diff --git a/Makefile b/Makefile
index 66f00cfb30..7571b3fcd8 100644
--- a/Makefile
+++ b/Makefile
@@ -604,3 +604,10 @@ frontier890-verify: selected-record-check
 frontier942-verify: selected-record-check
 	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-frontier942.XXXXXX"); \
 	python3 -B scripts/verify_frontier942.py --work "$$work/replay"
+
+# Research note: restoration deferral and coverage identity on the selected T37 payload (no new kappa).
+.PHONY: t37-restoration-deferral-verify
+t37-restoration-deferral-verify:
+	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-t37-restoration.XXXXXX"); \
+	python3 -B research/t37-restoration-deferral/verify.py --work "$$work/replay" && \
+	python3 -B -m unittest discover -s research/t37-restoration-deferral -p test_package.py
diff --git a/research/t37-restoration-deferral/CENSUS.json b/research/t37-restoration-deferral/CENSUS.json
new file mode 100644
index 0000000000..5bfebfb18b
--- /dev/null
+++ b/research/t37-restoration-deferral/CENSUS.json
@@ -0,0 +1,4544 @@
+{
+ "T21": {
+  "construction": "T21",
+  "coverage": {
+   "R": 504,
+   "calls": 189,
+   "coverage_values": {
+    "73": 18816
+   },
+   "data_coordinates": 357504,
+   "data_incidences_per_family": {
+    "2": 14112,
+    "3": 4704
+   },
+   "deficit": 6720,
+   "hosted_coordinates": 714042,
+   "idle_coordinates": 302022,
+   "live": 18816,
+   "m": 73,
+   "private_centre_families": [
+    18816,
+    18824
+   ],
+   "total_rank_mass": 1366848,
+   "v": 112
+  },
+  "identity": {
+   "calls": 189,
+   "deficit": 6720,
+   "live": 18816,
+   "rank_mass": 1366848,
+   "statement": "data_climb*k_f + 1 + hosted_f + idle_f = m for every live family f; rank mass = (m-1)*W + 64*N; deficit = W - 64*N"
+  }
+ },
+ "T37": {
+  "construction": "T37",
+  "coverage": {
+   "R": 504,
+   "calls": 333,
+   "coverage_values": {
+    "73": 33152
+   },
+   "data_coordinates": 629888,
+   "data_incidences_per_family": {
+    "2": 24864,
+    "3": 8288
+   },
+   "deficit": 11840,
+   "hosted_coordinates": 1258074,
+   "idle_coordinates": 532134,
+   "live": 33152,
+   "m": 73,
+   "private_centre_families": [
+    33152,
+    33160
+   ],
+   "total_rank_mass": 2408256,
+   "v": 112
+  },
+  "emitted_programs": {
+   "backward": {
+    "final_climbs": {
+     "1": 350,
+     "2": 18,
+     "3": 64,
+     "4": 2,
+     "5": 56
+    },
+    "phases": [
+     "zero_frame_precondition",
+     "entry_adapters",
+     "A",
+     "centers",
+     "B",
+     "cleanup_tail",
+     "final",
+     "exit_adapters",
+     "full_frame_cleanup",
+     "done"
+    ]
+   },
+   "forward": {
+    "final_climbs": {
+     "1": 350,
+     "2": 18,
+     "3": 64,
+     "4": 2,
+     "5": 56
+    },
+    "phases": [
+     "zero_frame_precondition",
+     "entry_adapters",
+     "A",
+     "centers",
+     "B",
+     "cleanup_tail",
+     "final",
+     "exit_adapters",
+     "full_frame_cleanup",
+     "done"
+    ]
+   }
+  },
+  "global_profile": {
+   "1": 848490,
+   "2": 112554,
+   "3": 148518,
+   "4": 53946,
+   "48": 11086,
+   "5": 23976,
+   "8": 2664
+  },
+  "identity": {
+   "calls": 333,
+   "deficit": 11840,
+   "live": 33152,
+   "rank_mass": 2408256,
+   "statement": "data_climb*k_f + 1 + hosted_f + idle_f = m for every live family f; rank mass = (m-1)*W + 64*N; deficit = W - 64*N"
+  },
+  "index_binding": {
+   "helper_restoration_by_index": "native word = canonical provider word bound by the template",
+   "helper_widths_by_index": "native word = hosted template provider (504 helpers)",
+   "source_restoration": "equal as a multiset (sources are relabelled in the canonical word)"
+  },
+  "local": {
+   "R": 504,
+   "centre_children": {
+    "8": 8
+   },
+   "data_climb_per_incidence": 8,
+   "h": 9,
+   "mass": 5634,
+   "phase_mass": {
+    "A": 1160,
+    "B": 3288,
+    "early_cleanup": 256,
+    "final": 866
+   },
+   "profile": {
+    "1": 2548,
+    "2": 338,
+    "3": 446,
+    "4": 162,
+    "5": 72,
+    "8": 8
+   },
+   "roles": {
+    "helper": {
+     "full_cleanup_gates_on_positive_restoration": 8492,
+     "paid_endpoint_mass": 3778,
+     "positive_restoration": 378,
+     "positive_restoration_touched_by_full_cleanup": 378,
+     "registers": 504,
+     "restoration_mass": 636,
+     "restoration_profile": {
+      "1": 272,
+      "2": 12,
+      "3": 64,
+      "4": 2,
+      "5": 28
+     },
+     "zero_restoration_low_ends": 126
+    },
+    "source": {
+     "full_cleanup_gates_on_positive_restoration": 3618,
+     "paid_endpoint_mass": 896,
+     "positive_restoration": 112,
+     "positive_restoration_touched_by_full_cleanup": 112,
+     "registers": 112,
+     "restoration_mass": 230,
+     "restoration_profile": {
+      "1": 78,
+      "2": 6,
+      "5": 28
+     },
+     "zero_restoration_low_ends": 0
+    },
+    "target": {
+     "full_cleanup_gates_on_positive_restoration": 0,
+     "paid_endpoint_mass": 896,
+     "positive_restoration": 0,
+     "positive_restoration_touched_by_full_cleanup": 0,
+     "registers": 112,
+     "restoration_mass": 0,
+     "restoration_profile": {},
+     "zero_restoration_low_ends": 0
+    }
+   },
+   "v": 112
+  }
+ },
+ "base_commit": "bbc600db2fc15007b7c914f4f2b2ed55fa909c87",
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+   "15": 12,
+   "2": 112554,
+   "20": 9,
+   "3": 148518,
+   "4": 53946,
+   "48": 11086,
+   "5": 23828,
+   "8": 2664
+  },
+  "91": {
+   "1": 848418,
+   "2": 112573,
+   "3": 148524,
+   "4": 53950,
+   "48": 11086,
+   "5": 23976,
+   "8": 2664
+  },
+  "92": {
+   "1": 848418,
+   "2": 112573,
+   "3": 148524,
+   "4": 53950,
+   "48": 11086,
+   "5": 23976,
+   "8": 2664
+  },
+  "93": {
+   "1": 848490,
+   "10": 19,
+   "15": 10,
+   "2": 112554,
+   "3": 148518,
+   "4": 53946,
+   "48": 11086,
+   "5": 23908,
+   "8": 2664
+  },
+  "94": {
+   "1": 848422,
+   "2": 112573,
+   "3": 148528,
+   "4": 53946,
+   "48": 11086,
+   "5": 23976,
+   "8": 2664
+  },
+  "95": {
+   "1": 848490,
+   "2": 112486,
+   "3": 148518,
+   "4": 53965,
+   "48": 11086,
+   "5": 23976,
+   "6": 10,
+   "8": 2664
+  },
+  "96": {
+   "1": 848422,
+   "2": 112573,
+   "3": 148528,
+   "4": 53946,
+   "48": 11086,
+   "5": 23976,
+   "8": 2664
+  },
+  "98": {
+   "1": 848422,
+   "2": 112573,
+   "3": 148528,
+   "4": 53946,
+   "48": 11086,
+   "5": 23976,
+   "8": 2664
+  }
+ },
+ "single_helper_unchanged": [
+  395,
+  397,
+  398,
+  399,
+  443,
+  445,
+  446,
+  447,
+  459,
+  461,
+  462,
+  463,
+  467,
+  469,
+  470,
+  471,
+  475,
+  477,
+  478,
+  479,
+  483,
+  485,
+  486,
+  487,
+  491,
+  493,
+  494,
+  495,
+  499,
+  501,
+  502,
+  503
+ ],
+ "status": "PASS_T37_RESTORATION_CENSUS"
+}
diff --git a/research/t37-restoration-deferral/CLAIM.json b/research/t37-restoration-deferral/CLAIM.json
new file mode 100644
index 0000000000..4426a5c947
--- /dev/null
+++ b/research/t37-restoration-deferral/CLAIM.json
@@ -0,0 +1,43 @@
+{
+ "ai_assistance": "substantial: Claude (Anthropic) via Claude Code",
+ "assignment_seed": 57,
+ "base_commit": "bbc600db2fc15007b7c914f4f2b2ed55fa909c87",
+ "claims": [
+  "Coverage identity on the selected T37 payload: 8*k_f + 1 + hosted_f + idle_f = 73 for all 33152 live families (and all 18816 T21 families); hence rank mass = 72W + 64N and deficit = W - 64N.",
+  "Every positive U8 helper restoration climb (378 helpers, 636 mass) belongs to a register touched by the full-frame inverse cleanup and equals, index by index, the canonical provider word bound by the template; the 112 sources (230 mass) have full endpoints fixed by the data contract. Both emitted programs have 490 final climbs with exactly the replay rank multiset, before full_frame_cleanup.",
+  "Restoration deferral is rank-mass neutral; under the selected owner map deferring all helper restoration gives at most kappa = 0.001708640379500299; under free concentration the PR589 bit side binds at 0.001730427469823602.",
+  "The best single helper index gives 0.001662126446464193; as a relaxation that no re-hosting realizes, one rank-one climb per call merged into a rank-48 idle child gives at most 0.001662339932746932, versus 0.001708820303553035 for a PR974-style zero-cost deletion that leaves live coordinates unadvanced."
+ ],
+ "contributor": "Sagar Thakrar (thakrarsagar)",
+ "deficit_T21": 6720,
+ "deficit_T37": 11840,
+ "expected_last_line": "PASS_T37_RESTORATION_DEFERRAL_REPLAY",
+ "kappa_rows": {
+  "baseline": "1661960547713947/1000000000000000000",
+  "baseline_free_concentration": "41549076555561/25000000000000000",
+  "defer_all_free_concentration": "865213734911801/500000000000000000",
+  "defer_all_selected_hosting": "1708640379500299/1000000000000000000",
+  "exchange_merge_rank1_into_48": "415584983186733/250000000000000000",
+  "zero_cost_delete_rank1": "341764060710607/200000000000000000"
+ },
+ "license": "Apache-2.0",
+ "mechanism": "restoration deferral: a helper ends at its pre-restoration frame; its host coordinates return to the same hosting window and are advanced by that window's idle child",
+ "not_claimed": [
+  "a construction or admitted word",
+  "a new selected kappa",
+  "validity of any low end, cleanup retiming, phase recipe, hosting admission or invoice for the deferred helpers",
+  "a lower bound for any mechanism",
+  "a proof of the inherited all-size, realization, hosting, precision/tape, analytic or bit H1-H5 assumptions"
+ ],
+ "rebased_and_reverified_on": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+ "reproduce": "make t37-restoration-deferral-verify",
+ "results": {
+  "census": "CENSUS.json",
+  "prices": "PRICES.json"
+ },
+ "review": "Independent adversarial review (AI-assisted subagent) of commit 2a4480a4: no blocking issues; should-fix items addressed in the follow-up commit.",
+ "seed_source": "Python secrets (OS CSPRNG)",
+ "selected_kappa_unchanged": "1661960547713947/1000000000000000000",
+ "status": "research note / scoped negative result; no new kappa",
+ "track": "50-59 recursive interfaces"
+}
diff --git a/research/t37-restoration-deferral/PRICES.json b/research/t37-restoration-deferral/PRICES.json
new file mode 100644
index 0000000000..01662906fc
--- /dev/null
+++ b/research/t37-restoration-deferral/PRICES.json
@@ -0,0 +1,140 @@
+{
+ "base_commit": "bbc600db2fc15007b7c914f4f2b2ed55fa909c87",
+ "bit_lower": "1733427039589844234749/1000000000000000000000000",
+ "engines": {
+  "base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+ },
+ "scenarios": {
+  "baseline": {
+   "binding": "complex",
+   "complex_decimal": "0.001664727258740678855772",
+   "complex_lower": "416181814685169713943/250000000000000000000000",
+   "kappa": "1661960547713947/1000000000000000000",
+   "kappa_decimal": "0.001661960547713947",
+   "kappa_gain": "0",
+   "kappa_gain_percent": "0",
+   "rank_mass": 2408256,
+   "rank_mass_neutral": true,
+   "realizable_in_selected_windows": true
+  },
+  "baseline_free_concentration": {
+   "binding": "complex",
+   "complex_decimal": "0.001664729781628087931514",
+   "complex_lower": "832364890814043965757/500000000000000000000000",
+   "kappa": "41549076555561/25000000000000000",
+   "kappa_decimal": "0.00166196306222244",
+   "kappa_gain": "2.514508493E-9",
+   "kappa_gain_percent": "0.000151297724634",
+   "rank_mass": 2408256,
+   "rank_mass_neutral": true,
+   "realizable_in_selected_windows": false
+  },
+  "defer_all_free_concentration": {
+   "binding": "bit",
+   "complex_decimal": "0.001836621859873056285676",
+   "complex_lower": "459155464968264071419/250000000000000000000000",
+   "kappa": "865213734911801/500000000000000000",
+   "kappa_decimal": "0.001730427469823602",
+   "kappa_gain": "0.000068466922109655",
+   "kappa_gain_percent": "4.11964785830",
+   "rank_mass": 2408256,
+   "rank_mass_neutral": true,
+   "realizable_in_selected_windows": false
+  },
+  "defer_all_selected_hosting": {
+   "binding": "complex",
+   "complex_decimal": "0.001711564828278027772823",
+   "complex_lower": "1711564828278027772823/1000000000000000000000000",
+   "kappa": "1708640379500299/1000000000000000000",
+   "kappa_decimal": "0.001708640379500299",
+   "kappa_gain": "0.000046679831786352",
+   "kappa_gain_percent": "2.80872081173",
+   "rank_mass": 2408256,
+   "rank_mass_neutral": true,
+   "realizable_in_selected_windows": true
+  },
+  "exchange_merge_rank1_into_48": {
+   "binding": "complex",
+   "complex_decimal": "0.001665107908114924955942",
+   "complex_lower": "832553954057462477971/500000000000000000000000",
+   "kappa": "415584983186733/250000000000000000",
+   "kappa_decimal": "0.001662339932746932",
+   "kappa_gain": "3.79385032985E-7",
+   "kappa_gain_percent": "0.0228275595054",
+   "rank_mass": 2408256,
+   "rank_mass_neutral": true,
+   "realizable_in_selected_windows": false
+  },
+  "zero_cost_delete_rank1": {
+   "binding": "complex",
+   "complex_decimal": "0.001711745368793742811272",
+   "complex_lower": "213968171099217851409/125000000000000000000000",
+   "kappa": "341764060710607/200000000000000000",
+   "kappa_decimal": "0.001708820303553035",
+   "kappa_gain": "0.000046859755839088",
+   "kappa_gain_percent": "2.81954682399",
+   "rank_mass": 2407923,
+   "rank_mass_neutral": false,
+   "realizable_in_selected_windows": false
+  }
+ },
+ "single_helper_deferral": {
+  "best_complex_lower": "332978742066137137057/200000000000000000000000",
+  "best_helper": 9,
+  "best_kappa": "1662126446464193/1000000000000000000",
+  "best_kappa_decimal": "0.001662126446464193",
+  "best_kappa_gain": "1.65898750246E-7",
+  "best_kappa_gain_percent": "0.00998211121643",
+  "best_moment_drop_times_mW": "1.187341707397",
+  "changed_profiles": 346,
+  "joint_moment_drop_times_mW": "324.975386392",
+  "ranking": "60-digit Decimal drop of m*W*moment at the baseline endpoint; only the best row is certified exactly",
+  "sum_of_single_moment_drops_times_mW": "53.927087289",
+  "top10": [
+   {
+    "helper": 9,
+    "moment_drop_times_mW": "1.187341707397"
+   },
+   {
+    "helper": 13,
+    "moment_drop_times_mW": "1.077218197256"
+   },
+   {
+    "helper": 29,
+    "moment_drop_times_mW": "1.065634256185"
+   },
+   {
+    "helper": 25,
+    "moment_drop_times_mW": "1.065634256185"
+   },
+   {
+    "helper": 41,
+    "moment_drop_times_mW": "0.936732577323"
+   },
+   {
+    "helper": 45,
+    "moment_drop_times_mW": "0.804946230156"
+   },
+   {
+    "helper": 61,
+    "moment_drop_times_mW": "0.742663529411"
+   },
+   {
+    "helper": 57,
+    "moment_drop_times_mW": "0.742663529411"
+   },
+   {
+    "helper": 77,
+    "moment_drop_times_mW": "0.640019976991"
+   },
+   {
+    "helper": 73,
+    "moment_drop_times_mW": "0.640019976991"
+   }
+  ],
+  "unchanged": 32
+ },
+ "status": "PASS_T37_RESTORATION_PRICES"
+}
diff --git a/research/t37-restoration-deferral/README.md b/research/t37-restoration-deferral/README.md
new file mode 100644
index 0000000000..5602739512
--- /dev/null
+++ b/research/t37-restoration-deferral/README.md
@@ -0,0 +1,202 @@
+# Restoration deferral in the selected T37 complex supplier
+
+**Status: research note and scoped negative result. No new κ; the selected result is unchanged.**
+Track 50–59 (recursive interfaces), assignment seed 57 (OS CSPRNG via Python `secrets`).
+Analysis base `bbc600db2fc15007b7c914f4f2b2ed55fa909c87`, where PR942's T37 record
+(κ = 0.001661960547713947) is selected. Rebased onto `29218749` and re-verified there: the selected
+record is unchanged and all pinned inputs are byte-identical.
+
+## Question
+
+At the end of every U8 invocation, 378 helpers and all 112 sources climb back to the full
+frame. PR974 calls these 866 mass units per call "pure boundary climbs" and prices their
+deletion with zero parent cost. This note prices one explicit way to remove the helper part,
+counting every child the change creates.
+
+**Mechanism (restoration deferral).** A helper ends at the frame it holds before its
+restoration climb, as a low end. The host coordinates that the climb advanced go back to the
+pending set of the same hosting window. That window's idle child then advances them, as in the
+hosting lemma of `research/idle-axis-hosting/PROOF.md` §2. Coordinates returned to one window
+form a single child, merged with any remainder the window already has.
+
+## Findings
+
+1. **Coverage identity (exact, every live family).** On the selected T37 payload, every one of
+   the 33,152 live families satisfies
+
+   ```
+   8·k_f + 1 + hosted_f + idle_f = 73,     k_f ∈ {2, 3} data incidences.
+   ```
+
+   The same holds for all 18,816 families of T21. So rank mass = 72W + 64N, and the deficit is
+   exactly **D = W − 64N** (T37: 33,152 − 64·333 = 11,840; T21: 18,816 − 64·189 = 6,720). This is
+   the per-family form of the per-replica relation `8v − 9C` in Dominik Scholz's
+   `research/larger-gain/geometry`. Outside the eight centre paths, paid mass equals advanced
+   live coordinates family by family: 8 per data incidence, the hosted residual widths and the
+   idle ranks. One coordinate per family is unpaid. The centre paths act on private work
+   families `[W, W+8)`.
+
+2. **The full-frame inverse cleanup consumes every helper restoration climb.** 378 helpers carry
+   636 mass of restoration, with children `{1:272, 2:12, 3:64, 4:2, 5:28}`, and every one of them
+   is touched by a full-frame cleanup gate (8,492 incidences). The other 126 helpers are already
+   low ends with zero restoration, and targets have none. The 112 sources carry another 230; the
+   data contract fixes their full endpoint, and the cleanup also touches them (3,618
+   incidences). Index by index, the helper restoration equals that of the canonical provider
+   word bound by the hosted template. In both emitted programs, the 490 `final` climbs have
+   exactly the replay's rank multiset `{1:350, 2:18, 3:64, 4:2, 5:56}` and run in a phase that
+   precedes `full_frame_cleanup`, with only exit adapters between.
+
+3. **Deferral is mass-neutral, and its whole value is consolidation.** Removing a restoration
+   climb returns the same number of coordinates to an idle child, so total rank mass is
+   unchanged. Only the shape of the profile can move. Deferring one helper index alone changes
+   nothing unless that index recurs in a window: 32 of the 378 indices leave the profile
+   unchanged. The best single index (helper 9, all 333 calls) is worth +0.00998%. The value is
+   strongly superadditive. Single-helper moment drops sum to 53.9 (× mW), while joint deferral
+   drops the moment by 325.0.
+
+4. **Exact ceilings.** The table below uses the pinned engines and the selected outer witness.
+   With the selected owner map, deferring all 636 restoration mass per call is worth at most
+   **κ = 0.001708640379500299 (+2.81%)**. That is about what PR974's model assigns to deleting
+   *one* rank-one child per call. Under ideal re-hosting into capacity-48 windows, the complex
+   side passes the PR589 bit side, and κ stops at the bit cap 0.001730427469823602.
+   As a relaxation, one rank-one climb merged into an existing rank-48 idle child is worth at
+   most about 1/124 of a zero-cost deletion. No re-hosting realizes that merge: every selected
+   window has capacity at most 48, and every rank-48 child already fills a whole idle window.
+
+5. **Source restoration has no deferral target in this template.** A source's restoration
+   coordinates belong to the current invocation level of its own family. In the fixed nine-stage
+   template, no idle window of that family contains them, and later bridges touch the family.
+   This note therefore does not price source deferral. This finding is argued from the
+   template's level structure and is not machine-checked here.
+
+## Exact prices
+
+Every row is certified the same way. Both pinned moment engines accept the complex endpoint b
+and reject b + 10⁻²⁴. All 47 outer inequalities pass at κ, and κ + 10⁻¹⁸ is rejected.
+The bit endpoint is the unchanged PR589 value 0.001733427039589844234749.
+
+| Scenario | Rank-mass neutral | Realizable in selected windows | Complex b | κ | Gain |
+|---|:---:|:---:|---|---|---:|
+| selected baseline (reproduced exactly) | yes | yes | 0.0016647272587406788557 | 0.001661960547713947 | — |
+| baseline under free concentration (relaxation control) | yes | no | 0.0016647297816280879 | 0.001661963062222440 | +0.00015% |
+| defer all helper restoration, selected owner map | yes | yes* | 0.0017115648282780278 | **0.001708640379500299** | +2.809% |
+| same, free concentration into capacity-48 windows | yes | no | 0.0018366218598730563 | 0.001730427469823602 (bit binds) | +4.120% |
+| best single helper index (9), all calls | yes | yes* | 0.0016648937103306857 | 0.001662126446464193 | +0.00998% |
+| one rank-one climb per call into an existing 48-child (48 → 49) | yes | no | 0.0016651079081149250 | 0.001662339932746932 | +0.0228% |
+| PR974-style deletion of one rank-one child per call | **no** | no | 0.0017117453687937428 | 0.001708820303553035 | +2.820% |
+
+\* The window placement is realizable. The local obligations listed below are not attempted.
+
+"Free concentration" places all idle coordinates in children of rank 48. It ignores helper
+indivisibility, window capacities and chronology, so it bounds every re-hosting from above.
+On the unchanged word it moves κ by only +0.00015%, so the selected packing is already
+nearly concentrated. The last row reproduces PR974's T37 value for comparison. It leaves 333
+live coordinates unadvanced, so it does not correspond to any coverage-preserving mechanism.
+
+## What this means for interface work
+
+- In the hosted recursion, helper and source restoration climbs are **coverage-productive
+  work**, not removable boundary overhead. PR974's rows "final helper climbs to FULL", "final
+  source climbs", "all final endpoint climbs", "early cleanup tails", "target delivery climbs"
+  and "all helper width" all delete live advances. A coverage-preserving version has mass value
+  zero and keeps only the shape value priced above.
+- Of PR974's classes, only the **centre path** (64 per call, on private work families) is
+  non-productive. Its existing obstructions are recorded in `research/larger-gain/geometry`.
+  Apart from the centre path, the deficit can grow only through the template, by giving each
+  family more unpaid coordinates or each invocation more families (D = W − 64N).
+- Restoration deferral could still be worth up to +2.81% with the current owner map. Getting
+  there needs most of the 378 helpers deferred **jointly**, because the value comes from
+  merging inside shared windows. Retiming a few helpers at a time is nearly worthless.
+
+## Remaining obligations (none attempted here)
+
+Realizing any part of the ceiling requires all of the following:
+
+1. Retime the full-frame inverse cleanup so that the deferred helpers are never needed at the
+   full frame. PR601 did this with commuting-prefix cleanup for 46 hyperplane-ended helpers per
+   call at the time. PR935's bounded retiming census found no local gain, but it held the final
+   caps fixed, which excludes this mechanism.
+2. Establish low-end validity: inverse-row and dirt-column cone conditions and dirty
+   compensation, as checked in PR881.
+3. Supply exact phase recipes and adapters for the changed word, in both orientations.
+4. Pass hosting-window and owner admission for the changed residual widths.
+5. Recompute the finite invoice and assembly, including prefix bits, row coefficient and
+   idle-child count.
+
+## Scope and limits
+
+- These are exact identities on the frozen payload and exact model prices, **not a construction
+  and not a new κ**. Neither ceiling is a lower bound for any mechanism.
+- The census checks that one coordinate per live family is unpaid. It does not re-derive the
+  route by which the nine-stage template supplies that coordinate.
+- The frame semantics follow `audit_local.py` and PR881's independent checker: monotone nested
+  F₂⁹ frames, one paid child per climb, a centre path at the cut and fixed endpoint frames. The
+  implementation here is new. Scalar maps, compensation and cones are not rechecked.
+- All inherited assumptions of the selected result remain: all-size compilation,
+  common-label/mutable-source realization, whole-call hosting, precision/tape, analytic transfer
+  and the bit H1–H5 interface. This is not a Lean proof of anything.
+
+## Reproduce
+
+```sh
+make t37-restoration-deferral-verify
+```
+
+The same check without make:
+
+```sh
+python3 -B research/t37-restoration-deferral/verify.py --work /new/empty/dir
+python3 -B -m unittest discover -s research/t37-restoration-deferral -p test_package.py -v
+```
+
+The expected last line is `PASS_T37_RESTORATION_DEFERRAL_REPLAY`. It takes about 8 s with
+standard-library Python 3.10+ and no network. The pinned engine files are loaded from the
+repository and hash-checked. `verify.py` reads five members of the committed T37 archive and
+two of the T21 archive in memory, without extracting them. It recomputes `CENSUS.json` and
+`PRICES.json` and requires them to equal the committed files. A double-precision bisection
+that shares no code with the pinned engines must then agree with every certified endpoint and
+κ to within 10⁻¹³, including the best single-helper row. Finally it runs nine negative
+controls. C4, C5 and C7 test this package's own checks; the others test the inputs and the
+certification:
+
+| Control | Rejected because |
+|---|---|
+| C1 one rank-48 idle child dropped | coverage identity fails (a family covers 25) |
+| C2 one idle child shrunk to rank 47 | coverage identity fails |
+| C3 one idle child duplicated | coverage identity fails |
+| C4 full-frame cleanup removed for one restoration helper | its restoration climb is no longer consumed |
+| C5 zero-cost deletion presented as a deferral | rank mass changes |
+| C6 corrupted payload pin | payload digest mismatch |
+| C7 a child of rank 52 | halving guard `73² > 2r²` fails |
+| C8 complex endpoint b + 10⁻²⁴ | both engines exceed one |
+| C9 one extra rank-one child | baseline κ no longer equals the selected record |
+
+## Sources and pins
+
+[`SOURCES.json`](SOURCES.json) records every input. The selected T37 archive is
+`research/community-frontier942-audit/t37-replay.tar.gz` (`48285025…`). From it, the census
+reads the hosted template (payload `956e0c0e…`, equal to the `template_sha256` of the selected
+`ASSEMBLY.json`), the U8 word (content `090fd574…`) and the emitted local programs (container
+`8b6a9e3a…`, bound by the template) and the canonical provider word (container `387a2266…`,
+bound by the template). T21 is read from `t21-replay.tar.gz` (`6dcd7040…`). The engines
+`moment.py`, `base_two_moment.py` and `outer.py` are taken from
+`research/native-complex-moment552/engines` and carry the SHA-256 digests recorded in the
+selected assembly. `price.py` transcribes `outer_witness` from the archive's
+`runtime/code/assemble.py`. It checks that file's digest (`d89ed7a6…`) and the literal lines it
+transcribes, and it cross-checks the bit endpoint against the selected `ASSEMBLY.json`.
+
+## Credit
+
+- **Selected construction:** Jonathan Capalbo (PR942); Chafik Boukhalfa (PR890); Jeremy Kothe
+  and NewBArch (PR869/PR870); Hao Yan (PR858); DreamingOfClouds (PR589) on eumemic (PR555).
+- **Concurrent work, PR974 (avirazza, open, same track).** It supplies the role/phase partition
+  and the zero-parent-cost budget. This note reproduces its T37 one-unit price independently and
+  adds the coverage-preserving recurrence for its restoration rows.
+- **Building blocks:**
+  - Dominik Scholz's `research/larger-gain` (`8v − 9C`, centre obstructions).
+  - DaysSky's idle-axis hosting (PR442) and its hosting lemma.
+  - Jeremy Kothe's hyperplane-ended helpers (PR601).
+  - goatliamia's cleanup retiming census (PR935).
+  - SethBurkart123's U8 independent cross-check (PR881).
+- **This note:** prepared by Sagar Thakrar (thakrarsagar) with substantial AI assistance from
+  Claude (Anthropic) via Claude Code. New material is Apache-2.0.
diff --git a/research/t37-restoration-deferral/SOURCES.json b/research/t37-restoration-deferral/SOURCES.json
new file mode 100644
index 0000000000..87cd0fd0fb
--- /dev/null
+++ b/research/t37-restoration-deferral/SOURCES.json
@@ -0,0 +1,59 @@
+{
+  "base_commit": "bbc600db2fc15007b7c914f4f2b2ed55fa909c87",
+  "selected_record": {
+    "path": "certificates/selected-result.json",
+    "kappa": "1661960547713947/1000000000000000000",
+    "source_pr": 942
+  },
+  "constructions": {
+    "T37": {
+      "role": "selected construction (PR942 on PR890/PR869/PR870/PR858, PR589 bit supplier)",
+      "archive": "research/community-frontier942-audit/t37-replay.tar.gz",
+      "archive_sha256": "48285025105210b56a32d3d4d57a21b7591760acc709d38073e4dca339eb06fe",
+      "template_member": "strict/global/hosted/GLOBAL-TEMPLATE.json.gz",
+      "template_payload_sha256": "956e0c0e9b083806268bf93525441ccea143d5f78e46c5f6b793b22cfe11113d",
+      "template_binding": "equals template_sha256 recorded in research/community-frontier942-audit/ASSEMBLY.json",
+      "word_member": "native/local/FULL-WORD.json.gz",
+      "word_payload_sha256": "090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a",
+      "assembly": "research/community-frontier942-audit/ASSEMBLY.json",
+      "assembly_sha256": "4b2894956e594e408e111d806c842f2ed2c32aefcadff93fad69ff0b46f1991a",
+      "program_member": "strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz",
+      "program_container_sha256": "8b6a9e3a2411a04e5ca79ba6cd1dd449b21c95f65ca127475167d9b97c80a1ce",
+      "program_payload_sha256": "a073d8d6a561cf5c8148d8b29ae2800bbe3978377c016b549edd7523eb3cf7e5",
+      "program_binding": "container digest equals local_providers.gauge44.local_programs_sha256 of the pinned hosted template",
+      "canonical_member": "strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz",
+      "canonical_container_sha256": "387a2266ffe006d20042221d967f67a4b18d9bb8de1cd1e01d4031b539fa74a5",
+      "canonical_payload_sha256": "24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c",
+      "canonical_binding": "container digest equals local_providers.gauge44.canonical_word_sha256 of the pinned hosted template; its register numbering is the template numbering"
+    },
+    "T21": {
+      "role": "preceding checkpoint (PR890), second instance of the coverage identity only",
+      "archive": "research/community-frontier890-audit/t21-replay.tar.gz",
+      "archive_sha256": "6dcd7040109174918fe25a631e349741e5d7fa1740e063e2bdd5ea77b054b6b4",
+      "template_member": "global/hosted/GLOBAL-TEMPLATE.json.gz",
+      "template_payload_sha256": "d7074fb509f61cf6d62bda4b3bec2419d5baaafcb8ceeed8c5ce295db6f5b82d",
+      "word_member": "native/local/FULL-WORD.json.gz",
+      "word_payload_sha256": "090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a",
+      "assembly": "research/community-frontier890-audit/ASSEMBLY.json",
+      "assembly_sha256": "190110b509dc87d38b72ad37c3290efcc245ce26df4cae3d7e2d6dcf0bac2c43"
+    }
+  },
+  "engines": {
+    "directory": "research/native-complex-moment552/engines",
+    "moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "binding": "the same SHA-256 digests are recorded under input_sha256 in research/community-frontier942-audit/ASSEMBLY.json"
+  },
+  "outer_witness": {
+    "source": "runtime/code/assemble.py inside the T37 archive (sha256 d89ed7a68f19e6d0dbb9d1bd75805433b1dc000bd89649fb598ef381c3887925), function outer_witness",
+    "eta": "1/1000000000000000000000000",
+    "beta": "1/1000000000000000000000000",
+    "bootstrap_start": "384599/10000000000",
+    "bootstrap_steps": 7,
+    "charged_complex_prefix_bits": 1024,
+    "bit_lower": "1733427039589844234749/1000000000000000000000000",
+    "source_sha256": "d89ed7a68f19e6d0dbb9d1bd75805433b1dc000bd89649fb598ef381c3887925",
+    "source_member": "runtime/code/assemble.py"
+  }
+}
diff --git a/research/t37-restoration-deferral/census.py b/research/t37-restoration-deferral/census.py
new file mode 100644
index 0000000000..b838dc7efc
--- /dev/null
+++ b/research/t37-restoration-deferral/census.py
@@ -0,0 +1,189 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Coverage identity, restoration census and deferral profiles for T37.
+
+Usage: census.py OUT.json
+
+Reads only the hash-pinned committed replay archives (no extraction to disk).
+Writes the census and every scenario profile that price.py certifies.
+"""
+import json
+import sys
+from collections import Counter
+
+from common import (ROOT, SOURCES, canonical, canonical_restoration, concentrated, coverage_census,
+                    emitted_restoration, global_profile, load_canonical, load_construction, load_programs,
+                    rank_mass, require, restoration_census, sha256, window_deferral)
+
+CENTRE_RANK = 8
+HALVING_CAP = 48          # every idle window has capacity <= 48; 2*48^2 < 73^2
+
+
+def counter_json(c):
+    return {str(k): c[k] for k in sorted(c) if c[k]}
+
+
+def role_summary(registers):
+    out = {}
+    for role in ('source', 'target', 'helper'):
+        rs = [r for r in registers if r['role'] == role]
+        pos = [r for r in rs if r['restoration'] > 0]
+        out[role] = dict(registers=len(rs),
+                         paid_endpoint_mass=sum(r['end'] - r['start'] for r in rs),
+                         positive_restoration=len(pos),
+                         restoration_mass=sum(r['restoration'] for r in pos),
+                         restoration_profile=counter_json(Counter(r['restoration'] for r in pos)),
+                         positive_restoration_touched_by_full_cleanup=sum(r['full_cleanup_gates'] > 0 for r in pos),
+                         zero_restoration_low_ends=sum(r['restoration'] == 0 and r['low_end'] for r in rs),
+                         full_cleanup_gates_on_positive_restoration=sum(r['full_cleanup_gates'] for r in pos))
+    return out
+
+
+def census(name):
+    template, word = load_construction(name)
+    local = restoration_census(word)
+    rep = word['report']
+    local_profile = Counter({int(k): n for k, n in rep['local_profile'].items()})
+    require(local['paid'] == local_profile, f'{name}: replayed local profile differs from the word report')
+    require(local['widths'] == Counter({int(k): n for k, n in rep['width_inventory'].items()}), 'width inventory')
+    require(dict(local['centre_children']) == {CENTRE_RANK: 8}, 'eight rank-eight centre paths')
+    data_steps = {r['end'] - r['start'] for r in local['registers'] if r['role'] != 'helper'}
+    require(len(data_steps) == 1, 'every data register pays the same climb')
+    data_step, = data_steps
+    local_mass = rank_mass(local_profile)
+    cov = coverage_census(template, local_mass, data_step)
+    W, N, m = cov['live'], cov['calls'], cov['m']
+    require(cov['coverage_values'] == {str(m): W}, f'{name}: coverage identity fails')
+    require(cov['total_rank_mass'] == (m - 1) * W + local['centre_children'][CENTRE_RANK] * CENTRE_RANK * N,
+            f'{name}: mass identity fails')
+    require(cov['deficit'] == W - CENTRE_RANK * 8 * N, f'{name}: deficit identity fails')
+    centres = cov['private_centre_families']
+    require(centres[0] >= W, 'centre work families lie outside the live stock')
+    H = global_profile(template, local_profile)
+    assembly = json.loads((ROOT / SOURCES['constructions'][name]['assembly']).read_text())
+    require(sha256((ROOT / SOURCES['constructions'][name]['assembly']).read_bytes())
+            == SOURCES['constructions'][name]['assembly_sha256'], f'{name}: assembly digest')
+    require(counter_json(H) == assembly['complex_profile'], f'{name}: global profile differs from the selected assembly')
+    emitted = None
+    binding = None
+    if 'canonical_member' in SOURCES['constructions'][name]:
+        (prov,) = template['local_providers'].values()
+        native = [r for r in local['registers'] if r['role'] == 'helper']
+        require([r['end'] - r['start'] for r in native] == prov['widths'], 'helper widths differ by index from the template')
+        canon = canonical_restoration(load_canonical(name, template))
+        v = local['v']
+        require(canon[2 * v:] == [r['restoration'] for r in native],
+                'helper restoration differs by index between the native and canonical words')
+        require(sorted(canon[:v]) == sorted(r['restoration'] for r in local['registers'] if r['role'] == 'source'),
+                'source restoration multiset differs between the native and canonical words')
+        local['template_helper_restoration'] = canon[2 * v:]
+        binding = dict(helper_widths_by_index='native word = hosted template provider (504 helpers)',
+                       helper_restoration_by_index='native word = canonical provider word bound by the template',
+                       source_restoration='equal as a multiset (sources are relabelled in the canonical word)')
+    if 'program_member' in SOURCES['constructions'][name]:
+        restored = Counter()
+        for r in local['registers']:
+            if r['restoration'] > 0:
+                restored[r['restoration']] += 1
+        no_centres = Counter(local_profile)
+        no_centres.subtract(local['centre_children'])
+        emitted = {}
+        for orientation, e in emitted_restoration(load_programs(name, template)).items():
+            require(e['final'] == restored, f'{name} {orientation}: emitted final climbs differ from the replay')
+            require(+e['climbs'] == +no_centres and e['centres'] == 8, f'{name} {orientation}: emitted children')
+            ph = e['phases']
+            require(ph.index('final') < ph.index('full_frame_cleanup'), 'final climbs precede the full-frame cleanup')
+            emitted[orientation] = dict(phases=ph, final_climbs=counter_json(e['final']))
+    out = dict(construction=name, emitted_programs=emitted, index_binding=binding, local=dict(
+        h=local['h'], v=local['v'], R=local['R'], profile=counter_json(local_profile), mass=local_mass,
+        data_climb_per_incidence=data_step, centre_children=counter_json(local['centre_children']),
+        phase_mass=counter_json(local['phase_mass']), roles=role_summary(local['registers'])),
+        coverage=cov, global_profile=counter_json(H),
+        identity=dict(statement='data_climb*k_f + 1 + hosted_f + idle_f = m for every live family f; '
+                                'rank mass = (m-1)*W + 64*N; deficit = W - 64*N',
+                      rank_mass=cov['total_rank_mass'], deficit=cov['deficit'], live=W, calls=N))
+    return out, template, local, local_profile, H
+
+
+def scenarios(template, local, local_profile, H):
+    N = len(template['calls'])
+    restoration = dict(enumerate(local['template_helper_restoration']))
+    positive = sorted(i for i, d in restoration.items() if d > 0)
+    idle_ranks = Counter(c['rank'] for c in template['idle_children'])
+    base_mass = rank_mass(H)
+    out = {}
+
+    def add(key, profile, realizable, **meta):
+        require(73 * 73 > 2 * max(profile) ** 2, f"{key}: child above the halving cap")
+        if realizable:
+            require(max(profile) <= HALVING_CAP, f"{key}: child above every window capacity")
+        out[key] = dict(profile=counter_json(profile), rank_mass=rank_mass(profile),
+                        rank_mass_neutral=rank_mass(profile) == base_mass,
+                        realizable_in_selected_windows=realizable, **meta)
+
+    add('baseline', H, True, description='Selected T37 profile.')
+    H1, removed, returned = window_deferral(template, local_profile, restoration, set(positive))
+    require(rank_mass(H1) == base_mass, 'deferral must be mass neutral')
+    add('defer_all_selected_hosting', H1, True,
+        description='Every positive helper restoration climb (all calls) is deferred; its host '
+                    'coordinates return to the same hosting window and are advanced by that '
+                    "window's idle child, merged per window. Owner map unchanged.",
+        deferred_helpers_per_call=len(positive), deferred_children=counter_json(removed),
+        windows_receiving=sum(returned.values()), returned_window_ranks=counter_json(returned))
+    H3 = concentrated(H, removed, idle_ranks, HALVING_CAP)
+    add('defer_all_free_concentration', H3, False,
+        description='Relaxation of the previous row: all idle coordinates, including the returned '
+                    'ones, placed in capacity-48 children, ignoring helper indivisibility, windows '
+                    'and chronology.')
+    H4 = concentrated(H, Counter(), idle_ranks, HALVING_CAP)
+    add('baseline_free_concentration', H4, False,
+        description='The same relaxation with no deferral (control for the relaxation itself).')
+    # One rank-one restoration climb per call moved into an existing rank-48 idle child.
+    H5 = Counter(H)
+    H5[1] -= N
+    H5[48] -= N
+    H5[49] += N
+    require(idle_ranks[48] >= N, 'enough rank-48 children')
+    add('exchange_merge_rank1_into_48', +H5, False,
+        description='Relaxation: per call, one rank-one climb is removed and its coordinate joins an '
+                    'existing rank-48 idle child (48 -> 49; halving 2*49^2 < 73^2). Every selected window '
+                    'has capacity at most 48 and every rank-48 child fills a whole idle window, so no '
+                    're-hosting realizes this; it over-estimates one deferred rank-one climb per call.')
+    H6 = Counter(H)
+    H6[1] -= N
+    out['zero_cost_delete_rank1'] = dict(
+        profile=counter_json(+H6), rank_mass=rank_mass(H6), rank_mass_neutral=False,
+        realizable_in_selected_windows=False,
+        description='PR974-style relaxation: one rank-one child per call deleted with zero parent '
+                    'cost. It leaves N live coordinates unadvanced; priced only for comparison.')
+    single = {}
+    for i in positive:
+        Hi, rem, _ = window_deferral(template, local_profile, restoration, {i})
+        single[i] = Hi
+    return out, single, positive, restoration
+
+
+def main():
+    target = sys.argv[1]
+    t37, template, local, local_profile, H = census('T37')
+    t21 = census('T21')[0]
+    rows, single, positive, restoration = scenarios(template, local, local_profile, H)
+    changed = {str(i): counter_json(Hi) for i, Hi in single.items() if Hi != H}
+    result = dict(status='PASS_T37_RESTORATION_CENSUS', base_commit=SOURCES['base_commit'],
+                  T37=t37, T21=dict(construction='T21', coverage=t21['coverage'], identity=t21['identity']),
+                  helper_restoration={str(i): restoration[i] for i in sorted(restoration)},
+                  positive_restoration_helpers=positive,
+                  scenarios=rows,
+                  single_helper_profiles=changed,
+                  single_helper_unchanged=sorted(int(i) for i in single if single[i] == H))
+    with open(target, 'w') as f:
+        f.write(canonical(result))
+    print(result['status'])
+    for role, s in t37['local']['roles'].items():
+        print(f"{role:7s} restoration mass {s['restoration_mass']:4d} in {s['positive_restoration']:3d} registers, "
+              f"{s['positive_restoration_touched_by_full_cleanup']:3d} touched by full-frame cleanup")
+    print('T37 coverage', t37['coverage']['coverage_values'], 'deficit', t37['coverage']['deficit'],
+          '| T21 coverage', t21['coverage']['coverage_values'], 'deficit', t21['coverage']['deficit'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/t37-restoration-deferral/common.py b/research/t37-restoration-deferral/common.py
new file mode 100644
index 0000000000..144323b941
--- /dev/null
+++ b/research/t37-restoration-deferral/common.py
@@ -0,0 +1,383 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Shared, standard-library-only helpers for the T37 restoration-deferral note.
+
+Nothing here imports producer, auditor or checker code from the selected
+packages.  Inputs are read directly from the committed, hash-pinned replay
+archives without extracting them to disk.
+"""
+import gzip
+import hashlib
+import json
+import tarfile
+from collections import Counter, defaultdict
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[2]
+HERE = Path(__file__).resolve().parent
+
+SOURCES = json.loads((HERE / 'SOURCES.json').read_text())
+
+
+def sha256(data):
+    return hashlib.sha256(data).hexdigest()
+
+
+def require(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def canonical(obj):
+    return json.dumps(obj, indent=1, sort_keys=True) + '\n'
+
+
+def read_member(archive, member, payload_sha256):
+    """Return the decompressed JSON payload of one gzip member of a pinned tar archive."""
+    with tarfile.open(archive, 'r:gz') as tar:
+        info = tar.getmember(member)
+        require(info.isfile(), f'{member} is not a regular file')
+        payload = gzip.decompress(tar.extractfile(info).read())
+    require(sha256(payload) == payload_sha256, f'{member}: payload digest mismatch')
+    return json.loads(payload)
+
+
+def bound_member(name, template_key, member_key, container_key, payload_key, template, root=ROOT):
+    """A gzip JSON member whose container digest is bound by the hosted template."""
+    src = SOURCES['constructions'][name]
+    with tarfile.open(Path(root) / src['archive'], 'r:gz') as tar:
+        info = tar.getmember(src[member_key])
+        require(info.isfile(), f'{src[member_key]} is not a regular file')
+        container = tar.extractfile(info).read()
+    (prov,) = template['local_providers'].values()
+    require(sha256(container) == src[container_key] == prov[template_key],
+            f'{name}: {src[member_key]} is not the one bound by the hosted template')
+    payload = gzip.decompress(container)
+    require(sha256(payload) == src[payload_key], f'{name}: {src[member_key]} payload digest mismatch')
+    return json.loads(payload)
+
+
+def load_canonical(name, template, root=ROOT):
+    return bound_member(name, 'canonical_word_sha256', 'canonical_member', 'canonical_container_sha256',
+                        'canonical_payload_sha256', template, root)
+
+
+def archive_text(name, member_key, digest_key, root=ROOT):
+    src = SOURCES['constructions'][name]
+    with tarfile.open(Path(root) / src['archive'], 'r:gz') as tar:
+        data = tar.extractfile(tar.getmember(SOURCES['outer_witness'][member_key])).read()
+    require(sha256(data) == SOURCES['outer_witness'][digest_key], 'outer witness source digest')
+    return data.decode()
+
+
+def load_programs(name, template, root=ROOT):
+    """Emitted forward/backward local programs, bound to the hosted template by container digest."""
+    src = SOURCES['constructions'][name]
+    archive = Path(root) / src['archive']
+    with tarfile.open(archive, 'r:gz') as tar:
+        info = tar.getmember(src['program_member'])
+        require(info.isfile(), 'program member is not a regular file')
+        container = tar.extractfile(info).read()
+    (prov,) = template['local_providers'].values()
+    require(sha256(container) == src['program_container_sha256'] == prov['local_programs_sha256'],
+            f'{name}: program container is not the one bound by the hosted template')
+    payload = gzip.decompress(container)
+    require(sha256(payload) == src['program_payload_sha256'], f'{name}: program payload digest mismatch')
+    return json.loads(payload)
+
+
+def emitted_restoration(programs):
+    """Rank profile of the emitted 'final' climbs and the phase order, per orientation."""
+    out = {}
+    for orientation in ('forward', 'backward'):
+        prog = programs[orientation]
+        phases = [e[1] for e in prog if e[0] == 'phase']
+        final = Counter(e[5] for e in prog if e[0] == 'climb' and e[1] == 'final')
+        climbs = Counter(e[5] for e in prog if e[0] == 'climb')
+        centres = sum(1 for e in prog if e[0] == 'center')
+        out[orientation] = dict(phases=phases, final=final, climbs=climbs, centres=centres)
+    return out
+
+
+def load_construction(name, root=ROOT):
+    """Load the hosted global template and the local U8 word of a pinned construction."""
+    src = SOURCES['constructions'][name]
+    archive = Path(root) / src['archive']
+    require(sha256(archive.read_bytes()) == src['archive_sha256'], f'{name}: archive digest mismatch')
+    template = read_member(archive, src['template_member'], src['template_payload_sha256'])
+    word = read_member(archive, src['word_member'], src['word_payload_sha256'])
+    return template, word
+
+
+# ---------------------------------------------------------------------------
+# Local frame semantics (monotone nested F2^h frames).
+
+class Span:
+    """A subspace of F2^h held as a list of basis vectors in reduced echelon form."""
+    __slots__ = ('basis',)
+
+    def __init__(self, vectors=()):
+        self.basis = []
+        for x in vectors:
+            self.insert(x)
+
+    def residue(self, x):
+        for b in self.basis:                      # basis sorted by decreasing leading bit
+            if x ^ b < x:
+                x ^= b
+        return x
+
+    def insert(self, x):
+        x = self.residue(x)
+        if not x:
+            return False
+        lead = x.bit_length() - 1
+        self.basis = [b ^ x if (b >> lead) & 1 else b for b in self.basis]
+        self.basis.append(x)
+        self.basis.sort(reverse=True)
+        return True
+
+    @property
+    def rank(self):
+        return len(self.basis)
+
+    def within(self, other):
+        return all(other.residue(b) == 0 for b in self.basis)
+
+    def same(self, other):
+        return self.rank == other.rank and self.within(other)
+
+
+def hyperplane(port, h):
+    """{x in F2^h : <x, port> = 0}."""
+    require(0 < port < 1 << h, 'port out of range')
+    vectors = [x for x in (1 << i for i in range(h))]
+    pivot = port & -port
+    out = []
+    for x in vectors:
+        if x == pivot:
+            continue
+        out.append(x ^ (pivot if bin(x & port).count('1') % 2 else 0))
+    U = Span(out)
+    require(U.rank == h - 1, 'hyperplane rank')
+    return U
+
+
+def gate_registers(g):
+    return list(g[1:3]) if g[0] == 'add' else list(g[1:2])
+
+
+def canonical_restoration(cw):
+    """Per-register restoration climbs of the template's canonical provider word.
+
+    The canonical word indexes its frames through cw['frames'] and numbers its
+    registers as the hosted template does, so its helper k is the template's
+    pooled_slots helper k.  Same semantics as restoration_census.
+    """
+    h = cw['h']
+    F = [Span(f) for f in cw['frames']]
+    full = Span([1 << i for i in range(h)])
+    require(not cw['target_levels'], 'canonical word has target levels')
+    frame = [F[i] for i in cw['start']]
+
+    def climb(q, U):
+        require(frame[q].within(U), f'canonical word: non-monotone frame for register {q}')
+        frame[q] = U
+
+    for g in cw['A']:
+        for q in gate_registers(g):
+            climb(q, F[g[-1]])
+    for q, i in zip(cw['centers'], cw['center_frames']):
+        require(frame[q].same(F[i]), 'canonical word: centre frame at the cut')
+    for g in cw['B'] + cw['tail']:
+        for q in gate_registers(g):
+            climb(q, F[g[-1]])
+    restoration = []
+    for q, i in enumerate(cw['final']):
+        restoration.append(F[i].rank - frame[q].rank)
+        climb(q, F[i])
+    for g in cw['cleanup']:
+        require(F[g[-1]].same(full), 'canonical cleanup gate is not full-frame')
+    return restoration
+
+
+def restoration_census(word):
+    """Replay the literal frame chains of a local word.
+
+    Returns the paid child profile, the width inventory, and for every register
+    its start/end ranks, its final restoration climb (the climb from its last
+    gate frame to its endpoint frame) and the number of full-frame cleanup
+    gates that touch it.
+    """
+    rep = word['report']
+    h, v, R = rep['h'], rep['v'], rep['R']
+    n = 2 * v + R
+    require(not word['target_levels'], 'this replay assumes empty target levels')
+    full = Span([1 << i for i in range(h)])
+    frame = [Span([p]) for p in word['ports']] + [Span() for _ in range(v + R)]
+    for q, U in word['start_extra'].items():
+        frame[int(q)] = Span(U)
+    start = [f.rank for f in frame]
+    paid = Counter()
+    phase_mass = Counter()
+
+    def climb(q, U, phase):
+        require(frame[q].within(U), f'non-monotone frame for register {q} in {phase}')
+        step = U.rank - frame[q].rank
+        if step:
+            paid[step] += 1
+            phase_mass[phase] += step
+        frame[q] = U
+
+    for g in word['A']:
+        for q in gate_registers(g):
+            climb(q, Span(g[-1]), 'A')
+    centre_children = Counter()
+    for q, U in zip(word['centers'], word['center_frames']):
+        U = Span(U)
+        require(frame[q].same(U), 'centre frame at the cut')
+        if any(g[2] == q for g in word['cut']):
+            centre_children[U.rank] += 1
+    paid.update(centre_children)
+    for g in word['B']:
+        for q in gate_registers(g):
+            climb(q, Span(g[-1]), 'B')
+    early = {}
+    for i, U in word['early_cleanup']:
+        early[i] = U
+        for q in gate_registers(word['cleanup'][i]):
+            climb(q, Span(U), 'early_cleanup')
+    end = [full] * v + [hyperplane(p, h) for p in word['ports']] + [full] * R
+    for q, U in word['helper_final'].items():
+        end[int(q)] = Span(U)
+    before_final = [f.rank for f in frame]
+    for q in range(n):
+        climb(q, end[q], 'final')
+    full_touch = Counter()
+    for i, g in enumerate(word['cleanup']):
+        if i in early:
+            continue
+        require(Span(g[-1]).same(full), 'non-early cleanup gate is not full-frame')
+        for q in gate_registers(g):
+            require(end[q].same(full), 'full-frame cleanup touches a low end')
+            full_touch[q] += 1
+    registers = []
+    for q in range(n):
+        role = 'source' if q < v else 'target' if q < 2 * v else 'helper'
+        registers.append(dict(register=q, role=role, start=start[q], end=end[q].rank,
+                              restoration=end[q].rank - before_final[q],
+                              low_end=str(q) in word['helper_final'],
+                              full_cleanup_gates=full_touch[q]))
+    widths = Counter(r['end'] - r['start'] for r in registers if r['role'] == 'helper')
+    return dict(h=h, v=v, R=R, paid=paid, centre_children=centre_children,
+                phase_mass=phase_mass, widths=widths, registers=registers)
+
+
+# ---------------------------------------------------------------------------
+# Global coverage semantics of the hosted nine-stage template.
+
+def coverage_census(template, local_mass, data_step):
+    """Per-family coordinate coverage of every live family.
+
+    data_step is the paid frame climb of one data register per incidence,
+    taken from the local word; the identity checked is
+        data_step*k_f + 1 + hosted_f + idle_f = m      for every live family f.
+    """
+    W, m = template['live'], template['m']
+    provider = template['local_providers']
+    require(len(provider) == 1, 'one local provider expected')
+    (pid, prov), = provider.items()
+    v, R, widths = prov['v'], prov['R'], prov['widths']
+    require(len(widths) == R, 'width list')
+    k, hosted = Counter(), Counter()
+    for call in template['calls']:
+        require(call['provider_id'] == pid, 'provider dispatch')
+        owners = call['owners']
+        require(len(owners) == 2 * v + R, 'owner count')
+        for i, (family, route) in enumerate(owners):
+            require((route[0] == 1) == (i < 2 * v), 'data routes are exactly the data registers')
+            if i < 2 * v:
+                k[family] += 1
+            else:
+                hosted[family] += widths[i - 2 * v]
+    pooled = Counter()
+    for s in template['hosting']['pooled_slots']:
+        require(widths[s['helper']] == s['width'], 'pooled slot width')
+        pooled[s['family']] += s['width']
+    require(pooled == hosted, 'pooled slots differ from call owners')
+    idle = Counter()
+    for c in template['idle_children']:
+        require(c['replicas'] == 1 and c['rank'] > 0, 'idle child shape')
+        idle[c['family']] += c['rank']
+    outside = [f for f in set(k) | set(hosted) | set(idle) if not 0 <= f < W]
+    require(not outside, 'coverage outside the live families')
+    values = Counter(data_step * k[f] + 1 + hosted[f] + idle[f] for f in range(W))
+    N = len(template['calls'])
+    idle_mass = sum(idle.values())
+    total = N * local_mass + idle_mass
+    centres = template['private_namespace']['centers']
+    return dict(live=W, m=m, calls=N, v=v, R=R,
+                coverage_values={str(x): n for x, n in sorted(values.items())},
+                data_incidences_per_family={str(x): n for x, n in sorted(Counter(k[f] for f in range(W)).items())},
+                data_coordinates=data_step * sum(k.values()) + W,
+                hosted_coordinates=sum(hosted.values()),
+                idle_coordinates=idle_mass,
+                total_rank_mass=total,
+                deficit=m * W - total,
+                private_centre_families=centres)
+
+
+def global_profile(template, local_profile):
+    H = Counter()
+    for _ in template['calls']:
+        H.update(local_profile)
+    for c in template['idle_children']:
+        H[c['rank']] += 1
+    return H
+
+
+# ---------------------------------------------------------------------------
+# Restoration deferral: the explicit mechanism and its complete recurrence.
+
+def window_deferral(template, local_profile, restoration_by_helper, chosen):
+    """Profile after deferring the restoration climbs of the chosen helper indices.
+
+    Each deferred climb of rank d leaves the local profile.  Its d host
+    coordinates are returned to the pending set of the same hosting window
+    (family, idle child), where they are advanced by that window's idle child.
+    Coordinates returned to one window form one child, merged with any
+    existing remainder of that window.  Rank mass is unchanged by construction.
+    """
+    H = global_profile(template, local_profile)
+    remainder = {(c['family'], c['child']): c['rank'] for c in template['idle_children']}
+    returned = defaultdict(int)
+    removed = Counter()
+    for s in template['hosting']['pooled_slots']:
+        d = restoration_by_helper[s['helper']]
+        if s['helper'] in chosen and d > 0:
+            returned[(s['family'], s['child'])] += d
+            removed[d] += 1
+    H.subtract(removed)
+    for w, d in returned.items():
+        r0 = remainder.get(w, 0)
+        if r0:
+            H[r0] -= 1
+        H[r0 + d] += 1
+    H = +H
+    return H, removed, Counter(returned.values())
+
+
+def concentrated(H, removed, idle_ranks, cap):
+    """Free-concentration relaxation: all idle coordinates in children of rank cap."""
+    out = Counter(H)
+    out.subtract(removed)
+    out.subtract(idle_ranks)
+    mass = sum(r * n for r, n in idle_ranks.items()) + sum(r * n for r, n in removed.items())
+    q, r = divmod(mass, cap)
+    out[cap] += q
+    if r:
+        out[r] += 1
+    return +out
+
+
+def rank_mass(H):
+    return sum(int(r) * n for r, n in H.items())
diff --git a/research/t37-restoration-deferral/price.py b/research/t37-restoration-deferral/price.py
new file mode 100644
index 0000000000..6805a3fbda
--- /dev/null
+++ b/research/t37-restoration-deferral/price.py
@@ -0,0 +1,172 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Exact prices of the census scenarios with the pinned rational engines.
+
+kappa() is a transcription of outer_witness in the T37 archive's runtime/code/assemble.py;
+check_transcription() binds it to that file's digest and to the literal lines it transcribes.
+
+Usage: price.py CENSUS.json OUT.json
+
+The complex endpoint b of a profile is accepted by both pinned interval
+engines at b and rejected at b + 10^-24.  kappa is the largest 10^-18 grid
+point accepted by the selected T37 outer witness (seven bootstrap steps and
+all 47 strict inequalities), and the next grid point must be rejected.
+The baseline must reproduce the selected record exactly.
+"""
+import importlib.util
+import json
+import sys
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+
+from common import ROOT, SOURCES, archive_text, canonical, require, sha256
+
+M_COMPLEX = 73
+
+
+def engine(name):
+    path = ROOT / SOURCES['engines']['directory'] / (name + '.py')
+    require(sha256(path.read_bytes()) == SOURCES['engines'][name + '.py'], f'engine pin {name}')
+    spec = importlib.util.spec_from_file_location('pinned_' + name, path)
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+MOMENT, BASE_TWO, OUTER = engine('moment'), engine('base_two_moment'), engine('outer')
+OW = SOURCES['outer_witness']
+BIT = Q(OW['bit_lower'])
+ETA, BETA = Q(OW['eta']), Q(OW['beta'])
+GRID = 10 ** 18
+BRIDGE = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1},
+          'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+
+
+def dec(x, prec=40):
+    with localcontext() as ctx:
+        ctx.prec = prec
+        return str(Decimal(x.numerator) / Decimal(x.denominator))
+
+
+def endpoint(H, W):
+    """Certified complex lower endpoint on the 10^-24 grid (native recurrence, no surcharge)."""
+    b = Q(MOMENT.certify(H, M_COMPLEX, W, False)['lower'])
+    for z, accept in ((b, True), (b + Q(1, 10 ** 24), False)):
+        lo, hi = MOMENT.moment(H, M_COMPLEX, W, z, False)
+        blo, bhi = BASE_TWO.moment(M_COMPLEX, W, list(H.items()), z)
+        require((hi < 1 and bhi < 1) if accept else (lo > 1 and blo > 1), 'endpoint certification')
+    return b
+
+
+def check_transcription():
+    text = archive_text('T37', 'source_member', 'source_sha256')
+    for line in ("eta=beta=Q(1,10**24);s=min(c,(1-beta)*bb)-Q(1,10**27)",
+                 "chain=[Q(384599,10**10)];cuts=[]", "for _ in range(7):",
+                 "old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s)",
+                 "q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;"
+                 "k=Q((ticks.numerator-1)//ticks.denominator,10**18)",
+                 "bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},"
+                 "'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}"):
+        require(line in text, 'transcribed outer_witness line not found: ' + line)
+
+
+def kappa(b):
+    """Replays outer_witness of the selected T37 assembly for complex endpoint b."""
+    s = min(BIT, (1 - BETA) * b) - Q(1, 10 ** 27)
+    require(0 < s < BIT and s < (1 - BETA) * b, 'effective saving')
+    chain = [Q(OW['bootstrap_start'])]
+    for _ in range(OW['bootstrap_steps']):
+        old = chain[-1]
+        a = (1 - s) * s + s * old
+        gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s)
+        require(old < a < s < 1 - a and gap > 0, 'bootstrap step')
+        chain.append(a)
+    q = chain[-1] * (1 - 2 * ETA)
+    margin = (1 - ETA) * q / (1 + q)
+    ticks = margin * GRID
+    k = Q((ticks.numerator - 1) // ticks.denominator, GRID)
+    out = OUTER.assembly(chain[-1], b, BRIDGE, k, eta=ETA, beta=BETA)
+    require(len(out['strict_constraints']) == 47 and all(v > 0 for v in out['strict_constraints'].values()),
+            'outer inequalities')
+    try:
+        OUTER.assembly(chain[-1], b, BRIDGE, k + Q(1, GRID), eta=ETA, beta=BETA)
+    except AssertionError:
+        pass
+    else:
+        raise ValueError('next kappa grid point accepted')
+    return k, ('bit' if BIT <= (1 - BETA) * b else 'complex')
+
+
+def drop(H0, H, W, b):
+    """60-digit Decimal value of moment(H0) - moment(H) at exponent b, times m*W (ranking only)."""
+    with localcontext() as ctx:
+        ctx.prec = 60
+        bd = Decimal(b.numerator) / Decimal(b.denominator)
+        g = lambda P: sum(Decimal(r * n) * ((Decimal(M_COMPLEX) / Decimal(r)).ln() * bd).exp()
+                          for r, n in P.items())
+        return g(H0) - g(H)
+
+
+def main():
+    check_transcription()
+    census = json.loads(open(sys.argv[1]).read())
+    W = census['T37']['coverage']['live']
+    selected = json.loads((ROOT / SOURCES['selected_record']['path']).read_text())
+    assembly = json.loads((ROOT / SOURCES['constructions']['T37']['assembly']).read_text())
+    require(Q(assembly['bit_lower']) == BIT, 'bit endpoint differs from the selected assembly')
+    rows = {}
+    for key, row in census['scenarios'].items():
+        H = {int(r): n for r, n in row['profile'].items()}
+        b = endpoint(H, W)
+        k, binding = kappa(b)
+        rows[key] = dict(complex_lower=str(b), complex_decimal=dec(b), kappa=str(k), kappa_decimal=dec(k),
+                         binding=binding, rank_mass_neutral=row['rank_mass_neutral'],
+                         realizable_in_selected_windows=row['realizable_in_selected_windows'],
+                         rank_mass=row['rank_mass'])
+    base = rows['baseline']
+    require(base['complex_lower'] == assembly['complex_lower'], 'baseline complex endpoint differs from selected')
+    require(base['kappa'] == selected['kappa'] == SOURCES['selected_record']['kappa'], 'baseline kappa differs')
+    k0 = Q(base['kappa'])
+    for row in rows.values():
+        dk = Q(row['kappa']) - k0
+        row['kappa_gain'] = dec(dk)
+        row['kappa_gain_percent'] = dec(100 * dk / k0, 12)
+    # Single-helper deferrals: rank by a 60-digit proxy, certify the best one exactly.
+    H0 = {int(r): n for r, n in census['scenarios']['baseline']['profile'].items()}
+    b0 = Q(base['complex_lower'])
+    singles = []
+    for i, prof in census['single_helper_profiles'].items():
+        singles.append((drop(H0, {int(r): n for r, n in prof.items()}, W, b0), int(i)))
+    singles.sort(reverse=True)
+    best_gain, best = singles[0]
+    Hb = {int(r): n for r, n in census['single_helper_profiles'][str(best)].items()}
+    bb = endpoint(Hb, W)
+    kb, _ = kappa(bb)
+    joint = drop(H0, {int(r): n for r, n in census['scenarios']['defer_all_selected_hosting']['profile'].items()},
+                 W, b0)
+    with localcontext() as ctx:
+        ctx.prec = 60
+        total_single = sum(x for x, _ in singles)
+    q = lambda x, e: str(x.quantize(Decimal(e)))
+    single = dict(changed_profiles=len(singles), unchanged=len(census['single_helper_unchanged']),
+                  best_helper=best, best_moment_drop_times_mW=q(best_gain, '1e-12'),
+                  sum_of_single_moment_drops_times_mW=q(total_single, '1e-9'),
+                  joint_moment_drop_times_mW=q(joint, '1e-9'),
+                  best_complex_lower=str(bb), best_kappa=str(kb), best_kappa_decimal=dec(kb),
+                  best_kappa_gain=dec(kb - k0), best_kappa_gain_percent=dec(100 * (kb - k0) / k0, 12),
+                  ranking='60-digit Decimal drop of m*W*moment at the baseline endpoint; '
+                          'only the best row is certified exactly',
+                  top10=[dict(helper=i, moment_drop_times_mW=q(x, '1e-12')) for x, i in singles[:10]])
+    result = dict(status='PASS_T37_RESTORATION_PRICES', base_commit=SOURCES['base_commit'],
+                  engines={k: v for k, v in SOURCES['engines'].items() if k.endswith('.py')},
+                  bit_lower=OW['bit_lower'], scenarios=rows, single_helper_deferral=single)
+    with open(sys.argv[2], 'w') as f:
+        f.write(canonical(result))
+    print(result['status'])
+    for key, row in rows.items():
+        print(f"{key:32s} b {row['complex_decimal'][:22]}  kappa {row['kappa_decimal'][:21]}  "
+              f"gain {row['kappa_gain_percent'][:9]}%  {row['binding']}")
+    print(f"best single helper {best}: kappa {single['best_kappa_decimal'][:21]} gain {single['best_kappa_gain_percent'][:10]}%")
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/t37-restoration-deferral/test_package.py b/research/t37-restoration-deferral/test_package.py
new file mode 100644
index 0000000000..a4fadabd10
--- /dev/null
+++ b/research/t37-restoration-deferral/test_package.py
@@ -0,0 +1,151 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Unit tests for the T37 restoration-deferral note.
+
+Run: python3 -B -m unittest discover -s research/t37-restoration-deferral -p test_package.py -v
+"""
+import json
+import sys
+import unittest
+from collections import Counter
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+
+from common import (Span, concentrated, coverage_census, hyperplane, load_construction, rank_mass,
+                    restoration_census, window_deferral)
+
+FULL3 = [0b100, 0b010, 0b001]
+
+
+def toy_word():
+    """h=3, one source (port 001), one target, two helpers; helper 3 is a low end."""
+    return dict(report=dict(h=3, v=1, R=2), ports=[0b001], start_extra={},
+                A=[['add', 0, 2, 1, 1, [0b001, 0b010]]], centers=[], center_frames=[], cut=[],
+                B=[['add', 3, 1, 1, 1, [0b010]]], early_cleanup=[],
+                cleanup=[['add', 0, 2, -1, 1, FULL3]], helper_final={'3': [0b010]}, target_levels={})
+
+
+def toy_template():
+    """Two calls; helper 0 is hosted twice in one window, helper 1 in two windows,
+    helper 2 in a window that already has an idle remainder of rank 3."""
+    slots = [dict(helper=0, family=2, child=0, width=2), dict(helper=0, family=2, child=0, width=2),
+             dict(helper=1, family=3, child=1, width=1), dict(helper=1, family=4, child=2, width=1),
+             dict(helper=2, family=5, child=3, width=2), dict(helper=2, family=5, child=3, width=2)]
+    return dict(calls=[{}, {}], hosting=dict(pooled_slots=slots),
+                idle_children=[dict(family=5, child=3, rank=3, replicas=1)])
+
+
+class SpanTests(unittest.TestCase):
+    def test_rank_and_containment(self):
+        U = Span([0b011, 0b001, 0b011])
+        self.assertEqual(U.rank, 2)
+        self.assertTrue(Span([0b010]).within(U))
+        self.assertFalse(Span([0b100]).within(U))
+        self.assertTrue(Span([0b001, 0b010]).same(U))
+
+    def test_hyperplane_is_orthogonal_complement(self):
+        for p in range(1, 1 << 5):
+            U = hyperplane(p, 5)
+            self.assertEqual(U.rank, 4)
+            self.assertTrue(all(bin(b & p).count('1') % 2 == 0 for b in U.basis))
+
+
+class RestorationTests(unittest.TestCase):
+    def test_toy_word(self):
+        r = restoration_census(toy_word())
+        self.assertEqual(r['paid'], Counter({1: 6, 2: 1}))
+        regs = r['registers']
+        self.assertEqual([x['restoration'] for x in regs], [1, 1, 1, 0])
+        self.assertEqual([x['full_cleanup_gates'] for x in regs], [1, 0, 1, 0])
+        self.assertTrue(regs[3]['low_end'])
+        self.assertEqual(r['widths'], Counter({3: 1, 1: 1}))
+
+    def test_non_monotone_frame_rejected(self):
+        w = toy_word()
+        w['B'].append(['add', 2, 3, 1, 1, [0b100]])   # helper 2 sits at rank 2 and cannot drop to <100>
+        with self.assertRaisesRegex(ValueError, 'non-monotone'):
+            restoration_census(w)
+
+    def test_target_levels_rejected(self):
+        w = toy_word()
+        w['target_levels'] = {'1': 1}
+        with self.assertRaisesRegex(ValueError, 'target levels'):
+            restoration_census(w)
+
+    def test_full_cleanup_on_low_end_rejected(self):
+        w = toy_word()
+        w['cleanup'].append(['add', 3, 0, 1, 1, FULL3])
+        with self.assertRaisesRegex(ValueError, 'low end'):
+            restoration_census(w)
+
+
+class DeferralTests(unittest.TestCase):
+    local = Counter({1: 2, 2: 1, 4: 1})
+    restoration = {0: 1, 1: 1, 2: 2}
+
+    def run_case(self, chosen):
+        H, removed, _ = window_deferral(toy_template(), self.local, self.restoration, chosen)
+        base, _, _ = window_deferral(toy_template(), self.local, self.restoration, set())
+        self.assertEqual(rank_mass(H), rank_mass(base))
+        return H, base
+
+    def test_isolated_deferral_is_shape_neutral(self):
+        H, base = self.run_case({1})
+        self.assertEqual(H, base)
+
+    def test_same_window_deferrals_merge(self):
+        H, base = self.run_case({0})
+        self.assertEqual(base - H, Counter({1: 2}))
+        self.assertEqual(H - base, Counter({2: 1}))
+
+    def test_existing_remainder_absorbs(self):
+        H, base = self.run_case({2})
+        self.assertEqual(base - H, Counter({2: 2, 3: 1}))
+        self.assertEqual(H - base, Counter({7: 1}))
+
+    def test_concentration_preserves_mass(self):
+        H = Counter({1: 5, 48: 2})
+        out = concentrated(H, Counter({1: 3}), Counter({48: 2}), 48)
+        self.assertEqual(rank_mass(out), rank_mass(H))
+        self.assertEqual(out, Counter({1: 2, 48: 2, 3: 1}))
+
+
+class CoverageTests(unittest.TestCase):
+    def template(self):
+        prov = dict(v=1, R=2, widths=[2, 1])
+        call = dict(provider_id='p', owners=[[0, [1, 0, 0]], [1, [1, 1, 0]], [2, [3, 0, 0]], [3, [4, 0, 0]]])
+        return dict(live=4, m=5, local_providers={'p': prov}, calls=[call],
+                    hosting=dict(pooled_slots=[dict(helper=0, family=2, width=2), dict(helper=1, family=3, width=1)]),
+                    idle_children=[dict(family=0, rank=2, replicas=1), dict(family=1, rank=2, replicas=1),
+                                   dict(family=2, rank=2, replicas=1), dict(family=3, rank=3, replicas=1)],
+                    private_namespace=dict(centers=[4, 5]))
+
+    def test_identity_and_failure(self):
+        cov = coverage_census(self.template(), local_mass=7, data_step=2)
+        self.assertEqual(cov['coverage_values'], {'5': 4})
+        t = self.template()
+        t['idle_children'][3]['rank'] = 2
+        self.assertEqual(coverage_census(t, 7, 2)['coverage_values'], {'4': 1, '5': 3})
+
+
+class SelectedDataTests(unittest.TestCase):
+    def test_t37_census_claims(self):
+        template, word = load_construction('T37')
+        local = restoration_census(word)
+        pos = [r for r in local['registers'] if r['restoration'] > 0]
+        self.assertEqual(sum(r['restoration'] for r in pos if r['role'] == 'helper'), 636)
+        self.assertEqual(sum(r['restoration'] for r in pos if r['role'] == 'source'), 230)
+        self.assertTrue(all(r['full_cleanup_gates'] > 0 for r in pos))
+        cov = coverage_census(template, rank_mass(local['paid']), 8)
+        self.assertEqual(cov['coverage_values'], {'73': 33152})
+        self.assertEqual(cov['deficit'], 33152 - 64 * 333)
+
+    def test_committed_baseline_is_selected(self):
+        prices = json.loads((HERE / 'PRICES.json').read_text())
+        selected = json.loads((HERE.parents[1] / 'certificates/selected-result.json').read_text())
+        self.assertEqual(prices['scenarios']['baseline']['kappa'], selected['kappa'])
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/research/t37-restoration-deferral/verify.py b/research/t37-restoration-deferral/verify.py
new file mode 100644
index 0000000000..56aeed2281
--- /dev/null
+++ b/research/t37-restoration-deferral/verify.py
@@ -0,0 +1,190 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Replay the T37 restoration-deferral note and its negative controls.
+
+Usage: python3 -B research/t37-restoration-deferral/verify.py --work NEW_EMPTY_DIR
+
+Runs census.py and price.py into the new work directory, requires their
+outputs to equal the committed CENSUS.json and PRICES.json, and checks that
+every negative control is rejected for its stated reason.
+Expected last line: PASS_T37_RESTORATION_DEFERRAL_REPLAY
+"""
+import argparse
+import copy
+import json
+import subprocess
+import sys
+from collections import Counter
+from pathlib import Path
+
+from common import (HERE, ROOT, SOURCES, coverage_census, gate_registers, load_construction, rank_mass,
+                    read_member, require, restoration_census, window_deferral)
+
+
+def run(script, *args):
+    proc = subprocess.run([sys.executable, '-B', str(HERE / script), *map(str, args)],
+                          cwd=HERE, capture_output=True, text=True)
+    sys.stdout.write(proc.stdout)
+    require(proc.returncode == 0, f'{script} failed:\n{proc.stderr}')
+
+
+def same_json(a, b):
+    return json.loads(Path(a).read_text()) == json.loads(Path(b).read_text())
+
+
+def rejects(name, fn, reason):
+    try:
+        fn()
+    except ValueError as exc:
+        require(reason in str(exc), f'control {name} rejected for another reason: {exc}')
+        return name
+    raise SystemExit(f'FAIL control {name} was accepted')
+
+
+def consumed_by_cleanup(local):
+    """The note's claim: every positive restoration climb is consumed by full-frame cleanup."""
+    for r in local['registers']:
+        if r['restoration'] > 0:
+            require(r['full_cleanup_gates'] > 0, f"unconsumed restoration climb at register {r['register']}")
+    return True
+
+
+def controls():
+    template, word = load_construction('T37')
+    local = restoration_census(word)
+    local_mass = rank_mass(local['paid'])
+    W = template['live']
+    passed = []
+
+    def coverage_with(mutate):
+        t = copy.copy(template)
+        t['idle_children'] = copy.deepcopy(template['idle_children'])
+        mutate(t)
+        cov = coverage_census(t, local_mass, 8)
+        require(cov['coverage_values'] == {'73': W}, 'coverage identity fails')
+
+    big = next(i for i, c in enumerate(template['idle_children']) if c['rank'] == 48)
+    passed.append(rejects('C1_idle_child_dropped',
+                          lambda: coverage_with(lambda t: t['idle_children'].pop(big)), 'coverage identity fails'))
+    passed.append(rejects('C2_idle_child_rank_47',
+                          lambda: coverage_with(lambda t: t['idle_children'][big].update(rank=47)),
+                          'coverage identity fails'))
+    passed.append(rejects('C3_idle_child_duplicated',
+                          lambda: coverage_with(lambda t: t['idle_children'].append(dict(t['idle_children'][big]))),
+                          'coverage identity fails'))
+    # C4: delete every full-frame cleanup gate touching one restoration helper.
+    victim = next(r['register'] for r in local['registers'] if r['role'] == 'helper' and r['restoration'] > 0)
+    early = {i for i, _ in word['early_cleanup']}
+    w2 = dict(word)
+    keep, remap = [], {}
+    for i, g in enumerate(word['cleanup']):
+        if i in early or victim not in gate_registers(g):
+            remap[i] = len(keep)
+            keep.append(g)
+    w2['cleanup'] = keep
+    w2['early_cleanup'] = [[remap[i], U] for i, U in word['early_cleanup']]
+    passed.append(rejects('C4_cleanup_removed_for_one_helper',
+                          lambda: consumed_by_cleanup(restoration_census(w2)), 'unconsumed restoration climb'))
+    # C5: a 'deferral' that drops the returned coordinates is not coverage preserving.
+    restoration = {r['register'] - 2 * local['v']: r['restoration'] for r in local['registers'] if r['role'] == 'helper'}
+    H, removed, _ = window_deferral(template, local['paid'], restoration, {9})
+    base = Counter()
+    for _ in template['calls']:
+        base.update(local['paid'])
+    for c in template['idle_children']:
+        base[c['rank']] += 1
+    zero_cost = base - removed
+
+    def mass_neutral(P):
+        require(rank_mass(P) == rank_mass(base), 'deferral changes rank mass')
+    mass_neutral(H)
+    passed.append(rejects('C5_zero_cost_deletion', lambda: mass_neutral(zero_cost), 'deferral changes rank mass'))
+    # C6: a corrupted payload pin is rejected before parsing.
+    src = SOURCES['constructions']['T37']
+    passed.append(rejects('C6_payload_pin', lambda: read_member(ROOT / src['archive'], src['word_member'], '0' * 64),
+                          'payload digest mismatch'))
+    # C7: a child above the halving cap is rejected by the scenario guard.
+    def halving(P):
+        require(73 * 73 > 2 * max(P) ** 2, 'halving guard')
+    halving(Counter({48: 1}))
+    passed.append(rejects('C7_halving_cap', lambda: halving(Counter({52: 1})), 'halving guard'))
+    return passed
+
+
+def price_controls():
+    sys.path.insert(0, str(HERE))
+    import price
+    from fractions import Fraction as Q
+    census = json.loads((HERE / 'CENSUS.json').read_text())
+    W = census['T37']['coverage']['live']
+    H0 = {int(r): n for r, n in census['scenarios']['baseline']['profile'].items()}
+    passed = []
+    b0 = price.endpoint(H0, W)
+    # C8: at the next complex grid point both engines put the moment above one.
+    z = b0 + Q(1, 10 ** 24)
+    lo, hi = price.MOMENT.moment(H0, 73, W, z, False)
+    blo, bhi = price.BASE_TWO.moment(73, W, list(H0.items()), z)
+    require(lo > 1 and blo > 1, 'both engines must exceed one at the next endpoint')
+
+    def accept_next():
+        require(hi < 1 or bhi < 1, 'next complex endpoint rejected by both engines')
+    passed.append(rejects('C8_next_complex_endpoint', accept_next, 'next complex endpoint rejected by both engines'))
+    # C9: one extra rank-one child changes the baseline kappa, so the selected pin would fail.
+    H1 = dict(H0)
+    H1[1] += 1
+    k1, _ = price.kappa(price.endpoint(H1, W))
+    def pin():
+        require(str(k1) == SOURCES['selected_record']['kappa'], 'baseline kappa differs')
+    passed.append(rejects('C9_perturbed_baseline', pin, 'baseline kappa differs'))
+    return passed
+
+
+def float_crosscheck(census_path, prices_path):
+    """Double-precision bisection that shares no code with the pinned engines."""
+    import math
+    census = json.loads(Path(census_path).read_text())
+    prices = json.loads(Path(prices_path).read_text())
+    W, m = census['T37']['coverage']['live'], 73
+    bit = float(prices['bit_lower'].split('/')[0]) / float(prices['bit_lower'].split('/')[1])
+    for key, row in census['scenarios'].items():
+        H = {int(r): n for r, n in row['profile'].items()}
+        f = lambda a: sum(r * n / (m * W) * math.exp(a * math.log(m / r)) for r, n in H.items()) - 1
+        lo, hi = 0.0, 0.01
+        for _ in range(200):
+            mid = (lo + hi) / 2
+            lo, hi = (mid, hi) if f(mid) < 0 else (lo, mid)
+        exact = prices['scenarios'][key]
+        s = min(bit, lo)
+        require(abs(lo - float(exact['complex_decimal'])) < 1e-13, f'{key}: float endpoint disagrees')
+        require(abs(s / (1 + s) - float(exact['kappa_decimal'])) < 1e-13, f'{key}: float kappa disagrees')
+    best = prices['single_helper_deferral']
+    H = {int(r): n for r, n in census['single_helper_profiles'][str(best['best_helper'])].items()}
+    f = lambda a: sum(r * n / (m * W) * math.exp(a * math.log(m / r)) for r, n in H.items()) - 1
+    lo, hi = 0.0, 0.01
+    for _ in range(200):
+        mid = (lo + hi) / 2
+        lo, hi = (mid, hi) if f(mid) < 0 else (lo, mid)
+    b = best['best_complex_lower'].split('/')
+    require(abs(lo - int(b[0]) / int(b[1])) < 1e-13, 'best single helper: float endpoint disagrees')
+    return len(census['scenarios']) + 1
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument('--work', required=True)
+    work = Path(ap.parse_args().work).resolve()
+    require(not work.exists(), 'work directory must not exist')
+    work.mkdir(parents=True)
+    run('census.py', work / 'CENSUS.json')
+    require(same_json(work / 'CENSUS.json', HERE / 'CENSUS.json'), 'CENSUS.json differs from the committed result')
+    run('price.py', work / 'CENSUS.json', work / 'PRICES.json')
+    require(same_json(work / 'PRICES.json', HERE / 'PRICES.json'), 'PRICES.json differs from the committed result')
+    print('float cross-check agrees for', float_crosscheck(work / 'CENSUS.json', work / 'PRICES.json'), 'priced rows')
+    template, word = load_construction('T37')
+    consumed_by_cleanup(restoration_census(word))
+    passed = controls() + price_controls()
+    print('controls rejected as expected:', ', '.join(passed))
+    print('PASS_T37_RESTORATION_DEFERRAL_REPLAY')
+
+
+if __name__ == '__main__':
+    main()