diff --git a/research/frontier1305-kernel-census/NOTICE.md b/research/frontier1305-kernel-census/NOTICE.md
new file mode 100644
index 0000000000..5450afc5da
--- /dev/null
+++ b/research/frontier1305-kernel-census/NOTICE.md
@@ -0,0 +1,19 @@
+# Notice
+
+`inputs/BASE-WORD.json.gz`, `inputs/EXTRA-WORD.json.gz` and `inputs/CONTROL-WORD.json.gz` are unmodified copies of
+files from PR #1297 (rohanarun, head 4abf710a7f0d2a46f522f3f13c15769d003f9495, research/global-mixed-four-cold-kernels/),
+Apache-2.0, with that package's retained ancestry (#1286, #1274 Jeremy Kothe, #1218, #1193 Jeremy Diviney, #1148 Thomas
+DiFiore, #1196 chafreaky, #1195, PR564/571/589/645 lineage). The base and extra words are the same Git blobs in PR #1305
+(jeremykothe2, head a96a5d959672752026292ba5024664b436879fe7). Exact pins: inputs/PINS.json.
+
+`census.py` is an independent re-implementation of the relation rule of #1297's `search_relations.py`, with its edit
+format, extended to pivots never written in B and to a before-first-write restoration. `idle_optimum.py` re-implements
+#1305's `idle_overlay.py` group enumeration with exact axis selection; its admissibility class is #1305's
+`verify_idle_overlay.py` (adapted there from Gonzalo-Mier's #1252). `price.py`, `deletion.py` and `retime.py` call the
+pricing harness of PR #1186 (research/exact-frame-toolkit), which is not vendored here.
+
+New files: Marius-Paul Dumitrean, Apache-2.0, prepared with substantial AI assistance (Anthropic Claude, via Claude Code).
+
+Revision 2 (2026-10-14) answers the maintainer's review continuation point on #1337 (Mister-Meeseeks, [batch review](https://github.com/CrocSwap/integer-mult-bounds/blob/main/docs/research/community-efficient400-review.md)). It re-prices the evidence with PR #1186 revision 2's true-moment interval certificate (head 3855fd41). Prepared with substantial AI assistance (Anthropic Claude, via Claude Code).
+
+Revision 3 (2026-10-14) re-pins `regenerate.py` to PR #1186 revision 3 (head c37dfb07) and moves `deletion.py` to that toolkit's `compat.deadline`; the evidence is unchanged. Prepared with substantial AI assistance (Anthropic Claude, via Claude Code).
diff --git a/research/frontier1305-kernel-census/README.md b/research/frontier1305-kernel-census/README.md
new file mode 100644
index 0000000000..167a52df55
--- /dev/null
+++ b/research/frontier1305-kernel-census/README.md
@@ -0,0 +1,125 @@
+# Helper-donor kernel census on the #1297/#1305/#1324 words (no new κ)
+
+**Scoped negative result.** The census uses #1297's two local words, which #1305, #1324 and #1319's T74 exact fill use byte-identically. #1305 and #1324 were later withdrawn by their author, because their idle overlays move axes across Z4 families that the retained recipes fix. On these words, neither the #1274/#1297 two-shock helper-donor family nor exact re-timing of early reads improves the frames. The surrogate optimum is certified, and revision 2 adds a rigorous true-moment bound: no candidate can lower the per-call moment at b by more than 1e-6 cost units. The search covers **all 306 helper pivots read before their first B write**; #1297 searched four. #1305's idle overlay is the exact optimum of the donor-star class its own verifier admits, which is now a statement about a withdrawn class. No construction is proposed and no selected-record change is suggested.
+
+Kernels in richer families were later found on these same words: #1625's pivot-566 kernel (this author) and #1672's pivot-554 kernel. Both lie outside the two families searched here, consistent with the scope below.
+
+Coordination: [discussion #1314](https://github.com/CrocSwap/integer-mult-bounds/discussions/1314) (claim and results).
+
+## Starting point (validated)
+
+These validations predate the withdrawal of #1305 and #1324; they are kept as historical records.
+
+- **#1305 head `a96a5d95`** (jeremykothe2): its `verify.py` was run locally from a fresh checkout. It covers fresh native replays of both words, local controls, literal owner construction and strict global admission with the idle overlay. Result: `PASS_GLOBAL_MIXED_X54_IDLE_EXCHANGES_NATIVE_AND_STRICT_ADMISSION 0.001677162029073474` (127 s, macOS/Python 3.14, no Boost).
+- **#1324 head `43c19465`** (jeremykothe2, posted 22:40Z while this census ran): its `verify.py` was also run locally from a fresh checkout, with fresh native replays and strict admission. Result: `PASS_GLOBAL_MIXED_X54_IDLE_EXCHANGES_NATIVE_AND_STRICT_ADMISSION 0.001677380107853623` (156 s). The #1186 pricer reproduces this κ exactly from #1324's profile: H39=1530, H42=244, H45=1477, H48=1568, H51=6555 replace #1305's idle part.
+- **Independent pricing:** the #1186 `kappa.kappa(H, 37)` pricer reproduces 0.001677162029073474 from #1305's profile, and 0.001676854978651125 (#1297) without the overlay.
+- **Words:** `inputs/BASE-WORD.json.gz` (125 calls) and `inputs/EXTRA-WORD.json.gz` (208 calls) are #1297's `gauge44-word.json.gz` / `extra-word.json.gz`, which are the same blobs in #1305. `inputs/CONTROL-WORD.json.gz` is #1297's input base word, before pivots 555/567 were given kernels. Pins are in [inputs/PINS.json](inputs/PINS.json).
+
+## Searched families and results
+
+Pricing uses PR #1186's harness, pinned at revision 3 (head `c37dfb07`; its pricing code is revision 2's, `3855fd41`):
+- the auditor's static program rules;
+- an exact program-map screen;
+- an unchanged derived compensation;
+- recomputed cone caps, tail-mutable surrogate-optimal frames and cut equality;
+- `audit_local` on every negative delta;
+- per-rank weights at b = 0.001679979627113687, which is #1305's certified complex lower endpoint.
+
+Repricing the 61 + 292 + 803 base-word candidates at #1324's endpoint, 0.001680198439292940, gives identical verdicts and profiles. `ok` means the surrogate optimum is certified: zero integer duality gap for the floored weights `floor(2^40 · lo_r(b))`. A screen rejection is exact: a dyadic map that differs modulo an odd prime differs over Q. `infeasible` means there is no legal frame assignment in the model. Both words give identical tallies.
+
+| Family (per word) | Pivots with matches | Candidates | Neutral (`ok`, Δ = 0) | Frame-infeasible | Inexact | Gains |
+|---|---:|---:|---:|---:|---:|---:|
+| #1297 two-shock relation, restore at end of early cleanup (`--restore tail`, the #1297 rule) | 25 | 61 | 32 | 8 | 21 | **0** |
+| Same relation, helper restored just before the pivot's first write (`--restore first`, exact by construction) | 43 | 292 | 52 | 240 | 0 | **0** |
+| Exact re-timing of early reads within the target's suffix segment (single moves to three slots plus the joint move per pivot; the 152 pivots with a positive deletion price) | — | 803 | 635 | 168 | 0 | **0** |
+
+**True-moment bound (revision 2).** The surrogate certificate alone does not establish true-moment optimality: each jump's floor rounding can hide up to one unit. Revision 2 therefore prices every candidate again with PR #1186 revision 2's interval certificate. Of the 1,438 neutral candidates (the `ok` rows above, both words), none can lower the per-call moment at b below the base word's frames by more than **1e-6 units**; one unit is 2^-40 of the per-call moment. The exact rational bounds are about 1e-11 units and are rounded up to the 1e-6 grid. Each of these candidates leaves the paid profile unchanged, so its realized true delta is exactly 0. Every verdict, delta and profile equals revision 1's evidence. `infeasible` and `inexact` rows involve no cost and need no bound.
+
+**Positive control.** On the control word, `census.py` reproduces #1297's five hooks for each of pivots 555 and 567, including its committed donors 620 and 628 with partners 383 and 399. Every hook is priced at −11,707 surrogate units, which is H1 −3, H3 +1: the realized #1297 kernel, worth 2.616e-7 κ over 333 calls. Its true realized delta is −11,707.88 units, a certified gain, and `audit_local` passes all ten hook words.
+
+**Deletion screen, a heuristic and not a bound.** `deletion.py` prices the word with every early read of one pivot deleted and no compensation. 152 pivots have a positive price. The largest are:
+
+| Pivots | Surrogate price (units) | Notes |
+|---|---:|---|
+| 439, 444 | −67,944 | the X=439/444 slot sites of #1195's fusions |
+| 438, 440 | −62,316 | |
+| 230, 238, 226, 228, 231, 232, 236, 434, 436, 446 | −51,648 each | read early by two helpers and one output |
+| 12 further pivots | −44,075 each | |
+
+Under exact pricing, a −51,648 profile change (H1 −12, H2 +4, H3 −4, H4 +4 per call) would be worth +1.16e-6 κ.
+
+This is **not** an upper bound on kernels. On the control word the uncompensated deletion of 555 or 567 is frame-infeasible, yet the exact kernels are feasible and gain. Deletion changes the map-derived constraints that compensation restores. Use the screen only to choose where richer compensations are worth attempting.
+
+**Idle overlay of #1305 (historical: #1305 was withdrawn).** `idle_optimum.py` reruns #1305's group enumeration over 3,687 (replica, port) groups and 11,374 eligible children. Each group has at most four completely idle rank-48 non-owner children. Unlike #1305's builder, it picks axis triples by exact backtracking rather than greedily. The optimum equals #1305's selection in every group: 3,251 donors and 5,025 receivers. No size-4 group admits one donor serving three receivers, and 963 groups admit no exchange. A further idle gain therefore needed a larger class, not a better selection. #1324 supplies one: simultaneous axis reassignments inside each group, with its own operator check. Its 4-child groups reach (51,51,51,39), so this part is superseded as a frontier statement and remains a closure statement for #1305's class.
+
+## What is and is not established
+
+- **Established:** finite exhaustive results for the families above, on these two fixed words, in #1186's frame model, at b:
+  - surrogate optimality certified;
+  - true-moment gains bounded by 1e-6 units.
+
+  Census replays are exact rational arithmetic, standard library only.
+- **Not established:**
+  - exact true-moment optimality: the bound is 1e-6 units, not 0, and holds at the stated b only;
+  - anything about other compensation families: three or more shocks, window donors on helper readers, or cleanup-side corrections. #1625 and #1672 later found kernels in such families;
+  - other words, other owner maps or hosting changes;
+  - any impossibility theorem.
+- **Not run, since nothing is admitted:** native replay and strict admission of candidates.
+- The idle statement holds only inside `verify_idle_overlay.py`'s admitted class.
+
+## Reproduce
+
+Standard-library check, about 30 s. It replays every census exactly, binds every priced record to a census match, recounts all evidence against [RESULT.json](RESULT.json), runs the positive control, and checks that four failure controls are rejected:
+
+```sh
+python3 -B research/frontier1305-kernel-census/verify.py
+python3 scripts/research_package.py --package research/frontier1305-kernel-census
+```
+
+**Coverage.** `verify.py` recounts and binds the stored evidence. It does not rerun the frame optimization or the interval certificates. `regenerate.py` reruns all of them; it needs PR #1186's toolkit at revision 3 (head `c37dfb07`) and checks the toolkit's pinned `MANIFEST.json` and every file it lists. With 12 workers it takes about 10 minutes. Two consecutive regenerations reproduced `evidence/` byte for byte. Against revision 1's evidence, 8 of 15 files are byte-identical. The other 7 differ only by the added bound fields: no verdict, delta or profile changed.
+
+```sh
+python3 -B research/frontier1305-kernel-census/regenerate.py \
+  --toolkit <checkout of PR #1186 at c37dfb07>/research/exact-frame-toolkit --out /absolute/new/dir --workers 12 \
+  [--idle-run <#1305 verify work dir> --idle-owners <#1305 package>/OWNERS.json.gz]
+```
+
+## Revision 2 (2026-10-14)
+
+This revision answers the maintainer's review continuation point: supply a rigorous rounding or separation bound, or narrow
+the optimality claim to the integer objective.
+
+- **Rigorous bound.** Every census and re-timing candidate is re-priced with PR #1186 revision 2's interval certificate
+  (`bounds.py`, `price.py`, `retime.py`). The bound and the positive control's true delta are recorded in `RESULT.json`
+  (`true_moment_bound`, `tallies.intervals`, `tallies.control`), and `verify.py` checks them, with a new forged-bound control.
+- **Narrowed wording.** "Exactly optimal" now reads as surrogate-optimal plus the stated true-moment bound.
+- **Coverage.** The distinction between the recount (`verify.py`) and the full regeneration (`regenerate.py`) is stated.
+- **Frontier text.** It records the withdrawal of #1305 and #1324.
+
+## Revision 3 (2026-10-14)
+
+PR #1186 revision 3 (head `c37dfb07`) made the toolkit portable. It changed only timeouts, memory readings, the worker
+start method and text encoding; `frames.py` and the pricing code are unchanged. This revision follows it, so that
+`regenerate.py` keeps working if #1186 merges as is.
+
+- `regenerate.py` now pins revision 3's `MANIFEST.json`.
+- `deletion.py` used the harness's private SIGALRM handler, which revision 3 replaced with `compat.deadline`. It now
+  uses `deadline` and `Timeout` from the toolkit's `compat.py`.
+- `verify.py` and `regenerate.py` now refuse to run under `-O`. Before, `verify.py`'s guard was itself an `assert`,
+  which `-O` strips, and `regenerate.py` had none.
+- A fresh regeneration with revision 3 (12 workers, about 8 minutes) reproduced all 16 evidence files byte for
+  byte. No verdict, price, bound or tally changes; `RESULT.json` changes only in its toolkit pin.
+
+## Open next questions
+
+- **Do three-shock or window-donor relations exist for the high-screen pivots** (438/440 and the ten −51,648 pivots)? #1625's pivot-566 and #1672's pivot-554 kernels show that such richer relations do exist on these words.
+  - *Why it matters:* their screens are four to five times a realized kernel. The two-shock family is now exhausted on these words.
+  - *First step:* extend `census.py`'s dictionary from output-read donor pairs to windows `x += c·q … x −= c·q` on any register x, closing before the pivot's first write. Solve d as a sparse dyadic combination of at most three terms, then price with `price.py`.
+  - *Blocker:* each pivot has roughly 2,500 distinct suffix vectors, so the search needs support-guided enumeration rather than all triples.
+#1324 has since answered the idle question that was here: a larger simultaneous-swap class does admit (51,51,51,39) groups.
+
+## Credit
+
+The words, relation rule and edit format are from rohanarun's #1297 (`search_relations.py`), built on Jeremy Kothe's #1274 helper-donor kernel mechanism. Jeremy Kothe's #1305 and #1324 contribute the idle overlay compositions and strict packages, after Gonzalo-Mier's #1252 idle exchanges. The lineage also includes #1218/#1193/#1148/#1195. Prior saturation sweeps on the #1218 words are Wronskode's #1288, and the idle ceiling on #1094 is PatatePatatePatate's #1276. The pricing harness is #1186. See [NOTICE.md](NOTICE.md).
+
+Prepared by Marius-Paul Dumitrean with substantial AI assistance (Anthropic Claude, via Claude Code). Apache-2.0.
diff --git a/research/frontier1305-kernel-census/RESULT.json b/research/frontier1305-kernel-census/RESULT.json
new file mode 100644
index 0000000000..8a48132008
--- /dev/null
+++ b/research/frontier1305-kernel-census/RESULT.json
@@ -0,0 +1,293 @@
+{
+  "status": "NO_GAIN_IN_SEARCHED_FAMILIES",
+  "kappa_claim": null,
+  "frontier": {
+    "note": "Updated 2026-10-14. #1305 and #1324 were withdrawn by their author: their idle overlays move axes across Z4 families that the retained recipes fix. #1297's two words are also those of #1319's T74 exact fill. Later kernels in richer families were found on them: #1625 (pivot 566, this author) and #1672 (pivot 554). Both lie outside the two families searched here.",
+    "words": "PR #1297 head 4abf710a (same blobs in #1305, #1324 and #1319)",
+    "selected": "PR #1094 kappa 0.001672660197076918 (main)",
+    "historical": {
+      "pr1324": "kappa 0.001677380107853623 (head 43c19465), withdrawn",
+      "pr1305": "kappa 0.001677162029073474 (head a96a5d95), withdrawn"
+    }
+  },
+  "cost_weights_b": "0.001679979627113687 (certified complex lower endpoint of #1305 profile)",
+  "kappa_scale": {
+    "one_1274_type_kernel_H1m3_H3p1_on_333_calls": "2.616e-07",
+    "cost_units_per_kappa_note": "about 2.24e-11 kappa per per-call cost unit at these weights"
+  },
+  "tallies": {
+    "census": {
+      "base-tail": {
+        "pivots": 306,
+        "with_matches": 25,
+        "matches": 61
+      },
+      "base-first": {
+        "pivots": 306,
+        "with_matches": 43,
+        "matches": 292
+      },
+      "extra-tail": {
+        "pivots": 306,
+        "with_matches": 25,
+        "matches": 61
+      },
+      "extra-first": {
+        "pivots": 306,
+        "with_matches": 43,
+        "matches": 292
+      }
+    },
+    "prices": {
+      "base-tail": {
+        "inexact:None": 21,
+        "infeasible:None": 8,
+        "ok:0": 32
+      },
+      "base-first": {
+        "infeasible:None": 240,
+        "ok:0": 52
+      },
+      "extra-tail": {
+        "inexact:None": 21,
+        "infeasible:None": 8,
+        "ok:0": 32
+      },
+      "extra-first": {
+        "infeasible:None": 240,
+        "ok:0": 52
+      }
+    },
+    "retime": {
+      "base": {
+        "infeasible:None": 168,
+        "ok:0": 635
+      },
+      "extra": {
+        "infeasible:None": 168,
+        "ok:0": 635
+      }
+    },
+    "deletion": {
+      "base": {
+        "statuses": {
+          "infeasible": 22,
+          "ok": 272,
+          "uncertified": 12
+        },
+        "negative": 152
+      },
+      "extra": {
+        "statuses": {
+          "infeasible": 22,
+          "ok": 272,
+          "uncertified": 12
+        },
+        "negative": 152
+      }
+    },
+    "control": {
+      "matches": 10,
+      "delta": -11707,
+      "true_delta_units": [
+        -11707.881657641952,
+        -11707.881657641952
+      ],
+      "audit_local": true,
+      "deletion": [
+        "infeasible",
+        "infeasible"
+      ]
+    },
+    "idle": {
+      "eligible": 11374,
+      "groups": 3687,
+      "group_sizes": {
+        "1": 632,
+        "2": 480,
+        "3": 518,
+        "4": 2057
+      },
+      "improvable_groups": 0,
+      "donors": 3251,
+      "receivers": 5025
+    },
+    "intervals": {
+      "prices-base-tail": {
+        "bounded": 32,
+        "max_gain_units_ceil": "0.000001"
+      },
+      "prices-base-first": {
+        "bounded": 52,
+        "max_gain_units_ceil": "0.000001"
+      },
+      "retime-base": {
+        "bounded": 635,
+        "max_gain_units_ceil": "0.000001"
+      },
+      "prices-extra-tail": {
+        "bounded": 32,
+        "max_gain_units_ceil": "0.000001"
+      },
+      "prices-extra-first": {
+        "bounded": 52,
+        "max_gain_units_ceil": "0.000001"
+      },
+      "retime-extra": {
+        "bounded": 635,
+        "max_gain_units_ceil": "0.000001"
+      }
+    }
+  },
+  "deletion_screen_top": [
+    {
+      "pivot": 439,
+      "early_read_targets": [
+        584,
+        126,
+        10,
+        186
+      ],
+      "price": -67944
+    },
+    {
+      "pivot": 444,
+      "early_read_targets": [
+        590,
+        150,
+        34,
+        210
+      ],
+      "price": -67944
+    },
+    {
+      "pivot": 438,
+      "early_read_targets": [
+        586,
+        118,
+        178
+      ],
+      "price": -62316
+    },
+    {
+      "pivot": 440,
+      "early_read_targets": [
+        588,
+        158,
+        218
+      ],
+      "price": -62316
+    },
+    {
+      "pivot": 226,
+      "early_read_targets": [
+        449,
+        473,
+        145
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 228,
+      "early_read_targets": [
+        451,
+        497,
+        217
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 230,
+      "early_read_targets": [
+        450,
+        496,
+        221
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 231,
+      "early_read_targets": [
+        448,
+        472,
+        149
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 232,
+      "early_read_targets": [
+        452,
+        520,
+        157
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 236,
+      "early_read_targets": [
+        454,
+        544,
+        213
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 238,
+      "early_read_targets": [
+        455,
+        545,
+        209
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 434,
+      "early_read_targets": [
+        585,
+        287,
+        187
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 436,
+      "early_read_targets": [
+        587,
+        319,
+        115
+      ],
+      "price": -51648
+    },
+    {
+      "pivot": 446,
+      "early_read_targets": [
+        591,
+        303,
+        211
+      ],
+      "price": -51648
+    }
+  ],
+  "scope": "Finite searched families on the two fixed #1297/#1305 local words: #1297 two-shock helper-donor relations (end-of-early-cleanup and before-first-write restorations) over all 306 early-read helper pivots, and exact single/joint re-timings of the early reads of the 152 pivots with a positive deletion price. Exact frame model of PR #1186 (cone caps, tail-mutable frames, cut equality). Uncompensated deletion prices are a screen, not a bound. Idle part: #1305 selection versus the exact optimum of the donor-star class admitted by its verify_idle_overlay.py. Not an impossibility theorem for other kernel families, other words or other hosting.",
+  "robustness": "Verdicts and profiles of all 61 + 292 + 803 base-word candidates are identical at #1324 endpoint weights b = 0.001680198439292940.",
+  "true_moment_bound": {
+    "max_gain_units_ceil": "0.000001",
+    "candidates_bounded": 1438,
+    "statement": "No priced or re-timed candidate without a surrogate gain can lower the per-call moment at b below the base word's surrogate-optimal frames by more than 1e-6 units (one unit = 2^-40 of the per-call moment). The exact rational bounds, about 1e-11 units, are rounded up to the 1e-6 grid. Every such candidate has an unchanged paid profile, so its realized true delta is exactly 0.",
+    "method": "PR #1186 revision 2 Pricer(interval=True): chain-dual or exact-elimination lower bound on floor(2^224 (lo_r - lam r)) in Python integers plus lam * (rank mass), against the engines' upper bound of the base assignment",
+    "toolkit": {
+      "pr": 1186,
+      "head": "c37dfb077ad77ef391cefa56c98db87a40b7e28c",
+      "tree": "389ebe11c44f6aa58fd026d84ebfa79d4afe69be",
+      "manifest_sha256": "658331a6f03d1ca4eb0ae7f186b0da2aa694d70619af3c83a77e051cca85fd8e"
+    },
+    "revision1_verdicts_unchanged": true,
+    "earlier_toolkit": {
+      "pr": 1186,
+      "head": "3855fd413a3ccfc31988033801b9648c25aee783",
+      "manifest_sha256": "0c390838893e3170169657220bbf56132df0372f77b87059f7bb0b601971249f",
+      "evidence": "byte-identical (revision 2 of this package)"
+    }
+  }
+}
diff --git a/research/frontier1305-kernel-census/SOURCES.json b/research/frontier1305-kernel-census/SOURCES.json
new file mode 100644
index 0000000000..43693ebc24
--- /dev/null
+++ b/research/frontier1305-kernel-census/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb",
+      "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce"
+    }
+  ]
+}
diff --git a/research/frontier1305-kernel-census/TASK.json b/research/frontier1305-kernel-census/TASK.json
new file mode 100644
index 0000000000..b9464e38e5
--- /dev/null
+++ b/research/frontier1305-kernel-census/TASK.json
@@ -0,0 +1,60 @@
+{
+  "schema_version": 1,
+  "task_id": "selected-packing",
+  "priority_revision": 2,
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "original_card": {
+    "id": "selected-packing",
+    "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/heterogeneous-owner-assembly/README.md"
+    ],
+    "methods": [
+      "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+      "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+    ],
+    "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+    "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+    "allowed_variations": [
+      "One bounded residual packing instance or exact relaxation."
+    ],
+    "scope_change_triggers": [
+      "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+    ],
+    "overlap_terms": [
+      "T16",
+      "owner exchange",
+      "packing"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "On the two fixed local words of the highest open claims (#1324 and #1305, both on #1297's words, owners and dispatch), do the #1274/#1297 two-shock helper-donor kernels (both restoration rules) or exact re-timings of early reads improve the exactly optimal frames for any of the 306 helper pivots read before their first write; and is #1305's idle selection optimal within its admitted donor-star class?",
+  "scope_change_reason": "The card asks about the selected packing; the selected #1094 is superseded by open claims on the same lineage, and #1288 already reports packing/width-neutral saturation on the #1218 words. The open question that matters for the highest claim is #1297's own next question: whether the helper-donor kernel family extends beyond its four analogous pivots on the final words, plus whether #1305's idle selection leaves headroom in its class.",
+  "bottleneck_link": "The complex supplier binds; every recent gain on this line came from width-neutral local word changes (kernels) or idle repartitions. This bounds both families on the incumbent words and maps where a richer compensation would have to act.",
+  "budget_minutes": 120,
+  "stop_rule": "Stop after exhaustive two-shock (both restoration rules) and re-timing censuses on both words with exact pricing; build an admitted construction only if a gain appears; one bounded pivot only.",
+  "outcome": "negative-result",
+  "evidence": "evidence/CENSUS-*, PRICES-* (0 gains in 2 x (61 + 292) exact relation candidates), RETIME-* (0 gains in 2 x 803 exact moves), DELETION-* (screen only; control shows it is not a bound), IDLE-OPTIMUM-1305.json (#1305 selection = exact group optimum in all 3,687 groups); RESULT.json tallies; verify.py replays the censuses exactly and runs one positive and four failure controls. #1324 (posted during the census) uses the same word blobs; verdicts are unchanged at its endpoint weights, and it supersedes the idle part with a larger swap class.",
+  "author": "Marius-Paul Dumitrean",
+  "ai_assistance": "Substantial assistance from Anthropic Claude (Claude Code): search design, code, runs, analysis and text.",
+  "open_questions": [
+    {
+      "question": "Do three-shock or window-donor relations exist for the high-screen pivots (438/440 and the ten -51,648 pivots 226/228/230/231/232/236/238/434/436/446)?",
+      "why_it_matters": "Their uncompensated deletion prices are 4-5x a realized #1274-type kernel (about +1.2e-6 kappa each if fully realized), and the two-shock family is now exhausted on these words.",
+      "first_step": "Extend census.py from output-read donor pairs to windows x += c*q ... x -= c*q on any register x closing before the first write of q; solve d as a sparse dyadic combination of at most three terms; price with price.py.",
+      "blocked_by": "About 2,500 distinct suffix vectors per pivot; all-triples enumeration is too large without support-guided pruning."
+    }
+  ]
+}
diff --git a/research/frontier1305-kernel-census/VERIFY.json b/research/frontier1305-kernel-census/VERIFY.json
new file mode 100644
index 0000000000..8ae7f690a8
--- /dev/null
+++ b/research/frontier1305-kernel-census/VERIFY.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "input SHA256/Git-blob pins; exact rational replay of all five censuses against evidence; every priced record bound to exactly one census match; evidence tallies equal RESULT.json with no negative price; every surrogate-optimal candidate carries PR #1186 revision 2 true-moment bounds, none above the declared 1e-6 units; positive control reproduces #1297's 5+5 hooks for pivots 555/567 at -11707 (true -11707.88, audit_local PASS); five failure controls (byte change, coefficient change, forged price, unbound edit, forged bound) rejected. Recount only: the frame optimization and interval certificates are rerun by regenerate.py, not by this command"
+    }
+  ]
+}
diff --git a/research/frontier1305-kernel-census/bounds.py b/research/frontier1305-kernel-census/bounds.py
new file mode 100644
index 0000000000..29ff20da86
--- /dev/null
+++ b/research/frontier1305-kernel-census/bounds.py
@@ -0,0 +1,24 @@
+"""bounds.py: true-moment bounds for each priced candidate, from PR #1186 revision 2's Pricer(interval=True).
+
+The stored fields do not depend on the platform:
+  realized_delta_units  bounds of (H_candidate - H_base) . T(b) from the engines' exact per-rank bounds (exactly 0 for an
+                        unchanged profile);
+  gain_certified        the upper end of realized_delta_units is negative;
+  max_gain_units_ceil   rigorous: no frame assignment of the candidate program has a per-call moment at b below the base
+                        word's surrogate-optimal frames by more than this (exact rational value rounded UP to 1e-6 units);
+  interval_width_units_ceil  width of the candidate's own true-moment interval, rounded up likewise.
+One unit is 2^-40 of the per-call moment (frames.Costs)."""
+import math
+from fractions import Fraction as Q
+GRID = 10 ** 6
+def up(x):
+    n = math.ceil(Q(x) * GRID); assert n >= 0
+    return f"{n // GRID}.{n % GRID:06d}"
+def pricer(H):
+    class Pricer(H.Pricer):
+        def compare(self, profile, iv):
+            out = super().compare(profile, iv); unit = 1 << self.costs.unit_bits
+            gain = max(Q(0), self.base_interval['upper'] - iv['lower']) * unit
+            return dict(realized_delta_units=list(out['realized_delta_units']), gain_certified=out['gain_certified'],
+                        max_gain_units_ceil=up(gain), interval_width_units_ceil=up((iv['upper'] - iv['lower']) * unit))
+    return Pricer
diff --git a/research/frontier1305-kernel-census/census.py b/research/frontier1305-kernel-census/census.py
new file mode 100644
index 0000000000..b222a0e5ca
--- /dev/null
+++ b/research/frontier1305-kernel-census/census.py
@@ -0,0 +1,105 @@
+"""census.py: exact two-shock helper-donor relations for EVERY helper pivot read in B before its first write.
+Independent re-implementation of the #1274/#1297 rule (rohanarun's search_relations.py): delete the early reads of a
+pivot q, then compensate the exact rational output difference d with one helper cut (h += a*q after an output read of h,
+restored h -= a*q at the end of early cleanup) and one donor pair (x += c*q / x -= c*q around an output read of x),
+all coefficients dyadic and both nonzero.  Adds pivots never written in B (first write = len(B)).
+--restore first: the helper cut is restored just before the pivot's first B write instead of at the end of early cleanup
+(exact by construction, since the pivot still holds its initial value there).  Output records carry no timing fields, so a
+rerun is byte-identical.  Credit: rule and edit format from rohanarun's #1297 search_relations.py and Jeremy Kothe's #1274.
+usage: python3 -B census.py WORD.json.gz OUT.json [--workers 12] [--pivots ...] [--restore tail|first]"""
+import argparse, gzip, json, os, resource, signal, sys, time, multiprocessing as mp
+from fractions import Fraction as Q
+W = None
+RESTORE = 'tail'
+def coef(g): return Q(g[3], g[4]) if g[0] == 'add' else Q(g[2], g[3])
+def dyadic(c): return c.denominator & (c.denominator - 1) == 0
+def addv(a, b, c):
+    d = dict(a)
+    for k, v in b.items():
+        x = d.get(k, 0) + c * v
+        if x: d[k] = x
+        else: d.pop(k, None)
+    return d
+def col(seq, q):
+    r = {q: Q(1)}
+    for g in seq:
+        t = g[1]
+        if g[0] == 'add':
+            if g[2] in r:
+                x = r.get(t, 0) + coef(g) * r[g[2]]
+                if x: r[t] = x
+                else: r.pop(t, None)
+        elif t in r:
+            r[t] = r[t] * coef(g)
+    return r
+def mask(v):
+    m = 0
+    for k in v: m |= 1 << k
+    return m
+def solve(u, v, d):
+    keys = sorted(set(u) | set(v) | set(d)); i = keys[0]; ui, vi, di = u.get(i, 0), v.get(i, 0), d.get(i, 0)
+    for j in keys:
+        uj, vj, dj = u.get(j, 0), v.get(j, 0), d.get(j, 0); det = ui * vj - uj * vi
+        if det:
+            a = (di * vj - dj * vi) / det; b = (ui * dj - uj * di) / det
+            if not a or not b or not dyadic(a) or not dyadic(b): return None
+            return (a, b) if all(a * u.get(k, 0) + b * v.get(k, 0) == d.get(k, 0) for k in keys) else None
+    return None
+def init(path, restore='tail'):
+    global W, RESTORE; W = json.loads(gzip.decompress(open(path, 'rb').read())); RESTORE = restore
+def relations(q):
+    signal.alarm(900)
+    t0 = time.monotonic(); w = W; B = w['B']; ne = len(w['early_cleanup']); tail = [w['cleanup'][i] for i, U in w['early_cleanup']]
+    seq = B + tail
+    first = next((i for i, g in enumerate(B) if g[1] == q), len(B))
+    dele = {i for i in range(first) if B[i][0] == 'add' and B[i][2] == q}
+    if not dele: return dict(pivot=q, early=0, matches=[])
+    new = [g for i, g in enumerate(seq) if i not in dele]
+    d = addv(col(seq, q), col(new, q), -1)
+    cols = {}; hs = []; ts = []; snap = None
+    for i in range(len(seq) - 1, -1, -1):
+        g = seq[i]
+        if i == first - 1 and RESTORE == 'first': snap = {k: dict(v) for k, v in cols.items()}
+        if i < first and g[0] == 'add' and 112 <= g[1] < 224 and g[2] >= 224 and g[2] != q and i not in dele:
+            h = g[2]
+            base_h = (snap.get(h, {h: Q(1)}) if snap is not None else {h: Q(1)}) if RESTORE == 'first' else {h: Q(1)}
+            eff = addv(cols.get(h, {h: Q(1)}), base_h, -1)
+            if eff: hs.append((i + 1, h, eff))
+            ts.append((i, g, dict(cols.get(g[1], {g[1]: Q(1)}))))
+        if i in dele: continue
+        if g[0] == 'add':
+            t, s = g[1], g[2]; cols[s] = addv(cols.get(s, {s: Q(1)}), cols.get(t, {t: Q(1)}), coef(g))
+        else:
+            t = g[1]; c = coef(g); cols[t] = {k: x * c for k, x in cols.get(t, {t: Q(1)}).items()}
+    md = mask(d); tm = [mask(v) for _, _, v in ts]; out = []; tried = 0
+    for cut, h, u in hs:
+        need = md & ~mask(u)
+        for (i, g, v), mv in zip(ts, tm):
+            if h == g[2] or need & ~mv: continue
+            tried += 1; sol = solve(u, v, d)
+            if not sol: continue
+            a, b = sol; c = b / coef(g)
+            if not dyadic(c): continue
+            ins = [[i, ['add', g[2], q, c.numerator, c.denominator, []]], [i + 1, ['add', g[2], q, -c.numerator, c.denominator, []]], [cut, ['add', h, q, a.numerator, a.denominator, []]]]
+            if RESTORE == 'first':
+                ed = dict(delete=sorted(dele), insert=ins + [[first, ['add', h, q, -a.numerator, a.denominator, []]]], tail=[], prepend=[])
+            else:
+                ed = dict(delete=sorted(dele), insert=ins, tail=[[ne, ['add', h, q, -a.numerator, a.denominator, []]]], prepend=[])
+            out.append(dict(pivot=q, helper=h, cut=cut, output=g[1], hook=i, donor=g[2], amount=str(a), correction=str(b), ed=ed))
+    signal.alarm(0)
+    return dict(pivot=q, early=len(dele), first=first, d_support=len(d), hs=len(hs), ts=len(ts), solved=tried, matches=out)
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(); ap.add_argument('word'); ap.add_argument('out'); ap.add_argument('--workers', type=int, default=12)
+    ap.add_argument('--pivots', nargs='*', type=int); ap.add_argument('--restore', choices=('tail', 'first'), default='tail'); a = ap.parse_args()
+    RESTORE = a.restore
+    init(a.word, a.restore); B = W['B']; first = {}
+    for i, g in enumerate(B): first.setdefault(g[1], i)
+    piv = a.pivots or sorted({g[2] for i, g in enumerate(B) if g[0] == 'add' and g[2] >= 224 and i < first.get(g[2], len(B))})
+    print('pivots', len(piv), flush=True); res = []; t0 = time.time()
+    with mp.get_context('fork').Pool(a.workers, initializer=init, initargs=(a.word, a.restore), maxtasksperchild=8) as pool:
+        for n, r in enumerate(pool.imap_unordered(relations, piv), 1):
+            res.append(r)
+            if r['matches']: print(f"  {n}/{len(piv)} {time.time()-t0:.0f}s pivot {r['pivot']} early {r['early']} matches {len(r['matches'])}", flush=True)
+    res.sort(key=lambda r: r['pivot'])
+    json.dump(res, open(a.out, 'w'), sort_keys=True)
+    print('done', len(res), 'pivots with matches', sum(1 for r in res if r['matches']), 'matches', sum(len(r['matches']) for r in res), f'{time.time()-t0:.0f}s')
diff --git a/research/frontier1305-kernel-census/deletion.py b/research/frontier1305-kernel-census/deletion.py
new file mode 100644
index 0000000000..61a782f47d
--- /dev/null
+++ b/research/frontier1305-kernel-census/deletion.py
@@ -0,0 +1,45 @@
+"""deletion.py: uncompensated deletion price per pivot (a screening heuristic, NOT a bound; see README).  Exact optimal frames (#1186 model: cone caps, tail-mutable, cut equality) of the
+word with ALL early reads of pivot q deleted, WITHOUT any compensation and without the program-map screen.  Any exact
+compensating kernel adds gates, so (cost after deletion - base cost) bounds below the delta of every kernel for q that
+keeps the remaining frame structure ONLY when the deletion leaves the map-derived constraints (cone caps, cut equality)
+unchanged; it does not in general: on #1297's input word the uncompensated deletion of pivot 555/567 is frame-infeasible while
+the exact kernels gain.  usage: deletion.py TOOLKIT WORD OUT [--workers N]"""
+import argparse, json, sys, time, multiprocessing as mp
+ap = argparse.ArgumentParser(); ap.add_argument('toolkit'); ap.add_argument('word'); ap.add_argument('out'); ap.add_argument('--workers', type=int, default=12)
+ap.add_argument('--pivots', nargs='*', type=int); a = ap.parse_args()
+sys.path.insert(0, a.toolkit)
+import harness as H, frames as F
+from word import inline
+from model import cone_caps
+from compat import Timeout, deadline
+P = None
+def init():
+    global P; P = H.Pricer(a.word, check_literal=True)
+def run(q):
+    w = P.base; B = w['B']; first = next((i for i, g in enumerate(B) if g[1] == q), len(B))
+    dele = [i for i in range(first) if B[i][0] == 'add' and B[i][2] == q]
+    w1 = H.compile_edits(w, dict(delete=dele))
+    try:
+        with deadline(300):
+            caps, comp = cone_caps(w1)
+            g = F.Graph(inline(w1, True), check_literal=False, tail_mutable=True, caps=caps, cut_equality=True)
+            r = F.optimal_frames(inline(w1, True), P.costs, check_literal=False, graph=g)
+        res = dict(status='ok' if r['certified'] else 'uncertified', delta=r['cost'] - P.base_cost, profile=dict(sorted(r['profile'].items())))
+    except F.Infeasible as e: res = dict(status='infeasible')
+    except Timeout: res = dict(status='timeout')
+    except ValueError as e: res = dict(status='error:' + str(e)[:60])
+    return dict(pivot=q, early=len(dele), targets=[B[i][1] for i in dele], **res)
+if __name__ == '__main__':
+    init(); B = P.base['B']; first = {}
+    for i, g in enumerate(B): first.setdefault(g[1], i)
+    piv = a.pivots or sorted({g[2] for i, g in enumerate(B) if g[0] == 'add' and g[2] >= 224 and i < first.get(g[2], len(B))})
+    print('base', P.base_cost, P.base_profile, 'pivots', len(piv), flush=True); out = []; t0 = time.time()
+    with mp.get_context('fork').Pool(a.workers, initializer=init, maxtasksperchild=10) as pool:
+        for n, r in enumerate(pool.imap_unordered(run, piv), 1):
+            out.append(r)
+            if n % 50 == 0: print(f'  {n}/{len(piv)} {time.time()-t0:.0f}s', flush=True)
+    out.sort(key=lambda r: (r.get('delta') if r.get('delta') is not None else 10 ** 30, r['pivot']))
+    json.dump(out, open(a.out, 'w'), sort_keys=True)
+    neg = [r for r in out if r.get('delta') is not None and r['delta'] < 0]
+    print('pivots with a deletion gain', len(neg), 'of', len(out), {s: sum(1 for r in out if r['status'] == s) for s in {r['status'] for r in out}})
+    for r in neg[:40]: print('  ', r['pivot'], 'early', r['early'], r['targets'], 'delta', r['delta'], r['profile'])
diff --git a/research/frontier1305-kernel-census/evidence/CENSUS-base-first.json b/research/frontier1305-kernel-census/evidence/CENSUS-base-first.json
new file mode 100644
index 0000000000..f1b71cb1c1
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/CENSUS-base-first.json
@@ -0,0 +1 @@
+[{"d_support": 10, "early": 3, "first": 1844, "hs": 368, "matches": [], "pivot": 226, "solved": 0, "ts": 655}, {"d_support": 10, "early": 3, "first": 1844, "hs": 368, "matches": [], "pivot": 228, "solved": 0, "ts": 655}, {"d_support": 10, "early": 3, "first": 1844, "hs": 368, "matches": [], "pivot": 230, "solved": 0, "ts": 655}, {"d_support": 10, "early": 3, "first": 1844, "hs": 368, "matches": [], "pivot": 231, "solved": 0, "ts": 655}, {"d_support": 10, "early": 3, "first": 1844, "hs": 368, "matches": [], "pivot": 232, "solved": 0, "ts": 655}, {"d_support": 4, "early": 1, "first": 640, "hs": 197, "matches": [], "pivot": 233, "solved": 0, "ts": 331}, {"d_support": 11, "early": 3, "first": 1844, "hs": 367, "matches": [], "pivot": 235, "solved": 0, "ts": 654}, {"d_support": 10, "early": 3, "first": 1844, "hs": 368, "matches": [], "pivot": 236, "solved": 0, "ts": 655}, {"d_support": 11, "early": 3, "first": 1844, "hs": 367, "matches": [], "pivot": 237, "solved": 0, "ts": 654}, 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diff --git a/research/frontier1305-kernel-census/evidence/CENSUS-base-tail.json b/research/frontier1305-kernel-census/evidence/CENSUS-base-tail.json
new file mode 100644
index 0000000000..501d0cf88c
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/CENSUS-base-tail.json
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diff --git a/research/frontier1305-kernel-census/evidence/CENSUS-control-tail.json b/research/frontier1305-kernel-census/evidence/CENSUS-control-tail.json
new file mode 100644
index 0000000000..6b563d46f7
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/CENSUS-control-tail.json
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diff --git a/research/frontier1305-kernel-census/evidence/CENSUS-extra-first.json b/research/frontier1305-kernel-census/evidence/CENSUS-extra-first.json
new file mode 100644
index 0000000000..f1b71cb1c1
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/CENSUS-extra-first.json
@@ -0,0 +1 @@
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diff --git a/research/frontier1305-kernel-census/evidence/CENSUS-extra-tail.json b/research/frontier1305-kernel-census/evidence/CENSUS-extra-tail.json
new file mode 100644
index 0000000000..501d0cf88c
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new file mode 100644
index 0000000000..1e11bd15fc
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\ No newline at end of file
diff --git a/research/frontier1305-kernel-census/evidence/DELETION-control.json b/research/frontier1305-kernel-census/evidence/DELETION-control.json
new file mode 100644
index 0000000000..ee923b5ea1
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/DELETION-control.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/research/frontier1305-kernel-census/evidence/DELETION-extra.json b/research/frontier1305-kernel-census/evidence/DELETION-extra.json
new file mode 100644
index 0000000000..a8803b932e
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/DELETION-extra.json
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diff --git a/research/frontier1305-kernel-census/evidence/IDLE-OPTIMUM-1305.json b/research/frontier1305-kernel-census/evidence/IDLE-OPTIMUM-1305.json
new file mode 100644
index 0000000000..fc58d09c02
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/IDLE-OPTIMUM-1305.json
@@ -0,0 +1,100 @@
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diff --git a/research/frontier1305-kernel-census/evidence/PRICES-base-first.json b/research/frontier1305-kernel-census/evidence/PRICES-base-first.json
new file mode 100644
index 0000000000..f8c38bc528
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/PRICES-base-first.json
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diff --git a/research/frontier1305-kernel-census/evidence/PRICES-base-tail.json b/research/frontier1305-kernel-census/evidence/PRICES-base-tail.json
new file mode 100644
index 0000000000..6cfec0b908
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/PRICES-base-tail.json
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\ No newline at end of file
diff --git a/research/frontier1305-kernel-census/evidence/PRICES-control-tail.json b/research/frontier1305-kernel-census/evidence/PRICES-control-tail.json
new file mode 100644
index 0000000000..46d6443677
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/PRICES-control-tail.json
@@ -0,0 +1 @@
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diff --git a/research/frontier1305-kernel-census/evidence/PRICES-extra-first.json b/research/frontier1305-kernel-census/evidence/PRICES-extra-first.json
new file mode 100644
index 0000000000..25477239ee
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/PRICES-extra-first.json
@@ -0,0 +1 @@
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diff --git a/research/frontier1305-kernel-census/evidence/PRICES-extra-tail.json b/research/frontier1305-kernel-census/evidence/PRICES-extra-tail.json
new file mode 100644
index 0000000000..3e95a7aadd
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/PRICES-extra-tail.json
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diff --git a/research/frontier1305-kernel-census/evidence/RETIME-base.json b/research/frontier1305-kernel-census/evidence/RETIME-base.json
new file mode 100644
index 0000000000..39c2432e21
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/RETIME-base.json
@@ -0,0 +1 @@
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diff --git a/research/frontier1305-kernel-census/evidence/RETIME-extra.json b/research/frontier1305-kernel-census/evidence/RETIME-extra.json
new file mode 100644
index 0000000000..b7205144c6
--- /dev/null
+++ b/research/frontier1305-kernel-census/evidence/RETIME-extra.json
@@ -0,0 +1 @@
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701], [9, 701]], "pivot": 452, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[8, 10]], "pivot": 452, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[8, 354]], "pivot": 452, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[8, 701]], "pivot": 452, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[9, 11]], "pivot": 452, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[9, 355]], "pivot": 452, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[9, 701]], "pivot": 452, "profile": null, "status": "infeasible"}, {"delta": null, "kind": "joint-end", "moves": [[12, 703], [13, 703]], "pivot": 454, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[12, 14]], "pivot": 454, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[12, 357]], "pivot": 454, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[12, 703]], "pivot": 454, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[13, 15]], "pivot": 454, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[13, 358]], "pivot": 454, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[13, 703]], "pivot": 454, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[17, 19]], "pivot": 473, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[17, 372]], "pivot": 473, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[17, 727]], "pivot": 473, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[21, 23]], "pivot": 497, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[21, 392]], "pivot": 497, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[21, 764]], "pivot": 497, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[25, 27]], "pivot": 521, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[25, 413]], "pivot": 521, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[25, 802]], "pivot": 521, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[29, 31]], "pivot": 545, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[29, 433]], "pivot": 545, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[29, 838]], "pivot": 545, "profile": null, "status": "infeasible"}, {"delta": null, "kind": "joint-end", "moves": [[32, 885], [34, 885]], "pivot": 585, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[32, 34]], "pivot": 585, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[32, 458]], "pivot": 585, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[32, 885]], "pivot": 585, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[34, 36]], "pivot": 585, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[34, 459]], "pivot": 585, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[34, 885]], "pivot": 585, "profile": null, "status": "infeasible"}, {"delta": null, "kind": "joint-end", "moves": [[38, 889], [39, 889]], "pivot": 587, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[38, 40]], "pivot": 587, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[38, 463]], "pivot": 587, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[38, 889]], "pivot": 587, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[39, 41]], "pivot": 587, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[39, 464]], "pivot": 587, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[39, 889]], "pivot": 587, "profile": null, "status": "infeasible"}, {"delta": null, "kind": "joint-end", "moves": [[43, 893], [44, 893]], "pivot": 589, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[43, 45]], "pivot": 589, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[43, 468]], "pivot": 589, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[43, 893]], "pivot": 589, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[44, 46]], "pivot": 589, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[44, 468]], "pivot": 589, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[44, 893]], "pivot": 589, "profile": null, "status": "infeasible"}, {"delta": null, "kind": "joint-end", "moves": [[45, 897], [47, 897]], "pivot": 591, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[45, 47]], "pivot": 591, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[45, 471]], "pivot": 591, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[45, 897]], "pivot": 591, "profile": null, "status": "infeasible"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[47, 49]], "pivot": 591, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": 0, "gain_certified": false, "interval_width_units_ceil": "0.000001", "kind": "single", "max_gain_units_ceil": "0.000001", "moves": [[47, 472]], "pivot": 591, "profile": {"1": 2338, "2": 512, "3": 418, "4": 126, "5": 82}, "realized_delta_units": [0.0, 0.0], "status": "ok"}, {"delta": null, "kind": "single", "moves": [[47, 897]], "pivot": 591, "profile": null, "status": "infeasible"}]
\ No newline at end of file
diff --git a/research/frontier1305-kernel-census/idle_optimum.py b/research/frontier1305-kernel-census/idle_optimum.py
new file mode 100644
index 0000000000..f79604495a
--- /dev/null
+++ b/research/frontier1305-kernel-census/idle_optimum.py
@@ -0,0 +1,79 @@
+"""idle_optimum.py: group census of #1305's completely idle rank-48 non-owner children and exact per-group optimum of the
+donor-star class admitted by verify_idle_overlay.py (receiver gets exactly one 3-axis triple -> rank 51).
+Every assignment of donors to receivers in each (replica, port) group is enumerated (as #1305's builder does), but axis triples
+are chosen by exact backtracking instead of greedily.  Group weights are #1305's own selection weights.
+usage: idle_optimum.py STRICT_GLOBAL_DIR OWNERS.json.gz OUT.json  (STRICT_GLOBAL_DIR = <#1305 verify work>/strict/global)"""
+import gzip, json, sys, itertools, collections
+from pathlib import Path
+import hashlib
+G = Path(sys.argv[1]); OWN = Path(sys.argv[2]); OUT = Path(sys.argv[3])
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+rd = lambda p: json.loads(gzip.decompress(p.read_bytes()) if p.suffix == '.gz' else p.read_bytes())
+dot = lambda a, b: (int(a) & int(b)).bit_count() & 1
+frames = rd(G / 'hosted-baseline/IDLE-REMAINDER-FRAMES.json.gz')
+phases = rd(G / 'base/work/complex-nine-native/DATA-PHASES.json'); recipes = {r['port']: r for r in phases['recipes']}
+owners = rd(OWN); owner_slots = {(x['owner_replica'], x['port'], x['child']) for x in owners}
+ov = json.loads((G / 'hosted/IDLE-PAIR-OVERLAY.json').read_text())
+print('idle frames', len(frames), 'rank hist', sorted(collections.Counter(r['rank'] for r in frames).items())[:12], '...')
+elig = collections.defaultdict(list); why = collections.Counter()
+for r in frames:
+    k = (r['replica'], r['port'], r['child'])
+    if r['rank'] != 48: why['rank!=48'] += 1; continue
+    if r['hosted'] != 0: why['hosted'] += 1; continue
+    if r['pending_offset'] != 0: why['pending'] += 1; continue
+    if k in owner_slots: why['owner'] += 1; continue
+    elig[r['replica'], r['port']].append(r)
+print('rank48 exclusions', dict(why), 'eligible', sum(map(len, elig.values())), 'groups', len(elig))
+print('group sizes', sorted(collections.Counter(map(len, elig.values())).items()))
+Gw = {36: -2.4520183911866953e-09, 39: -1.9171680322068257e-09, 42: -1.3276966099980976e-09, 45: -6.875123312271499e-10, 48: 0.0, 51: 7.318804853566615e-10}
+cur = collections.defaultdict(list)
+for d in ov['donors']: cur[d['replica'], d['port']].append(len(d['receivers']))
+def feasible(lists):
+    """disjoint 3-subsets, one per receiver, from the given axis lists (exact backtracking)."""
+    lists = sorted(lists, key=len)
+    def bt(i, used):
+        if i == len(lists): return True
+        cand = [v for v in lists[i] if v not in used]
+        if len(cand) < 3: return False
+        for t in itertools.combinations(cand, 3):
+            if bt(i + 1, used | set(t)): return True
+        return False
+    return bt(0, frozenset())
+better = []; stats = collections.Counter(); tot_cur = tot_opt = 0.0
+for (rep, port), rows in sorted(elig.items()):
+    rec = recipes[port]; m = len(rows)
+    ys = [int(s[k]) for s in rec['stage_alignment'] for k in ('entry_Y', 'exit_Y')] + [int(rec['terminal_Y_translation'])]
+    xs = [int(s[k]) for s in rec['stage_alignment'] for k in ('entry_X', 'exit_X')]
+    ax = [list(map(int, r['orthogonal_axes'])) for r in rows]
+    mov = {}
+    for i in range(m):
+        for j in range(m):
+            if i != j:
+                tr = [int(rec['idle_children'][c]['translation_after']) for c in (rows[i]['child'], rows[j]['child'])]
+                mov[i, j] = [v for v in ax[i] if all(dot(v, x) == 0 for x in ax[j] + ys + xs + tr)]
+    best = 0.0; bestshape = ()
+    for assign in itertools.product(range(-1, m), repeat=m):
+        if any(assign[j] == j for j in range(m)): continue
+        donors = set(d for d in assign if d >= 0)
+        if any(assign[d] >= 0 for d in donors): continue
+        serve = {d: [j for j in range(m) if assign[j] == d] for d in donors}
+        val = sum(Gw[48 - 3 * len(v)] + len(v) * Gw[51] for v in serve.values())
+        if val <= best + 1e-30: continue
+        if all(feasible([mov[d, j] for j in rs]) for d, rs in serve.items()):
+            best = val; bestshape = tuple(sorted(len(v) for v in serve.values()))
+    c = sum(Gw[48 - 3 * k] + k * Gw[51] for k in cur.get((rep, port), []))
+    tot_cur += c; tot_opt += best
+    stats[(m, tuple(sorted(cur.get((rep, port), []))), bestshape)] += 1
+    if best > c + 1e-25: better.append(((rep, port), m, sorted(cur.get((rep, port), [])), bestshape, best - c))
+print('value current %.6e optimum %.6e  groups improvable %d' % (tot_cur, tot_opt, len(better)))
+for k, v in sorted(stats.items()): print('  m=%d current=%s optimum=%s : %d groups' % (k[0], k[1], k[2], v))
+for b in better[:10]: print('  better', b)
+
+rec = dict(status='PASS_1305_IDLE_SELECTION_EQUALS_EXACT_GROUP_OPTIMUM' if not better else 'IMPROVABLE_GROUPS_FOUND',
+           inputs={n: sha(G / n) for n in ('hosted-baseline/IDLE-REMAINDER-FRAMES.json.gz', 'hosted/IDLE-PAIR-OVERLAY.json', 'base/work/complex-nine-native/DATA-PHASES.json')},
+           owners_sha256=sha(OWN), eligible=sum(map(len, elig.values())), groups=len(elig),
+           group_sizes={str(k): v for k, v in sorted(collections.Counter(map(len, elig.values())).items())},
+           shapes=[dict(size=k[0], current=list(k[1]), optimum=list(k[2]), groups=v) for k, v in sorted(stats.items())],
+           value_current=repr(tot_cur), value_optimum=repr(tot_opt), improvable_groups=len(better),
+           donors=len(ov['donors']), receivers=sum(len(d['receivers']) for d in ov['donors']), profile=ov['profile'])
+OUT.write_text(json.dumps(rec, indent=2, sort_keys=True) + '\n'); print(rec['status'])
diff --git a/research/frontier1305-kernel-census/inputs/BASE-WORD.json.gz b/research/frontier1305-kernel-census/inputs/BASE-WORD.json.gz
new file mode 100644
index 0000000000..eacf8c773c
Binary files /dev/null and b/research/frontier1305-kernel-census/inputs/BASE-WORD.json.gz differ
diff --git a/research/frontier1305-kernel-census/inputs/CONTROL-WORD.json.gz b/research/frontier1305-kernel-census/inputs/CONTROL-WORD.json.gz
new file mode 100644
index 0000000000..ed6248e6b7
Binary files /dev/null and b/research/frontier1305-kernel-census/inputs/CONTROL-WORD.json.gz differ
diff --git a/research/frontier1305-kernel-census/inputs/EXTRA-WORD.json.gz b/research/frontier1305-kernel-census/inputs/EXTRA-WORD.json.gz
new file mode 100644
index 0000000000..4d464f55a2
Binary files /dev/null and b/research/frontier1305-kernel-census/inputs/EXTRA-WORD.json.gz differ
diff --git a/research/frontier1305-kernel-census/inputs/PINS.json b/research/frontier1305-kernel-census/inputs/PINS.json
new file mode 100644
index 0000000000..605303a255
--- /dev/null
+++ b/research/frontier1305-kernel-census/inputs/PINS.json
@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "license": "Apache-2.0 (rohanarun, PR #1297; retained ancestry)",
+  "files": {
+    "BASE-WORD.json.gz": {
+      "sha256": "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e",
+      "git_blob": "eacf8c773cb50637f93a762342b3b5f0853fe29a",
+      "source_pr": 1297,
+      "source_commit": "4abf710a7f0d2a46f522f3f13c15769d003f9495",
+      "source_path": "research/global-mixed-four-cold-kernels/gauge44-word.json.gz",
+      "also_in": "PR #1305 a96a5d959672752026292ba5024664b436879fe7 research/global-mixed-four-cold-kernels-idle/ (identical blob)"
+    },
+    "EXTRA-WORD.json.gz": {
+      "sha256": "7b0e9fbda32749aabc7e156d9fe09bceb0624a178628fe69e5dfea783462f905",
+      "git_blob": "4d464f55a2955e5c832b5ce789d5d0e0a39fb4e1",
+      "source_pr": 1297,
+      "source_commit": "4abf710a7f0d2a46f522f3f13c15769d003f9495",
+      "source_path": "research/global-mixed-four-cold-kernels/extra-word.json.gz",
+      "also_in": "PR #1305 a96a5d959672752026292ba5024664b436879fe7 research/global-mixed-four-cold-kernels-idle/ (identical blob)"
+    },
+    "CONTROL-WORD.json.gz": {
+      "sha256": "b87c706d14a7e1972514ee901002a930908073811ef38761def31c8e36351916",
+      "git_blob": "ed6248e6b7a1dfad3e40b5b82eaab38ccced0f7e",
+      "source_pr": 1297,
+      "source_commit": "4abf710a7f0d2a46f522f3f13c15769d003f9495",
+      "source_path": "research/global-mixed-four-cold-kernels/inputs/base.json.gz",
+      "role": "#1297's input base word (pivots 555/567 not yet kerneled): positive control"
+    }
+  }
+}
\ No newline at end of file
diff --git a/research/frontier1305-kernel-census/price.py b/research/frontier1305-kernel-census/price.py
new file mode 100644
index 0000000000..388829afb6
--- /dev/null
+++ b/research/frontier1305-kernel-census/price.py
@@ -0,0 +1,29 @@
+"""price.py: frame pricing of census matches on one word with PR #1186 revision 2's harness: static program rules, map screen,
+unchanged derived compensation, cone caps, tail-mutable surrogate-optimal frames, cut equality, audit_local on negative
+deltas, and true-moment interval bounds (bounds.py).  Needs research/exact-frame-toolkit of PR #1186 (revision 3, pinned by regenerate.py).
+usage: price.py TOOLKIT_DIR WORD.json.gz CENSUS.json OUT.json [--workers N]"""
+import argparse, json, os, resource, sys, time, multiprocessing as mp
+ap = argparse.ArgumentParser(); ap.add_argument('toolkit'); ap.add_argument('word'); ap.add_argument('census'); ap.add_argument('out')
+ap.add_argument('--workers', type=int, default=8); ap.add_argument('--check-literal', type=int, default=1); a = ap.parse_args()
+sys.path.insert(0, a.toolkit)
+import harness as H, bounds
+P = None
+def init():
+    global P; P = bounds.pricer(H)(a.word, check_literal=bool(a.check_literal), interval=True)
+def run(m):
+    r = P.price(m['ed'], timeout=300)
+    if resource.getrusage(resource.RUSAGE_SELF).ru_maxrss / 1024 ** 3 > 8: r['rss_exit'] = True
+    return dict({k: v for k, v in m.items() if k != 'ed'}, ed=m['ed'], price=r)
+if __name__ == '__main__':
+    cen = json.load(open(a.census)); ms = [m for r in cen for m in r['matches']]
+    t0 = time.time(); init(); print('base cost', P.base_cost, 'profile', P.base_profile, 'interval width', bounds.up(P.base_interval['width_units']), f'{time.time()-t0:.1f}s', flush=True)
+    out = []
+    with mp.get_context('fork').Pool(a.workers, initializer=init, maxtasksperchild=6) as pool:
+        for n, r in enumerate(pool.imap_unordered(run, ms), 1):
+            out.append(r); p = r['price']
+            print(f"  {n}/{len(ms)} {time.time()-t0:.0f}s pivot {r['pivot']} h {r['helper']} donor {r['donor']} -> {p.get('status')} delta {p.get('delta')} {p.get('profile')}", flush=True)
+    out.sort(key=lambda r: (r['pivot'], r['helper'], r['donor'], r['cut'], r['hook']))
+    json.dump(out, open(a.out, 'w'), sort_keys=True)
+    g = sorted([r for r in out if r['price'].get('delta') is not None and r['price']['delta'] < 0], key=lambda r: r['price']['delta'])
+    print('priced', len(out), 'gains', len(g), 'pivots with gains', sorted({r['pivot'] for r in g}))
+    for r in g[:40]: print('   gain', r['pivot'], r['helper'], r['donor'], r['price']['delta'], r['price']['profile'])
diff --git a/research/frontier1305-kernel-census/regenerate.py b/research/frontier1305-kernel-census/regenerate.py
new file mode 100644
index 0000000000..4a296bf604
--- /dev/null
+++ b/research/frontier1305-kernel-census/regenerate.py
@@ -0,0 +1,53 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Rebuild every evidence file into a new directory and compare it byte-for-byte with evidence/.
+
+Stages: census.py (standard library) for both #1297/#1305 final words with both restoration rules and for the #1297
+input word (positive control); price.py, deletion.py and retime.py with the #1186 exact frame harness; optionally
+idle_optimum.py on a completed #1305 verify run.  Cost weights use IMB_B = 0.001679979627113687, the certified complex
+lower endpoint of #1305's profile (kappa itself is never taken from these weights).
+
+The toolkit must be PR #1186 revision 3 (head c37dfb07): its MANIFEST.json and every file it lists are checked first.
+Revision 3 changed only the toolkit's portability layer; frames.py and the pricing and interval code are revision 2's.
+
+usage: python3 -B regenerate.py --toolkit <PR #1186 checkout at c37dfb07>/research/exact-frame-toolkit --out NEW_DIR [--workers 12]
+       [--idle-run <#1305 verify work dir> --idle-owners <#1305 package>/OWNERS.json.gz]
+"""
+import argparse, filecmp, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+PKG = Path(__file__).resolve().parent
+if not __debug__:
+    raise SystemExit('regenerate.py: run without -O; its assert statements are the pin and exit-code checks')
+TOOLKIT = dict(pr=1186, head='c37dfb077ad77ef391cefa56c98db87a40b7e28c', tree='389ebe11c44f6aa58fd026d84ebfa79d4afe69be',
+               manifest_sha256='658331a6f03d1ca4eb0ae7f186b0da2aa694d70619af3c83a77e051cca85fd8e')
+IMB_B = '0.001679979627113687'
+WORDS = dict(base=PKG / 'inputs/BASE-WORD.json.gz', extra=PKG / 'inputs/EXTRA-WORD.json.gz', control=PKG / 'inputs/CONTROL-WORD.json.gz')
+ap = argparse.ArgumentParser(); ap.add_argument('--toolkit', type=Path, required=True); ap.add_argument('--out', type=Path, required=True)
+ap.add_argument('--workers', type=int, default=12); ap.add_argument('--idle-run', type=Path); ap.add_argument('--idle-owners', type=Path)
+a = ap.parse_args(); out = a.out.resolve(); assert not out.exists(), 'output directory must be new'; out.mkdir(parents=True)
+env = dict(os.environ, IMB_B=IMB_B, IMB_ROOT=str(PKG.parents[1]), PYTHONDONTWRITEBYTECODE='1')   # the toolkit reads vendored PR551 gk modules from this checkout
+env.pop('PYTHONOPTIMIZE', None)
+def run(*args):
+    t0 = time.time(); log = out / 'regenerate.log'
+    with log.open('a') as f:
+        f.write('$ ' + ' '.join(map(str, args)) + '\n'); f.flush()
+        rc = subprocess.run([sys.executable, '-B', *map(str, args)], env=env, stdout=f, stderr=subprocess.STDOUT).returncode
+    assert rc == 0, (args, log.read_text()[-3000:]); print('PASS', Path(args[0]).name, Path(str(args[-1])).name if not str(args[-1]).startswith('-') else '', f'{time.time()-t0:.0f}s', flush=True)
+W = str(a.workers); T = a.toolkit.resolve()
+sha = lambda p: hashlib.sha256(Path(p).read_bytes()).hexdigest()
+assert sha(T / 'MANIFEST.json') == TOOLKIT['manifest_sha256'], 'toolkit is not PR #1186 revision 3 (MANIFEST.json differs)'
+for name, h in json.loads((T / 'MANIFEST.json').read_text()).items(): assert sha(T / name) == h, ('toolkit file drift', name)
+for w in ('base', 'extra'):
+    for rule in ('tail', 'first'):
+        run(PKG / 'census.py', WORDS[w], out / f'CENSUS-{w}-{rule}.json', '--workers', W, '--restore', rule)
+        run(PKG / 'price.py', T, WORDS[w], out / f'CENSUS-{w}-{rule}.json', out / f'PRICES-{w}-{rule}.json', '--workers', W)
+    run(PKG / 'deletion.py', T, WORDS[w], out / f'DELETION-{w}.json', '--workers', W)
+    run(PKG / 'retime.py', T, WORDS[w], out / f'DELETION-{w}.json', out / f'RETIME-{w}.json', '--workers', W)
+run(PKG / 'census.py', WORDS['control'], out / 'CENSUS-control-tail.json', '--workers', W, '--pivots', '555', '567')
+run(PKG / 'price.py', T, WORDS['control'], out / 'CENSUS-control-tail.json', out / 'PRICES-control-tail.json', '--workers', W)
+run(PKG / 'deletion.py', T, WORDS['control'], out / 'DELETION-control.json', '--workers', W, '--pivots', '555', '567')
+if a.idle_run:
+    run(PKG / 'idle_optimum.py', a.idle_run.resolve() / 'strict/global', a.idle_owners.resolve(), out / 'IDLE-OPTIMUM-1305.json')
+names = sorted(p.name for p in out.glob('*.json'))
+same = [n for n in names if (PKG / 'evidence' / n).exists() and filecmp.cmp(out / n, PKG / 'evidence' / n, shallow=False)]
+print('identical to evidence/:', len(same), 'of', len(names)); [print('  DIFFERS or new:', n) for n in names if n not in same]
diff --git a/research/frontier1305-kernel-census/retime.py b/research/frontier1305-kernel-census/retime.py
new file mode 100644
index 0000000000..65442abf59
--- /dev/null
+++ b/research/frontier1305-kernel-census/retime.py
@@ -0,0 +1,51 @@
+"""retime.py: exact re-timing of early pivot reads.  An early read g_j = (t += c*q) at B position j < first(q) may move to
+any position p in (j, first(q)] such that no B gate in (j, p) reads t or scales t (t's suffix effect is then unchanged) and
+q is still unwritten (its value is the initial one), so the program map is unchanged exactly.  Prices (PR #1186 revision 2
+harness, surrogate-optimal frames and true-moment interval bounds, bounds.py): every single move to the segment end and
+to every intermediate slot; then, per pivot, the joint move of all its early reads to their segment ends.
+usage: retime.py TOOLKIT WORD ORACLE.json OUT.json [--top N] [--workers N]"""
+import argparse, json, sys, time, multiprocessing as mp
+ap = argparse.ArgumentParser(); ap.add_argument('toolkit'); ap.add_argument('word'); ap.add_argument('oracle'); ap.add_argument('out')
+ap.add_argument('--top', type=int, default=160); ap.add_argument('--workers', type=int, default=14); a = ap.parse_args()
+sys.path.insert(0, a.toolkit)
+import harness as H, bounds
+P = None
+def init():
+    global P; P = bounds.pricer(H)(a.word, check_literal=True, interval=True)
+def segment_end(B, j, q, first):
+    t = B[j][1]; p = j + 1
+    while p < first:
+        g = B[p]
+        if (g[0] == 'add' and g[2] == t) or (g[0] == 'scale' and g[1] == t) or (g[0] == 'add' and g[1] == q) or (g[0] == 'scale' and g[1] == q): break
+        p += 1
+    return p   # insert before base index p (exclusive end); p == j+1 means no room
+def run(job):
+    kind, q, moves = job
+    ed = dict(delete=[j for j, p in moves], insert=[[p, list(P.base['B'][j][:-1]) + [[]]] for j, p in moves])
+    r = P.price(ed, timeout=300)
+    extra = {k: r[k] for k in ('realized_delta_units', 'gain_certified', 'max_gain_units_ceil', 'interval_width_units_ceil', 'audit') if k in r}
+    return dict(kind=kind, pivot=q, moves=moves, status=r.get('status'), delta=r.get('delta'), profile=r.get('profile'), **extra)
+if __name__ == '__main__':
+    init(); B = P.base['B']; ora = [r for r in json.load(open(a.oracle)) if r.get('delta') is not None and r['delta'] < 0][:a.top]
+    jobs = []
+    for r in ora:
+        q = r['pivot']; first = next((i for i, g in enumerate(B) if g[1] == q), len(B))
+        dele = [i for i in range(first) if B[i][0] == 'add' and B[i][2] == q]
+        ends = []
+        for j in dele:
+            e = segment_end(B, j, q, first)
+            if e > j + 1:
+                ends.append((j, e))
+                for p in sorted({j + 2, (j + e) // 2, e}):
+                    if j + 1 < p <= e: jobs.append(('single', q, [(j, p)]))
+        if len(ends) > 1: jobs.append(('joint-end', q, ends))
+    print('pivots', len(ora), 'jobs', len(jobs), flush=True); out = []; t0 = time.time()
+    with mp.get_context('fork').Pool(a.workers, initializer=init, maxtasksperchild=12) as pool:
+        for n, r in enumerate(pool.imap_unordered(run, jobs), 1):
+            out.append(r)
+            if r['delta'] is not None and r['delta'] < 0: print('  GAIN', r, flush=True)
+            if n % 100 == 0: print(f'  {n}/{len(jobs)} {time.time()-t0:.0f}s', flush=True)
+    out.sort(key=lambda r: (r['pivot'], r['kind'], r['moves']))
+    json.dump(out, open(a.out, 'w'), sort_keys=True)
+    import collections
+    print('done', len(out), collections.Counter((r['status'], (r['delta'] > 0) - (r['delta'] < 0) if r['delta'] is not None else None) for r in out))
diff --git a/research/frontier1305-kernel-census/verify.py b/research/frontier1305-kernel-census/verify.py
new file mode 100644
index 0000000000..c150173403
--- /dev/null
+++ b/research/frontier1305-kernel-census/verify.py
@@ -0,0 +1,140 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Standard-library replay of the #1297/#1305 helper-donor kernel census (no new kappa).
+
+Checks:
+  1. inputs: SHA256 and Git blob ids of the three vendored words equal inputs/PINS.json (the #1297/#1305 blobs);
+  2. census replay: census.py (exact rational two-shock relations, both restoration rules) is rerun on both final words
+     and on the control word; every result equals evidence/CENSUS-*.json exactly;
+  3. binding: every record of evidence/PRICES-*.json is exactly one census match, and every match is priced once;
+  4. tallies: PRICES, RETIME, DELETION and IDLE-OPTIMUM evidence recount to RESULT.json; no priced or re-timed
+     candidate has a negative delta (no gain);
+  5. positive control: on #1297's input word the census reproduces #1297's five hooks for each of pivots 555 and 567
+     (including its committed donors 620 and 628), each priced at the realized kernel gain -11707 (H1 -3, H3 +1);
+  6. true-moment bounds (revision 2): every priced or re-timed candidate with a surrogate optimum carries PR #1186
+     revision 2's interval bounds, and none of them can lower the per-call moment at b by more than the bound declared in
+     RESULT.json (max_gain_units_ceil, rounded up from exact rationals);
+  7. failure controls: a one-byte input change, a changed early-read coefficient, a forged negative price, a priced edit
+     absent from the census and a forged true-gain bound are each rejected at the intended check.
+Coverage: this script recounts and binds the stored evidence; it does not rerun the frame optimization or the interval
+certificates.  regenerate.py reruns every price with PR #1186 revision 3 and compares the evidence byte for byte.
+"""
+import collections, copy, gzip, hashlib, json, sys
+from fractions import Fraction
+from pathlib import Path
+if not __debug__:
+    raise SystemExit('verify.py: assertions are the checks; do not run with -O')
+PKG = Path(__file__).resolve().parent
+sys.path.insert(0, str(PKG))
+import census  # noqa: E402
+EV = PKG / 'evidence'
+rd = lambda p: json.loads(Path(p).read_text())
+canon = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':'))
+def blob(b): return hashlib.sha1(b'blob %d\0' % len(b) + b).hexdigest()
+
+def check_pins(raw):
+    pins = rd(PKG / 'inputs/PINS.json')['files']
+    for name, pin in pins.items():
+        b = raw[name]
+        assert hashlib.sha256(b).hexdigest() == pin['sha256'], 'input pin: ' + name
+        assert blob(b) == pin['git_blob'], 'input git blob: ' + name
+    return pins
+
+def pivots(w):
+    B = w['B']; first = {}
+    for i, g in enumerate(B): first.setdefault(g[1], i)
+    return sorted({g[2] for i, g in enumerate(B) if g[0] == 'add' and g[2] >= 224 and i < first.get(g[2], len(B))})
+
+def run_census(word_json, restore, only=None):
+    census.W = word_json; census.RESTORE = restore
+    return json.loads(canon(sorted((census.relations(q) for q in (only or pivots(word_json))), key=lambda r: r['pivot'])))
+
+def match_key(m): return canon({k: v for k, v in m.items() if k != 'price'})
+
+def check_binding(cen, priced):
+    a = collections.Counter(match_key(m) for r in cen for m in r['matches'])
+    b = collections.Counter(match_key(m) for m in priced)
+    assert a == b, 'priced records must be exactly the census matches'
+
+def tally(records, key):
+    return dict(sorted(collections.Counter(key(r) for r in records).items()))
+
+def price_key(r): return '%s:%s' % (r['price']['status'], r['price'].get('delta'))
+
+def check_no_gain(priced, label):
+    assert all(r['price'].get('delta') is None or r['price']['delta'] >= 0 for r in priced), 'negative price in ' + label
+
+BOUND_FIELDS = ('realized_delta_units', 'gain_certified', 'max_gain_units_ceil', 'interval_width_units_ceil')
+def check_bounds(records, get, label, declared):
+    """every candidate with a surrogate optimum carries the interval bounds; returns (bounded, largest possible true gain)."""
+    worst = Fraction(0); n = 0
+    for r in records:
+        p = get(r)
+        if p.get('status') not in ('ok', 'uncertified'): continue
+        assert all(k in p for k in BOUND_FIELDS), 'missing interval bounds in ' + label
+        if p['delta'] < 0: continue
+        g = Fraction(p['max_gain_units_ceil']); n += 1; worst = max(worst, g)
+        assert g <= declared, 'possible true gain above the declared bound in ' + label
+    return n, worst
+
+def main():
+    res = rd(PKG / 'RESULT.json'); raw = {n: (PKG / 'inputs' / n).read_bytes() for n in ('BASE-WORD.json.gz', 'EXTRA-WORD.json.gz', 'CONTROL-WORD.json.gz')}
+    check_pins(raw)
+    words = {k: json.loads(gzip.decompress(raw[f])) for k, f in (('base', 'BASE-WORD.json.gz'), ('extra', 'EXTRA-WORD.json.gz'), ('control', 'CONTROL-WORD.json.gz'))}
+    out = dict(census={}, prices={}, retime={}, deletion={}, intervals={})
+    declared = Fraction(res['true_moment_bound']['max_gain_units_ceil'])
+    def bound(name, n_worst):
+        n = n_worst[1] * 10 ** 6; assert n.denominator == 1
+        out['intervals'][name] = dict(bounded=n_worst[0], max_gain_units_ceil=f'{n.numerator // 10 ** 6}.{n.numerator % 10 ** 6:06d}')
+    for w in ('base', 'extra'):
+        for rule in ('tail', 'first'):
+            name = f'{w}-{rule}'; cen = run_census(words[w], rule)
+            assert cen == rd(EV / f'CENSUS-{name}.json'), 'census replay differs: ' + name
+            priced = rd(EV / f'PRICES-{name}.json'); check_binding(cen, priced); check_no_gain(priced, name)
+            out['census'][name] = dict(pivots=len(cen), with_matches=sum(1 for r in cen if r['matches']), matches=sum(len(r['matches']) for r in cen))
+            out['prices'][name] = tally(priced, price_key)
+            bound('prices-' + name, check_bounds(priced, lambda r: r['price'], name, declared))
+        rt = rd(EV / f'RETIME-{w}.json'); assert all(r['delta'] is None or r['delta'] >= 0 for r in rt), 'negative re-timing price'
+        out['retime'][w] = tally(rt, lambda r: '%s:%s' % (r['status'], r['delta']))
+        bound('retime-' + w, check_bounds(rt, lambda r: r, 'retime-' + w, declared))
+        dl = rd(EV / f'DELETION-{w}.json')
+        out['deletion'][w] = dict(statuses=tally(dl, lambda r: r['status']), negative=sum(1 for r in dl if r.get('delta') is not None and r['delta'] < 0))
+    cen = run_census(words['control'], 'tail', [555, 567]); assert cen == rd(EV / 'CENSUS-control-tail.json'), 'control census replay differs'
+    priced = rd(EV / 'PRICES-control-tail.json'); check_binding(cen, priced)
+    by = {r['pivot']: r['matches'] for r in cen}
+    assert [len(by[555]), len(by[567])] == [5, 5] and 620 in {m['donor'] for m in by[555]} and 628 in {m['donor'] for m in by[567]}, 'control hooks'
+    assert {m['helper'] for m in by[555]} == {383} and {m['helper'] for m in by[567]} == {399}, 'control partners'
+    assert all({k: r['price'][k] for k in ('status', 'delta', 'profile')} == dict(status='ok', delta=-11707, profile={'1': 2349, '2': 504, '3': 413, '4': 130, '5': 82})
+               and r['price']['audit'] is True and r['price']['gain_certified'] is True for r in priced), 'control prices'
+    true = sorted({tuple(r['price']['realized_delta_units']) for r in priced}); assert len(true) == 1 and true[0][1] < 0, 'control true delta'
+    out['control'] = dict(matches=len(priced), delta=-11707, true_delta_units=list(true[0]), audit_local=True,
+                          deletion=[r['status'] for r in rd(EV / 'DELETION-control.json')])
+    idle = rd(EV / 'IDLE-OPTIMUM-1305.json')
+    assert idle['status'] == 'PASS_1305_IDLE_SELECTION_EQUALS_EXACT_GROUP_OPTIMUM' and idle['improvable_groups'] == 0
+    assert all(s['current'] == s['optimum'] for s in idle['shapes']) and sum(s['groups'] for s in idle['shapes']) == idle['groups']
+    out['idle'] = {k: idle[k] for k in ('eligible', 'groups', 'group_sizes', 'improvable_groups', 'donors', 'receivers')}
+    assert out == res['tallies'], 'evidence tallies differ from RESULT.json'
+    # failure controls
+    rejected = {}
+    def expect(fn, needle, label):
+        try: fn()
+        except AssertionError as e:
+            assert needle in str(e), (label, str(e)); rejected[label] = str(e); return
+        raise AssertionError('control accepted: ' + label)
+    bad = dict(raw); b = bytearray(bad['BASE-WORD.json.gz']); b[-5] ^= 1; bad['BASE-WORD.json.gz'] = bytes(b)
+    expect(lambda: check_pins(bad), 'input pin', 'one-byte input change')
+    w2 = copy.deepcopy(words['control']); first = next(i for i, g in enumerate(w2['B']) if g[1] == 555)
+    j = next(i for i in range(first) if w2['B'][i][0] == 'add' and w2['B'][i][2] == 555); w2['B'][j][3] *= 3
+    def mutated():
+        assert run_census(w2, 'tail', [555]) == [r for r in rd(EV / 'CENSUS-control-tail.json') if r['pivot'] == 555], 'census replay differs: mutated coefficient'
+    expect(mutated, 'census replay differs', 'changed early-read coefficient')
+    forged = copy.deepcopy(rd(EV / 'PRICES-base-tail.json')); next(r for r in forged if r['price']['status'] == 'ok')['price']['delta'] = -1
+    expect(lambda: check_no_gain(forged, 'forged'), 'negative price', 'forged negative price')
+    moved = copy.deepcopy(rd(EV / 'PRICES-base-tail.json')); moved[0]['ed']['insert'][2][0] += 1
+    expect(lambda: check_binding(rd(EV / 'CENSUS-base-tail.json'), moved), 'exactly the census matches', 'priced edit absent from census')
+    loose = copy.deepcopy(rd(EV / 'RETIME-base.json')); next(r for r in loose if r['status'] == 'ok')['max_gain_units_ceil'] = '1.000000'
+    expect(lambda: check_bounds(loose, lambda r: r, 'forged', declared), 'above the declared bound', 'forged true-gain bound')
+    print(json.dumps(dict(status='PASS_FRONTIER1305_KERNEL_CENSUS_NO_GAIN', tallies=out, controls_rejected=sorted(rejected)), indent=2))
+
+if __name__ == '__main__':
+    main()