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new file mode 100644
index 0000000000..db5442bd54
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new file mode 100644
index 0000000000..53d7fd9219
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diff --git a/research/high-carry-streams/PROOF.md b/research/high-carry-streams/PROOF.md
new file mode 100644
index 0000000000..2c42df2eb5
--- /dev/null
+++ b/research/high-carry-streams/PROOF.md
@@ -0,0 +1,143 @@
+# Direct bounded carry rotation
+
+This is a source-level argument for `rotation.py` and the opt-in adapter, not a
+formal proof of the complete multiplication theorem. Jose Manuel's PR2915
+supplies the reached high-field route, its complete affine compiler, and its
+inherited primitive/caller contracts. We change one bounded carry operation.
+The exact base and executable/archive pins are in SOURCES.json.
+
+## Contract and exact coordinates
+
+Let B,Q,S be positive canonical encoded counts, with Q>1 for the actual Ring
+interface, and V=BQS. A complete input contains the Boolean cells
+`source[(b Q+x) S+s]`, in that order, for 0<=b<B, 0<=x<Q, 0<=s<S.
+The source and cardinalities enter at their origins. The output must satisfy
+
+    output[(b Q+((x+a) mod Q)) S+s] = source[(b Q+x) S+s],
+
+where the compiled integer a is in {-4,-3,-2,-1,1,2,3,4}. Neither the source,
+counts nor numerical Ring are disposable. The factory supplies distinct blank
+owned scratch leases. Capacity and successful underlying operations are
+premises. Existing occupied leases are excluded from allocation and preserved.
+No general interrupted-operation rollback guarantee is asserted.
+
+`split_lengths` keeps a canonical countdown initially equal to Q and a count
+initially zero. After j bounded iterations they represent Q-r and r, where
+r=j mod Q, including the representation Q,0 when r=0. Decrement/increment
+preserves this invariant until the countdown reaches zero, when both are reset.
+This proves the returned pair Q-r,r for r=abs(a) mod Q. There are at most four
+iterations. The runtime modulus is never decoded to a host integer; only the
+already compiled carry chooses a bounded finite-control loop.
+
+For a>0, split each Q-field row into intervals L=[0,Q-r), R=[Q-r,Q). Store all
+L blocks in one sequential bucket and all R blocks in another, retaining the
+complete S-bit suffix and the order of the B prefixes. Emit R then L for each
+prefix. An old x<Q-r is emitted at r+x, and an old x>=Q-r at x-(Q-r), exactly
+x+a mod Q. For a<0 split at r instead: L=[0,r), R=[r,Q); emit R then L. These
+coordinates are x-r mod Q. The bucket cursors advance by their exact per-prefix
+lengths, so no suffix or neighboring prefix is interchanged.
+
+When r=0, the result is the identity but is still copied to a distinct owned
+output. This covers, for example, carries ±3 at Q=3. The helper split itself
+also has a valid Q=1 identity, but Ring rejects Q=1 and the enclosing PR2915
+executor skips all high operations there. The complete-route zero-high fixture
+checks that unchanged boundary; no Q=1 Ring execution is claimed.
+
+The code checks input exhaustion at the actual end of the first pass, and both
+bucket ends at the end of the second. It rewinds the source, clears both private
+buckets and every count, and returns only the output lease at its origin. The
+numerical bank is only read to obtain the modulus. Thus the column identity
+holds on arbitrary Boolean input, without zero-filled-source assumptions.
+
+## Complete local cost and storage
+
+Count every Tape read, write and unit movement, including encoded setup,
+countdown allocation/normalization, payload copies, rewinds, erasure and pool
+acquisitions. Let I be the fixed encoded width scanned when copying the Ring
+modulus. The direct kernel costs
+
+    T_rotate(B,Q,S,I,a) = O(BQS + I),   0<|a|<=4.
+
+Here is the complete decomposition, with all constants independent of B,Q,S.
+The initial modulus copy and normalization cost O(I). The bounded split uses
+O(log Q) copying, at most four decrements and bounded zero-counter resets. Its
+final copy and all split-count disposal cost O(log Q). A canonical countdown
+from m through zero costs O(m+log(m+1)) including construction and disposal:
+bit toggles and head travel have a geometric sum, and the final erasure costs
+its encoded length. This is the actual retained Counter algorithm, not an
+assumption of constant-time arbitrary integer subtraction.
+
+Each nonidentity route has two phases. Each phase has one B-countdown and at
+most two Q-row subloops per prefix. There are exactly BQ suffix copies per
+phase; each suffix copy costs O(S), including its S-countdown when S>1. The
+one-bit branch is constant. Since log(m+1)<=m for positive integer m, all row,
+prefix and suffix initialization costs are absorbed into O(BQS). There are two
+full payload copy passes (2V copied bits), O(V) total bucket rewind/clear work,
+O(V) source/output rewinds, and a fixed number of end checks and acquisitions.
+The identity path uses one complete copy pass. Returned-output disposal is an
+additional O(V) charge at the caller. No recursive child, source access, sign,
+frame change, or restoration is hidden in this expression.
+
+For the reached canonical high bank I=O(log Q), this becomes O(V). Arbitrarily
+padded encodings retain the separate I term. This is a constant-factor execution
+change; it does not improve the recursive exponent or provide a total stock,
+backing-capacity, uniform primitive coefficient or machine-admission theorem.
+
+At the nonidentity streaming peak there are three payload leases (left, right,
+output), two split counts, and at most three nested counters (prefix, field,
+suffix): **eight additional scratch roles**. The temporary modulus has already
+been erased. Split construction uses at most four roles, including the temporary
+literal constructor. For S=1 the deepest suffix counter is absent. An occupied
+entry lease is not one of these eight. A literal fixture attains eight, and a
+one-role-short allocator rejects. The kernel allocates **zero numerical words**.
+Payload storage is at most V in the two buckets plus V in the output; including
+the borrowed source gives 3V occupied payload cells. Count tapes, markers,
+retained blank extents and enclosing caller payloads remain separate categories.
+This is not a bound on the entire recursive machine's backing capacity.
+
+## Adapter and whole-route accounting
+
+`CarryAdapter` retains PR2915's complete execute lifecycle: source copy,
+modulus setup, affine-operation order, intermediate disposal, final bank erasure
+and source return. Only translations with a!=1 use the new kernel. All other
+operations, including +1, use the original dispatcher. +1 already uses a single
+translation pass; retaining it avoids the small setup regression observed at
+B=S=1. This is a static opcode selection, not a benchmark-dependent guard.
+
+For compiled operations o_1,...,o_k the whole charge is
+
+    T_new = T_setup_and_return
+            + sum_{unchanged o_j} T_original(o_j)
+            + sum_{replaced carries a_j} T_rotate(B_j,Q,S_j,I,a_j).
+
+The inherited setup term includes every original input copy, intermediate clear
+and high-bank lifecycle. Every swap and reversed-ADD native interval is identical
+and fully charged. There is no additional native child or new recursive profile.
+We prove the replacement's completed contract and linear cost. We do not infer
+an all-domain numerical speed ratio from this big-O statement or finite timings.
+
+Before replacement a positive carry a uses a calls to `translate_one`, whereas
+a negative carry uses |a| repetitions of sign/translate/sign, or 3|a| full-field
+primitive calls. The new path uses one direct kernel (including both buckets),
+with +1 unchanged. The catalogue receipt counts these calls in one precisely
+named source specialization. These different primitives have different costs;
+that count is neither a runtime ratio nor a κ calculation.
+
+## Verification boundary
+
+The independent oracle maps each input column using host modular arithmetic,
+separately from the encoded implementation. Random Boolean values are only an
+additional check: the provenance observer propagates a distinct formal column
+for every input cell, and a wrong-direction control also fails on all-zero data.
+All input bits, old prefixes and suffixes are included. A raw Tape observer
+meters setup through complete kernel/route return. Native route intervals are
+additionally reported but are not subtracted from totals.
+
+The package checks 96 complete before/after kernel pairs, seven complete route
+pairs, 2,056 independently decoded split identities, source pins, cardinality and
+ownership restoration, occupied dirty leases, erased buckets, invalid carries,
+trailing input and endpoint-preserving extra-traffic controls. Complete selected
+GL64 payload execution, supplier admission, whole caller stock and inherited
+native/analytic assumptions remain outside this result. No new κ is claimed.
+
+Tekalign (tekuuu), with substantial OpenAI Codex assistance. Apache-2.0.
diff --git a/research/high-carry-streams/README.md b/research/high-carry-streams/README.md
new file mode 100644
index 0000000000..c052eabbf1
--- /dev/null
+++ b/research/high-carry-streams/README.md
@@ -0,0 +1,117 @@
+# Direct signed carry streams for selected BIT routes
+
+PR2915 implements a negative high-field carry by repeating sign/shift/sign,
+up to twelve complete primitive calls for a carry of −4. This package adds an
+opt-in physical kernel that performs the same rotation with two sequential
+buckets. It uses encoded counters, preserves complete prefix/suffix coordinates,
+returns a distinct owned output and clears its private state. The existing +1
+path remains in use: replacing it exposed a small setup regression on tiny
+packets. Frozen sources and the default adapter remain unchanged.
+
+On the 486-bit −4 fixture, complete kernel traffic falls from **1,105,367 to
+54,064 tape operations (95.1%)**. A complete signed-scale route falls from
+**881,379 to 410,237 operations (53.5%)**. Every read, write and unit movement
+between entry and return is counted, including setup, rewinds, bucket erasure
+and native intervals. Initial fixture creation and disposal of the returned
+output are outside the measured interval; output disposal stays paid by the
+caller. No mathematical coverage is dropped between the two implementations.
+
+The source proof gives `O(BQS + I)` physical work for a complete B×Q×S packet
+and encoded modulus width I, hence `O(BQS)` for the reached canonical high bank.
+The direct kernel requires at most **eight additional scratch roles** and no
+numerical words. Borrowed source and occupied scratch roles are additional to
+that local inventory. This is not a total backing-capacity or supplier proof.
+
+## Exact evidence
+
+- **96 complete kernel pairs:** all eight signed carries, Q in 3,5,7,9,25,81,
+  unit/nonunit suffixes, multiple prefixes, wrapping and zero-residue cases.
+  Every independent input column, borrowed count, source and dirty lease is
+  checked; success leaves only the distinct output lease owned.
+- **Seven complete route pairs:** dyadic/scalar/noncommuting words, signed low
+  carries, two high radix digits, multiple old prefixes and spectators, and
+  the unchanged zero-high-width branch. Native calls are unchanged and remain
+  in the measured totals. All seven complete pairs pass the original independent
+  coordinate oracle with the new adapter.
+- **2,056 split identities and controls:** exact separate modular arithmetic;
+  wrong direction also rejected on all-zero payloads; trailing input in active
+  and identity cases; one scratch role too few; extra endpoint-preserving I/O;
+  invalid carries, zero modulus and source corruption.
+- **Actual selected registry exposure:** 1,123 chart types, 2,246 orientations,
+  q=3 and identity low class, using source occurrence multiplicities. Carries
+  take **34,450,048 old full-field primitive calls → 11,858,368 kernel calls**.
+  These different primitives have different prices. This is one finite low-class
+  specialization, not a distribution over all low classes, a runtime ratio or
+  executed selected GL64 payloads.
+
+[PROOF.md](PROOF.md) gives the all-width coordinate argument, role lifetimes,
+complete cost decomposition and explicit inherited scope. [KERNEL.json](KERNEL.json),
+[ROUTES.json](ROUTES.json) and [CATALOGUE.json](CATALOGUE.json) retain complete typed
+receipts; replay compares their contents as well as their digests in
+[RESULT.json](RESULT.json). [BENCHMARK.json](BENCHMARK.json) records three alternating
+fresh-process Python 3.12 pairs on identical inputs: median instrumented kernel
+execution is **19.68×** faster and complete signed-scale route execution **2.13×**
+faster. Including process startup gives **2.75×** and **1.47×**, respectively.
+These are instrumented reference fixtures, not multiplication timings.
+
+## Reproduce and use
+
+From the repository root with standard-library CPython 3.12:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/high-carry-streams
+```
+
+Expected: all four `PASS_HIGH_CARRY_*` suites and successful registered replay.
+The control suite runs with optimization enabled. The same committed verifiers
+can run from a source export with all declared inputs present. The generic
+metadata/pin launcher additionally needs Git history. [VALIDATION.md](VALIDATION.md)
+records actual checks and environments.
+
+In an authenticated PR2915 namespace, construct `adapter.CarryAdapter` instead
+of `stage.Adapter`, with the same native backend, registry and capacity. Its
+`StagePool` and enclosing `route_packet` interface are unchanged. The replacement
+uses no runtime module patch; test-only observers patch the fixture namespace
+to compare the two adapters. This adapter has not been combined with PR3330's
+optional frame scheduler in this package, and their measured savings must not
+be added. The changed carry map is independent of that schedule.
+
+Base: `6f100d4bb5083f8c35d96fd95a539811c62f245c`, priority revision 6,
+OS assignment seed **6**. [TASK.json](TASK.json) records three candidates,
+changed card scope, bounded coverage and stopping rule. [SOURCES.json](SOURCES.json)
+pins every executable/archive input before predecessor loading.
+[Canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/2319#discussioncomment-19007093).
+
+No new κ, recursive child profile, selected frontier, complete fitted GL64
+execution or supplier admission is claimed. Source-level proof and exact finite
+replay do not discharge inherited native, numerical-capacity, whole-caller stock,
+physical backing, analytic or formal-refinement obligations. Concurrent
+[PR3340](https://github.com/CrocSwap/integer-mult-bounds/pull/3340)'s fitted-B1 bridge
+addresses a separate boundary and is not used as an assumption here.
+
+## Open next questions
+
+1. Can one reached dyadic scale/carry pair be executed with fewer complete
+   passes? First derive its actual prefix/suffix permutation and full bucket,
+   scratch and restoration bill. The present kernel deliberately changes only
+   bounded translations.
+2. Before adoption, independently review this kernel and join its eight-role
+   reserve and actual encoded width to one enclosing caller. The remaining
+   stock/backing and native-refinement obligations prevent a component benchmark
+   from serving as a whole-supplier admission. Structured handoffs are in TASK.json.
+
+## Credit
+
+Tekalign (`tekuuu`), with substantial OpenAI Codex assistance in source analysis,
+implementation, proof, verification and writing. New material is Apache-2.0;
+no independent human or formal-kernel review is claimed.
+
+Jose Manuel (`jmbarrancoml`) supplied PR2915's executor, kernel vocabulary and
+registry, PR2899's backend, and the retained physical source chain. The execute
+lifecycle is adapted with attribution, rather than attributed as a new algorithm.
+David Arias supplied PR2753's recursive caller. The physical observer follows
+this account's PR3330. Credit Nick Petalas, commdata2338, Sagar Thakrar, Arham
+Tahir, ywz65, Ross Richardson and Krzysztof Wójt for the predecessor cost,
+countdown, physical-lifetime and caller work, and the PR2157/PR589/PR555 lineage
+for the retained factor words and geometry. Original notices remain in the
+unchanged authenticated archives.
diff --git a/research/high-carry-streams/RESULT.json b/research/high-carry-streams/RESULT.json
new file mode 100644
index 0000000000..c4b18a5863
--- /dev/null
+++ b/research/high-carry-streams/RESULT.json
@@ -0,0 +1,6 @@
+{
+  "kernel": "4d0230b41e688e23cabf3547076fba81526b680203a8fdc1035447a35b85cd44",
+  "routes": "d77cc2b15d5dc623e8af5431830a58b5c2e728be81ef92b8ee6e80757202a3ee",
+  "catalogue": "ed26829392d85fd8afcc377e3a68a5e3bccd80bb3588856fd25e7312f28d3f3c",
+  "controls": "960e219d8c74f5a6d6078779f7c038bcfdc78eb45cb3484cdc91b35c998880cc"
+}
diff --git a/research/high-carry-streams/ROUTES.json b/research/high-carry-streams/ROUTES.json
new file mode 100644
index 0000000000..3d7cbade46
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diff --git a/research/high-carry-streams/SOURCES.json b/research/high-carry-streams/SOURCES.json
new file mode 100644
index 0000000000..3db5fdb8d4
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+++ b/research/high-carry-streams/SOURCES.json
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+    },
+    {
+      "path": "research/pr589-five-helper-hosting/PROOF.md",
+      "usage": "input",
+      "git_blob": "bbd3f12b9a32b3ad3cba85a2d5a1b3054214fa02",
+      "sha256": "59cae781bfbe1a01ed9e66a8efeeb5a2b995e5ecdf908586b23ecc39f2b8d647"
+    },
+    {
+      "path": "research/pr589-five-helper-hosting/verify.py",
+      "usage": "input",
+      "git_blob": "dbc71f56bb4205ebe378ada1f9f4ea88630d1d39",
+      "sha256": "cf90e19ae9991b0698be03d395a8cc29061ecb307eb7fea19adfb2d23c25a367"
+    },
+    {
+      "path": "research/recursive-parking-boundary/README.md",
+      "usage": "input",
+      "git_blob": "251f335ebaccc11d69393ee7aeb5a2e84526d0bb",
+      "sha256": "491aa208391ee4c2936510b1a5c5c018dd5509d9a0e88687c72ab8406cd77b18"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_caller.py",
+      "usage": "input",
+      "git_blob": "c3085e1d648ff2ba8d774d1739854306b84e5798",
+      "sha256": "75808ef9a1b65d620109717ab4af88598777a39cfc4d4bc2e42d3788233f029b"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_catalogue.py",
+      "usage": "input",
+      "git_blob": "7368d63e1a7c54c29d622324e35f4115884adc10",
+      "sha256": "f7cc1c7907fd1877e310ba41904110a40e52f091ad38442ab2398c798afd3644"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_complete.py",
+      "usage": "input",
+      "git_blob": "d4db3439979d347a1ab6a96b978c8d3dbfa5cb7e",
+      "sha256": "0751dd27a129823894cd7ade7ba73fcc84c825ecf5fcdd1fedac11ca08526d9d"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_controls.py",
+      "usage": "input",
+      "git_blob": "bee3f603c989358b8e6169bd7770ebf9280b3a00",
+      "sha256": "d0b41aec46462f6b351935efdd8b200eb4de72fa2f8784cfa672fe3607711d91"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_handoff.py",
+      "usage": "input",
+      "git_blob": "96051d7ca03bd38541d86289cdb6ec5fed98e707",
+      "sha256": "be1436e32bfad474330b69905aa6e4bfdb1a3538c295ace0f0ef96f40a34661a"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_kernels.py",
+      "usage": "input",
+      "git_blob": "f4525ca47b90151f5461b01ed33ff80d64931ffe",
+      "sha256": "dd35d535e6986687bee112cef2003569252fc473acbce98f1a64b66e84083cc2"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_outer.py",
+      "usage": "input",
+      "git_blob": "013b959cc9fc4a37f0c109cda4ffc37d639a5473",
+      "sha256": "b303f94091b1a09333532c57182808e5e049ad8b00dc77d491c664f5c5351ee3"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/check_routes.py",
+      "usage": "input",
+      "git_blob": "0b05ab1e4de1e10fe651c72da883887cb44a643d",
+      "sha256": "28803eb270202e2742c713bf14ead47f44c8b5341a380c156bce7392ebed642d"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/compile_routes.py",
+      "usage": "input",
+      "git_blob": "37263fdc327b4a300ccfaa0b7ad650012ab3d59c",
+      "sha256": "1bfef464dfb3e33d9d57f53b657b2d1fe3598bc453be49000a5e782b622e8585"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/high_route.py",
+      "usage": "input",
+      "git_blob": "ec7481f890147be7763f4da729fd879a88a87e8e",
+      "sha256": "13d9c706e7bad2fa3b7d2a97d19b58f2c4efac06d2bb76b613b40069c38b1cd2"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/inputs/pr2157.tar",
+      "usage": "input",
+      "git_blob": "9504807466071f56519f8663ccb532076a42a273",
+      "sha256": "db202c7b91b5b8b9340f96f870d54e275854f0b73839451c7c15bd7895ac3639"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/inputs/pr2899.tar",
+      "usage": "input",
+      "git_blob": "e85ce82745879141e416ac6d9e3551ff959871aa",
+      "sha256": "fc4a2e07423835737c8fb3872664b16ff12aa4cf83b1e26e49878debef40c531"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/kernels.py",
+      "usage": "input",
+      "git_blob": "de9fb08c35e92c8354ae622276866385fd07e3d2",
+      "sha256": "c4b91333817f7fcea44b1d32e01095cd71aeb673ed3608d2e25f4c06d56bb420"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/stage.py",
+      "usage": "input",
+      "git_blob": "765ae9e11af3acb9458d7a1444a9e79112b72d96",
+      "sha256": "44e334162d12868ce6bb50c501cd2eba8c527f59ce7a144614edd8cd6f533647"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/stage_sources.py",
+      "usage": "input",
+      "git_blob": "27383dd1553672f9c82139f80b628b2a094628d8",
+      "sha256": "55c6631cce4f76e14b66b6195468c36b544e2374cc6c59702135c664bff10822"
+    },
+    {
+      "path": "research/selected-bit-fast-primitives/verify.py",
+      "usage": "input",
+      "git_blob": "a2f602c15cd413638116b4ea9bcffe613e4e3a7d",
+      "sha256": "90760db1526f73cfffc34eb8af3f2e5ec83f8f1015a780caa61d156f0d850c68"
+    },
+    {
+      "path": "research/selected-bit-local-ring-sweeps/PROOF.md",
+      "usage": "input",
+      "git_blob": "4330de85dd9862ed15d84ab917887d249753df99",
+      "sha256": "846c59440cc99e28bae93ad2af99525bc769de29368080071b8427141215b4f7"
+    },
+    {
+      "path": "research/selected-bit-recursive-closure/PROOF.md",
+      "usage": "input",
+      "git_blob": "6c410cab5713979214a45835091fbeb9ee9b8531",
+      "sha256": "74cc8de20f21acb5123fe2d20996fe0925ea6e51b3dec633bd5221fb719b3344"
+    },
+    {
+      "path": "upstream/build/sections/02-streams.tex",
+      "usage": "input",
+      "git_blob": "088fceea1867abc76271d7efe7532b779fee9039",
+      "sha256": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab"
+    },
+    {
+      "path": "research/high-route-permutation-frames/check_physical.py",
+      "usage": "provenance",
+      "git_blob": "85d4501b8fcc5df5b7d02d4958b4f1e3381c857e",
+      "sha256": "96911c5a55387bed6d252c1ac39f55b65da5c65c52e8fea327288b259b7b2c0b"
+    }
+  ],
+  "predecessors": [
+    {
+      "pr": 2915,
+      "head": "fecc5a87574df441ddc3dad44f99fca9bd7fdd92",
+      "author": "Jose Manuel (jmbarrancoml)",
+      "scope": "reached executor and selected registry; main includes the documented catalogue cache adaptation"
+    },
+    {
+      "pr": 2899,
+      "head": "2f0911ad735643a069b9790302fbf179e49f74f8",
+      "author": "Jose Manuel (jmbarrancoml)",
+      "scope": "B1 in the authenticated PR2915 archive"
+    },
+    {
+      "pr": 3330,
+      "head": "aa14cb3a57a6170f645f13d140543b941227fca9",
+      "author": "Tekalign (tekuuu)",
+      "scope": "reused complete-route physical observer; schedule itself is unchanged and unused"
+    }
+  ]
+}
diff --git a/research/high-carry-streams/TASK.json b/research/high-carry-streams/TASK.json
new file mode 100644
index 0000000000..752a189329
--- /dev/null
+++ b/research/high-carry-streams/TASK.json
@@ -0,0 +1,75 @@
+{
+  "schema_version": 1,
+  "task_id": "bit-helper-contract",
+  "priority_revision": 6,
+  "base_commit": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+  "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": [
+      "docs/research/research-family-status.md",
+      "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. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "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": "Direct encoded signed carry rotation in the reached PR2915 BIT high route, with complete ownership, traffic and cleanup accounting.",
+  "scope_change_reason": "OS seed 6 assigns the Bit supplier track. The current route implementation exposes a distinct repeated sign/shift/sign expense; the fitted-B1 audit is separately claimed. This changes a reached implementation rather than the generic helper-star card.",
+  "bottleneck_link": "Remove repeated whole-field passes from the reached route without changing its map, recursive native calls or paid profile.",
+  "budget_minutes": 60,
+  "stop_rule": "One direct signed carry implementation; 96 complete kernel pairs, seven route pairs, fixed q=3 identity-low catalogue census, split identities and controls. No search for a new supplier.",
+  "outcome": "completed",
+  "evidence": "PROOF.md, RESULT.json, KERNEL.json, ROUTES.json, CATALOGUE.json and registered replay.",
+  "author": "Tekalign (tekuuu), with substantial OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance in derivation, implementation, source inspection, verification and writing; no independent human review or proof-assistant verification.",
+  "open_questions": [
+    {
+      "question": "Can adjacent dyadic scale and carry operations be completed with fewer complete stream passes?",
+      "why_it_matters": "The present change eliminates repeated carry passes but preserves every scalar factor.",
+      "first_step": "Pin one reached scalar/carry pair and derive its complete prefix/suffix permutation and ownership budget before implementation.",
+      "blocked_by": "a complete bounded bucket/scratch and physical-cost proof"
+    },
+    {
+      "question": "Should the opt-in adapter be adopted by an enclosing selected caller?",
+      "why_it_matters": "Component correctness and faster fixtures do not establish the full physical supplier.",
+      "first_step": "Independently review the source proof, then join its eight-role inventory and actual encoded width to the enclosing reserve.",
+      "blocked_by": "enclosing stock/backing, native refinement and independent admission review"
+    }
+  ],
+  "assignment_seed": 6,
+  "assignment_rng": "secrets.randbelow(100), operating-system randomness, drawn once on 2026-10-17",
+  "candidate_tasks": [
+    "Direct signed carry streams.",
+    "Remove the initial high-cube copy using borrowed/owned lifetime tracking.",
+    "Fuse dyadic scale/carry factors."
+  ],
+  "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2319#discussioncomment-19007093"
+}
diff --git a/research/high-carry-streams/VALIDATION.md b/research/high-carry-streams/VALIDATION.md
new file mode 100644
index 0000000000..b796e1dae3
--- /dev/null
+++ b/research/high-carry-streams/VALIDATION.md
@@ -0,0 +1,40 @@
+# Validation
+
+Implementation and receipt freeze: `8376965a54f12604c23c45ca458d606d1c1f6f28`.
+The complete registered CPython 3.12.14 replay passed at this commit. The
+publication amendment changes only this validation record.
+Base: 6f100d4bb5083f8c35d96fd95a539811c62f245c. Priority revision 6, seed 6.
+
+The author ran the complete kernel, route, catalogue and optimized control
+suites with CPython 3.12.14 on Linux. The same-input benchmark uses that runtime
+and three alternating fresh-process pairs. See BENCHMARK.json for every sample.
+No formal kernel, independent human review, selected cold replay, whole-machine
+execution or new κ is claimed.
+
+Overlap metadata at entry covered 249 open PRs, 2,761 closed/merged PRs and
+2,171 Discussion records with complete pagination. A later refresh covered 256
+open PRs and the latest #2319 replies; main was unchanged. PR3340 addresses the
+separate fitted native bridge. These metadata checks do not cover unpublished
+work or every code diff. The only open issue remained #913's clarity concern.
+
+## Committed verification
+
+- All four registered suites pass, including the 1,123-chart catalogue census
+  and optimized controls; no artifact generation occurs during verification.
+- A read-only Git-free export of all 51 package/input files passes the optimized
+  CPython 3.14.7 control suite and all 96 complete kernel comparisons. Every
+  exported byte matches the scientific commit.
+- An AST comparison verifies that the adapted execute function is identical
+  to PR2915 except for the intended dispatch name. This was a separate local
+  check, not a formal proof or a registered additional suite.
+- `git diff --check` passes. Runtime constructors and numerical inspection are
+  forbidden inside the physical fixtures. Counter traffic and source-column
+  provenance are observed together, without replacing the semantic observer.
+
+The registered comparison covers 6,624 independent kernel columns and 8,893
+complete-route columns. The opt-in path has no measured I/O regression in the
+96 retained pairs; that finite observation is not a universal timing theorem.
+The direct negative-carry cases use 66.8–95.1% less physical I/O in these inputs.
+
+The source/archive merge and hosted CI remain separate from scientific admission.
+Hosted CI status is reported in the PR rather than inferred from local success.
diff --git a/research/high-carry-streams/VERIFY.json b/research/high-carry-streams/VERIFY.json
new file mode 100644
index 0000000000..efed187208
--- /dev/null
+++ b/research/high-carry-streams/VERIFY.json
@@ -0,0 +1,90 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/bit2234-stock-threshold/README.md",
+    "research/community-frontier1094-audit/ASSEMBLY.json",
+    "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL-TEMPLATE.json.gz",
+    "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL.json",
+    "research/community-hyperplane599-audit/pr589/bit589/v9/nine/GEOMETRY.json",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz",
+    "research/idle-axis-hosting/PROOF.md",
+    "research/pr589-five-helper-hosting/PROOF.md",
+    "research/pr589-five-helper-hosting/verify.py",
+    "research/recursive-parking-boundary/README.md",
+    "research/selected-bit-fast-primitives/check_caller.py",
+    "research/selected-bit-fast-primitives/check_catalogue.py",
+    "research/selected-bit-fast-primitives/check_complete.py",
+    "research/selected-bit-fast-primitives/check_controls.py",
+    "research/selected-bit-fast-primitives/check_handoff.py",
+    "research/selected-bit-fast-primitives/check_kernels.py",
+    "research/selected-bit-fast-primitives/check_outer.py",
+    "research/selected-bit-fast-primitives/check_routes.py",
+    "research/selected-bit-fast-primitives/compile_routes.py",
+    "research/selected-bit-fast-primitives/high_route.py",
+    "research/selected-bit-fast-primitives/inputs/pr2157.tar",
+    "research/selected-bit-fast-primitives/inputs/pr2899.tar",
+    "research/selected-bit-fast-primitives/kernels.py",
+    "research/selected-bit-fast-primitives/stage.py",
+    "research/selected-bit-fast-primitives/stage_sources.py",
+    "research/selected-bit-fast-primitives/verify.py",
+    "research/selected-bit-local-ring-sweeps/PROOF.md",
+    "research/selected-bit-recursive-closure/PROOF.md",
+    "upstream/build/sections/02-streams.tex"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py",
+        "--suite",
+        "kernel"
+      ],
+      "timeout_seconds": 120,
+      "checks": "96 complete signed-carry baseline/candidate pairs with exact columns, borrowed and dirty state, scratch and all physical I/O"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py",
+        "--suite",
+        "routes"
+      ],
+      "timeout_seconds": 180,
+      "checks": "Seven complete PR2915 routes through the opt-in adapter with independent columns and every native interval retained"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py",
+        "--suite",
+        "catalogue"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Actual 1123 chart source specialization at q=3 identity low class; exact weighted carry exposure"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "-O",
+        "{package}/verify.py",
+        "--suite",
+        "controls"
+      ],
+      "timeout_seconds": 30,
+      "checks": "2056 exact split identities, invalid/extra input, wrong sign including all-zero payload, one-role-short, extra-traffic and source-corruption controls"
+    }
+  ]
+}
diff --git a/research/high-carry-streams/adapter.py b/research/high-carry-streams/adapter.py
new file mode 100644
index 0000000000..5584ff973a
--- /dev/null
+++ b/research/high-carry-streams/adapter.py
@@ -0,0 +1,69 @@
+"""Opt-in adapter. Execute lifecycle retained from Jose Manuel, PR2915.
+
+Apache-2.0. The only changed dispatch is the bounded carry kernel.
+"""
+import bindings
+bindings.activate()
+from cardinal_counts import Count
+from high_route import apply, extents
+from routes import copy_rows
+from session import initialize_marker
+from words import BLANK, Ring, need
+from stage import Adapter
+from rotation import translated
+
+
+def apply_carry(source, operation, route, ring, modulus, fibre, adapter, factory):
+    if operation[0] != "translate" or operation[2] == 1:
+        return apply(source, operation, route, ring, modulus, fibre, adapter, factory)
+    before, suffix = extents(modulus, fibre, route.dimension, operation[1])
+    try:
+        return translated(source, ring, before, suffix, operation[2], factory)
+    finally:
+        before.close()
+        suffix.close()
+
+
+def execute(source, route, context, fibre, adapter, factory):
+    need((route.q, route.dimension) == (context.q, context.dimension), "route/context binding")
+    operations = adapter.registry.compile(route)
+    current = factory()
+    source.rewind()
+    ring = modulus_word = None
+    modulus = Count(context.cap)
+    bank = adapter.high_bank
+    try:
+        copy_rows(source, current, context.highs, fibre)
+        need(source.read() == BLANK, "complete source high cube")
+        source.rewind()
+        current.rewind()
+        if context.raw.compare(context.cap, context.ring.one) > 0:
+            for word in (*bank.words, bank.template):
+                initialize_marker(word.tape)
+            bank.prepare(modulus)
+            modulus_word = bank.load(modulus)
+            ring = Ring(modulus_word)
+            for operation in operations:
+                following = apply_carry(current, operation, route, ring, modulus, fibre, adapter, factory)
+                current.clear()
+                current = following
+        result, current = current, None
+        return result
+    finally:
+        source.rewind()
+        if current is not None:
+            current.clear()
+        if ring is not None:
+            ring.close()
+            bank.free(modulus_word)
+            bank.erase_owned()
+        modulus.close()
+
+
+class CarryAdapter(Adapter):
+    def route_cube(self, source, route, context, fibre, factory=None):
+        need(not self.in_base and self.scope is not None, "successor route stage")
+        result = execute(source, route, context, fibre, self,
+                         self.scope.acquire if factory is None else factory)
+        self.calls["cubes"] += 1
+        return result
diff --git a/research/high-carry-streams/benchmark.py b/research/high-carry-streams/benchmark.py
new file mode 100644
index 0000000000..4280ff4958
--- /dev/null
+++ b/research/high-carry-streams/benchmark.py
@@ -0,0 +1,53 @@
+"""Alternating fresh-process comparisons; exact results remain checked."""
+import argparse
+import json
+from pathlib import Path
+import statistics
+import subprocess
+import sys
+from time import perf_counter
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE))
+
+
+def worker(kind,optimized):
+    if kind=='kernel':
+        from check_kernel import one_case
+        result,elapsed=one_case(81,2,3,-4,optimized)
+    else:
+        # Explicit loading avoids the predecessor's equally named check_routes.
+        import importlib.util
+        spec=importlib.util.spec_from_file_location('carry_benchmark_routes',HERE/'check_routes.py')
+        module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+        result,elapsed=module.run_case(module.cases()[0],optimized)
+    print(json.dumps(dict(result=result,seconds=elapsed)))
+
+
+def main():
+    parser=argparse.ArgumentParser()
+    parser.add_argument('--worker',choices=('kernel','route'))
+    parser.add_argument('--optimized',action='store_true')
+    parser.add_argument('--repeats',type=int,default=3)
+    args=parser.parse_args()
+    if args.worker:return worker(args.worker,args.optimized)
+    rows=[]
+    for kind in ('kernel','route'):
+        for repeat in range(args.repeats):
+            for opt in ((False,True) if repeat%2==0 else (True,False)):
+                command=[sys.executable,'-I','-B',str(Path(__file__).resolve()),'--worker',kind]
+                if opt:command.append('--optimized')
+                start=perf_counter()
+                output=subprocess.check_output(command,text=True)
+                row=json.loads(output);row.update(kind=kind,optimized=opt,repeat=repeat,process_seconds=perf_counter()-start)
+                rows.append(row)
+    summary={}
+    for kind in ('kernel','route'):
+        summary[kind]={}
+        for field in ('seconds','process_seconds'):
+            medians=[statistics.median(row[field] for row in rows if row['kind']==kind and row['optimized']==opt)
+                     for opt in (False,True)]
+            summary[kind][field]=dict(before=medians[0],after=medians[1],speedup=medians[0]/medians[1])
+    print(json.dumps(dict(python=sys.version,rows=rows,summary=summary),indent=2,sort_keys=True))
+
+
+if __name__=='__main__':main()
diff --git a/research/high-carry-streams/bindings.py b/research/high-carry-streams/bindings.py
new file mode 100644
index 0000000000..19391eb1e6
--- /dev/null
+++ b/research/high-carry-streams/bindings.py
@@ -0,0 +1,40 @@
+"""Authenticate every declared executable/archive before predecessor imports."""
+from hashlib import sha256
+import json
+from pathlib import Path
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def authenticate(root=ROOT, package=HERE):
+    manifest = json.loads((HERE / "SOURCES.json").read_text())
+    for row in manifest["files"]:
+        if row["usage"] == "input":
+            data = (root / row["path"]).read_bytes()
+            if sha256(data).hexdigest() != row["sha256"]:
+                raise ValueError("source changed: " + row["path"])
+    for row in manifest.get("external_proofs", []):
+        if sha256((package/row["path"]).read_bytes()).hexdigest() != row["sha256"]:
+            raise ValueError("inherited proof changed: " + row["path"])
+
+
+def activate():
+    authenticate()
+    path = ROOT / "research/selected-bit-fast-primitives"
+    sys.path.insert(0, str(path))
+    # This module is deliberately not named 'source' when imported: the
+    # unchanged archive loader reserves that name for its own predecessor.
+    import stage_sources
+    return stage_sources.activate()
+
+
+def route_checks():
+    import importlib.util
+    activate()
+    path = ROOT / "research/selected-bit-fast-primitives/check_routes.py"
+    spec = importlib.util.spec_from_file_location("carry_source_route_checks", path)
+    result = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(result)
+    return result
diff --git a/research/high-carry-streams/check_catalogue.py b/research/high-carry-streams/check_catalogue.py
new file mode 100644
index 0000000000..666b3014ff
--- /dev/null
+++ b/research/high-carry-streams/check_catalogue.py
@@ -0,0 +1,53 @@
+"""Carry exposure in the actual selected registry at identity low class, q=3.
+
+This is a finite source specialization, not a selected GL64 payload execution
+or a distribution over every low class. Occurrence weights are source weights.
+"""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import json
+from unittest.mock import patch
+
+import bindings
+
+
+def run():
+    _source,retained,data=bindings.activate()
+    from catalogue import Catalogue
+    from compile_routes import selected_registry,matrix_key,inverse_word
+    from routes import Route
+    from words import need
+    names=(retained.GEOMETRY,retained.TEMPLATE,retained.GLOBAL,retained.WORD,retained.EXPECTED,retained.ASSEMBLY)
+    routes,source_receipt=retained.compile_catalog({name:data[name] for name in names})
+    catalogue=Catalogue(3)
+    matrix=type(catalogue).chart_matrix.__wrapped__
+    with patch.object(catalogue,'chart_matrix',lambda chart:matrix(catalogue,chart)):
+        registry,binding_receipt=selected_registry(catalogue)
+    identity=tuple(tuple(int(i==j) for j in range(64)) for i in range(64))
+    histograms={}
+    digest=sha256()
+    for chart in sorted(registry.words,key=repr):
+        target=tuple(tuple(v.numerator*pow(v.denominator,-1,3)%3 for v in row) for row in chart)
+        route=Route(3,64,identity,target,chart)
+        operations=registry.compile(route)
+        carries=Counter(op[2] for op in operations if op[0]=='translate')
+        need(all(type(a) is int and 0<abs(a)<=4 for a in carries),'entire compiled carry domain')
+        histograms[chart]=carries
+        digest.update(json.dumps(operations,separators=(',',':')).encode())
+        registry.compiled.clear()
+    total=Counter()
+    for key,row in sorted(routes.items()):
+        word=tuple((k,t,c,F(v)) for k,t,c,v in row['word'])
+        for oriented in (word,inverse_word(word)):
+            matrix=matrix_key(retained.replay(oriented,64))
+            for carry,count in histograms[matrix].items():total[carry]+=count*row['occurrences']
+    before=sum(count*(a if a>0 else -3*a) for a,count in total.items())
+    after=sum(total.values())
+    need(before>after,'nontrivial selected carry exposure')
+    return dict(q=3,low='identity',chart_types=len(routes),registry_matrices=len(registry.words),
+                orientations=2*len(routes),weighted_carries={str(k):v for k,v in sorted(total.items())},
+                weighted_old_full_field_primitive_calls=before,weighted_new_kernel_calls=after,
+                saved_primitive_calls=before-after,operations_sha256=digest.hexdigest(),
+                source_catalogue_sha256=source_receipt['catalogue_sha256'],
+                bound_source_types=binding_receipt['source_types'])
diff --git a/research/high-carry-streams/check_controls.py b/research/high-carry-streams/check_controls.py
new file mode 100644
index 0000000000..bdb641c7be
--- /dev/null
+++ b/research/high-carry-streams/check_controls.py
@@ -0,0 +1,76 @@
+"""Small independent identities and rejection tests, also run under -O."""
+from pathlib import Path
+from tempfile import TemporaryDirectory
+from unittest.mock import patch
+import json
+
+import bindings
+bindings.activate()
+from cardinal_counts import Count
+from words import need
+from check_kernel import one_case
+import rotation
+
+
+def reject(call, fragment):
+    try:
+        call()
+    except ValueError as error:
+        need(fragment in str(error), "intended control rejection: " + str(error))
+        return
+    raise ValueError("mutation unexpectedly accepted: " + fragment)
+
+
+def split_checks():
+    total=0
+    for q in range(1,258):
+        modulus=Count.literal(q)
+        for amount in (-4,-3,-2,-1,1,2,3,4):
+            large,small=rotation.split_lengths(modulus,amount)
+            def value(count):
+                bits=count.tape.cells[1:]
+                digits=[]
+                for bit in bits:
+                    if bit not in (0,1):break
+                    digits.append(bit)
+                return sum(bit<<i for i,bit in enumerate(digits))
+            need((value(large),value(small)) == (q-abs(amount)%q,abs(amount)%q),
+                 "independent exact modular split")
+            large.close();small.close();total+=1
+        for amount in (0,5,-5,True,1.0):
+            reject(lambda:rotation.split_lengths(modulus,amount),'fixed selected carry')
+        modulus.close()
+    zero=Count.literal(0)
+    reject(lambda:rotation.split_lengths(zero,1),'positive cardinality')
+    zero.close()
+    return total
+
+
+def run():
+    split=split_checks()
+    reject(lambda:one_case(5,2,3,-4,True,wrong_sign=True),'independent input columns')
+    reject(lambda:one_case(5,2,3,-4,True,extra_bit=True),'complete rotation input')
+    reject(lambda:one_case(3,2,3,-3,True,extra_bit=True),'complete identity rotation source')
+    reject(lambda:one_case(5,2,3,-4,True,capacity=10),'inventory exhausted')
+    good,_=one_case(5,2,3,-4,True,capacity=11)
+    need(good['scratch']==8,'eight additional roles suffice and are attained')
+    original=rotation.translated
+    def extra_read(source,*args,**kwargs):
+        source.read()
+        return original(source,*args,**kwargs)
+    with patch.object(rotation,'translated',extra_read):
+        changed,_=one_case(5,2,3,-4,True)
+    need(changed['total']==good['total']+1 and changed['physical']['reads']==good['physical']['reads']+1,
+         'endpoint-preserving extra traffic detected')
+    # The independent column check must still reject even on all-zero data.
+    with patch('random.Random.randrange',return_value=0):
+        reject(lambda:one_case(5,2,3,-4,True,wrong_sign=True),'independent input columns')
+    # The source loader must reject an altered input before importing it.
+    manifest=json.loads((bindings.HERE/'SOURCES.json').read_text())
+    first=next(row for row in manifest['files'] if row['usage']=='input')
+    with TemporaryDirectory() as path:
+        root=Path(path)
+        target=root/first['path'];target.parent.mkdir(parents=True)
+        target.write_bytes((bindings.ROOT/first['path']).read_bytes()+b'\n')
+        reject(lambda:bindings.authenticate(root=root),'source changed')
+    return dict(split_cases=split,controls=9,scratch_peak=8,seed=6)
diff --git a/research/high-carry-streams/check_kernel.py b/research/high-carry-streams/check_kernel.py
new file mode 100644
index 0000000000..9b673e9836
--- /dev/null
+++ b/research/high-carry-streams/check_kernel.py
@@ -0,0 +1,120 @@
+"""Independent modular column oracle and complete physical-I/O measurement."""
+from time import perf_counter
+from unittest.mock import patch
+import random
+
+import bindings
+bindings.activate()
+from cardinal_counts import Count
+from check_support import no_decode
+import kernels
+from physical_words import PhysicalArena, PhysicalWord
+from provenance import Provenance
+from records import Tape
+from scratch_pool import ScratchPool
+from session import sealed_constructors
+from words import BLANK, Ring, Word, need
+import rotation
+
+
+def body(tape):
+    physical = getattr(tape, "physical", tape)
+    return bytes(physical.cells[1:]).rstrip(bytes([BLANK]))
+
+
+def one_case(q, b, s, amount, optimized, capacity=40, extra_bit=False, wrong_sign=False):
+    bank, pool = PhysicalArena(64), ScratchPool(capacity)
+    maximum = Count.literal(q)
+    bank.prepare(maximum)
+    modulus = bank.load(maximum)
+    ring = Ring(modulus)
+    before, suffix = Count.literal(b), Count.literal(s)
+    source = Tape()
+    rng = random.Random(6 + 1000*q + 100*b + 10*s + amount)
+    length = b*q*s
+    for _ in range(length + int(extra_bit)):
+        source.append(rng.randrange(2))
+    source.rewind()
+    initial = body(source)
+    observer = Provenance(length)
+    observer.mark(source)
+    occupied = []
+    for index in range(3):
+        lease = pool.acquire()
+        for bit in (1, index & 1, 0, 1):
+            lease.append(bit)
+        lease.rewind()
+        lease.step(1)
+        occupied.append((lease, bytes(lease.physical.cells), lease.physical.head))
+    count_bytes = tuple(bytes(c.tape.cells) for c in (before,suffix))
+    source_bytes = bytes(source.cells)
+    numerical = tuple(bytes(word.tape.cells) for word in (*bank.words, bank.template))
+    counts = dict(reads=0, writes=0, moves=0)
+    def wrap(key):
+        def observed(*args, **kw):
+            counts[key] += 1
+            return methods[key](*args, **kw)
+        return observed
+    def forbidden(*_args, **_kwargs):
+        raise ValueError("fixture-only operation in physical carry")
+    with no_decode(), sealed_constructors(), pool.install(), observer.installed(), \
+            patch.object(Word, "__init__", forbidden), patch.object(PhysicalWord, "inspect", forbidden):
+        methods = {"reads":Tape.read, "writes":Tape.write, "moves":Tape.step}
+        with patch.object(Tape,"read",wrap("reads")), patch.object(Tape,"write",wrap("writes")), \
+                patch.object(Tape,"step",wrap("moves")):
+            start = perf_counter()
+            if optimized and amount != 1:
+                output = rotation.translated(source, ring, before, suffix,
+                                             -amount if wrong_sign else amount, pool.acquire)
+            else:
+                output = kernels.translated(source, ring, 3, before, suffix, amount)
+            seconds = perf_counter()-start
+        expected, masks = bytearray(length), [0]*length
+        for origin, bit in enumerate(initial[:length]):
+            block, tail = divmod(origin, s)
+            prefix, x = divmod(block, q)
+            target = (prefix*q + (x+amount)%q)*s + tail
+            expected[target], masks[target] = bit, 1 << origin
+        need(body(output) == expected and observer.masks(output.physical,length) == tuple(masks),
+             "complete modular carry and independent input columns")
+        need(output is not source and pool.live.get(output.slot) is output,
+             "distinct owned carry output")
+        need(bytes(source.cells) == source_bytes and source.head == output.head == 1,
+             "borrowed source bytes and heads restored")
+        need(tuple(bytes(c.tape.cells) for c in (before,suffix)) == count_bytes
+             and before.tape.head == suffix.tape.head == 1, "borrowed cardinalities preserved")
+        if optimized and amount != 1:
+            need(tuple(bytes(word.tape.cells) for word in (*bank.words,bank.template)) == numerical,
+                 "no numerical bank mutation")
+        peak = pool.peak - len(occupied)
+        need(len(pool.live) == len(occupied)+1, "only output lease remains")
+        output.clear()
+        for lease, data, head in occupied:
+            need(bytes(lease.physical.cells) == data and lease.physical.head == head,
+                 "occupied dirty bytes and heads restored")
+            need(pool.live.get(lease.slot) is lease, "occupied ownership preserved")
+            lease.clear()
+        pool.empty()
+    ring.close()
+    bank.free(modulus)
+    bank.erase_owned()
+    source.clear()
+    for count in (maximum,before,suffix):count.close()
+    return dict(q=q,b=b,s=s,amount=amount,columns=length,physical=counts,
+                total=sum(counts.values()),scratch=peak,dirty=3), seconds
+
+
+def cases():
+    amounts = (-4,-3,-2,-1,1,2,3,4)
+    return [(q,b,s,a) for q in (3,5) for b,s in ((1,1),(2,1),(1,3),(2,3)) for a in amounts] + \
+           [(q,2,3,a) for q in (7,9,25,81) for a in amounts]
+
+
+def run():
+    rows=[]
+    for case in cases():
+        before,_=one_case(*case,False)
+        after,_=one_case(*case,True)
+        need(before['columns']==after['columns'],'same complete domain')
+        rows.append(dict(before=before,after=after))
+    return rows
diff --git a/research/high-carry-streams/check_routes.py b/research/high-carry-streams/check_routes.py
new file mode 100644
index 0000000000..c6d71377e0
--- /dev/null
+++ b/research/high-carry-streams/check_routes.py
@@ -0,0 +1,117 @@
+"""PR2915 complete-route harness, with the PR3330 physical observer.
+
+Only the opt-in carry adapter differs between baseline and candidate.
+"""
+from fractions import Fraction as F
+from time import perf_counter
+from unittest.mock import patch
+
+import bindings
+bindings.activate()
+from words import need
+from adapter import CarryAdapter
+
+
+def run_case(case, optimized):
+    bindings.activate()
+    old = bindings.route_checks()
+    from records import Tape
+    from words import BLANK
+
+    class DirtyPool(old.ScratchPool):
+        def __init__(self, capacity):
+            super().__init__(capacity)
+            self.borrowed = []
+            for i in range(3):
+                lease = self.acquire()
+                for bit in (i & 1, 1, 0, 1, (i+1) & 1):
+                    lease.append(bit)
+                lease.rewind()
+                lease.step(1)
+                self.borrowed.append((lease, bytes(lease.physical.cells), lease.physical.head))
+
+        def empty(self):
+            for lease, data, head in self.borrowed:
+                need(bytes(lease.physical.cells) == data and lease.physical.head == head,
+                     "occupied scratch bytes and heads restored")
+                need(self.live.get(lease.slot) is lease, "occupied lease ownership")
+                lease.clear()
+            self.borrowed.clear()
+            super().empty()
+
+    class CheckedAdapter(CarryAdapter if optimized else old.Adapter):
+        def close(self):
+            super().close()
+            need(not self.high_bank.live, "high numerical bank empty")
+            need(all(x == BLANK for w in (*self.high_bank.words, self.high_bank.template)
+                     for x in w.tape.cells), "high numerical roles erased")
+
+    counts = dict(reads=0, writes=0, moves=0)
+    native = dict(reads=0, writes=0, moves=0, calls=0)
+    elapsed = []
+    original_route = old.route_packet
+
+    def observed_route(*args, **kwargs):
+        methods = {"reads":Tape.read, "writes":Tape.write, "moves":Tape.step}
+        def wrap(key):
+            def call(*a, **kw):
+                counts[key] += 1
+                return methods[key](*a, **kw)
+            return call
+        original_native = old.Ordinary.run
+        def observed_native(*a, **kw):
+            before = counts.copy()
+            result = original_native(*a, **kw)
+            for k in counts:
+                native[k] += counts[k]-before[k]
+            native["calls"] += 1
+            return result
+        with patch.object(Tape,"read",wrap("reads")), \
+             patch.object(Tape,"write",wrap("writes")), \
+             patch.object(Tape,"step",wrap("moves")), \
+             patch.object(old.Ordinary,"run",observed_native):
+            start = perf_counter()
+            result = original_route(*args, **kwargs)
+            elapsed.append(perf_counter()-start)
+            return result
+
+    with patch.object(old,"ScratchPool",DirtyPool), \
+         patch.object(old,"Adapter",CheckedAdapter), patch.object(old,"route_packet",observed_route):
+        result = old.one_case(**case)
+    need(native["calls"] == result["calls"]["swaps"], "all complete B1 intervals counted")
+    total = sum(counts.values())
+    paid_native = sum(native[k] for k in counts)
+    need(total >= paid_native, "nonoverlapping paid intervals")
+    result.update(physical=counts, native=native, total=total,
+                  outside_native=total-paid_native, dirty_roles=3)
+    return result, sum(elapsed)
+
+
+def cases():
+    word = (("add",0,1,F(1,2)), ("scale",1,1,F(-2)), ("swap",0,1,F(1)))
+    dense = (("add",0,1,F(-4)), ("scale",1,1,F(-1,2)),
+             ("add",0,1,F(1,2)), ("add",1,0,F(2)), ("swap",0,1,F(1)))
+    return [
+        dict(q=3,width=2,low=((2,1),(1,1)),word=(("scale",0,0,F(-4)),),
+             old_prefixes=2,fibre_value=3),
+        dict(q=3,width=2,low=((1,2),(2,2)),word=(("add",0,1,F(1)),)*9,
+             old_prefixes=2,fibre_value=3),
+        dict(q=3,width=2,low=((1,2),(2,2)),word=word,old_prefixes=2,fibre_value=3),
+        dict(q=5,width=2,low=((1,4),(2,1)),word=word,old_prefixes=1,fibre_value=1),
+        dict(q=3,width=1,low=((1,2),(2,2)),word=dense,old_prefixes=2,fibre_value=3),
+        dict(q=3,width=3,low=((2,1),(1,1)),word=word,old_prefixes=1,fibre_value=1),
+        dict(q=3,width=2,low=((2,1),(1,1)),word=dense,old_prefixes=1,fibre_value=3),
+    ]
+
+
+def run():
+    results = []
+    for index, case in enumerate(cases()):
+        before, _ = run_case(case, False)
+        after, _ = run_case(case, True)
+        need(before["columns"] == after["columns"], "same complete input")
+        need(after["calls"] == before["calls"], "unchanged complete route native call bill")
+        results.append(dict(case=index, before=before, after=after))
+    need(results[0]["after"]["total"] < results[0]["before"]["total"],
+         "physical saving on compiled signed scale/carry fixture")
+    return results
diff --git a/research/high-carry-streams/rotation.py b/research/high-carry-streams/rotation.py
new file mode 100644
index 0000000000..12d84ff8cc
--- /dev/null
+++ b/research/high-carry-streams/rotation.py
@@ -0,0 +1,98 @@
+"""Encoded bounded cyclic rotation with complete spectator blocks.
+
+Tekalign, with substantial OpenAI Codex assistance. Apache-2.0.
+Uses the authenticated PR2915/PR2753 Count, Counter and copy operations.
+No host integer is reconstructed from a tape.
+"""
+import bindings
+bindings.activate()
+from cardinal_counts import Count, positive
+from routes import copy_rows
+from stream import Counter
+from words import BLANK, need
+
+
+def split_lengths(modulus, amount):
+    """Return Q-r,r where r=abs(amount) mod Q, using at most four decrements."""
+    need(type(amount) is int and 0 < abs(amount) <= 4, "fixed selected carry")
+    positive(modulus)
+    remaining = Counter(modulus)
+    small = Count.literal(0)
+    try:
+        for _ in range(abs(amount)):
+            remaining.decrement()
+            small.increment()
+            if remaining.finished:
+                remaining.close()
+                small.close()
+                remaining = Counter(modulus)
+                small = Count.literal(0)
+        large = Count(remaining.tape)
+        result, small = (large, small), None
+        return result
+    finally:
+        remaining.close()
+        if small is not None:
+            small.close()
+
+
+def translated(source, ring, before, suffix, amount, factory):
+    """Borrow B*Q*S bits, return a distinct owned x -> x+amount mod Q cube."""
+    need(type(amount) is int and 0 < abs(amount) <= 4, "fixed selected carry")
+    positive(before)
+    positive(suffix)
+    modulus = Count(ring.modulus)
+    large = small = left = right = output = None
+    try:
+        large, small = split_lengths(modulus, amount)
+        modulus.close()
+        modulus = None
+        output = factory()
+        if small.zero():
+            outer = Counter(before)
+            try:
+                while not outer.finished:
+                    copy_rows(source, output, large, suffix)
+                    outer.decrement()
+            finally:
+                outer.close()
+        else:
+            left = factory()
+            right = factory()
+            first, second = (large, small) if amount > 0 else (small, large)
+            outer = Counter(before)
+            try:
+                while not outer.finished:
+                    copy_rows(source, left, first, suffix)
+                    copy_rows(source, right, second, suffix)
+                    outer.decrement()
+            finally:
+                outer.close()
+            need(source.read() == BLANK, "complete rotation input")
+            source.rewind()
+            left.rewind()
+            right.rewind()
+            outer = Counter(before)
+            try:
+                while not outer.finished:
+                    copy_rows(right, output, second, suffix)
+                    copy_rows(left, output, first, suffix)
+                    outer.decrement()
+            finally:
+                outer.close()
+            need(left.read() == right.read() == BLANK, "complete rotation buckets")
+        # The general path already rewound its source. Check the identity path
+        # at its actual end; never infer completeness from a known bit count.
+        if small.zero():
+            need(source.read() == BLANK, "complete identity rotation source")
+        output.rewind()
+        result, output = output, None
+        return result
+    finally:
+        source.rewind()
+        for value in (left, right, output):
+            if value is not None:
+                value.clear()
+        for value in (large, small, modulus):
+            if value is not None:
+                value.close()
diff --git a/research/high-carry-streams/verify.py b/research/high-carry-streams/verify.py
new file mode 100644
index 0000000000..39fa67b367
--- /dev/null
+++ b/research/high-carry-streams/verify.py
@@ -0,0 +1,40 @@
+"""Read-only registered replay of complete typed receipts."""
+import argparse
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+import sys
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE))
+
+
+def canonical(value):
+    return json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False)
+
+
+def main():
+    parser=argparse.ArgumentParser()
+    parser.add_argument('--suite',required=True,choices=('kernel','routes','catalogue','controls'))
+    parser.add_argument('--emit',action='store_true')
+    args=parser.parse_args()
+    import bindings
+    bindings.authenticate()
+    # The predecessor loader places its packages first in sys.path. Load our
+    # checker by explicit path to keep similarly named frozen checkers distinct.
+    spec=importlib.util.spec_from_file_location('carry_check_'+args.suite,HERE/('check_'+args.suite+'.py'))
+    check=importlib.util.module_from_spec(spec);spec.loader.exec_module(check)
+    result=check.run()
+    digest=sha256(canonical(result).encode()).hexdigest()
+    if args.emit:print(canonical(result))
+    else:
+        expected=json.loads((HERE/'RESULT.json').read_text())
+        if digest!=expected[args.suite]:raise ValueError('complete typed receipt differs: '+args.suite)
+        if args.suite!='controls':
+            saved=json.loads((HERE/(args.suite.upper()+'.json')).read_text())
+            if canonical(result)!=canonical(saved):raise ValueError('saved full receipt differs: '+args.suite)
+        print(canonical(dict(suite=args.suite,sha256=digest,cases=len(result))))
+    print('PASS_HIGH_CARRY_'+args.suite.upper())
+
+
+if __name__=='__main__':main()