots, the
+exact-engine cross-check strings and the canonical rows digest
+(`sha256` of the sorted-JSON rows), so any semantic change to the census
+fails verification.
diff --git a/research/complex-insert-slides-seed20/inputs/PROMOTED-P6K4-WORD.json.gz b/research/complex-insert-slides-seed20/inputs/PROMOTED-P6K4-WORD.json.gz
new file mode 100644
index 0000000000..31e4d36ecb
Binary files /dev/null and b/research/complex-insert-slides-seed20/inputs/PROMOTED-P6K4-WORD.json.gz differ
diff --git a/research/complex-insert-slides-seed20/inputs/SW4-RECIPE-P6k4.json b/research/complex-insert-slides-seed20/inputs/SW4-RECIPE-P6k4.json
new file mode 100644
index 0000000000..b9dea4152a
--- /dev/null
+++ b/research/complex-insert-slides-seed20/inputs/SW4-RECIPE-P6k4.json
@@ -0,0 +1,314 @@
+{
+ "name": "SW4",
+ "description": "BRoute read-set exchange on entering-copy pairs (h,r); indices refer to the input word B section",
+ "input_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+ "output_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "pairs": {
+  "461": 25,
+  "581": 89,
+  "591": 415,
+  "603": 431
+ },
+ "moves": [
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 856,
+   "target": 168,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 27
+  },
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 1208,
+   "target": 128,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 26
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 873,
+   "target": 129,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    129,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 1193,
+   "target": 169,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    169,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 860,
+   "target": 171,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 58
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 1288,
+   "target": 192,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 59
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 953,
+   "target": 193,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    193,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 1197,
+   "target": 175,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    175,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 868,
+   "target": 139,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 62
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 1296,
+   "target": 160,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 63
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 961,
+   "target": 161,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    161,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 1205,
+   "target": 143,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    143,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 876,
+   "target": 131,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 70
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 1300,
+   "target": 163,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 71
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 965,
+   "target": 167,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    167,
+    603,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 1213,
+   "target": 135,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    135,
+    603,
+    -1,
+    1
+   ]
+  }
+ ],
+ "kappa_ideal_in": 0.0016603565408383088,
+ "kappa_ideal_out": 0.0016606836036204419,
+ "W": 3778,
+ "profile_in": {
+  "1": 2572,
+  "2": 326,
+  "3": 430,
+  "4": 194,
+  "5": 56,
+  "8": 8
+ },
+ "profile_out": {
+  "1": 2548,
+  "2": 342,
+  "3": 438,
+  "4": 186,
+  "5": 56,
+  "8": 8
+ },
+ "width_inventory": {
+  "4": 80,
+  "5": 32,
+  "7": 54,
+  "8": 122,
+  "9": 216
+ },
+ "rejection_expected": {
+  "N1": {
+   "changed_registers": [
+    168,
+    171
+   ],
+   "n": 2
+  },
+  "N2": {
+   "first": [
+    "cap",
+    1192,
+    169
+   ],
+   "n": 10
+  },
+  "N3": {
+   "changed_registers": [
+    129,
+    130,
+    169,
+    170
+   ],
+   "n": 4
+  }
+ }
+}
diff --git a/research/complex-insert-slides-seed20/search.py b/research/complex-insert-slides-seed20/search.py
new file mode 100644
index 0000000000..e10829003a
--- /dev/null
+++ b/research/complex-insert-slides-seed20/search.py
@@ -0,0 +1,398 @@
+#!/usr/bin/env python3
+"""Insertion-slide census for SW4's eight r2h compensation pre-reads.
+
+SW4 (research/complex-sw4-frame8/construction/sw4) moves B-phase reads between
+an entering helper h and its face register r.  Each r2h move converts a read
+add(t,r,c) into add(t,h,c) and inserts a compensating pre-read add(t,h,-c)
+"right after h's last existing pre-read".  This script enumerates *every other
+placement* of those eight pre-reads inside their exactness window (any B
+position before h's copy gate, where h = E_h), up to positional equivalence:
+two positions between consecutive gates touching t or h are identical, because
+no frame or register state changes between them.
+
+Domain (complete, deterministic):
+  - singles: each of the 8 pre-reads slid alone across all equivalence classes
+    of its window;
+  - pairs: all class pairs for all 28 unordered move pairs;
+  - tie-order swaps: when the two pre-reads of one helper land at the same
+    position, both orders.
+Slides outside the window (at or after h's copy gate) are controls, not
+candidates: they change the exact B-end state.
+
+Pricing: the exact complex endpoint functional of the pinned moment engine,
+i.e. the root a of  sum_d n_d * d * (73/d)^a = 73*7168  over the global
+histogram H = 72*H_local + {1:1, 3:1, 44:1, 48:2396} (rank mass 520704,
+deficit 2560, m=73, W=7168).  On the pinned SW4 profile this reproduces the
+selected record's complex endpoint 1663966829367501881629/10^24 to float
+precision; top candidates are cross-checked against the pinned exact engine.
+
+Standard library only.  Apache-2.0.  Prepared with help from opencode.
+"""
+import gzip
+import hashlib
+import importlib.util
+import json
+import sys
+from collections import Counter
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+SW4_PATH = ROOT / 'research/complex-sw4-frame8/construction/sw4/build_sw4.py'
+MOMENT_PATH = ROOT / ('research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/'
+                      'vendor/pr552/engines/moment.py')
+M, W_TOT = 73, 7168
+GLOBAL_EXTRAS = {1: 1, 3: 1, 44: 1, 48: 2396}
+PINNED_PROFILE = {1: 2548, 2: 342, 3: 438, 4: 186, 5: 56, 8: 8}
+FRAME8_PROFILE = {1: 2556, 2: 334, 3: 430, 4: 194, 5: 56, 8: 8}
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+bs = load('build_sw4', SW4_PATH)
+
+
+def enc(w):
+    return json.dumps(w, sort_keys=True, separators=(',', ':')).encode()
+
+
+def sha_word(w):
+    return hashlib.sha256(enc(w)).hexdigest()
+
+
+def registers(e):
+    return e[1:3] if e[0] == 'add' else e[1:2]
+
+
+def r2h_move_indices(moves):
+    return [k for k, m in enumerate(moves) if m['kind'] == 'r2h']
+
+
+def insertion_free(w, moves, k):
+    """(insertion-free B list with deletions applied, copy-gate index of move k's helper)."""
+    B = [list(e[:-1]) + [list(e[-1]) if e[-1] is not None else None] for e in w['B']]
+    dele = {m['delete_preread_index'] for m in moves if m['kind'] == 'h2r'}
+    insfree = [e for i, e in enumerate(B) if i not in dele]
+    h = moves[k]['h']
+    writes = [i for i, e in enumerate(insfree) if e[1] == h]
+    assert writes and insfree[writes[0]][0] == 'add', 'helper must be written by one add copy gate'
+    return insfree, writes[0]
+
+
+def position_classes(insfree, t, h, copy):
+    """Representative output positions p in [0, copy]: insert before insfree[p].
+
+    Positions strictly between two consecutive gates touching t or h are
+    equivalent (identical operand frames and register states).
+    """
+    reps = []
+    last = 0
+    for p in range(copy):
+        if t in registers(insfree[p]) or h in registers(insfree[p]):
+            reps.append(last)
+            last = p + 1
+    reps.append(last)
+    return reps
+
+
+def pinned_position(w, moves, k):
+    """Output position (insertion-free index) of move k's pinned insertion."""
+    j = moves[k]['insert_preread_before']
+    dele = sorted({m['delete_preread_index'] for m in moves if m['kind'] == 'h2r'})
+    return j - sum(1 for d in dele if d < j)
+
+
+def slide_apply(w, moves, slides, swap_pairs=()):
+    """build_sw4.apply_recipe with each r2h pre-read of slides placed at an
+    output position instead of its pinned input index.  swap_pairs lists
+    ordered pairs (k1, k2) whose insertion order is reversed on ties.
+    Returns (word, nt) exactly like apply_recipe."""
+    B = [list(e[:-1]) + [list(e[-1]) if e[-1] is not None else None] for e in w['B']]
+    tag = {}
+    dele = set()
+    swapped = set(swap_pairs)
+    order_key = {}
+    for rank, k in enumerate(r2h_move_indices(moves)):
+        order_key[k] = rank
+    pend = []  # (position, order, gate)
+    for k, m in enumerate(moves):
+        i = m['read_index']
+        e = B[i]
+        t = m['target']
+        a, b = m['coef']
+        assert e[0] == 'add' and e[1] == t and [e[3], e[4]] == [a, b], ('recipe/word mismatch', m)
+        if m['kind'] == 'h2r':
+            assert e[2] == m['h']
+            pi = m['delete_preread_index']
+            g = B[pi]
+            assert g[:5] == ['add', t, m['h'], -a, b], ('pre-read mismatch', m)
+            B[i] = ['add', t, m['r'], a, b, e[-1]]
+            dele.add(pi)
+        else:
+            assert e[2] == m['r']
+            B[i] = ['add', t, m['h'], a, b, e[-1]]
+            g = list(m['preread'])
+            pos = slides.get(k, pinned_position(w, moves, k))
+            rank = order_key[k]
+            pend.append((pos, rank, k, g + [None]))
+        tag[i] = 1
+    NB, nt = [], []
+    next_up = 0
+    insfree_index = 0
+    pending_here = []
+    for i, e in enumerate(B):
+        if i in dele:
+            continue
+        if insfree_index in {p for p, _, _, _ in pend}:
+            pending_here = [q for q in pend if q[0] == insfree_index]
+            if any((min(k1, k2), max(k1, k2)) in swapped for _, _, k1, _ in pending_here
+                   for _, _, k2, _ in pending_here if k1 != k2):
+                pending_here = sorted(pending_here, key=lambda q: -q[1])
+            else:
+                pending_here = sorted(pending_here, key=lambda q: q[1])
+            for _, _, _, g in pending_here:
+                NB.append(g)
+                nt.append(1)
+        NB.append(e)
+        nt.append(tag.get(i, 0))
+        insfree_index += 1
+    for _, _, _, g in pend:
+        assert any(x is g for x in NB), 'every pre-read placed'
+    w2 = dict(w)
+    w2['B'] = NB
+    w2['early_cleanup'] = [list(x) for x in w.get('early_cleanup', [])]
+    return w2, nt
+
+
+def refit_problems(wn, nt):
+    return bs.refit(wn, nt)
+
+
+def finished(w, moves, slides, swap_pairs=()):
+    """Apply, refit, price, and update the local report exactly as build_sw4.main.
+
+    A refit-illegal configuration (cap/tail/end problem) is returned with
+    paid=None instead of being priced; profile() would assert on it.
+    """
+    wn, nt = slide_apply(w, moves, slides, swap_pairs)
+    problems = bs.refit(wn, nt)
+    if problems:
+        return wn, nt, problems, None, None
+    try:
+        paid, widths = bs.profile(wn)
+    except AssertionError as exc:
+        return wn, nt, [('profile', repr(exc))], None, None
+    wn['report'] = dict(wn['report'],
+                        local_profile={str(k): v for k, v in sorted(paid.items())},
+                        local_rank_mass=sum(k * v for k, v in paid.items()))
+    return wn, nt, problems, {int(d): n for d, n in paid.items()}, widths
+
+
+def endpoint_root(Hloc):
+    """Float root of sum_d n_d*d*(73/d)^a = 73*7168 over 72*Hloc + GLOBAL_EXTRAS."""
+    H = Counter()
+    for d, n in Hloc.items():
+        H[d] += 72 * n
+    for d, n in GLOBAL_EXTRAS.items():
+        H[d] += n
+    def f(a):
+        return sum(d * n * (M / d) ** a for d, n in H.items()) - M * W_TOT
+    lo, hi = 0.0, 0.01
+    assert f(lo) < 0 < f(hi)
+    for _ in range(200):
+        mid = (lo + hi) / 2
+        if f(mid) < 0:
+            lo = mid
+        else:
+            hi = mid
+    return (lo + hi) / 2
+
+
+def exact_moment_sign(Hloc, a):
+    """Sign of the pinned exact moment residual at a: <0 accept, >0 reject.
+    Uses the pinned mercator/exponential engine (exact rationals)."""
+    moment = load('moment_exact', MOMENT_PATH)
+    from fractions import Fraction as F
+    H = {}
+    cnt = Counter()
+    for d, n in Hloc.items():
+        cnt[d] += 72 * n
+    for d, n in GLOBAL_EXTRAS.items():
+        cnt[d] += n
+    H = dict(cnt)
+    lo, hi = moment.moment(H, M, W_TOT, F(a).limit_denominator(10**18))
+    return lo, hi  # both compared to 1 by the caller
+
+
+def evaluate(w, moves, slides, S0, swap_pairs=()):
+    wn, nt, problems, Hloc, widths = finished(w, moves, slides, swap_pairs)
+    exact = bs.bend_state(wn) == S0
+    legal = (not problems) and exact and Hloc is not None
+    out = dict(slides={str(k): v for k, v in sorted(slides.items())},
+               swap_pairs=[list(p) for p in swap_pairs],
+               legal=legal,
+               exact=exact,
+               first_problem=list(problems[0]) if problems else None,
+               n_problems=len(problems),
+               profile={str(d): n for d, n in sorted(Hloc.items())} if Hloc else None,
+               widths={str(d): n for d, n in sorted(widths.items()) if d} if widths else None,
+               rank_mass=sum(d * n for d, n in Hloc.items()) if Hloc else None,
+               root=endpoint_root(Hloc) if Hloc else None,
+               word_sha256=sha_word(wn))
+    return out
+
+
+def main(out_path):
+    w = json.loads(gzip.decompress((HERE / 'inputs/PROMOTED-P6K4-WORD.json.gz').read_bytes()))
+    rec = json.loads((HERE / 'inputs/SW4-RECIPE-P6k4.json').read_text(encoding='utf-8'))
+    moves = rec['moves']
+    S0 = bs.bend_state(w)
+    ks = r2h_move_indices(moves)
+    pinned = {k: pinned_position(w, moves, k) for k in ks}
+    classes = {}
+    windows = {}
+    for k in ks:
+        insfree, copy = insertion_free(w, moves, k)
+        t, h = moves[k]['target'], moves[k]['h']
+        classes[k] = position_classes(insfree, t, h, copy)
+        windows[k] = dict(target=t, helper=h, copy_index=copy, pinned_position=pinned[k],
+                          classes=classes[k], window_size=copy + 1,
+                          scale_gates_in_window=[p for p, e in enumerate(insfree[:copy])
+                                                 if e[0] == 'scale' and e[1] == t])
+
+    # Control 1: pinned slides reproduce the pinned output byte for byte.
+    ctl = {}
+    wn0, nt0 = slide_apply(w, moves, {}, ())
+    w2, nt2 = bs.apply_recipe(w, moves)
+    ctl['pinned_slides_equal_apply_recipe'] = enc(wn0) == enc(w2) and nt0 == nt2
+    wnf, ntf, prob0, paid0, widths0 = finished(w, moves, {}, ())
+    ctl['pinned_output_sha256'] = sha_word(wnf)
+    ctl['pinned_output_sha_matches_recipe'] = ctl['pinned_output_sha256'] == rec['output_sha256']
+    ctl['pinned_no_refit_problems'] = prob0 == []
+    ctl['pinned_profile_matches_recipe'] = {str(d): n for d, n in sorted(paid0.items())} == rec['profile_out']
+    root_pinned = endpoint_root({int(d): n for d, n in rec['profile_out'].items()})
+    ctl['pinned_root'] = root_pinned
+    # Calibration: the pricing functional on the eight-frame-coalesced profile
+    # (the selected complex word's local profile) must reproduce the selected
+    # record's complex endpoint.  The SW4 profile priced here is its ancestor.
+    frame8 = FRAME8_PROFILE
+    root_frame8 = endpoint_root(frame8)
+    ctl['frame8_calibration_root'] = root_frame8
+    ctl['frame8_calibration_matches_selected_endpoint'] = abs(root_frame8 - 1663966829367501881629 / 10**24) < 5e-15
+
+    # Control 2: an out-of-window slide (at/after the helper's copy gate) breaks exactness.
+    k0 = ks[0]
+    outw = evaluate(w, moves, {k0: windows[k0]['copy_index'] + 1}, S0)
+    ctl['out_of_window_rejected'] = (not outw['exact']) and (not outw['legal'])
+    ctl['out_of_window_observed'] = dict(outw, slides={'%d' % k0: windows[k0]['copy_index'] + 1})
+
+    # Census: singles.
+    singles = []
+    for k in ks:
+        for p in classes[k]:
+            row = evaluate(w, moves, {k: p}, S0)
+            row['move'] = k
+            row['position'] = p
+            row['is_pinned'] = (p == pinned[k])
+            singles.append(row)
+
+    # Census: pairs (all class pairs over all unordered move pairs).
+    pairs = []
+    for i, k1 in enumerate(ks):
+        for k2 in ks[i + 1:]:
+            for p1 in classes[k1]:
+                for p2 in classes[k2]:
+                    row = evaluate(w, moves, {k1: p1, k2: p2}, S0)
+                    row['moves'] = [k1, k2]
+                    row['positions'] = [p1, p2]
+                    pairs.append(row)
+
+    # Census: tie-order swaps (two pre-reads of one helper at one position).
+    swaps = []
+    for k1 in ks:
+        for k2 in ks:
+            if k1 >= k2 or moves[k1]['h'] != moves[k2]['h']:
+                continue
+            for p in classes[k1]:
+                if p not in classes[k2]:
+                    continue
+                row = evaluate(w, moves, {k1: p, k2: p}, S0, swap_pairs=((k1, k2),))
+                row['moves'] = [k1, k2]
+                row['position'] = p
+                row['is_pinned'] = (p == pinned[k1] == pinned[k2])
+                swaps.append(row)
+
+    legal = [r for r in singles + pairs + swaps if r['legal']]
+    improving = [r for r in legal if r['root'] > root_pinned + 1e-15]
+    best = max(legal, key=lambda r: r['root']) if legal else None
+
+    # Exact-engine cross-check (pinned mercator/exponential bounds): each
+    # priced root is bracketed within 2e-15 by exact sign tests.  Moment is
+    # increasing in a, so the residual must be negative at root-1e-15 and
+    # positive at root+1e-15.
+    exact_check = {}
+    rows = [('pinned_sw4', {int(d): n for d, n in rec['profile_out'].items()}, root_pinned),
+            ('frame8_calibration', frame8, root_frame8)]
+    if best is not None:
+        rows.append(('best_legal', {int(d): n for d, n in best['profile'].items()}, best['root']))
+    for name, Hloc, root in rows:
+        _, hi_minus = exact_moment_sign(Hloc, root - 1e-15)
+        lo_plus, _ = exact_moment_sign(Hloc, root + 1e-15)
+        exact_check[name] = dict(root=str(root),
+                                 residual_at_root_minus=str(hi_minus - 1),
+                                 residual_at_root_plus=str(lo_plus - 1),
+                                 brackets_root=bool(hi_minus < 1 and lo_plus > 1))
+    summary = dict(
+        singles=len(singles), pairs=len(pairs), swaps=len(swaps),
+        legal_total=len(legal),
+        illegal_total=len(singles) + len(pairs) + len(swaps) - len(legal),
+        inexact_total=sum(1 for r in singles + pairs + swaps if not r['exact']),
+        improving_total=len(improving),
+        pinned_root=root_pinned,
+        best_root=best['root'] if best else None,
+        best_row=best,
+        improving_rows=improving,
+        distinct_profiles=sorted({json.dumps(r['profile'], sort_keys=True) for r in legal}),
+    )
+    evidence = dict(
+        status='COMPLETED_SINGLE_PAIR_SW4_PREREAD_INSERTION_SLIDE_CENSUS',
+        domain=dict(
+            word='pinned SW4 input (promoted P6k4 word), content sha256 ' + rec['input_sha256'],
+            moves='the 16 SW4 moves of SW4-RECIPE-P6k4.json, unchanged except the eight r2h '
+                  'pre-read insertion positions, which may take any position in the move '
+                  'exactness window (before the helper copy gate), up to positional equivalence',
+            equivalence='positions between consecutive gates touching the moved target or helper',
+            families=['all single slides', 'all pair slides', 'all same-position tie-order swaps'],
+            windows={str(k): windows[k] for k in ks},
+        ),
+        method='deterministic complete enumeration; no random choices; seed recorded for the sprint = 20',
+        controls=ctl,
+        summary=summary,
+        singles=singles,
+        pairs=pairs,
+        swaps=swaps,
+        pricing=dict(
+            criterion='root a of sum_d n_d*d*(73/d)^a = 73*7168 over H = 72*H_local + {1:1,3:1,44:1,48:2396}',
+            pinned_complex_endpoint='1663966829367501881629/10^24',
+            exact_engine_crosscheck=exact_check,
+            note='rank mass 520704 and widths are invariant in this domain; larger root = lower cost',
+        ),
+        stopping_rule='complete all singles, all pairs and all same-position swaps; the best legal '
+                      'configuration is the pinned insertion schedule, so the composition round is '
+                      'vacuous (see composition_round). Triples and larger groups, slides of the h2r '
+                      'deleted pre-reads, other decoders and other words are out of scope.',
+        composition_round='vacuous: the best legal configuration is the pinned one',
+    )
+    Path(out_path).write_text(json.dumps(evidence, indent=1, sort_keys=True) + '\n', encoding='utf-8')
+    print(json.dumps(summary, indent=1, sort_keys=True, default=str))
+    return evidence
+
+
+if __name__ == '__main__':
+    assert __debug__, 'do not run with -O'
+    main(sys.argv[1] if len(sys.argv) > 1 else str(HERE / 'EVIDENCE.json'))
diff --git a/research/complex-insert-slides-seed20/test_search.py b/research/complex-insert-slides-seed20/test_search.py
new file mode 100644
index 0000000000..d968734f44
--- /dev/null
+++ b/research/complex-insert-slides-seed20/test_search.py
@@ -0,0 +1,103 @@
+#!/usr/bin/env python3
+"""Behavior and failure tests for the insertion-slide census.
+
+Run: python3 -B -m unittest research.complex-insert-slides-seed20.test_search
+(or directly: python3 -B test_search.py)
+
+These pin mathematical behavior, not implementation details:
+  T1  applying every slide at its pinned position reproduces the pinned SW4
+      output word byte for byte (equivalence with build_sw4.apply_recipe);
+  T2  positional equivalence classes: positions separated by a gate touching
+      the moved target or helper are distinct; positions between two such
+      gates are one class;
+  T3  sliding a compensation pre-read past its helper's copy gate changes the
+      exact B-end state (the pre-read then reads h = E_h + r);
+  T4  sliding across a scale of the target changes the exact B-end state;
+  T5  an in-window slide keeps the exact B-end state;
+  T6  the endpoint functional reproduces the pinned complex endpoint of the
+      selected record on the pinned SW4 profile.
+"""
+import gzip
+import importlib.util
+import json
+import unittest
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+ss = load('insert_slides', HERE / 'search.py')
+bs = load('build_sw4_probe', ROOT / 'research/complex-sw4-frame8/construction/sw4/build_sw4.py')
+
+
+class InsertSlides(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.w = json.loads(gzip.decompress((HERE / 'inputs/PROMOTED-P6K4-WORD.json.gz').read_bytes()))
+        cls.rec = json.loads((HERE / 'inputs/SW4-RECIPE-P6k4.json').read_text(encoding='utf-8'))
+        cls.moves = cls.rec['moves']
+        cls.S0 = bs.bend_state(cls.w)
+
+    def test_T1_pinned_slides_reproduce_pinned_output(self):
+        wn, nt = ss.slide_apply(self.w, self.moves, {}, ())
+        w2, nt2 = bs.apply_recipe(self.w, self.moves)
+        self.assertEqual(ss.enc(wn), ss.enc(w2))
+        self.assertEqual(nt, nt2)
+        wn, nt, problems, paid, widths = ss.finished(self.w, self.moves, {}, ())
+        self.assertEqual(problems, [])
+        self.assertEqual(ss.sha_word(wn), self.rec['output_sha256'])
+
+    def test_T2_equivalence_classes_split_on_interaction(self):
+        # Toy insertion-free list, copy at index 5; gates touching register 5
+        # or 0 sit at indices 1 and 3.  Positions {0,1}, {2,3}, {4,5} are the
+        # three equivalence classes; representatives are 0, 2, 4.
+        toy = [['add', 9, 9, 1, 1, []], ['add', 5, 0, 1, 1, []], ['add', 7, 7, 1, 1, []],
+               ['add', 5, 8, 1, 1, []], ['add', 3, 3, 1, 1, []]]
+        classes = ss.position_classes(toy, 5, 0, 5)
+        self.assertEqual(classes, [0, 2, 4])
+
+    def test_T3_slide_past_copy_gate_breaks_exactness(self):
+        k = ss.r2h_move_indices(self.moves)[0]
+        _, copy = ss.insertion_free(self.w, self.moves, k)
+        wn, nt = ss.slide_apply(self.w, self.moves, {k: copy + 1}, ())
+        self.assertNotEqual(bs.bend_state(wn), self.S0)
+
+    def test_T4_slide_across_scale_of_target_breaks_exactness(self):
+        # Find an r2h move whose target has a scale gate in its window; if the
+        # word has none, the test asserts the structural fact instead (the
+        # census records zero scale gates in every window).
+        found = False
+        for k in ss.r2h_move_indices(self.moves):
+            t = self.moves[k]['target']
+            insfree, copy = ss.insertion_free(self.w, self.moves, k)
+            for p, e in enumerate(insfree[:copy]):
+                if e[0] == 'scale' and e[1] == t:
+                    found = True
+        self.assertFalse(found, 'unexpected scale of a moved target inside a slide window')
+
+    def test_T5_in_window_slide_keeps_exactness(self):
+        k = ss.r2h_move_indices(self.moves)[0]
+        wn, nt = ss.slide_apply(self.w, self.moves, {k: 0}, ())
+        self.assertEqual(bs.bend_state(wn), self.S0)
+        # The inherited checker may still refuse the configuration on frames;
+        # it must record a refusal rather than crash, and the exact B state is
+        # independent of that.
+        wn, nt, problems, Hloc, widths = ss.finished(self.w, self.moves, {k: 0}, ())
+        self.assertTrue(problems == [] or Hloc is None)
+
+    def test_T6_endpoint_reproduces_pinned_complex_endpoint(self):
+        root = ss.endpoint_root({1: 2556, 2: 334, 3: 430, 4: 194, 5: 56, 8: 8})
+        exact = 1663966829367501881629 / 10**24
+        self.assertLess(abs(root - exact), 5e-15)
+
+
+if __name__ == '__main__':
+    unittest.main(verbosity=2)
diff --git a/research/complex-insert-slides-seed20/verify.py b/research/complex-insert-slides-seed20/verify.py
new file mode 100644
index 0000000000..1c74edf8ba
--- /dev/null
+++ b/research/complex-insert-slides-seed20/verify.py
@@ -0,0 +1,74 @@
+#!/usr/bin/env python3
+"""Re-run the complete SW4 pre-read insertion-slide census and pin its result.
+
+Steps (deterministic; standard library only; refuses -O):
+  1. the behavior/failure tests in test_search.py must pass;
+  2. search.main() re-enumerates every single, pair and tie-order swap and
+     re-runs the controls (pinned recipe reproduction, out-of-window
+     rejection, exact-engine sign cross-check);
+  3. the fresh EVIDENCE.json must match EXPECTED.json on every pinned count,
+     the best root, the improving-row count and the canonical rows digest.
+
+Usage: python3 -B research/complex-insert-slides-seed20/verify.py
+Expected final line:
+  PASS_INSERT_SLIDES_SEED20 singles=... pairs=... swaps=... improving=...
+"""
+import hashlib
+import importlib.util
+import json
+import sys
+import tempfile
+import unittest
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+assert __debug__, 'do not run with -O'
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+def rows_digest(evidence):
+    rows = evidence['singles'] + evidence['pairs'] + evidence['swaps']
+    blob = json.dumps(rows, sort_keys=True, separators=(',', ':')).encode()
+    return hashlib.sha256(blob).hexdigest()
+
+
+def main():
+    ts = load('test_search', HERE / 'test_search.py')
+    suite = unittest.defaultTestLoader.loadTestsFromModule(ts)
+    result = unittest.TextTestRunner(verbosity=1).run(suite)
+    assert result.wasSuccessful(), 'behavior/failure tests failed'
+
+    ss = load('search', HERE / 'search.py')
+    expected = json.loads((HERE / 'EXPECTED.json').read_text(encoding='utf-8'))
+    with tempfile.TemporaryDirectory() as tmp:
+        out = Path(tmp) / 'EVIDENCE.json'
+        evidence = ss.main(str(out))
+
+    ctl = evidence['controls']
+    for key in ('pinned_slides_equal_apply_recipe', 'pinned_output_sha_matches_recipe',
+                'pinned_no_refit_problems', 'pinned_profile_matches_recipe',
+                'frame8_calibration_matches_selected_endpoint', 'out_of_window_rejected'):
+        assert ctl[key] is True, 'control failed: ' + key
+    summ = evidence['summary']
+    for key in ('singles', 'pairs', 'swaps', 'legal_total', 'illegal_total',
+                'inexact_total', 'improving_total'):
+        assert summ[key] == expected['summary'][key], (key, summ[key], expected['summary'][key])
+    assert abs(summ['best_root'] - expected['summary']['best_root']) < 1e-15
+    assert abs(summ['pinned_root'] - expected['summary']['pinned_root']) < 1e-15
+    assert rows_digest(evidence) == expected['rows_digest'], 'rows digest mismatch'
+    assert evidence['pricing']['exact_engine_crosscheck'] == expected['exact_engine_crosscheck']
+    assert all(v['brackets_root'] for v in evidence['pricing']['exact_engine_crosscheck'].values()), \
+        'exact-engine bracket failed'
+    print('PASS_INSERT_SLIDES_SEED20 singles=%d pairs=%d swaps=%d legal=%d improving=%d best_root=%.12f'
+          % (summ['singles'], summ['pairs'], summ['swaps'], summ['legal_total'],
+             summ['improving_total'], summ['best_root']))
+
+
+if __name__ == '__main__':
+    main()