diff --git a/research/r439-later-retirement-cuts/CERTIFICATE.json b/research/r439-later-retirement-cuts/CERTIFICATE.json
new file mode 100644
index 0000000000..ffce862911
--- /dev/null
+++ b/research/r439-later-retirement-cuts/CERTIFICATE.json
@@ -0,0 +1,2036 @@
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+  ],
+  "join_rank_counts": {
+    "7": 6,
+    "8": 433
+  },
+  "legal_helpers": [
+    469,
+    470,
+    476
+  ],
+  "no_new_kappa": true,
+  "rank_seven_cases": [
+    {
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+        474
+      ],
+      "endpoint_blockers": [
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+      "isolation_gates": [
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+          0
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+    {
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+      "isolation_gates": [
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+      "isolation_gates": [
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+        "registers": [
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+      "isolation_gates": [
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+      "legal": true,
+      "minimum_adds": 3,
+      "promotions": [
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+          "rank_increment": 6,
+          "register": 50,
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+        "registers": [
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+  ],
+  "schema_version": 1,
+  "seed": 17,
+  "status": "SCOPED_SINGLE_STATION_CLASSIFICATION",
+  "word_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f"
+}
diff --git a/research/r439-later-retirement-cuts/LATER-CUTS.json b/research/r439-later-retirement-cuts/LATER-CUTS.json
new file mode 100644
index 0000000000..4540d66ea3
--- /dev/null
+++ b/research/r439-later-retirement-cuts/LATER-CUTS.json
@@ -0,0 +1,572 @@
+{
+  "B_gate_count": 712,
+  "cut_convention": "cut k is after exactly the first k B records, with D/A/scatter fixed",
+  "cuts_per_helper": 713,
+  "helper_cut_pairs": 4278,
+  "helpers": [
+    {
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+      "joint_rank_seven_cuts": 49,
+      "necessary_condition_pass_count": 39,
+      "runs": [
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+            "lost_targets": [
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+            ],
+            "restoration_rank": 4,
+            "restore_donors": [
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+          "first_cut": 0,
+          "last_cut": 9
+        },
+        {
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+            "lost_targets": [],
+            "restoration_rank": 4,
+            "restore_donors": [
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+            ]
+          },
+          "first_cut": 10,
+          "last_cut": 48
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+        {
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+            "joint_rank": 8
+          },
+          "first_cut": 49,
+          "last_cut": 712
+        }
+      ],
+      "windows": [
+        [
+          10,
+          48
+        ]
+      ]
+    },
+    {
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+      "necessary_condition_pass_count": 0,
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+            "restore_donors": [
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+        {
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+        }
+      ],
+      "windows": []
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+    {
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+      "necessary_condition_pass_count": 58,
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+            "restoration_rank": 4,
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+          },
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+          "last_cut": 30
+        },
+        {
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+        {
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+          "last_cut": 712
+        }
+      ],
+      "windows": [
+        [
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+      ]
+    },
+    {
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+      "necessary_condition_pass_count": 0,
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+              200,
+              208
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+          "last_cut": 60
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+        {
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+              200,
+              208
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+          "last_cut": 288
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+        {
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+          "last_cut": 301
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+        {
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+        {
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+            "restore_donors": [
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+            ]
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+        },
+        {
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+          "last_cut": 555
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+        {
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+          },
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+          "last_cut": 712
+        }
+      ],
+      "windows": []
+    },
+    {
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+      "joint_rank_seven_cuts": 518,
+      "necessary_condition_pass_count": 518,
+      "runs": [
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+            "lost_targets": [],
+            "restoration_rank": 2,
+            "restore_donors": [
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+            ]
+          },
+          "first_cut": 0,
+          "last_cut": 289
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+        {
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+            "lost_targets": [],
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+            "restore_donors": [
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+          "last_cut": 294
+        },
+        {
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+            "lost_targets": [],
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+            "restore_donors": [
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+            ]
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+          "last_cut": 295
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+        {
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+            "lost_targets": [],
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+            "restore_donors": [
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+            ]
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+          "last_cut": 296
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+        {
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+            "lost_targets": [],
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+        {
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+            "lost_targets": [],
+            "restoration_rank": 4,
+            "restore_donors": [
+              17,
+              33,
+              77,
+              470
+            ]
+          },
+          "first_cut": 307,
+          "last_cut": 307
+        },
+        {
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+            "joint_rank": 7,
+            "lost_targets": [],
+            "restoration_rank": 4,
+            "restore_donors": [
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+              22,
+              33,
+              77,
+              470
+            ]
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+          "last_cut": 312
+        },
+        {
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+            "lost_targets": [],
+            "restoration_rank": 4,
+            "restore_donors": [
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+              33,
+              77,
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+            ]
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+          "first_cut": 313,
+          "last_cut": 517
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+        {
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+          },
+          "first_cut": 518,
+          "last_cut": 712
+        }
+      ],
+      "windows": [
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+        ]
+      ]
+    },
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+              385,
+              476
+            ]
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+          "first_cut": 0,
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+        {
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+          },
+          "first_cut": 285,
+          "last_cut": 712
+        }
+      ],
+      "windows": []
+    }
+  ],
+  "meaning": "Passing both necessary tests is not a legal suffix or new supplier.",
+  "no_new_kappa": true,
+  "schema_version": 1,
+  "source_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f"
+}
diff --git a/research/r439-later-retirement-cuts/README.md b/research/r439-later-retirement-cuts/README.md
new file mode 100644
index 0000000000..c2fec1d897
--- /dev/null
+++ b/research/r439-later-retirement-cuts/README.md
@@ -0,0 +1,187 @@
+# R439: complete later-cut retirement census
+
+**Scoped bit-supplier negative result and precise handoff; no new kappa.**
+For PR1128's six width-seven candidates, this package checks every boundary
+along the fixed PR589 B word: **713 cuts and 4,278 helper/cut pairs**. It supplies the complete
+necessary-condition census for the later-cut first-restoration question left
+explicitly open by Ross Richardson's concurrent PR1256.
+
+A cut numbered k is **after exactly the first k B records**. Thus cut 10 is
+after zero-based B[9]. The D/A/scatter prefix and B chronology are fixed.
+
+| Helper | Cuts with joint restoration/erasure rank seven | Cuts also passing first-restoration target access |
+|---:|---|---|
+| 465 | 0–48 | **10–48** (39 cuts) |
+| 466 | 0–78 | **none** |
+| 468 | 0–88 | **31–88** (58 cuts) |
+| 469 | 0–555 | **none** |
+| 470 | 0–517 | **0–517** (518 cuts) |
+| 476 | 0–284 | **none** |
+
+Every later cut outside the second column has joint rank eight. These are
+**necessary-condition windows**, not feasible suffixes or constructions.
+No B/C replacement, physical owner allocation or supplier invoice is supplied.
+
+The sharp chronology point is helper466: its blocking target208 is first
+read at B[88], but the joint bound has already risen to eight after B[78].
+Simply waiting for that target read cannot save it. Helpers465 and468 do
+escape their initial target-access obstruction after B[9] and B[30],
+respectively, but only until the joint bound rises after B[48] and B[88].
+For helpers469 and476, at least one inaccessible required target dependency
+remains at every cut with joint rank seven.
+
+## Exact contract and argument
+
+The sole mathematical input is the frozen PR589 tuned word. At each cut,
+write the 661-register scalar state as `w=M u` over F2. All source, target
+and helper inputs are independent. Each prefix gate is an invertible
+transvection, including the already-consumed retained scatter; no new access
+to its COPY channels is allowed. Current frames F_r are rational subspaces
+of Q^8. Frame changes must be monotone. Scalar operations must use a common
+frame, extra dirty workspace must start independently and be restored, and
+there is no new COPY, descent, reset or other high-to-low transport.
+
+We test a suffix whose **first restoration block** operates at a single
+rational frame J, with no lower-frame preprocessing after the chosen cut,
+and restores the designated helper h to its original dirty input s_h.
+After that block, arbitrary allowed multi-frame scalar work is permitted.
+The ultimate endpoint for h must have dimension at most seven; other source,
+target and helper endpoints and scalar values retain their original contract.
+This is the first-restoration model of PR1256, not arbitrary suffix synthesis.
+
+Let R_h be the support of `e_h^T M^-1`, and D_h the support of the h-th column
+of M. The restoration/erasure argument from PR1128 gives the necessary bound
+
+`U_h = span(F_h, {F_r : r in R_h union D_h}) <= final_frame(h)`.
+
+All these joins have rank seven or eight in the completed census. A rank-eight
+join excludes every proper final frame in this interface, even with arbitrary
+rational choices, target access and restored dirty scratch. For a rank-seven
+join, a first restoration block must use a frame containing
+
+`J_h = span(F_h, {F_r : r in R_h})`.
+
+The required final target value `y_t + x_(t-111)` has the unique boundary row
+`b_t = (e_t + e_(t-111))^T M^-1`. If b_t uses a coordinate forced into the
+restoration block, but J_h is not contained in t's final frame V_t, no allowed
+completion can supply that dependence to t. Every touched register has moved
+to J_h or a larger frame; monotonicity prevents any of its information from
+reaching V_t. Untouched boundary coordinates and fresh independent dirt cannot
+encode the missing independent coordinate. Enlarging the first restoration
+frame cannot cure a failed containment.
+
+This is PR1256's information-access implication. We apply it at **every**
+later B boundary, where both inverse rows and frames change. The complete
+certificate records contiguous runs with identical restoration donors, join
+rank, restoration rank and lost-target sets. No cut, rational station or
+support-size cutoff is sampled. The proof establishes the stated exclusions;
+passing the two tests supplies no sufficiency claim.
+
+For helper466, the target-access witness is target208 at every eligible cut
+0–78. At cut79 the joint rank is eight; at cut89, after target208's original
+read, it is still eight. The 469/476 lost-target sets are likewise nonempty
+through every rank-seven cut. Full sets and every transition are retained in
+[LATER-CUTS.json](LATER-CUTS.json).
+
+## Predecessors and evidence-driven scope change
+
+Ali Romman's PR1128 (`df29b159239b79d7e451d6ddda826a73e0e50a67`) establishes the
+boundary lemma and the six after-scatter candidates. Ross Richardson's
+PR1256 (`d6d5a994fcdcd8d04ec439ff988daa8f37b17ece`) establishes the initial
+six-case target-access obstruction and an explicit finite helper470 retirement
+using rank two before rank seven. Its construction is predecessor evidence,
+not implemented or repriced here. Its native/physical/H4 obligations remain.
+
+This session initially derived the same stationary stars and endpoint-cap
+failures independently. The final overlap refresh found PR1256 before any
+submission. That initial material is retained in [STATION-NOTE.md](STATION-NOTE.md)
+and `CERTIFICATE.json` as corroboration only. It is not the novelty claim.
+The one evidence-driven pivot is exactly PR1256's listed later-cut question;
+its README says no search there was performed. In particular, our no-window
+result for helper466 explains why its proposed target-read follow-up fails
+in the fixed chronology, while the two other suggested candidates retain
+precise finite windows. Earlier helper470 deletion belongs to Ali Romman's
+PR1043; its savings are not combined with anything here.
+
+Fresh OS seed **17** selected the original user's bit-supplier track. The
+three initial candidates, first scope, pivot and stopping rule are in
+`TASK.json`. There was no pinned sprint issue, so the authorized local-claim
+fallback was used. The initial snapshot covered 850 open PR bodies; the final
+pre-pivot refresh covered 855 and all 12 returned discussions. PR1253 concerns
+common-first-contact kernel entrances and PR1250 source-mask deletion; both
+are distinct and neither is a mathematical dependency here.
+
+## Reproduce and negative controls
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 scripts/research_package.py --package research/r439-later-retirement-cuts
+```
+
+The principal commands also run on Python 3.10+:
+
+```sh
+python3 -I -O -B research/r439-later-retirement-cuts/later_cuts.py
+python3 -I -O -B research/r439-later-retirement-cuts/check_later_cuts.py
+python3 -I -O -B research/r439-later-retirement-cuts/test_later_cuts.py
+```
+
+Expected markers include `PASS_LATER_BIT_CUTS pairs=4278` and
+`PASS_INDEPENDENT_LATER_CUTS full_inverse_rebuilds=713 helper_cut_pairs=4278`,
+followed by passing tests and `PASS_REGISTERED_RESEARCH_PACKAGE`.
+
+The primary engine incrementally updates inverse rows with each B
+transvection, using packed binary rows and rational geometry. The separate
+checker imports no primary engine, reconstructs the **entire inverse from
+scratch at every one of the 713 boundaries**, and uses independently replayed
+set-valued scalar states and fraction-free integer geometry. It checks each
+restoration identity directly and agrees on every run and boundary, not just
+the total counts. Both inherit only the exact raw word; no predecessor
+executable code is imported. Separate code paths are not independent human
+review.
+
+The test suite rejects wrong boundary indexing, shifted donor support,
+missing target obligations, false pass windows, incomplete cut coverage and
+changed source bytes. It checks optimized source-only relocation and parsed
+certificate regeneration. The retained stationary suite adds all ten legal
+witness-gate omissions, three endpoint-cap failures with relaxed positive
+controls, six certificate mutations in both engines, a wrong station, damaged
+original cleanup and source-corruption tests.
+
+Base `dadfea6e8a78ff6ba901705f87532a71c6f5bbb8`; input SHA256
+`e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f`.
+`SOURCES.json` pins base Git blobs, historical context and both predecessor
+heads/documents. See `VALIDATION.md` for actual local runs and omitted work.
+
+## Scope, cost and credit
+
+This is an exact finite census plus the cited necessary-condition arguments.
+It is not a formal proof-assistant verification of the multiplication theorem.
+Even optimistically free suffix work cannot repair a failed information-access
+condition within this model. The surviving windows still require full source
+access, target effects, restoration, frame transitions, copies, recursive
+children, physical hosting, precision/tape and outer/all-size admission before
+any new paid profile or exponent can be claimed. The selected complex supplier
+remains binding. No native replay, complete cold supplier replay, production
+adoption, remote CI or new kappa is claimed. `upstream/`, frozen predecessor
+packages and the selected frontier are unchanged.
+
+Credit **Ali Romman** (PR1128 and earlier PR1043), **Ross Richardson**
+(PR1256), **Sagar Thakrar** (PR1023 width-seven hosting incentive),
+DreamingOfClouds (PR589/545), eumemic (PR555/543), and their retained
+compiler/hosting lineage. Prepared for **Philipp (@mightyOil)** with substantial
+**OpenAI Codex / GPT-6 Astra** assistance in proof, code, tests and writing.
+New material is Apache-2.0.
+
+## Open next questions
+
+Can helper465 at cut10 or helper468 at cut31 be restored through a fully
+priced legal suffix? Those are the earliest new necessary-condition windows;
+start there and preserve all dirty columns, pending target reads and physical
+frame paths. The census supplies no such suffix and does not justify a new
+search outside the 39/58 windows without a changed assumption. For helper470,
+PR1256 already gives a finite cut-zero continuation; native H4, owner-window
+and precision admission are the more useful next checks. Changes to the prefix,
+lower-frame preparation, target-read reordering or added transport are outside
+this census and require a new explicit contract and complete cost.
diff --git a/research/r439-later-retirement-cuts/SOURCES.json b/research/r439-later-retirement-cuts/SOURCES.json
new file mode 100644
index 0000000000..fd76caad17
--- /dev/null
+++ b/research/r439-later-retirement-cuts/SOURCES.json
@@ -0,0 +1,85 @@
+{
+  "schema_version": 1,
+  "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8",
+  "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"
+    },
+    {
+      "path": "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz",
+      "usage": "input",
+      "git_blob": "85a4499bf9e4911a705d50567a2c2ef6cf23739a",
+      "sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f"
+    },
+    {
+      "path": "research/bit589-width-packing/README.md",
+      "usage": "provenance",
+      "git_blob": "a915381a7a38d3728205a2120aa034f94537ca0f",
+      "sha256": "671ca8a9d9e78348eae1e5c605ead1606df3d5e23d251600f0bdf60175479f1e"
+    },
+    {
+      "path": "docs/research/community-batch1099-review.md",
+      "usage": "provenance",
+      "git_blob": "6cb6ec061a071a06a2d18cd4dc3e9a2b05d28099",
+      "sha256": "7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb"
+    },
+    {
+      "path": "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+      "usage": "provenance",
+      "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8",
+      "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+    }
+  ],
+  "predecessors": [
+    {
+      "pr": 1128,
+      "head": "df29b159239b79d7e451d6ddda826a73e0e50a67",
+      "author": "Ali Romman (@aliromman)",
+      "role": "Boundary lemma and six-survivor premise; independently replayed, no executable code imported.",
+      "documents": [
+        {
+          "path": "research/bit-width-seven-boundary/README.md",
+          "git_blob": "f1930385706e38cc3b9995b8ba01f3ac9d06034b",
+          "sha256": "29b61651091c0870f9762efb6f93ebfa358d7bb8206d04012b18192cf4dabfab"
+        },
+        {
+          "path": "research/bit-width-seven-boundary/PROOF.md",
+          "git_blob": "b3bedffde3ee5f1914873ec7918039ab6614678c",
+          "sha256": "f9fb4706dd523229e8351646c5ef011d8bd16eebc3dd6c35a778b352c123b387"
+        },
+        {
+          "path": "research/bit-width-seven-boundary/CERTIFICATE.json",
+          "git_blob": "6982d303d1ba1dfa0b33a2a7f1a1acc9b8a5b2ee",
+          "sha256": "06ea7280e8a0829b283e352d5590a7cc832ee0973335c24dbac02505d493fa36"
+        }
+      ]
+    },
+    {
+      "pr": 1256,
+      "head": "d6d5a994fcdcd8d04ec439ff988daa8f37b17ece",
+      "author": "Ross Richardson",
+      "role": "First-restoration target-access lemma, after-scatter classification, finite470 continuation; later-cut question. No executable code imported.",
+      "documents": [
+        {
+          "path": "research/bit-early-retirement-cut/README.md",
+          "git_blob": "4f3716685c7a22ec4c1b8a68c8beb69021acd0a9",
+          "sha256": "57b952674aefc3fb6287ceaab7c940c100916dba8ba97104e1838c785e3d8e9f"
+        },
+        {
+          "path": "research/bit-early-retirement-cut/CERTIFICATE.json",
+          "git_blob": "b7a8d17755711ccb901742c59dd775c586be1c8d",
+          "sha256": "735c507caf32715f978e9c0ca67cb056184c751593cd8c58e9dd97232def7a46"
+        }
+      ]
+    }
+  ]
+}
diff --git a/research/r439-later-retirement-cuts/STATION-NOTE.md b/research/r439-later-retirement-cuts/STATION-NOTE.md
new file mode 100644
index 0000000000..d56a412505
--- /dev/null
+++ b/research/r439-later-retirement-cuts/STATION-NOTE.md
@@ -0,0 +1,41 @@
+# Initial stationary fixtures: independent corroboration only
+
+The session began by replaying PR1128's 439-helper after-scatter boundary and
+checking a single rank-seven station. Concurrent Ross Richardson PR1256
+subsumes this question and gives the stronger future-target-access argument
+and finite two-frame helper470 continuation. This appendix claims no priority
+or new supplier result. README.md describes the later-cut contribution.
+
+433 helpers have rank-eight restoration/erasure joins. The other six are
+465/466/468/469/470/476. The first three cannot perform all isolation work at
+their forced station while retaining their dirty-carrying targets' final
+frames. The other three admit scalar/frame-local isolation:
+
+```
+station 517: 469 ^= 50; 413 ^= 469; 479 ^= 469
+station 513: 470 ^= 77; 444 ^= 470; 475 ^= 470
+station 514: 476 ^= 67; 476 ^= 328; 476 ^= 331; 476 ^= 385
+```
+
+These programs restore the designated independent dirty input and remove it
+from all other registers, preserving their other coefficients. Their counts
+3/3/4 are minimal in binary ADDs: the first two change three required
+destinations; the third computes the parity of five essential boundary
+coordinates, whose dependency graph requires four edges. All participating
+registers can reach the station and retain their final-frame cap. However,
+future target information may already have become inaccessible; none is an
+admitted suffix. In particular these stationary programs must not be confused
+with PR1256's two-frame helper470 program, which leaves source77 at rank two.
+
+`CERTIFICATE.json`, `verify.py`, `independent.py` and `test_package.py` retain
+this complete after-scatter replay and its controlled scalar fixtures. The
+primary also checks the original B/C map on all661 columns. The six test
+groups cover both complete engines, ten gate omissions, three target-cap
+failures plus relaxed positive controls, six receipt mutations, a wrong
+station, damaged original cleanup, exact regeneration, isolated relocation
+and source corruption. These checks support the later-cut implementations;
+they do not establish a complete physical supplier or new kappa.
+
+Credit Ali Romman's PR1128, Ross Richardson's PR1256 and the PR589/555 lineage.
+Prepared for Philipp (@mightyOil), with substantial OpenAI Codex assistance.
+Apache-2.0.
diff --git a/research/r439-later-retirement-cuts/TASK.json b/research/r439-later-retirement-cuts/TASK.json
new file mode 100644
index 0000000000..66355fa1d5
--- /dev/null
+++ b/research/r439-later-retirement-cuts/TASK.json
@@ -0,0 +1,95 @@
+{
+  "schema_version": 1,
+  "task_id": "bit-helper-contract",
+  "priority_revision": 2,
+  "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8",
+  "original_card": {
+    "id": "bit-helper-contract",
+    "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?",
+    "starting_points": [
+      "research/r439-bsection-stars-seed01/README.md",
+      "research/r439-copy-path-sharing-barrier/README.md"
+    ],
+    "methods": [
+      "Derive a replacement interface lemma and price its implementation.",
+      "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement."
+    ],
+    "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/r439-bsection-stars-seed01/verify.py"
+      ],
+      "expected": "PASS_R439_BSECTION_STARS",
+      "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.",
+    "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.",
+    "allowed_variations": [
+      "Choose one helper-star or quartet instance; narrow to one boundary implication."
+    ],
+    "scope_change_triggers": [
+      "Changing only source count or scalar addition count without an interface argument."
+    ],
+    "overlap_terms": [
+      "H2_D_frame0_targets_from_helpers",
+      "K_equals_D",
+      "helper-star"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Source-bound all-713-B-boundary first-restoration/target-access census for the six PR1128 survivors; fill the later-cut gap explicitly left by PR1256.",
+  "scope_change_reason": "The final refresh found PR1256 had subsumed the initial stationary classification. One evidence-driven pivot to its explicitly unsearched later B cuts; initial material is corroborative only.",
+  "bottleneck_link": "A narrower helper changes hosted residual width; these blocks expose the exact later source-access obstruction. Side mechanism result with no complete supplier price and no selected kappa gain.",
+  "budget_minutes": 40,
+  "stop_rule": "Exactly713 cuts for each of6 helpers; stop after joint-rank and first-restoration target-access classification. No arbitrary suffix rewriting or cost search.",
+  "outcome": "completed",
+  "evidence": "LATER-CUTS.json; independent full inverse rebuild at every boundary; primary incremental updates; full boundary and mutation/relocation suites.",
+  "author": "Philipp (@mightyOil)",
+  "ai_assistance": "Substantial OpenAI Codex / GPT-6 Astra assistance in proof, code, testing and writing.",
+  "open_questions": [
+    {
+      "question": "Can helper465 at cut10 or468 at cut31 be completed through a legal, fully priced suffix?",
+      "why_it_matters": "The census identifies the exact remaining necessary-condition windows, but passing them is not construction.",
+      "first_step": "Construct and replay all dirty columns starting from the stated earliest cut.",
+      "blocked_by": "Pending target dependencies, source access, frame schedules, H4 and physical hosting/precision costs."
+    }
+  ],
+  "seed": 17,
+  "assignment_track": "bit supplier, original user mapping 00-19",
+  "candidates": [
+    {
+      "scope": "PR1128 six-survivor single-station exit feasibility",
+      "decision": "selected"
+    },
+    {
+      "scope": "R439 fixed-profile scalar block optimization",
+      "decision": "overlaps PR1208/1221"
+    },
+    {
+      "scope": "Arbitrary source-mask helper deletion",
+      "decision": "already classified in PR1250"
+    }
+  ],
+  "coordination": {
+    "pinned_issue_present": false,
+    "claim": "local claim before implementation",
+    "overlap_snapshot_open_prs": 850,
+    "predecessor": 1128,
+    "distinct_from": [
+      1179,
+      1250,
+      1253
+    ],
+    "final_snapshot_open_prs": 855,
+    "final_snapshot_discussions": 12,
+    "concurrent_overlap": {
+      "pr": 1256,
+      "head": "d6d5a994fcdcd8d04ec439ff988daa8f37b17ece",
+      "treatment": "Credit initial stationary results and470 continuation; extend only explicitly unsearched later cuts."
+    },
+    "submission_refresh": "Latest100 open PR bodies through1268; no additional later-cut overlap."
+  }
+}
diff --git a/research/r439-later-retirement-cuts/VALIDATION.md b/research/r439-later-retirement-cuts/VALIDATION.md
new file mode 100644
index 0000000000..40bfe0921e
--- /dev/null
+++ b/research/r439-later-retirement-cuts/VALIDATION.md
@@ -0,0 +1,42 @@
+# Local verification receipt
+
+Date: 2026-10-13. Environment: macOS arm64, CPython 3.12.13 and 3.14.7.
+Base and refreshed main: `dadfea6e8a78ff6ba901705f87532a71c6f5bbb8`.
+
+Passed on Python 3.12.13:
+
+```
+python3.12 scripts/research_package.py --package research/r439-later-retirement-cuts
+```
+
+- Complete primary census: 4,278 pairs, 713 cuts per helper.
+- Separate checker: 713 complete inverse reconstructions and equality at every boundary.
+- Four later-cut test groups, including six corrupted census variants, boundary witnesses, source corruption, optimized relocation and exact regeneration.
+- Six stationary fixture groups, including ten gate omissions, three target-cap failures/relaxed positives, six receipt faults in both engines, wrong station, damaged original cleanup, source corruption, relocation and overwrite rejection.
+- Final marker: `PASS_REGISTERED_RESEARCH_PACKAGE research/r439-later-retirement-cuts outcome=completed`.
+
+The four later-cut groups also pass with CPython 3.14.7 under `-I -O -B`.
+The six stationary groups passed on the same interpreter before the directory
+was renamed; the complete registered replay after the rename passed on 3.12.13.
+
+Also passed:
+
+```
+python3 -B scripts/research_baseline.py
+python3 -B scripts/verify_selected_result.py
+python3 -m unittest discover -s tests -p test_selected_result.py
+```
+
+The baseline reports source bindings only, unchanged selected kappa
+`836330098538459/500000000000000000`, and the complex side binding. The five
+selected-result tests pass. No selected frontier file or upstream file changed.
+
+Overlap: initial complete850-PR snapshot; refreshed complete855-PR snapshot
+and12 discussions exposed PR1256 and caused the documented one-scope pivot.
+Final latest100-PR refresh through PR1268 found no additional later-cut census;
+newer work concerns other circuits, packing and ledger verification. These
+bounded live observations do not constitute a novelty guarantee.
+
+Not run or claimed: native 5/9/11-stage supplier replay, full selected cold
+replay, new suffix construction, hosted admission, complete paid profile,
+remote CI, proof-assistant verification or independent human review.
diff --git a/research/r439-later-retirement-cuts/VERIFY.json b/research/r439-later-retirement-cuts/VERIFY.json
new file mode 100644
index 0000000000..d0b8177ef4
--- /dev/null
+++ b/research/r439-later-retirement-cuts/VERIFY.json
@@ -0,0 +1,55 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/later_cuts.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Complete4278 pair census using incremental inverse updates."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/check_later_cuts.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent inverse rebuilt from scratch at all713 boundaries; compare every boundary."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/test_later_cuts.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Boundary, donor, target-access, coverage, source corruption and relocation controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/test_package.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Retained original439-helper stationary fixtures and their semantic controls."
+    }
+  ]
+}
diff --git a/research/r439-later-retirement-cuts/check_later_cuts.py b/research/r439-later-retirement-cuts/check_later_cuts.py
new file mode 100644
index 0000000000..5c0f46de39
--- /dev/null
+++ b/research/r439-later-retirement-cuts/check_later_cuts.py
@@ -0,0 +1,82 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent every-boundary inverse replay; no later_cuts/verify imports."""
+import gzip
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE=Path(__file__).resolve().parent
+spec=importlib.util.spec_from_file_location('integer_geometry',HERE/'independent.py')
+I=importlib.util.module_from_spec(spec);spec.loader.exec_module(I)
+
+
+def check(cert):
+    raw=(I.ROOT/I.WORD).read_bytes();I.need(hashlib.sha256(raw).hexdigest()==I.SHA,'source hash')
+    w=json.loads(gzip.decompress(raw));n=2*w['v']+w['R'];v=w['v']
+    state=[{r} for r in range(n)];current=w['start'][:]
+    prefix=w['D']+w['A']+[[0,v+t,[w['ret'][j]]] for t,js in enumerate(w['scatter']) for j in js]
+    for section in ['D','A']:
+        for f,t,ss in w[section]:
+            for r in [t]+ss:current[r]=f
+            for s in ss:state[t]^=state[s]
+    for t,js in enumerate(w['scatter']):
+        for j in js:state[v+t]^=state[w['ret'][j]]
+    frames=[I.reduce_rows([w['lines'][i] for i in f]) for f in w['frames']]
+    expanded={}
+    I.need([h['helper'] for h in cert['helpers']]==[465,466,468,469,470,476],'helper coverage')
+    for entry in cert['helpers']:
+        sequence=[]
+        for run in entry['runs']:
+            I.need(run['first_cut']==len(sequence) and run['last_cut']>=run['first_cut'],'run coverage')
+            sequence += [run['conditions']]*(run['last_cut']-run['first_cut']+1)
+        I.need(len(sequence)==713,'cut coverage')
+        passed=[k for k,r in enumerate(sequence) if r.get('lost_targets')==[]]
+        windows=[]
+        for k in passed:
+            if not windows or windows[-1][1]+1!=k:windows.append([k,k])
+            else:windows[-1][1]=k
+        I.need(windows==entry['windows'] and len(passed)==entry['necessary_condition_pass_count'],'windows')
+        I.need(sum(r['joint_rank']==7 for r in sequence)==entry['joint_rank_seven_cuts'],'join counts')
+        expanded[entry['helper']]=sequence
+    geometry,subset_cache={},{}
+    def join(registers):
+        key=tuple(sorted({current[r] for r in registers}))
+        if key not in geometry:geometry[key]=I.reduce_rows([x for f in key for x in frames[f]])
+        return geometry[key]
+    def subset(vecs,f):
+        key=(tuple(map(tuple,vecs)),f)
+        if key not in subset_cache:subset_cache[key]=len(I.reduce_rows(vecs+frames[f]))==len(frames[f])
+        return subset_cache[key]
+    def support(value):return [r for r in range(n) if value & (1<<r)]
+    for k in range(713):
+        # Deliberately recompute the entire inverse independently at EACH
+        # boundary; never use the primary incremental inverse update.
+        inverse=[1<<r for r in range(n)]
+        for _,dst,srcs in reversed(prefix+w['B'][:k]):
+            for src in srcs:inverse[dst]^=inverse[src]
+        for h,sequence in expanded.items():
+            donors=support(inverse[h]);dirt=[r for r in range(n) if h in state[r]]
+            test=set()
+            for r in donors:test^=state[r]
+            I.need(test=={h},'direct restoration identity')
+            U=join(donors+dirt+[h]);actual={'joint_rank':len(U)}
+            if len(U)<=7:
+                J=join(donors+[h]);touched=set(donors+[h]);lost=[]
+                for t in range(v):
+                    if not subset(J,w['final'][v+t]):
+                        row=inverse[v+t]^inverse[t]
+                        if any(row & (1<<r) for r in touched):lost.append(v+t)
+                actual.update(restoration_rank=len(J),lost_targets=lost,restore_donors=donors)
+            I.need(actual==sequence[k],f'boundary classification h={h} cut={k}')
+        if k<len(w['B']):
+            f,t,ss=w['B'][k]
+            for r in [t]+ss:current[r]=f
+            for s in ss:state[t]^=state[s]
+    I.need(cert['cuts_per_helper']==713 and cert['helper_cut_pairs']==4278 and cert['B_gate_count']==712,'coverage metadata')
+    I.need(cert['source_sha256']==I.SHA and cert['no_new_kappa'] is True,'source metadata')
+    return True
+
+if __name__=='__main__':
+    check(json.loads((HERE/'LATER-CUTS.json').read_text()))
+    print('PASS_INDEPENDENT_LATER_CUTS full_inverse_rebuilds=713 helper_cut_pairs=4278')
diff --git a/research/r439-later-retirement-cuts/independent.py b/research/r439-later-retirement-cuts/independent.py
new file mode 100644
index 0000000000..c185a8568a
--- /dev/null
+++ b/research/r439-later-retirement-cuts/independent.py
@@ -0,0 +1,122 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Separate set-state / integer-elimination replay; no primary imports."""
+import gzip
+import hashlib
+import json
+import math
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+WORD = 'research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz'
+SHA = 'e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f'
+
+
+def need(ok, label):
+    if not ok:
+        raise ValueError(label)
+
+
+def reduce_rows(vectors):
+    out = {}
+    for vector in vectors:
+        row = list(vector)
+        for p in sorted(out):
+            if row[p]:
+                a, b = row[p], out[p][p]
+                row = [b*x-a*y for x, y in zip(row, out[p])]
+                g = math.gcd(*row)
+                if g:
+                    row = [x//g for x in row]
+        p = next((i for i, x in enumerate(row) if x), None)
+        if p is not None:
+            g = math.gcd(*row)
+            out[p] = [x//g for x in row]
+        if len(out) == 8:
+            break
+    return list(out.values())
+
+
+def check(cert, root=ROOT):
+    raw = (root/WORD).read_bytes()
+    need(hashlib.sha256(raw).hexdigest() == SHA, 'source hash')
+    w = json.loads(gzip.decompress(raw))
+    n, v = 2*w['v']+w['R'], w['v']
+    rows = [{i} for i in range(n)]
+    current = w['start'][:]
+    for section in ['D', 'A']:
+        for frame, dst, srcs in w[section]:
+            for r in [dst]+srcs:
+                current[r] = frame
+            for r in srcs:
+                rows[dst].symmetric_difference_update(rows[r])
+    for t, js in enumerate(w['scatter']):
+        for j in js:
+            rows[v+t].symmetric_difference_update(rows[w['ret'][j]])
+    z = list(range(v))+list(range(2*v, n))
+    matrix = {r: set(rows[r]) for r in z}
+    inverse = {r: {r} for r in z}
+    for pivot in z:
+        donor = next(r for r in z if r >= pivot and pivot in matrix[r])
+        matrix[pivot], matrix[donor] = matrix[donor], matrix[pivot]
+        inverse[pivot], inverse[donor] = inverse[donor], inverse[pivot]
+        for r in z:
+            if r != pivot and pivot in matrix[r]:
+                matrix[r] ^= matrix[pivot]
+                inverse[r] ^= inverse[pivot]
+    need(all(matrix[r] == {r} for r in z), 'matrix inverse')
+    frames = [reduce_rows([w['lines'][i] for i in f]) for f in w['frames']]
+    def subset(a, b):
+        return len(reduce_rows(frames[a]+frames[b])) == len(frames[b])
+    ranks = []
+    cases = []
+    for h in range(2*v, n):
+        restore = sorted(inverse[h])
+        dirt = [r for r in range(n) if h in rows[r]]
+        involved = sorted(set(restore+dirt+[h]))
+        vectors = [x for r in involved for x in frames[current[r]]]
+        rank = len(reduce_rows(vectors))
+        ranks.append([h, rank])
+        if rank == 7:
+            candidates = [f for f in range(len(frames)) if len(frames[f]) == 7
+                          and len(reduce_rows(vectors+frames[f])) == 7]
+            station = min(candidates)
+            blocked = [r for r in involved if r != h and not subset(station, w['final'][r])]
+            gates = [[h, r] for r in restore if r != h]+[[r, h] for r in dirt if r != h]
+            case = {'helper':h, 'station':station, 'restore':restore, 'dirt':dirt,
+                    'endpoint_blockers':blocked, 'isolation_gates':gates, 'legal':not blocked}
+            if not blocked:
+                values, now = [set(row) for row in rows], current[:]
+                for dst, src in gates:
+                    for r in (dst, src):
+                        need(subset(now[r], station), 'arrival')
+                        need(subset(station, station if r == h else w['final'][r]), 'cap')
+                        now[r] = station
+                    values[dst] ^= values[src]
+                need(values[h] == {h}, 'restoration')
+                need(all(values[r] == rows[r]-{h} for r in range(n) if r != h), 'clean columns')
+                case['minimum_adds'] = max(len(dirt)-1+int(rows[h] != {h}), len(restore)-1)
+                need(case['minimum_adds'] == len(gates), 'optimality')
+                case['promotions'] = [{'register':r, 'from_frame':current[r], 'to_frame':station,
+                                       'rank_increment':7-len(frames[current[r]])}
+                                      for r in involved if not subset(station, current[r])]
+                for i, (f, dst, srcs) in enumerate(w['B']):
+                    bad = [r for r in [dst]+srcs if not subset(now[r], f)]
+                    if bad:
+                        case['first_fixed_B_conflict'] = {'gate_index':i,'frame':f,'registers':bad}
+                        break
+                    for r in [dst]+srcs:
+                        now[r] = f
+                need('first_fixed_B_conflict' in case, 'continuation conflict')
+            cases.append(case)
+    result = {'schema_version':1, 'status':'SCOPED_SINGLE_STATION_CLASSIFICATION',
+              'seed':17, 'word_sha256':SHA, 'join_rank_counts':{str(k):sum(r==k for _,r in ranks) for k in [7,8]},
+              'all_helper_join_ranks':ranks, 'rank_seven_cases':cases,
+              'legal_helpers':[r['helper'] for r in cases if r['legal']], 'no_new_kappa':True}
+    need(result == cert, 'independent certificate mismatch')
+    return result
+
+
+if __name__ == '__main__':
+    check(json.loads((HERE/'CERTIFICATE.json').read_text()))
+    print('PASS_INDEPENDENT_SINGLE_STATION sets=661 Gaussian_inverse=550 helpers=439 legal=3')
diff --git a/research/r439-later-retirement-cuts/later_cuts.py b/research/r439-later-retirement-cuts/later_cuts.py
new file mode 100644
index 0000000000..f687873634
--- /dev/null
+++ b/research/r439-later-retirement-cuts/later_cuts.py
@@ -0,0 +1,84 @@
+# SPDX-License-Identifier: Apache-2.0
+"""All fixed-B-prefix cuts; exact necessary conditions, not suffix synthesis."""
+import argparse
+import importlib.util
+import json
+from pathlib import Path
+
+HERE=Path(__file__).resolve().parent
+spec=importlib.util.spec_from_file_location('station_verify',HERE/'verify.py')
+V=importlib.util.module_from_spec(spec);spec.loader.exec_module(V)
+HELPERS=[465,466,468,469,470,476]
+
+
+def compute():
+    w=V.load(); n=2*w['v']+w['R']; v=w['v']; rows,current,_=V.cut(w)
+    fb=[V.basis([w['lines'][i] for i in f]) for f in w['frames']]
+    gates=w['D']+w['A']+[[0,v+t,[w['ret'][j]]] for t,js in enumerate(w['scatter']) for j in js]
+    inv=[1<<r for r in range(n)]
+    for _,t,ss in reversed(gates):
+        for s in ss:inv[t]^=inv[s]
+    restore={h:inv[h] for h in HELPERS}
+    target=[inv[v+t]^inv[t] for t in range(v)]
+    cache,contain={},{}
+    def join(regs):
+        key=tuple(sorted(set(current[r] for r in regs)))
+        if key not in cache:cache[key]=V.basis([x for f in key for x in fb[f]])
+        return cache[key]
+    def subset(b,f):
+        key=(tuple(tuple(x for x in r) for r in b),f)
+        if key not in contain:contain[key]=V.contained(b,fb[f])
+        return contain[key]
+    all_rows={h:[] for h in HELPERS}
+    for cut in range(len(w['B'])+1):
+        for h in HELPERS:
+            donors=list(V.bits(restore[h]))
+            dirt=[r for r,value in enumerate(rows) if value>>h&1]
+            U=join(donors+dirt+[h])
+            record={'joint_rank':len(U)}
+            if len(U)<=7:
+                J=join(donors+[h]);mask=sum(1<<r for r in set(donors+[h]))
+                lost=[t+v for t in range(v) if target[t]&mask and not subset(J,w['final'][v+t])]
+                record.update(restoration_rank=len(J),lost_targets=lost,restore_donors=donors)
+            all_rows[h].append(record)
+        if cut<len(w['B']):
+            f,t,ss=w['B'][cut]
+            # Source operands are distinct in the pinned word.
+            V.require(len(ss)==len(set(ss)) and t not in ss,'invalid B transvection')
+            sm=sum(1<<s for s in ss)
+            for r in [t,*ss]:current[r]=f
+            for s in ss:rows[t]^=rows[s]
+            for h in HELPERS:
+                if restore[h]>>t&1:restore[h]^=sm
+            for i in range(v):
+                if target[i]>>t&1:target[i]^=sm
+    result=[]
+    for h in HELPERS:
+        runs=[]
+        for cut,row in enumerate(all_rows[h]):
+            if not runs or runs[-1]['conditions']!=row:
+                runs.append({'first_cut':cut,'last_cut':cut,'conditions':row})
+            else:runs[-1]['last_cut']=cut
+        passed=[i for i,row in enumerate(all_rows[h]) if row.get('lost_targets')==[]]
+        windows=[]
+        for i in passed:
+            if not windows or windows[-1][1]+1!=i:windows.append([i,i])
+            else:windows[-1][1]=i
+        result.append({'helper':h,'joint_rank_seven_cuts':sum(r['joint_rank']==7 for r in all_rows[h]),
+                       'necessary_condition_pass_count':len(passed),'windows':windows,'runs':runs})
+    return {'schema_version':1,'source_sha256':V.DIGEST,'B_gate_count':len(w['B']),
+            'cuts_per_helper':len(w['B'])+1,'helper_cut_pairs':len(HELPERS)*(len(w['B'])+1),
+            'cut_convention':'cut k is after exactly the first k B records, with D/A/scatter fixed',
+            'meaning':'Passing both necessary tests is not a legal suffix or new supplier.',
+            'helpers':result,'no_new_kappa':True}
+
+
+def main():
+    ap=argparse.ArgumentParser();ap.add_argument('--output',type=Path);args=ap.parse_args()
+    result=compute()
+    if args.output:
+        with args.output.open('x') as out:json.dump(result,out,indent=2,sort_keys=True);out.write('\n')
+    else:V.require(result==json.loads((HERE/'LATER-CUTS.json').read_text()),'later-cut certificate mismatch')
+    print('PASS_LATER_BIT_CUTS pairs=4278 windows=465:10-48,468:31-88,470:0-517 excluded=466,469,476 no_new_kappa')
+
+if __name__=='__main__':main()
diff --git a/research/r439-later-retirement-cuts/test_later_cuts.py b/research/r439-later-retirement-cuts/test_later_cuts.py
new file mode 100644
index 0000000000..8a1ecb1743
--- /dev/null
+++ b/research/r439-later-retirement-cuts/test_later_cuts.py
@@ -0,0 +1,75 @@
+# SPDX-License-Identifier: Apache-2.0
+import copy
+import importlib.util
+import json
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tempfile
+import unittest
+
+HERE=Path(__file__).resolve().parent
+
+def module(name):
+    s=importlib.util.spec_from_file_location(name,HERE/(name+'.py'))
+    m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+
+P,Q=module('later_cuts'),module('check_later_cuts')
+
+class LaterCutTests(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):cls.cert=json.loads((HERE/'LATER-CUTS.json').read_text())
+
+    def test_complete_both_engines(self):
+        self.assertEqual(P.compute(),self.cert)
+        Q.check(self.cert)
+
+    def test_named_boundary_witnesses(self):
+        cases={e['helper']:e for e in self.cert['helpers']}
+        def row(h,k):return next(r['conditions'] for r in cases[h]['runs'] if r['first_cut']<=k<=r['last_cut'])
+        self.assertEqual(row(465,9)['lost_targets'],[122])
+        self.assertEqual(row(465,10)['lost_targets'],[])
+        self.assertEqual(row(465,48)['joint_rank'],7)
+        self.assertEqual(row(465,49)['joint_rank'],8)
+        self.assertEqual(row(468,30)['lost_targets'],[144])
+        self.assertEqual(row(468,31)['lost_targets'],[])
+        self.assertEqual(row(468,88)['joint_rank'],7)
+        self.assertEqual(row(468,89)['joint_rank'],8)
+        self.assertEqual(row(466,78)['lost_targets'],[208])
+        self.assertEqual(row(466,79)['joint_rank'],8)
+        self.assertEqual(row(466,89)['joint_rank'],8)
+
+    def test_mathematical_certificate_faults(self):
+        mutations=[lambda c:c['helpers'][0]['windows'][0].__setitem__(0,9),
+                   lambda c:c['helpers'][0]['runs'][0]['conditions']['lost_targets'].clear(),
+                   lambda c:c['helpers'][1]['runs'][0]['conditions']['restore_donors'].append(1),
+                   lambda c:c['helpers'][3]['runs'][0]['conditions'].update({'joint_rank':8}),
+                   lambda c:c['helpers'][4]['runs'][-1].update({'last_cut':711}),
+                   lambda c:c['helpers'].pop()]
+        for mut in mutations:
+            bad=copy.deepcopy(self.cert);mut(bad)
+            self.assertNotEqual(P.compute(),bad)
+            with self.assertRaises(ValueError):Q.check(bad)
+
+    def test_source_only_optimized_relocation_and_controls(self):
+        with tempfile.TemporaryDirectory(prefix='later bit cuts ') as tmp:
+            root=Path(tmp);pkg=root/'research/r439-later-retirement-cuts'
+            shutil.copytree(HERE,pkg)
+            raw=root/P.V.WORD;raw.parent.mkdir(parents=True,exist_ok=True)
+            shutil.copy2(P.V.ROOT/P.V.WORD,raw)
+            for script in ['later_cuts.py','check_later_cuts.py']:
+                run=subprocess.run([sys.executable,'-I','-O','-B',str(pkg/script)],cwd=root,capture_output=True,text=True)
+                self.assertEqual(run.returncode,0,run.stderr)
+            out=root/'later-regenerated.json'
+            cmd=[sys.executable,'-I','-O','-B',str(pkg/'later_cuts.py'),'--output',str(out)]
+            self.assertEqual(subprocess.run(cmd,capture_output=True).returncode,0)
+            self.assertEqual(json.loads(out.read_text()),self.cert)
+            self.assertNotEqual(subprocess.run(cmd,capture_output=True).returncode,0)
+            raw.write_bytes(raw.read_bytes()+b'corrupt')
+            for script in ['later_cuts.py','check_later_cuts.py']:
+                run=subprocess.run([sys.executable,'-I','-O','-B',str(pkg/script)],capture_output=True,text=True)
+                self.assertNotEqual(run.returncode,0)
+                self.assertIn('source hash',run.stderr)
+
+if __name__=='__main__':unittest.main(verbosity=2)
diff --git a/research/r439-later-retirement-cuts/test_package.py b/research/r439-later-retirement-cuts/test_package.py
new file mode 100644
index 0000000000..4ab08384f9
--- /dev/null
+++ b/research/r439-later-retirement-cuts/test_package.py
@@ -0,0 +1,110 @@
+# SPDX-License-Identifier: Apache-2.0
+import copy
+import importlib.util
+import json
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tempfile
+import unittest
+
+HERE = Path(__file__).resolve().parent
+
+def module(name):
+    spec = importlib.util.spec_from_file_location(name, HERE/(name+'.py'))
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+V, I = module('verify'), module('independent')
+
+class PackageTests(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.cert = json.loads((HERE/'CERTIFICATE.json').read_text())
+        cls.word = V.load()
+        cls.rows, cls.current, _ = V.cut(cls.word)
+        cls.fb = [V.basis([cls.word['lines'][i] for i in f]) for f in cls.word['frames']]
+
+    def test_complete_separate_replays(self):
+        V.verify(self.cert, self.word)
+        I.check(self.cert)
+
+    def test_all_ten_gate_omissions(self):
+        total = 0
+        for row in self.cert['rank_seven_cases']:
+            if row['legal']:
+                for j in range(len(row['isolation_gates'])):
+                    gates = row['isolation_gates'][:j]+row['isolation_gates'][j+1:]
+                    with self.assertRaisesRegex(ValueError, 'restoration|another column'):
+                        V.station_check(self.word, self.rows, self.current, self.fb,
+                                        row['helper'], row['station'], gates)
+                    total += 1
+        self.assertEqual(total, 10)
+
+    def test_three_target_caps_and_relaxed_positive_controls(self):
+        count = 0
+        for row in self.cert['rank_seven_cases']:
+            if not row['legal']:
+                with self.assertRaisesRegex(ValueError, 'final endpoint cap'):
+                    V.station_check(self.word, self.rows, self.current, self.fb,
+                                    row['helper'], row['station'], row['isolation_gates'])
+                relaxed = copy.deepcopy(self.word)
+                for r in row['endpoint_blockers']:
+                    relaxed['final'][r] = 1
+                V.station_check(relaxed, self.rows, self.current, self.fb,
+                                row['helper'], row['station'], row['isolation_gates'])
+                count += 1
+        self.assertEqual(count, 3)
+
+    def test_certificate_corruptions_both_engines(self):
+        mutations = [lambda c:c['join_rank_counts'].update({'8':432}),
+                     lambda c:c['legal_helpers'].append(465),
+                     lambda c:c['rank_seven_cases'][0]['endpoint_blockers'].clear(),
+                     lambda c:c['rank_seven_cases'][3].update({'minimum_adds':2}),
+                     lambda c:c['rank_seven_cases'][4]['isolation_gates'].pop(),
+                     lambda c:c['rank_seven_cases'][5]['first_fixed_B_conflict'].update({'gate_index':285})]
+        for mutation in mutations:
+            bad = copy.deepcopy(self.cert)
+            mutation(bad)
+            with self.assertRaisesRegex(ValueError, 'certificate mismatch'):
+                V.verify(bad, self.word)
+            with self.assertRaisesRegex(ValueError, 'certificate mismatch'):
+                I.check(bad)
+
+    def test_wrong_station_and_original_dirty_endpoint(self):
+        row = self.cert['rank_seven_cases'][3]
+        with self.assertRaisesRegex(ValueError, 'station arrival'):
+            V.station_check(self.word, self.rows, self.current, self.fb, 469, 513, row['isolation_gates'])
+        bad = copy.deepcopy(self.word)
+        bad['C'] = bad['C'][:-1]
+        with self.assertRaisesRegex(ValueError, 'baseline full endpoint'):
+            V.derive(bad)
+
+    def test_relocation_source_pin_regeneration_and_overwrite(self):
+        with tempfile.TemporaryDirectory(prefix='station exits ') as tmp:
+            root = Path(tmp)
+            pkg = root/'research/r439-later-retirement-cuts'
+            shutil.copytree(HERE, pkg)
+            raw = root/V.WORD
+            raw.parent.mkdir(parents=True, exist_ok=True)
+            shutil.copy2(V.ROOT/V.WORD, raw)
+            for script in ['verify.py','independent.py']:
+                run = subprocess.run([sys.executable,'-I','-O','-B',str(pkg/script)],
+                                     cwd=root, capture_output=True, text=True)
+                self.assertEqual(run.returncode, 0, run.stderr)
+            out = root/'regenerated.json'
+            command = [sys.executable,'-I','-O','-B',str(pkg/'verify.py'),'--output',str(out)]
+            self.assertEqual(subprocess.run(command, capture_output=True).returncode, 0)
+            self.assertEqual(json.loads(out.read_text()), self.cert)
+            self.assertNotEqual(subprocess.run(command, capture_output=True).returncode, 0)
+            raw.write_bytes(raw.read_bytes()+b'corrupt')
+            for script in ['verify.py','independent.py']:
+                run = subprocess.run([sys.executable,'-I','-O','-B',str(pkg/script)],
+                                     capture_output=True,text=True)
+                self.assertNotEqual(run.returncode, 0)
+                self.assertIn('source hash', run.stderr)
+
+if __name__ == '__main__':
+    unittest.main(verbosity=2)
diff --git a/research/r439-later-retirement-cuts/verify.py b/research/r439-later-retirement-cuts/verify.py
new file mode 100644
index 0000000000..99f7c75177
--- /dev/null
+++ b/research/r439-later-retirement-cuts/verify.py
@@ -0,0 +1,182 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Exact single-station classification. Philipp, with OpenAI Codex assistance."""
+import argparse
+import gzip
+import hashlib
+import json
+from fractions import Fraction
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+WORD = "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz"
+DIGEST = "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f"
+
+
+def require(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def basis(vectors):
+    pivots = {}
+    for vector in vectors:
+        row = list(map(Fraction, vector))
+        for p in sorted(pivots):
+            q = row[p]
+            if q:
+                row = [a - q*b for a, b in zip(row, pivots[p])]
+        p = next((i for i, x in enumerate(row) if x), None)
+        if p is not None:
+            q = row[p]
+            pivots[p] = [x/q for x in row]
+        if len(pivots) == 8:
+            break
+    return [pivots[p] for p in sorted(pivots)]
+
+
+def contained(left, right):
+    return len(basis(right + left)) == len(right)
+
+
+def bits(n):
+    while n:
+        b = n & -n
+        yield b.bit_length()-1
+        n ^= b
+
+
+def load(root=ROOT):
+    raw = (root / WORD).read_bytes()
+    require(hashlib.sha256(raw).hexdigest() == DIGEST, "source hash")
+    return json.loads(gzip.decompress(raw))
+
+
+def cut(word):
+    n, v = 2*word['v'] + word['R'], word['v']
+    rows, frames = [1 << r for r in range(n)], word['start'][:]
+    for section in ('D', 'A'):
+        for f, t, ss in word[section]:
+            for r in [t, *ss]:
+                frames[r] = f
+            for s in ss:
+                rows[t] ^= rows[s]
+    for t, totals in enumerate(word['scatter']):
+        for total in totals:
+            rows[v+t] ^= rows[word['ret'][total]]
+    inverse = [1 << r for r in range(n)]
+    for _, t, ss in reversed(word['A']):
+        if not v <= t < 2*v:
+            for s in ss:
+                inverse[t] ^= inverse[s]
+    return rows, frames, inverse
+
+
+def station_check(word, rows, current, fb, h, u, gates):
+    state, actual = rows[:], current[:]
+    for t, s in gates:
+        require(t != s, "self addition")
+        for r in (t, s):
+            require(contained(fb[actual[r]], fb[u]), "station arrival")
+            cap = u if r == h else word['final'][r]
+            require(contained(fb[u], fb[cap]), "final endpoint cap")
+            actual[r] = u
+        state[t] ^= state[s]
+    require(state[h] == 1 << h, "helper restoration")
+    for r in range(len(state)):
+        if r != h:
+            require(state[r] == rows[r] ^ (((rows[r] >> h) & 1) << h),
+                    "isolation changes another column")
+    return actual
+
+
+def derive(word):
+    rows, current, inverse = cut(word)
+    fb = [basis([word['lines'][i] for i in frame]) for frame in word['frames']]
+    baseline, frame_path = rows[:], current[:]
+    for section in ('B', 'C'):
+        for f, t, ss in word[section]:
+            for r in [t, *ss]:
+                require(contained(fb[frame_path[r]], fb[f]), 'baseline monotone frame')
+                frame_path[r] = f
+            for s in ss:
+                baseline[t] ^= baseline[s]
+    for r, value in enumerate(baseline):
+        expected = (1 << r) ^ ((1 << (r-word['v'])) if word['v'] <= r < 2*word['v'] else 0)
+        require(value == expected, 'baseline full endpoint')
+        require(contained(fb[frame_path[r]], fb[word['final'][r]]), 'baseline final cap')
+    counts, rank_rows, survivors = {}, [], []
+    for h in range(2*word['v'], len(rows)):
+        restore = list(bits(inverse[h]))
+        got = 0
+        for r in restore:
+            got ^= rows[r]
+        require(got == 1 << h, "inverse row")
+        dirt = [r for r, value in enumerate(rows) if value >> h & 1]
+        donors = sorted(set(restore + dirt + [h]))
+        join = basis([line for r in donors for line in fb[current[r]]])
+        rank = len(join)
+        counts[str(rank)] = counts.get(str(rank), 0) + 1
+        rank_rows.append([h, rank])
+        if rank != 7:
+            require(rank == 8, "unexpected join rank")
+            continue
+        require(h in restore, "missing pivot")
+        choices = [f for f, b in enumerate(fb) if len(b) == 7 and contained(join, b)]
+        require(bool(choices), "missing catalogued hyperplane")
+        u = min(choices)
+        blocked = [r for r in donors if r != h and not contained(fb[u], fb[word['final'][r]])]
+        gates = [[h, r] for r in restore if r != h] + [[r, h] for r in dirt if r != h]
+        row = {'helper': h, 'station': u, 'restore': restore, 'dirt': dirt,
+               'endpoint_blockers': blocked, 'isolation_gates': gates,
+               'legal': not blocked}
+        if not blocked:
+            actual = station_check(word, rows, current, fb, h, u, gates)
+            lower = max(len(dirt)-1 + int(rows[h] != 1 << h), len(restore)-1)
+            require(lower == len(gates), "non-sharp gate lower bound")
+            row['minimum_adds'] = lower
+            row['promotions'] = [{'register': r, 'from_frame': current[r],
+                                  'to_frame': u, 'rank_increment': 7-len(fb[current[r]])}
+                                 for r in donors if not contained(fb[u], fb[current[r]])]
+            conflict = None
+            for i, (f, t, ss) in enumerate(word['B']):
+                bad = [r for r in [t, *ss] if not contained(fb[actual[r]], fb[f])]
+                if bad:
+                    conflict = {'gate_index': i, 'frame': f, 'registers': bad}
+                    break
+                for r in [t, *ss]:
+                    actual[r] = f
+            require(conflict is not None, "unexpected unchanged-B continuation")
+            row['first_fixed_B_conflict'] = conflict
+        survivors.append(row)
+    return {'schema_version': 1, 'status': 'SCOPED_SINGLE_STATION_CLASSIFICATION',
+            'seed': 17, 'word_sha256': DIGEST, 'join_rank_counts': counts,
+            'all_helper_join_ranks': rank_rows, 'rank_seven_cases': survivors,
+            'legal_helpers': [r['helper'] for r in survivors if r['legal']],
+            'no_new_kappa': True}
+
+
+def verify(expected, word):
+    actual = derive(word)
+    require(actual == expected, "certificate mismatch")
+    require(actual['legal_helpers'] == [469, 470, 476], "legal set")
+    return actual
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--root', type=Path, default=ROOT)
+    parser.add_argument('--output', type=Path)
+    args = parser.parse_args()
+    result = derive(load(args.root))
+    if args.output:
+        with args.output.open('x') as stream:
+            json.dump(result, stream, indent=2, sort_keys=True)
+            stream.write('\n')
+    else:
+        require(result == json.loads((HERE/'CERTIFICATE.json').read_text()), 'certificate mismatch')
+    print('PASS_SINGLE_STATION_EXITS helpers=439 join8=433 endpoint_blocked=3 legal=469,470,476 adds=3,3,4 no_new_kappa')
+
+
+if __name__ == '__main__':
+    main()