Scoped negative result: R439 retirement windows across all 713 B cuts

research/r439-later-retirement-cuts/README.md

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+# 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.

research/r439-later-retirement-cuts/SOURCES.json

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+{
+  "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"
+        }
+      ]
+    }
+  ]
+}

research/r439-later-retirement-cuts/STATION-NOTE.md

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+# 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.