diff --git a/research/one-terminal-h3-prefix/HANDOFF.md b/research/one-terminal-h3-prefix/HANDOFF.md
new file mode 100644
index 0000000000..fc08d56d64
--- /dev/null
+++ b/research/one-terminal-h3-prefix/HANDOFF.md
@@ -0,0 +1,22 @@
+HANDOFF
+
+Research discussion / PR / artifact:
+LOCAL-ONLY `research/one-terminal-h3-prefix`, branch `research/one-terminal-h3-prefix-20261023`; final public artifact pending parent publication. Scope is one actual priced H3 split AND one phase-bound homogeneous tall4x3 U(q) native offer, with no complete second-call consumer,112-capacity or kappa claim. Previously published packages remain unchanged.
+
+Exact commit:
+Scientific provenance base `624de9dc66858af0945e5f8a0942488d62280d43`; final publication commit pending. Fresh canonical main checked at `cef4b52f2a59009865bf8eabde1be3f159063703`, including revised selected-baseline startup guidance; the source pins remain valid. Native source is `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`. All seven A files from local packet `954da4f1f8f2b84d84a6feed16fa5f10f971239d` and G's separately frozen nine-file subtree are retained byte-exact. Six vendored upstream inputs are ancestral20bb. G's local interval dependency is retained by exact hash as committed package bytes, with no fork-only runtime/history dependency.
+
+What is established:
+Actual backward helper496 event15372 H3(911→full1) becomes H2(911→181), owned-zero COPY, then H1(181→full1), with exact signed-tableau/absolute-phase identity in forward and primitive-wise raw dual. All old live values and inherited632-input endpoint are preserved. G independently propagated all632 columns to confirm clean prefixes and complete isolated X39/Y151/helper496 rows. Separately, exact monomials T=X510, N=S D^-1 and B=E Q normalize F=T Dq and S=ND, with Dq=qD, q^2=X162 and q^4=I. Input X=-B a, output normalizers and Y+=H produce (X0,Y0,C0)=D U(q)(a,y,h), H0=Dqh; restore T H0=Fh afterward. There are THREE original owners plus a dependent prefix, zero new productive credit, paid deltaH2+H1-H3, one owned array and at most36 finite passes (19 split/access+17 normalizers/ADD/helper restoration). Both separate frozen checkers replay portably in normal/O; their records, G's original-offer independent review and six new-interface guard controls remain distinct.
+
+What remains uncertain:
+No two-call endpoint,112-resource realization, extra productive reward, new kappa or transfer to #4929 is established. The224H17 positive moment is only an unrealized price screen. Raw Gamma^2 has grade2; separate two-sided monomial normalization recovers D/q and does not assert a monomial square for raw Gamma. A's COPY/CLEAR words are not automatically inverse-transposes under general raw duality. G's new U construction is author-checked and packaging-replayed, distinct from its independent review of A. The known #4698 controller reuses one third owner and has third targetH16, not automaticallyH17; two native calls have distinct original helpers h,k. Precision allocation, added-ADD amplification, finite compiler reserves, complete caller, stock and outer funding remain open. Whole modified632-column replay is inherited through exact local replacement, not freshly run.
+
+Smallest useful next task:
+Write one exact two-call endpoint with the actual third-owner policy, retaining both independent helper jobs or honestly repricing reuse. Bind all source headers, normalizers, residual queries, COPY/CLEAR and cleanup, then price the complete paid/finite invoice before extending capacity. The present package stops at the actual one-port tall offer and supplies no additional family search.
+
+Reproduction command and expected runtime:
+From repository root run `python3 -I -W error -B research/one-terminal-h3-prefix/verify.py` and `python3 -I -W error -B research/one-terminal-h3-prefix/verify_homogeneous.py`, then both with `-O`; each is about1–2 seconds locally. Registered replay is `python3 scripts/research_package.py --package research/one-terminal-h3-prefix`. Both launchers authenticate exact frozen science/source bytes, adapt only Git-loader AST nodes in memory and execute in private scratch. A's PATCH/RESULT regenerate byte-for-byte; G's read-only checker compares its frozen receipt. Direct launchers support Git-free export replay.
+
+Predecessor credit:
+Credit Cao Yifan /intqwq and retained native #4610/#4712 contributors; Cinna Davis /1337isnot1337 #4698 and retained #4694/#4470 lineage; zxv and the exact-phase/compiler/interval contributors; A for the literal physical prefix offer; G for independent source review and the separately frozen U-interface construction; and the parent for the source/header scope review. Prepared for Chris R / Clear1nsight with substantial OpenAI Codex gpt-6.1-sol/high assistance. Apache-2.0; no independent human or proof-kernel acceptance claimed.
diff --git a/research/one-terminal-h3-prefix/LICENSE b/research/one-terminal-h3-prefix/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/one-terminal-h3-prefix/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/one-terminal-h3-prefix/README.md b/research/one-terminal-h3-prefix/README.md
new file mode 100644
index 0000000000..d7bfa15070
--- /dev/null
+++ b/research/one-terminal-h3-prefix/README.md
@@ -0,0 +1,181 @@
+# One terminal H3 split and a phase-bound homogeneous native offer
+
+**One changed physical offer; no complete consumer or new kappa.** In the frozen
+#4610 backward supplier, split helper496's paid H3 at event15372 into H2 then
+H1 through actual chart181, and copy the intermediate into one new owned-zero
+array. The two children compose to the old H3 exactly, so every original live
+field and old632-input endpoint remains unchanged. The copied response matches
+actual Y151's source gauge at that cut. The exact paid change is
+`Delta P=H2+H1-H3`, with zero new productive reward. A separate source-bound
+construction normalizes this one copied prefix into a homogeneous tall4x3
+U(q) offer on three original owners, with its helper returned once.
+
+This is a distinct literal source offer after the separated-control ceilings.
+It is one resource, not a112-slot construction. The previously hypothetical
+224H17 target appears only in a necessary price screen and remains unrealized.
+No claim is transferred to the newer #4929 producer.
+
+## Literal patch and endpoint coverage
+
+Native source: `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, ancestral to canonical
+base `624de9dc66858af0945e5f8a0942488d62280d43`. The seven science files under
+`science/` are retained byte-for-byte from the local source packet at
+`954da4f1f8f2b84d84a6feed16fa5f10f971239d`; that local commit is attribution,
+not a runtime or Git-history dependency. The original replay uses five exact merged-source files; the separate
+homogeneous check adds one more. They are vendored under `inputs/`, with
+historical Git/SHA pins in SOURCES.json.
+
+The guarded old event is `['climb','warp_retimed',496,911,1,3]` at backward
+index15372. Helper496's last old write is13182. Actual Y151, port39/q162,
+is already in its final rank8 chart181 after event14597. Replace the H3 by:
+
+1. H2 on496, chart911 to181.
+2. COPY496 to new owned C1, tagged181.
+3. H1 on496, chart181 to full1.
+
+Initialize C1 separately and clear it after use. Original owned C0 is untouched.
+[PATCH.json](science/PATCH.json) records the guarded replacement and reset.
+
+For canonical frame operators FU,FM,FV, shared-frame cancellation proves
+`(FV FM*) (FM FU*) = FV FU*`, with rightmost operation first and star
+denoting adjoint. The unchanged checker
+verifies ranks2,1,3, signed tableaus, absolute zero-column phase and exact
+lowering. It separately checks the actual primitive-wise raw-dual convention,
+which preserves circuit order. General raw duality does not automatically make
+the added COPY/CLEAR access words inverse-transposes of one another.
+
+Reverse symbolic pullbacks bind the arbitrary-owner observations at the new cut:
+`C1=bar(F181)h496` and `Y151=bar(F181)y151`. Helper496 then returns its original
+`bar(F9)h496`. COPY reads only, and all later old events remain unchanged.
+This is an exact local replacement proof plus the authenticated old632-input
+endpoint receipt; a fresh whole modified632-column replay was not run.
+
+The actual rank1 tail `Gamma=bar(F9)bar(F181)^-1` is not bare C162 in either
+sign. The source's Y151 coefficient in returned mainX39 is `-bar(F9)`, or
+`-Gamma` relative to Y151's exit gauge. This binds one actual cross coefficient;
+it does not supply an arbitrary free query or complete multi-input consumer.
+The raw Gamma has square of grade2. The separate construction below uses
+two-sided monomial normalizers to recover a commuting D/q model; it does not
+claim that raw Gamma itself has a monomial square.
+
+## Separate actual one-port homogeneous construction
+
+The unchanged files under [homogeneous/](homogeneous/REPORT.md) contain G's
+independent original-offer review and its distinct new interface construction.
+Let E=bar(F41), S=bar(F181), F=bar(F9), Q=C162 and q=Q^-1. Actual source
+inputs have X in rank1 chart41=[162], while Y and helper enter empty. On three
+arbitrary independent physical inputs x,y,h, the isolated source equations are
+
+```text
+Xraw = F E^-1 x - F y,   Yraw = S y,
+Hraw = F h,              C = S h.
+```
+
+G's forward propagation of all632 original columns verifies these complete
+rows and that no other returned source row depends on the selected inputs.
+The native port39 transverse word is
+`D=C161 C4 C8 C16 C131 C64 C35 C256`. Exact phase-bound monomials
+`T=X510`, `N=S D^-1`, and `B=E Q` satisfy F=T D q and S=N D. D and q commute,
+q^2=X162 and q^4=I. N and B include their actual phases and source-derived
+literal monomial recipes. Raw Gamma^2 still has grade2; a common-conjugation
+square test would not establish these separate two-sided normalizations.
+
+Present X with x=-B a. Apply X0=-T^-1 Xraw, Y0=N^-1 Yraw,
+C0=N^-1 C and H0=T^-1 Hraw; then perform Y0+=H0. The resulting tall offer is
+
+```text
+(X0,Y0,C0) = D [ I q 0 ; 0 I q ; 0 0 I ] (a,y,h),
+H0         = D q h.
+```
+
+Restore Hraw=T H0 after reading it, returning the original helper Fh exactly.
+The inputs a,y,h are THREE original owners; C0 is dependent workspace, not a
+fourth independent input or extra productive job. Selected main outputs now
+form this changed interface and are not simultaneously credited as their old
+separate source main jobs. Scalar signs remain outside every columnwise tensor
+lift; all nonzero blocks are checked as individual absolute-phase Clifford
+words. No tensor of a width-one operator sum is used.
+
+This is one actual native homogeneous U(q) offer. It does not install the
+second-call controller. Two native calls have distinct original helpers h,k;
+the known #4698 same-third-owner template cannot identify them while retaining
+both rewards. Its documented third target is H16, not automatically H17.
+A four-owner endpoint or an honestly repriced reuse policy remains open.
+
+## Paid, storage and finite obligations
+
+All408 original helper jobs retain their reward once, including helper496's
+H9. C1 has no independent arbitrary input and earns no productive credit.
+One additional ordinary Gaussian child replaces the single H3, leaving rank
+mass unchanged. The added storage is one array, of size `2^(17f)` in the
+proposed17-axis embedding. The original split/access bill is19 full-array
+passes: initialization, COPY, CLEAR and up to16 monomial boundary passes,
+without subtracting removed old normalizers. Ordinary columnwise index/phase
+work retains its O(f) overhead. The homogeneous interface adds at most17
+passes for input/output normalizers, the borrow ADD and helper restoration,
+for a total conservative36 passes. The new ADD also needs its error reserve;
+this accounting does not fund a compiler or caller.
+
+The copied formal prefix has coefficient norm1, below the inherited169 bound.
+COPY/CLEAR and exact monomial operations add no arithmetic rounding. Replacing
+one approximate unitary child by two needs a new precision allocation: giving
+each error at most e/3 yields combined error at most `2e/3+e^2/9<e` for
+`0<e<=1`. Concrete source allocation, consumer amplification, finite compiler
+reserves and outer transfer remain unrun and unfunded.
+
+The surcharge `2^t+1-3^t` is positive at the funded comparisons. The exact
+intervals in [RESULT.json](science/RESULT.json) leave the hypothetical
+`224H17+2H` versus `2P` price-only screen positive after that surcharge. Those
+main targets have no endpoint here, so these are not complete-caller margins.
+[The original report](science/REPORT.md) retains the full local argument and
+its limitations.
+
+## Reproduce
+
+Python3.12 standard library, from repository root:
+
+```sh
+python3 -I -W error -B research/one-terminal-h3-prefix/verify.py
+python3 -I -O -W error -B research/one-terminal-h3-prefix/verify.py
+python3 -I -W error -B research/one-terminal-h3-prefix/verify_homogeneous.py
+python3 -I -O -W error -B research/one-terminal-h3-prefix/verify_homogeneous.py
+python3 scripts/research_package.py --package research/one-terminal-h3-prefix
+```
+
+The read-only wrapper authenticates all original science files and source
+inputs. It changes only the Git source-loader function in an in-memory AST,
+executes the otherwise unchanged checker in private scratch, and compares both
+emitted PATCH.json and RESULT.json byte-for-byte. The original checker is a
+writer; the registered wrapper does not write the published package. The same
+direct wrapper works after export without Git. Original normal/optimized logs
+remain archived unchanged. The separate homogeneous launcher changes only
+its Git-byte loader assignment and stages the exact local interval library at
+its expected relative path in private scratch. Six ancestral20bb sources are
+retained overall. The additional local interval code was not a Git source pin;
+its exact bytes are committed under inputs/local and authenticated against G
+DEPENDENCIES.json, so there is no external or fork-only runtime dependency.
+Both direct launchers support Git-free export replay. No compiler suite is invoked.
+
+## Open next questions
+
+The next useful task is an exact consumer for this one copied prefix, preserving
+both distinct productive helper jobs and all main owners. First write every
+arbitrary-input owner equation in the literal source gauges, including all
+normalizers, COPY/CLEAR, residual nonmonomial factors and chronological calls;
+then price the complete paid and finite bill. Stop before capacity expansion if
+that complete bill fails. TASK.json records this question and its blockers.
+The phase-bound normalizer construction resolves the one-off homogeneous
+interface; the distinct-helper two-call endpoint and full funding remain open.
+
+## Credit and review status
+
+Credit Cinna Davis /1337isnot1337 and the retained native #4610 lineage, #4712's
+arbitrary-owner protocol work, and the upstream exact-phase compiler and interval
+arithmetic contributors. A produced the exact changed offer and endpoint proof;
+G independently reviewed A's original offer and authored the separate frozen
+homogeneous construction. Its [review](homogeneous/REVIEW-A.md) and source-bound
+construction records are preserved distinctly; packaging replay does not turn
+G's new construction into an independently human- or kernel-reviewed theorem.
+Prepared for Chris R / Clear1nsight with substantial OpenAI Codex gpt-6.1-sol/high
+assistance. The source packet's seven files remain unchanged. Separate agent
+checks do not imply independent human or proof-kernel acceptance. Apache-2.0.
diff --git a/research/one-terminal-h3-prefix/SOURCES.json b/research/one-terminal-h3-prefix/SOURCES.json
new file mode 100644
index 0000000000..cf03d35e21
--- /dev/null
+++ b/research/one-terminal-h3-prefix/SOURCES.json
@@ -0,0 +1,68 @@
+{
+  "schema_version": 1,
+  "base_commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "usage": "provenance",
+      "pin": "head:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    },
+    {
+      "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py",
+      "usage": "provenance",
+      "pin": "head:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py",
+      "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    {
+      "path": "research/kappa-function-composition/complex/prune_native.py",
+      "usage": "provenance",
+      "pin": "head:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/kappa-function-composition/complex/prune_native.py",
+      "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b",
+      "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257"
+    },
+    {
+      "path": "research/higher-moment-strictification/verify.py",
+      "usage": "provenance",
+      "pin": "head:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/higher-moment-strictification/verify.py",
+      "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699",
+      "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json",
+      "usage": "provenance",
+      "pin": "head:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json",
+      "git_blob": "d8a2e0a915edce68cfe7472b94bb87dfb9dc24c0",
+      "sha256": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428"
+    },
+    {
+      "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json",
+      "usage": "provenance",
+      "pin": "head:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json",
+      "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70",
+      "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+    }
+  ],
+  "retained_local_sources": [
+    {
+      "path": "inputs/local/prefix-interval-library.py",
+      "origin": "G frozen outputs/split-helper-prefix-consumer/check.py, retained self-contained bytes",
+      "sha256": "18b2306ccbf1706f89800099c532551a792001b61ee57ffd752027739d67cdde",
+      "runtime_git_dependency": false
+    }
+  ]
+}
diff --git a/research/one-terminal-h3-prefix/TASK.json b/research/one-terminal-h3-prefix/TASK.json
new file mode 100644
index 0000000000..611773c559
--- /dev/null
+++ b/research/one-terminal-h3-prefix/TASK.json
@@ -0,0 +1,71 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 7,
+  "base_commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. 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/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "One actual backward paid-H3 split on helper496 plus separate phase-bound monomial normalizers yielding one homogeneous tall4x3 U(q) offer on three original owners and a dependent copied prefix, with the original helper returned once. Exact local source replacement, zero new productive reward,36 conservative finite passes; no second-call consumer,112-capacity or kappa.",
+  "scope_change_reason": "Explicit changed-physical-offer assignment narrows the helper-inventory card to a literal source child and access patch after earlier separated-control ceilings. This is one resource and changes one paid primitive; it is not a new row bank or a repeated chart search.",
+  "bottleneck_link": "The actual paid deltaH2+H1-H3 exposes one clean prefix; separate exact monomial normalizers and one ADD supply D U(q) from an actual native call. This resolves one native-interface premise but not repeated third-owner policy, complete caller, finite/compiler funding or capacity.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at one priced source split and one tall homogeneous interface. Preserve rawGamma-square grade2 warning and normalizedq-square monomial distinction. Do not identify two native helper inputs, add dependent-prefix reward, claim112 copies, a complete consumer or kappa.",
+  "outcome": "partial",
+  "evidence": "Seven original A science files unchanged; G independently propagated all632 original columns and verified cut/isolated endpoint, nested charts and phase/ranks. Separate G construction checks all absolute-phase word blocks, nonempty X header, commuting D/q, q-square/order, six discriminating controls and36-pass bill. Both portable normal/O checker pairs pass. New U construction is author-checked by G and replayed by packaging, distinct from G independent review of A.",
+  "author": "Prepared for Chris R / Clear1nsight",
+  "ai_assistance": "Substantial OpenAI Codex assistance. User-authorized gpt-6.1-sol/high agents separately produced the physical offer, independent review and packaging. No independent human or formal proof-kernel acceptance.",
+  "open_questions": [
+    {
+      "question": "Can two actual native calls consume the one-port tall U(q) interface with a correct third-owner policy, retaining both original helper jobs or honestly repricing reuse?",
+      "why_it_matters": "The paid prefix is physically exposed, but the hypothetical high-rank main reward still has no complete endpoint.",
+      "first_step": "Write the exact four-owner/two-call endpoint with both original helper inputs and every normalizer/copy/cleanup; derive the full paid/finite invoice before any capacity expansion.",
+      "blocked_by": "The known4698 template reuses one third owner across calls and has third targetH16, not automaticallyH17. No four-owner endpoint,112-resource realization, complete precision/compiler reserve or outer funding is supplied."
+    }
+  ],
+  "upstream_refresh": {
+    "commit": "cef4b52f2a59009865bf8eabde1be3f159063703",
+    "changed_guidance_read": "docs/research/agent-procedure.md startup selected-baseline substitution/sparse helper; this explicitly assigned source-bound module does not run a historical card orientation command.",
+    "scientific_pins_unchanged": true
+  }
+}
diff --git a/research/one-terminal-h3-prefix/VERIFY.json b/research/one-terminal-h3-prefix/VERIFY.json
new file mode 100644
index 0000000000..1accec5678
--- /dev/null
+++ b/research/one-terminal-h3-prefix/VERIFY.json
@@ -0,0 +1,59 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Authenticates seven unchanged science files and five vendored20bb sources; replaces only Git source-loader AST in memory; regenerates exact PATCH/RESULT in private scratch. Checks actual event15372, rank3=rank2+rank1 phase-exact identities, clean arbitrary-owner prefixes and raw price-only intervals. No complete consumer,112 capacity, fresh632-column or compiler/outer replay."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Authenticates seven unchanged science files and five vendored20bb sources; replaces only Git source-loader AST in memory; regenerates exact PATCH/RESULT in private scratch. Checks actual event15372, rank3=rank2+rank1 phase-exact identities, clean arbitrary-owner prefixes and raw price-only intervals. No complete consumer,112 capacity, fresh632-column or compiler/outer replay."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify_homogeneous.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Authenticates nine unchanged G files, four ancestral20bb sources and retained local interval dependency; changes only Git-byte loader assignment in memory and preserves expected relative dependency in scratch. Independently propagates all632 columns, verifies actual nonempty X header, phase-exact monomial normalizers, all tall4x3 Clifford-word blocks and six discriminating controls. One offer/three original owners/dependent prefix,36 passes; no second-call consumer or kappa."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify_homogeneous.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Authenticates nine unchanged G files, four ancestral20bb sources and retained local interval dependency; changes only Git-byte loader assignment in memory and preserves expected relative dependency in scratch. Independently propagates all632 columns, verifies actual nonempty X header, phase-exact monomial normalizers, all tall4x3 Clifford-word blocks and six discriminating controls. One offer/three original owners/dependent prefix,36 passes; no second-call consumer or kappa."
+    }
+  ]
+}
diff --git a/research/one-terminal-h3-prefix/homogeneous/DEPENDENCIES.json b/research/one-terminal-h3-prefix/homogeneous/DEPENDENCIES.json
new file mode 100644
index 0000000000..d854d173b1
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/DEPENDENCIES.json
@@ -0,0 +1,7 @@
+{
+  "local_interval_library": {
+    "path": "../check.py",
+    "sha256": "18b2306ccbf1706f89800099c532551a792001b61ee57ffd752027739d67cdde"
+  },
+  "local_only": true
+}
diff --git a/research/one-terminal-h3-prefix/homogeneous/FILES.json b/research/one-terminal-h3-prefix/homogeneous/FILES.json
new file mode 100644
index 0000000000..280af4883c
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/FILES.json
@@ -0,0 +1,36 @@
+{
+  "files": [
+    {
+      "path": "DEPENDENCIES.json",
+      "sha256": "8917b1b41e340f210cdd981243e71afc41f5052f348afdeeae7b16453fa4ec1b"
+    },
+    {
+      "path": "HANDOFF.md",
+      "sha256": "fcee273f7ff915f0931d5af3768648ba0a0807adc0a338442ce5a3e75ef06ad5"
+    },
+    {
+      "path": "REPORT.md",
+      "sha256": "f4d192ae906cf6d70b05ee134e806bfe0502ee4944a00024882bb042ac9fb2d3"
+    },
+    {
+      "path": "RESULT.json",
+      "sha256": "9d8e44b47ac6355b3265978d734e523890d7efa8851fc5121a48fb20b490afed"
+    },
+    {
+      "path": "REVIEW-A.json",
+      "sha256": "2ae5eae6ebb32e2dbf2f9f5a1224271519d6eb658c1a4ee71de61ac48b78ec86"
+    },
+    {
+      "path": "REVIEW-A.md",
+      "sha256": "a9978ed4f5a6265dbfd8e89d2193907081ddf952b78efccf353a0d0a12b039e4"
+    },
+    {
+      "path": "RUNS.json",
+      "sha256": "db1dae588849135a1b37a7a83bf1de07b944cc0277479dc9ae69790bb715ca1a"
+    },
+    {
+      "path": "check.py",
+      "sha256": "2a6a12650027407caea7037f309f33cd8d5ce043ab7dd41563b75d167040ab65"
+    }
+  ]
+}
diff --git a/research/one-terminal-h3-prefix/homogeneous/HANDOFF.md b/research/one-terminal-h3-prefix/homogeneous/HANDOFF.md
new file mode 100644
index 0000000000..3c0d50dfc1
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/HANDOFF.md
@@ -0,0 +1,52 @@
+# Handoff: actual one-port homogeneous prefix offer
+
+Status: local constructive finding and independent source-packet review PASS;
+not a complete consumer, new kappa, scientific admission or112-capacity claim.
+
+Owner: algebra agent G. Physical source-child offer A; publication/root and
+packaging D. This folder is new outputs-only work; frozen/public packages and
+native sources remain unchanged.
+
+Result: ONE actual backward helper496 H3 split exposes clean barF181 h. Exact
+separate monomial normalizers plus a postcall ADD give D U(q) on three original
+owners while returning the original helper Fh once. Source X39 header41=[162]
+and every absolute phase are explicit. See REPORT.md and RESULT.json.
+
+Sources: native20bb93cd990d2ff683e4d0fc56b87a42cd5d3296; physical ONE496
+packet954da4f1f; Cinna Davis #4698 conditional controller at
+9079ab66ba9a1717df478a08eb957c20d84d3e61. Source manifest in RESULT.json,
+peer reviewed hashes in REVIEW-A.json, and exact local bytes in FILES.json.
+The local verifier also requires ../check.py rational interval functions;
+its hash is in DEPENDENCIES.json. No frozen package was altered.
+
+Reproduce from this worktree:
+
+    python3 -I -W error outputs/split-helper-prefix-consumer/actual-h3-prefix/check.py
+    python3 -I -O -W error outputs/split-helper-prefix-consumer/actual-h3-prefix/check.py
+
+Default verification is read-only; --write is explicitly outside replay.
+Normal/O exact checks and independent copied-peer replays pass; peer RESULT
+and PATCH regenerate byte-identically. Timings/environment in RUNS.json.
+
+Complete cost qualification: real paid surcharge H2+H1-H3, no new helper
+reward; one split/COPY access bound19 passes plus new interface normalizers
+and ADD bound17 passes, total36. Precision allocation, full consumer,
+compiler, stock and outer transfer remain unproved. The old source's39-unit
+raw margin does not fund an unpriced repeated helper-owner substitution.
+
+Smallest next obligation: an exact two-call endpoint with the actual helper
+owner policy and full invoice. #4698's same-third-owner identity cannot
+silently identify two independent native helper inputs. Its documented third
+target isH16. A thirdH17 would require a new endpoint using the real retained
+qDh observation, not a second reward for copiedDh. New4929 collective demand
+must be derived from its own coupling/chart equations; old isolated ownY
+crosses do not transfer.
+
+Stop/expansion: no enumeration, native caller emission,112-capacity claim or
+new standalone PR follows from this offer. Root chooses the next changed
+physical contract. Independent review of G's new U-interface remains to be
+performed; G's independent review of A's physical packet is complete.
+
+Credit: Cao Yifan #4610/#4712, Cinna Davis #4698/#4694/#4470, zxv and the
+retained native, Clifford, controller, precision and outer lineage. New work
+has substantial OpenAI Codex assistance, Apache-2.0.
diff --git a/research/one-terminal-h3-prefix/homogeneous/REPORT.md b/research/one-terminal-h3-prefix/homogeneous/REPORT.md
new file mode 100644
index 0000000000..89bc05d40c
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/REPORT.md
@@ -0,0 +1,169 @@
+# One actual prefix gives a homogeneous three-field offer
+
+This source-bound construction supplies one homogeneous query chain from one
+actual backward #4610 invocation, while retaining its selected original helper
+job. It is not a two-call consumer, a capacity112 result or a new kappa.
+The copied prefix is dependent owned workspace and earns no productive credit.
+
+Source20bb93cd990d2ff683e4d0fc56b87a42cd5d3296; physical cut and local paid
+replacement are A's frozen ONE496 packet954da4f1f, checker cd9821de2e6cce4c,
+RESULT f62b9ca79788407d. Independent ALL632-column forward propagation and
+phase-word checks corroborate that packet, including explicit subspace
+containment not separately asserted in its checker. No source was changed.
+
+## Actual raw equations and legal paid change
+
+Use ordinary matrix products, rightmost operation first. Let
+
+    E = bar(F41),   S = bar(F181),   F = bar(F9).
+
+The bar is primitive-wise complex conjugation in chronological order. It is
+not adjoint. X39 enters frame41=[162]; Y151 and helper496 enter the empty
+frame. For arbitrary independent physical input arrays x,y,h, the isolated
+returned rows and the copied prefix are
+
+    Xraw = F E^-1 x - F y,
+    Yraw = S y,
+    Hraw = F h,
+    C    = S h.
+
+The complete source row of X39 has exactly its own input with coefficient+I
+and Y151 with coefficient-I, with no other owner or warp word. Y151 and
+helper496 have pure own-input rows. Independently propagating every original
+column shows that no other returned source field depends on these three
+inputs. This is stronger than checking the single cross coefficient alone.
+
+The real paid replacement is helper496 event15372, frame911 rank6 to full1:
+H3 becomes H2(911 to181), COPY into owned-zero C1, H1(181 tofull1). The
+explicit spans satisfy U911 strictly contained in U181 strictly contained
+in the full space, of sizes64,256,512. Both forward and actual raw-dual
+literal child products agree with the old child, including absolute phase.
+Every old live value after the replacement is its old value; the remaining
+suffix is identical. A's existing all632-owner endpoint receipt is inherited
+by this exact local replacement, rather than described as a fresh full
+modified-program replay. At this cut helper496 and Y151 are independently
+clean original-owner rows; the later reads of Y151 are untouched. The
+COPY is not asserted to dualize to a COPY under inverse transpose.
+
+## Exact separate monomial normalizers
+
+Let Q=C162 with the positive sign, q=Q^-1, and
+
+    D = C161 C4 C8 C16 C131 C64 C35 C256.
+
+The eight axes come from the frozen native DATA-PHASES port39 record. They
+are orthonormal and orthogonal to162. Thus D has rank8, q has rank1,
+Dq=qD phase-exactly, q^2=X162 is monomial and q^4=I.
+The exact native identities are
+
+    F = T D q,          T=X510,
+    S = N D,            N=S D^-1,
+    B = E Q.
+
+Both N and B are monomial including their absolute phase. In the source
+monomial recipe convention (diagonal, permutation, translation, phase), N is
+
+    rows [1,2,4,8,16,34,64,130,256], offset508,
+    quadratic_rows [0,0,0,0,0,0,0,0,0],
+    linear_Z4 [0,2,0,0,0,0,0,0,0], phase3.
+
+B is
+
+    rows [1,32,4,8,16,2,64,162,256], offset0,
+    quadratic_rows [0,34,0,0,0,34,0,0,0],
+    linear_Z4 [0,3,0,0,0,3,0,0,0], phase0.
+
+The checker emits literal source-derived words as well as these recipes.
+The original raw relative tail Gamma=F S^-1 has rank1 but Gamma^2 rank2;
+it is not bare Q in either sign. This does not prevent the separate
+normalizers above. Common conjugation alone would preserve that square
+rank and would be the wrong normalization test.
+
+At arbitrary column multiplicity f, each displayed Clifford word is lifted
+columnwise with its actual phase. All scalar signs between owner blocks
+remain outside those tensor powers. Each identity is an equality of single
+absolute-phase group words; there is no tensoring of a width1 operator sum.
+
+## Actual tall offer and original helper return
+
+Present X39 with physical input x=-B a. After the old call and saved COPY:
+
+    X0 = -T^-1 Xraw = D(a+q y),
+    Y0 = N^-1 Yraw  = D y,
+    C0 = N^-1 C     = D h,
+    H0 = T^-1 Hraw  = D q h.
+
+Perform the actual pointwise ADD Y0+=H0, which intentionally supplies the
+available qDh term. It does not pretend that Y and the helper had equal raw
+rank charts or that a logical identity transport was free. It gives
+
+    (X0,Y0,C0) = D [ I q 0 ; 0 I q ; 0 0 I ] (a,y,h),
+    H0         = D q h.
+
+The three inputs are exactly the original mainX, original mainY and original
+helper496. C0 is a second observation of h and is not another original
+owner. H0 survives the ADD; restore Hraw=T H0 to return the exact old Fh
+helper job. Every other autonomous helper remains its old original job.
+The selected main outputs now form a changed consumer interface and are not
+also credited as their old separate source main jobs.
+
+This is the homogeneous U(q) premise in Cinna Davis's #4698 controller, for
+ONE actual offer, with an extra dependent retained-helper output. It supplies
+an actual missing native interface in this limited case. It does not install
+the two-call identity: that identity needs the same third owner through two
+transverse stages. Two native invocations otherwise have independent original
+helper owners h and k. Replacing k by h changes the productive inventory;
+keeping both original helper rewards while doing that is invalid. A four-owner
+endpoint preserving both jobs or an honestly repriced reused-third-owner policy
+is still required. The published #4698 controller's third target is rank16,
+not automatically rank17. An additional use of the retained qDh observation
+would need an explicit endpoint before a third rank17 reward can be claimed.
+
+## Costs and qualifications
+
+The physical paid delta is H2+H1-H3; every original productive helper job is
+counted once. Its one-resource surcharge is enclosed exactly by rational
+logarithm/exponential series in RESULT.json at C=.0030217758 and .0034.
+It is approximately.005758080415496656 and .006477091731596653.
+This is not the withdrawn H8+H1-H9 endpoint-as-paid-node calculation.
+
+A's local split/COPY/initialize/eventualCLEAR bill is at most19 whole-array
+passes, one owned array, and no new productive reward. The new interface
+normalizers and ADD add at most17 more literal passes: input(-B)<=4,
+output(-T^-1)<=2, N^-1 on Y and C at most4 each, helper T^-1 and restoration
+at most1 each, plus one ADD. Total at most36 additional passes for this one
+offer, including eventual C1 clearing. Future source reads finish before the
+postcall changes. This finite accounting does not fund a compiler or caller.
+The new ADD can amplify inherited errors, so a real caller must assign its
+precision reserve as well as the two replacing child tolerances.
+
+Two FULLs on the old source with hypothetical224 rank17 main jobs have raw
+margin39.0639381148 at the source C. Even a useful one-port interface does not
+supply112 copies, a complete profitable caller, new precision reserves, stock
+or outer transfer. No claim transfers to #4929: its changed source demand and
+coupled ownership must be derived separately.
+
+## Verification and open next question
+
+From the worktree root:
+
+    python3 -I -W error outputs/split-helper-prefix-consumer/actual-h3-prefix/check.py
+    python3 -I -O -W error outputs/split-helper-prefix-consumer/actual-h3-prefix/check.py
+
+The default is read-only. Explicit --write regenerates the local receipt.
+The checker requires the pinned source Git objects and the retained rational
+interval helper at ../check.py. This is a local outputs finding, not a
+standalone portable publication package. Six discriminating boundaries cover
+omitted prefix normalization, the nonempty X header, the required Y+=H block,
+wrong raw query substitution/orientation, and erased absolute phase.
+
+The smallest useful next step is an exact consumer on two native calls with
+its actual third-owner policy, every remaining helper job and complete paid
+profile. If a changed #4929 collective consumer is attempted, first bind its
+nonuniform actual couplings and charts; do not import this old isolated
+own-Y-to-X row. No family search was run.
+
+Credit Cao Yifan / intqwq #4610 and #4712, Cinna Davis /1337isnot1337 #4698
+and its retained #4694/#4470 lineage, zxv, the retained Clifford/native
+controller/precision/outer contributors, and A's exact physical prefix gate.
+Substantial OpenAI Codex assistance; Apache-2.0. No new kappa is claimed.
diff --git a/research/one-terminal-h3-prefix/homogeneous/RESULT.json b/research/one-terminal-h3-prefix/homogeneous/RESULT.json
new file mode 100644
index 0000000000..f1e183902d
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/RESULT.json
@@ -0,0 +1,1117 @@
+{
+  "actual_child": {
+    "event": 15372,
+    "from": 911,
+    "mid": 181,
+    "paid_delta": {
+      "1": 1,
+      "2": 1,
+      "3": -1
+    },
+    "role": 496,
+    "to": 1
+  },
+  "additional_single_offer_pass_bound": 17,
+  "allwidth": "Every nonzero block checked as an individual absolute-phase Clifford word; tensor each word then add external scalar blocks, never tensor a sum.",
+  "capacity112_claim": false,
+  "consumer_complete": false,
+  "controls": {
+    "erase_normalizer_absolute_phase": true,
+    "omit_X_input_header_correction": true,
+    "omit_Y_plus_helper_ADD": true,
+    "omit_prefix_normalizer": true,
+    "replace_raw_Gamma_by_bare_query": true,
+    "wrong_query_orientation": true
+  },
+  "copied_prefix_independent_input": false,
+  "finite_scope": "Conservative literal passes: pre(-B)<=4; post X translation1+sign1; Y/C N^-1 at4 each; helper translation/restore2; ADD1. C init/COPY/CLEAR already in19. No complete caller/compiler precision proof.",
+  "grades": {
+    "D": 8,
+    "E": 1,
+    "F": 9,
+    "Gamma": 1,
+    "Gamma_squared": 2,
+    "S": 8,
+    "q_squared": 0
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+  "helper_productive_credit_once": true,
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+    ]
+  },
+  "new_kappa": false,
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+      ],
+      "offset": 0,
+      "phase": 0,
+      "quadratic_rows": [
+        0,
+        34,
+        0,
+        0,
+        0,
+        34,
+        0,
+        0,
+        0
+      ]
+    },
+    "N_S_Dinv": {
+      "linear_Z4": [
+        0,
+        2,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "matrix_rows": [
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+      ],
+      "offset": 508,
+      "phase": 3,
+      "quadratic_rows": [
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ]
+    },
+    "T": 510
+  },
+  "physical_split_pass_bound": 19,
+  "scalar_pre_post": "Input X=-B a; output X=-T^-1 rawX. Y=N^-1 rawY plus T^-1 rawH. C=N^-1 savedC. Original helper rawH restored after the ADD.",
+  "second_call_obligation": "Two FULL invocations have independent original helpers h and k. The three-field4698 template needs the same third owner, so identifying h with k loses a productive job. Need a four-owner exact endpoint with both helper jobs retained; none emitted here.",
+  "source_basis": {
+    "X_input_basis": [
+      162
+    ],
+    "X_input_header": 41,
+    "axes": [
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+      4,
+      8,
+      16,
+      131,
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+    ],
+    "q": 162
+  },
+  "source_commit": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296",
+  "sources": {
+    "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
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+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+  },
+  "split_surcharge": {
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+      "method": "exact rational Taylor bounds",
+      "upper": "0.005758080415496655457895"
+    },
+    "17/5000": {
+      "lower": "0.006477091731596653219921",
+      "method": "exact rational Taylor bounds",
+      "upper": "0.006477091731596653219922"
+    }
+  },
+  "status": "PASS_ONE_NATIVE_HOMOGENEOUS_TALL_OFFER_NOT_TWO_CALL_CONSUMER",
+  "tall_offer_rows": [
+    [
+      "D",
+      "Dq",
+      "0"
+    ],
+    [
+      "0",
+      "D",
+      "Dq"
+    ],
+    [
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+      "0",
+      "D"
+    ],
+    [
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+    ]
+  ],
+  "three_original_owners": [
+    "a",
+    "y",
+    "h496"
+  ],
+  "total_one_offer_extra_pass_bound": 36
+}
diff --git a/research/one-terminal-h3-prefix/homogeneous/REVIEW-A.json b/research/one-terminal-h3-prefix/homogeneous/REVIEW-A.json
new file mode 100644
index 0000000000..3a5c29cc39
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/REVIEW-A.json
@@ -0,0 +1,18 @@
+{
+  "verdict": "PASS_NO_CORRECTNESS_FINDING_WITHIN_SCOPE",
+  "peer_source": "954da4f1f",
+  "peer_sha256": {
+    "check.py": "cd9821de2e6cce4cd89e83ef1b1b8ceb5b4603e637d85ee5168c2706464e64a1",
+    "RESULT.json": "f62b9ca79788407dba125c1f612c4b245c2685cfd63256dbebbd677481337b8e",
+    "PATCH.json": "9935b03b917f97cee5cd18089b7f57383386e68d48d4511343215467cf0fd63e",
+    "REPORT.md": "5105dca9d8f2f69593d1d8cff4f8ccd005d8356c1043eaabe91472b33ed973a5",
+    "SOURCES.json": "3e0eaff1f992b59f9cce72523311bcc2b70897ed5765fc40dacaccb70f3c8aa3"
+  },
+  "independent_forward_all632": true,
+  "explicit_span_containment": true,
+  "literal_forward_rawdual_phase": true,
+  "complete_selected_owner_endpoints": true,
+  "new_homogeneous_offer": true,
+  "capacity112_claim": false,
+  "new_kappa": false
+}
diff --git a/research/one-terminal-h3-prefix/homogeneous/REVIEW-A.md b/research/one-terminal-h3-prefix/homogeneous/REVIEW-A.md
new file mode 100644
index 0000000000..c15c2e5be4
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/REVIEW-A.md
@@ -0,0 +1,37 @@
+# Independent read-only review of ONE496 packet954da4f1f
+
+PASS: no correctness finding within the declared local source20bb scope.
+
+Reviewed checker cd9821de2e6cce4cd89e83ef1b1b8ceb5b4603e637d85ee5168c2706464e64a1,
+RESULT f62b9ca79788407dba125c1f612c4b245c2685cfd63256dbebbd677481337b8e,
+PATCH9935b03b917f97cee5cd18089b7f57383386e68d48d4511343215467cf0fd63e.
+Every peer own-file manifest hash matched; the peer was never edited.
+
+A separately written all632-original-column FORWARD propagation independently
+verified both clean prefix rows at the cut, the complete isolated two-term
+X39 endpoint and pure Y151/helper496 endpoints. No other returned source
+row depends on these three selected inputs. Explicit subspace enumeration
+confirmed911⊂181⊂full with sizes64,256,512; thus both new climbs are legal,
+in addition to their exact rank2/rank1 phase certificates.
+
+Independent reconstruction from pinned canonical frames verified both literal
+forward and primitive-conjugate raw-dual child factor identities. Exact local
+replacement plus read-only COPY preserves every old live field after the
+replacement and the unchanged suffix. It correctly inherits original632-owner
+endpoint coverage rather than claiming a fresh modified all632 replay.
+
+Copied peer checkers ran in separate temporary directories under isolated
+normal and optimized Python. Both regenerated RESULT and PATCH byte-identical;
+all source/peer inputs remained read-only. RUNS.json records timings. The
+19-pass finite bound, one owned array, explicit eventual CLEAR, separate
+raw-dual checks, zero prefix reward and absence of any caller or112-capacity
+claim are appropriate. New recursive tolerances and actual caller precision,
+compiler reserves and outer transfer remain unrun obligations.
+
+The additional monomial/U-interface construction in REPORT.md is independent
+new work and was not asserted by the peer packet. Its normalizer/ADD cost is
+charged beyond the peer's19 passes. This review does not certify that new
+construction on behalf of another independent reviewer.
+
+Reviewer: OpenAI Codex gpt-6.1-sol/high, independent algebra agent.
+Apache-2.0. No source, peer or public-package edits.
diff --git a/research/one-terminal-h3-prefix/homogeneous/RUNS.json b/research/one-terminal-h3-prefix/homogeneous/RUNS.json
new file mode 100644
index 0000000000..5147d8e152
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/RUNS.json
@@ -0,0 +1,34 @@
+{
+  "utc": "2026-10-23T01:52:40.955256+00:00",
+  "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]",
+  "runs": [
+    {
+      "target": "independent_check",
+      "optimized": false,
+      "seconds": 1.3983095970470458,
+      "stdout": "PASS_ONE_NATIVE_HOMOGENEOUS_TALL_OFFER_NOT_TWO_CALL_CONSUMER",
+      "stderr": ""
+    },
+    {
+      "target": "A_exact_copied_checker_scratch",
+      "optimized": false,
+      "seconds": 0.9498719020048156,
+      "result_patch_byte_equal": true,
+      "stderr": ""
+    },
+    {
+      "target": "independent_check",
+      "optimized": true,
+      "seconds": 1.6084140840102918,
+      "stdout": "PASS_ONE_NATIVE_HOMOGENEOUS_TALL_OFFER_NOT_TWO_CALL_CONSUMER",
+      "stderr": ""
+    },
+    {
+      "target": "A_exact_copied_checker_scratch",
+      "optimized": true,
+      "seconds": 0.8929817660246044,
+      "result_patch_byte_equal": true,
+      "stderr": ""
+    }
+  ]
+}
diff --git a/research/one-terminal-h3-prefix/homogeneous/check.py b/research/one-terminal-h3-prefix/homogeneous/check.py
new file mode 100644
index 0000000000..4e11dfd54d
--- /dev/null
+++ b/research/one-terminal-h3-prefix/homogeneous/check.py
@@ -0,0 +1,166 @@
+#!/usr/bin/env python3
+"""One actual source prefix and a homogeneous tall interface, not a caller.
+Apache-2.0. Credit Cao Yifan #4610, Cinna Davis #4698, native/Clifford
+contributors; substantial OpenAI Codex assistance. Source files read-only.
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction
+from hashlib import sha256
+import ast, gzip, json, os, subprocess, sys, types
+
+HERE = Path(__file__).resolve().parent
+PIN = '20bb93cd990d2ff683e4d0fc56b87a42cd5d3296'
+PATHS = {
+ 'word': 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz',
+ 'ce': 'research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py',
+ 'prune': 'research/kappa-function-composition/complex/prune_native.py',
+ 'data': 'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json',
+}
+
+def need(v, m):
+    if not v:
+        raise ValueError(m)
+
+def load():
+    raw = {k: subprocess.check_output(['git', '--no-replace-objects', 'show', PIN+':'+v]) for k,v in PATHS.items()}
+    need(sha256(raw['word']).hexdigest() == '7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05', 'actual native payload')
+    need(sha256(raw['ce']).hexdigest() == '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', 'exact engine')
+    ce = types.ModuleType('one496_independent_ce')
+    sys.modules[ce.__name__] = ce
+    exec(compile(raw['ce'], PATHS['ce'], 'exec'), ce.__dict__)
+    definitions = [x for x in ast.parse(raw['prune']).body if isinstance(x, ast.FunctionDef) and x.name == 'conjugate']
+    env = {}
+    exec(compile(ast.Module(body=definitions, type_ignores=[]), PATHS['prune'], 'exec'), env)
+    return raw, ce, lambda op: env['conjugate'](ce, op)
+
+def forward(word, cut):
+    # Independently propagate ALL632 original columns, opposite to A's pullback.
+    rows = {('L',r): {(r, ()): Fraction(1)} for r in range(632)}
+    def plus(a,b,k):
+        result = a.copy()
+        for key,value in b.items():
+            result[key] = result.get(key, Fraction(0)) + k*value
+            if not result[key]: del result[key]
+        return result
+    for e in word[:cut]:
+        if e[0] == 'scalar':
+            s=e[1]; t=tuple(s[1]); v=rows.get(t,{})
+            if s[0]=='add': rows[t]=plus(v,rows.get(tuple(s[2]),{}),Fraction(s[3],s[4]))
+            elif s[0]=='scale': rows[t]={k:z*Fraction(s[2],s[3])for k,z in v.items()}
+            elif s[0]=='copy': rows[t]=rows.get(tuple(s[2]),{}).copy()
+            elif s[0]=='clear': rows[t]={}
+            else: raise ValueError(s)
+        elif e[0]=='warp':
+            t=tuple(e[1]); a=e[2]
+            rows[t]={(owner, (u[1:] if u and u[0]==-a else (a,)+u)):value for (owner,u),value in rows.get(t,{}).items()}
+    return rows
+
+def main():
+    raw,ce,bar=load()
+    p=json.loads(gzip.decompress(raw['word'])); c=p['canonical']; frames=c['frames']; w=p['programs']['backward']
+    need(w[15372]==['climb','warp_retimed',496,911,1,3], 'guard exact replaced child')
+    def span(v):
+        out={0}
+        for a in v: out|={x^a for x in tuple(out)}
+        return out
+    need(span(frames[911]) < span(frames[181]) < span(frames[1]), 'literal nested legal climb subspaces')
+    need([len(span(frames[j])) for j in (911,181,1)]==[64,256,512], 'true6/8/9 ranks')
+    state=forward(w,15372)
+    need(state[('L',496)]=={(496,()):Fraction(1)}, 'ALL632 columns independent clean helper at cut')
+    need(state[('L',151)]=={(151,()):Fraction(1)}, 'ALL632 columns independent clean Y at cut')
+    final=forward(w,len(w))
+    need(final[('L',39)]=={(39,()):Fraction(1),(151,()):Fraction(-1)}, 'complete actual X row')
+    need(final[('L',151)]=={(151,()):Fraction(1)} and final[('L',496)]=={(496,()):Fraction(1)}, 'complete Y/helper rows')
+    need({r for r,row in final.items() if any(owner in (39,151) for owner,u in row)}=={('L',39),('L',151)}, 'other original outputs do not depend on selected main inputs')
+    need({r for r,row in final.items() if any(owner==496 for owner,u in row)}=={('L',496)}, 'other original outputs do not depend on helper496')
+    I=ce.ident(9)
+    grade=lambda x:ce.rank([a for a,b,z in x.tab[9:]])
+    same=lambda a,b:a.tab==b.tab and a.zero_state()==b.zero_state()
+    # compose(A,B)=A*B, while source then is chronological.
+    def mul(*ops):
+        out=I
+        for op in reversed(ops): out=out.then(op)
+        return out
+    FU=ce.canonical_frame(9,frames[911]); FM=ce.canonical_frame(9,frames[181]); FV=ce.canonical_frame(9,frames[1])
+    for conv in (lambda z:z,bar):
+        old=conv(mul(FV,FU.adjoint())); first=conv(mul(FM,FU.adjoint())); last=conv(mul(FV,FM.adjoint()))
+        need([grade(z)for z in (old,first,last)]==[3,2,1] and same(mul(last,first),old), 'independent exact local split phase and ranks in both orientations')
+    F=bar(ce.canonical_frame(9,frames[1])); S=bar(ce.canonical_frame(9,frames[181])); E=bar(ce.canonical_frame(9,frames[41]))
+    need(c['start'][39]==41 and frames[41]==[162] and c['ports'][39]==162, 'actual nonempty X input header')
+    recipe=json.loads(raw['data'])['recipes'][39]; axes=recipe['idle_children'][0]['orthogonal_axes'][:8]
+    need(axes==[161,4,8,16,131,64,35,256] and recipe['q']==162, 'one native transverse basis')
+    need(all((a&162).bit_count()%2==0 for a in axes), 'transverse q-orthogonality')
+    need(all((a&b).bit_count()%2==(i==j) for i,a in enumerate(axes) for j,b in enumerate(axes)), 'orthonormal transverse basis')
+    D=I
+    for a in axes:D=D.then(ce.cgate(9,a))
+    Q=ce.cgate(9,162); q=Q.adjoint(); T=ce.xgate(9,510)
+    need(same(mul(D,q),mul(q,D)), 'phase-exact commuting central query')
+    need(same(F,mul(T,D,q)), 'actual full helper forward-sign translation in rawdual')
+    N=mul(S,D.adjoint()); B=mul(E,Q)
+    need(grade(N)==grade(B)==0, 'actual prefix and input normalization are monomial')
+    Nrec,Nword=ce.monomial(N)[1],ce.monomial(N)[0]
+    Brec,Bword=ce.monomial(B)[1],ce.monomial(B)[0]
+    need(same(N,Nword) and same(B,Bword), 'absolute phase of free maps')
+    need(same(mul(N.adjoint(),S),D), 'both actual prefix and Y normalize to D')
+    need(same(mul(T.adjoint(),F,E.adjoint(),B),D), 'header-normalized main self is exact D')
+    need(same(mul(T.adjoint(),F),mul(D,q)), 'main cross and independent helper are Dq')
+    Gamma=mul(F,S.adjoint())
+    need(grade(Gamma)==1 and grade(mul(Gamma,Gamma))==2, 'raw tail not a free-square central query')
+    need(same(mul(q,q),ce.xgate(9,162)), 'normalized q-square is a monomial involution')
+    need(same(mul(q,q,q,q),I), 'normalized q-order4')
+    # Each matrix entry below is a single literal Clifford unit, with scalar
+    # signs kept outside its tensor power. No width1 sum equality is lifted.
+    blocks={
+      'X_from_a':mul(T.adjoint(),F,E.adjoint(),B),
+      'X_from_y':mul(T.adjoint(),F),
+      'Y_from_y':mul(N.adjoint(),S),
+      'Y_from_h':mul(T.adjoint(),F),
+      'C_from_h':mul(N.adjoint(),S),
+      'H_from_h':mul(T.adjoint(),F),
+    }
+    expected={k:(mul(D,q) if k in ('X_from_y','Y_from_h','H_from_h') else D) for k in blocks}
+    def valid_tall(candidate):
+        return candidate.keys()==expected.keys() and all(same(v,expected[k])for k,v in candidate.items())
+    need(valid_tall(blocks), 'all tall4x3 group-word coefficients')
+    controls={
+      'omit_prefix_normalizer':not same(S,D),
+      'omit_X_input_header_correction':not same(mul(T.adjoint(),F,E.adjoint()),D),
+      'omit_Y_plus_helper_ADD':not valid_tall({k:v for k,v in blocks.items()if k!='Y_from_h'}),
+      'replace_raw_Gamma_by_bare_query':not same(Gamma,q),
+      'wrong_query_orientation':not same(mul(T.adjoint(),F),mul(D,Q)),
+    }
+    # Dedicated actual phase mutation: N has nonzero phase3, dropping it fails.
+    mutated=ce.Op(9,Nword.tab,[e for e in Nword.circuit if e[0]!='phase'])
+    controls['erase_normalizer_absolute_phase']=not same(mutated,N)
+    need(all(controls.values()), 'six discriminating mutation boundaries')
+    # Fixed source profile surcharge, via independently retained rational code.
+    iv={ '__name__':'one496_iv', '__file__':str(HERE.parent/'check.py') }; exec(compile((HERE.parent/'check.py').read_bytes(),'conditional_interval_library','exec'),iv)
+    costs={}
+    for C in (Fraction('.0030217758'),Fraction('.0034')):
+        delta=iv['add_intervals']([(1,iv['power_interval'](2,C)),(1,iv['power_interval'](1,C)),(-1,iv['power_interval'](3,C))])
+        costs[str(C)]=iv['decimal_interval'](delta)
+    out={
+      'status':'PASS_ONE_NATIVE_HOMOGENEOUS_TALL_OFFER_NOT_TWO_CALL_CONSUMER',
+      'source_commit':PIN,'sources':{PATHS[k]:sha256(v).hexdigest()for k,v in raw.items()},
+      'actual_child':{'role':496,'event':15372,'from':911,'mid':181,'to':1,'paid_delta':{'1':1,'2':1,'3':-1}},
+      'source_basis':{'q':162,'axes':axes,'X_input_header':41,'X_input_basis':frames[41]},
+      'normalizers':{'N_S_Dinv':Nrec,'B_E_Q':Brec,'T':510},
+      'grades':{'S':grade(S),'F':grade(F),'E':grade(E),'D':grade(D),'Gamma':grade(Gamma),'Gamma_squared':grade(mul(Gamma,Gamma)),'q_squared':grade(mul(q,q))},
+      'literal_word_blocks':{k:v.circuit for k,v in blocks.items()},
+      'tall_offer_rows':[['D','Dq','0'],['0','D','Dq'],['0','0','D'],['0','0','Dq']],
+      'scalar_pre_post':'Input X=-B a; output X=-T^-1 rawX. Y=N^-1 rawY plus T^-1 rawH. C=N^-1 savedC. Original helper rawH restored after the ADD.',
+      'three_original_owners':['a','y','h496'],'copied_prefix_independent_input':False,'helper_productive_credit_once':True,
+      'allwidth':'Every nonzero block checked as an individual absolute-phase Clifford word; tensor each word then add external scalar blocks, never tensor a sum.',
+      'controls':controls,'split_surcharge':costs,
+      'additional_single_offer_pass_bound':17,'physical_split_pass_bound':19,'total_one_offer_extra_pass_bound':36,
+      'finite_scope':'Conservative literal passes: pre(-B)<=4; post X translation1+sign1; Y/C N^-1 at4 each; helper translation/restore2; ADD1. C init/COPY/CLEAR already in19. No complete caller/compiler precision proof.',
+      'second_call_obligation':'Two FULL invocations have independent original helpers h and k. The three-field4698 template needs the same third owner, so identifying h with k loses a productive job. Need a four-owner exact endpoint with both helper jobs retained; none emitted here.',
+      'capacity112_claim':False,'new_kappa':False,'consumer_complete':False,
+    }
+    out=json.loads(json.dumps(out))
+    if '--write' in sys.argv:(HERE/'RESULT.json').write_text(json.dumps(out,indent=2,sort_keys=True)+'\n')
+    else:need(json.loads((HERE/'RESULT.json').read_text())==out,'frozen receipt')
+    print(out['status'])
+
+if __name__=='__main__':main()
diff --git a/research/one-terminal-h3-prefix/inputs/local/prefix-interval-library.py b/research/one-terminal-h3-prefix/inputs/local/prefix-interval-library.py
new file mode 100644
index 0000000000..70744305c4
--- /dev/null
+++ b/research/one-terminal-h3-prefix/inputs/local/prefix-interval-library.py
@@ -0,0 +1,150 @@
+#!/usr/bin/env python3
+"""Paid-node gate and exact CONDITIONAL prefix-split arithmetic; no search."""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip
+import hashlib
+import json
+import sys
+
+HERE = Path(__file__).resolve().parent
+
+
+def need(test, why):
+    if not test:
+        raise ValueError(why)
+
+
+def atanh_log(x):
+    """Exact rational bounds for log(x),1<=x<=2; positive Taylor tail."""
+    z = (x-1)/(x+1)
+    need(0 <= z <= F(1, 3), 'reduced logarithm domain')
+    value = F(0)
+    power = z
+    count = 64
+    for k in range(count):
+        value += 2*power/(2*k+1)
+        power *= z*z
+    tail = 2*power/((2*count+1)*(1-z*z))
+    return value, value+tail
+
+
+def log_interval(n):
+    if n == 1:
+        return F(0), F(0)
+    k = n.bit_length()-1
+    l2, u2 = atanh_log(F(2))
+    lr, ur = atanh_log(F(n, 1 << k))
+    return k*l2+lr, k*u2+ur
+
+
+def exp_minus(x):
+    """Alternating Taylor bounds: odd partial15 <= exp(-x) <= even16."""
+    need(0 <= x < F(1, 100), 'small exact exponential argument')
+    term, total = F(1), F(1)
+    lower = None
+    for k in range(1, 17):
+        term *= -x/k
+        total += term
+        if k == 15:
+            lower = total
+    return lower, total
+
+
+def power_interval(n, C):
+    lo, hi = log_interval(n)
+    low = n*exp_minus(C*hi)[0]
+    high = n*exp_minus(C*lo)[1]
+    return low, high
+
+
+def add_intervals(terms):
+    lo, hi = F(0), F(0)
+    for coefficient, (l, u) in terms:
+        lo += coefficient*(l if coefficient >= 0 else u)
+        hi += coefficient*(u if coefficient >= 0 else l)
+    return lo, hi
+
+
+def decimal_interval(interval):
+    scale = 10**24
+    l, u = interval
+    low = (l*scale).numerator//(l*scale).denominator
+    high = -((-u*scale).numerator//(-u*scale).denominator)
+    need(F(low, scale) <= l <= u <= F(high, scale), 'outward exact decimal enclosure')
+    def display(n):
+        sign = '-' if n < 0 else ''
+        n = abs(n)
+        return sign+str(n//scale)+'.'+str(n % scale).zfill(24)
+    return dict(lower=display(low), upper=display(high), method='exact rational Taylor bounds')
+
+
+def main():
+    sources = json.loads((HERE/'SOURCES.json').read_text())
+    for row in sources['files']:
+        raw = (HERE/row['path']).read_bytes()
+        need(hashlib.sha256(raw).hexdigest() == row['sha256'], 'source SHA256')
+        need(hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()
+             == row['git_blob'], 'full source Git blob')
+    word = json.loads(gzip.decompress((HERE/'source/ACTUAL-WORD.json.gz').read_bytes()))
+    profiles = {}
+    for direction in ('forward', 'backward'):
+        program = word['programs'][direction]
+        paid = Counter(e[5] for e in program if e[0] == 'climb')
+        paid.update(e[4] for e in program if e[0] == 'center')
+        need(dict(paid) == {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8},
+             'actual paid child profile')
+        need(paid.get(9, 0) == 0, 'NO existing paidH9 node to replace')
+        profiles[direction] = {str(r): paid[r] for r in sorted(paid)}
+    canonical = word['canonical']
+    rank8_paid_events = [dict(event=i, instruction=e) for i, e in enumerate(word['programs']['forward'])
+                        if (e[0] == 'climb' and e[5] == 8) or (e[0] == 'center' and e[4] == 8)]
+    need(len(rank8_paid_events) == 8 and all(r['instruction'][0] == 'center' for r in rank8_paid_events),
+         'all paidH8 children are centres, not mainB child observations')
+    helper = Counter(len(canonical['frames'][canonical['final'][r]])
+                     - len(canonical['frames'][canonical['start'][r]]) for r in range(224, 632))
+    need(dict(helper) == {4: 28, 7: 7, 8: 47, 9: 326}, 'productive helper census')
+    path = [dict(event=i, input=e[3], output=e[4], rank=e[5])
+            for i, e in enumerate(word['programs']['forward']) if e[0] == 'climb' and e[2] == 224]
+    need(Counter(e['rank'] for e in path) == {1: 5, 4: 1}, 'helper224 actual5H1+H4 path')
+    last = path[-1]['event']
+    later = [i for i, e in enumerate(word['programs']['forward']) if i > last
+             and e[0] == 'scalar' and e[1][0] == 'add' and e[1][1] == ['L', 224]]
+    need(path[-1] == dict(event=17722, input=279, output=1, rank=1) and later,
+         'terminalH1 has later writes; no clean-prefix inference')
+    endpoints = []
+    for C in (F(30217758, 10**10), F(34, 10**4)):
+        powers = {r: power_interval(r, C) for r in (1, 2, 3, 4, 5, 7, 8, 9, 17)}
+        split = add_intervals([(112, powers[8]), (112, powers[1]), (-112, powers[9])])
+        margin_terms = [(224, powers[17])]
+        margin_terms += [(2*n, powers[r]) for r, n in helper.items()]
+        margin_terms += [(-2*n, powers[int(r)]) for r, n in profiles['forward'].items()]
+        margin = add_intervals(margin_terms)
+        leftover = (margin[0]-split[1], margin[1]-split[0])
+        endpoints.append(dict(C=str(C), conditional112_split_surcharge=decimal_interval(split),
+                              original_optimistic_moment=decimal_interval(margin),
+                              conditional_moment_after_unrealized_split=decimal_interval(leftover)))
+    result = dict(status='PASS_SOURCE_GATE_NO_PAID_H9_SPLIT',
+                  source_commit=sources['source_commit'], paid_profiles=profiles,
+                  productive_helpers={str(r): n for r, n in sorted(helper.items())},
+                  helper224_paid_path=path, later_scalar_writes_to224=later,
+                  rank8_paid_events=rank8_paid_events,
+                  native_port0_frames=dict(Y_exit=canonical['final'][112],
+                                           helper224_exit=canonical['final'][224],
+                                           helper224_preterminal=path[-1]['input']),
+                  hypothetical_split_endpoints=endpoints,
+                  conditional_surcharge_monotone_in_C=True,
+                  accepted_profile_change=False, actual_prefix_access_proved=False,
+                  clean_prefix_assumed=False, new_kappa=False,
+                  missing_physical_premise='A replaceable paid subword with complete incident contacts and a phase-correct exposed prefix; the productive H9 endpoint is not a paidH9 node.')
+    if '--write' in sys.argv:
+        (HERE/'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    else:
+        need(json.loads((HERE/'RESULT.json').read_text()) == result, 'fixed exact receipt')
+    print('PASS_SOURCE_GATE_NO_PAID_H9_SPLIT conditional_surcharge_only '
+          'helper224=5H1+H4 later_writes_prefix_unproved no_new_kappa')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/one-terminal-h3-prefix/inputs/research/higher-moment-strictification/verify.py b/research/one-terminal-h3-prefix/inputs/research/higher-moment-strictification/verify.py
new file mode 100644
index 0000000000..4b24a50961
--- /dev/null
+++ b/research/one-terminal-h3-prefix/inputs/research/higher-moment-strictification/verify.py
@@ -0,0 +1,421 @@
+#!/usr/bin/env python3
+"""Higher-moment strictification and a polynomial-logarithm compiler bound.
+
+New arithmetic is independent of predecessor interval code. The unchanged
+invoice replay and two outer ledgers are credited, byte-pinned oracles.
+zxv with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+import ast
+from collections import Counter
+from contextlib import redirect_stdout
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256, sha1
+import io
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+GRID = 2**192
+C = Q('0.00268648')
+KAPPA = Q('0.00268647')
+T = {5:420, 6:270, 7:840, 8:1395, 9:3195,
+     25:448, 41:448, 57:448, 121:224}
+P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300,
+     8:1464, 16:448, 32:448, 48:448}
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def down(x):
+    return Q((x*GRID).__floor__(), GRID)
+
+
+def up(x):
+    return Q(-((-x*GRID).__floor__()), GRID)
+
+
+def rounded(lo, hi):
+    return down(lo), up(hi)
+
+
+def mul(a, b):
+    products = [x*y for x in a for y in b]
+    return rounded(min(products), max(products))
+
+
+def scale(a, x):
+    return mul(a, (x, x))
+
+
+def divide(a, b):
+    need(b[0] > 0, 'positive interval denominator')
+    return mul(a, rounded(1/b[1], 1/b[0]))
+
+
+@lru_cache(None)
+def log_bounds(n):
+    """Exact atanh series, binary reduction; round only the final interval."""
+    need(isinstance(n, int) and n >= 1, 'positive integer logarithm')
+
+    def series(x):
+        u = (x-1)/(x+1)
+        term, total = u, Q(0)
+        for j in range(80):
+            total += 2*term/(2*j+1)
+            term *= u*u
+        tail = 2*term/(161*(1-u*u))
+        return total, total+tail
+
+    k = n.bit_length()-1
+    a, b = series(Q(2))
+    c, d = series(Q(n, 2**k))
+    return rounded(k*a+c, k*b+d)
+
+
+def exp_point(x):
+    """Outward fixed-point Taylor enclosure, with binary scaling/squaring."""
+    need(abs(x) < 16, 'bounded exponential argument')
+    if x < 0:
+        a, b = exp_point(-x)
+        return rounded(1/b, 1/a)
+    divisions = 0
+    while x > Q(1, 2):
+        x /= 2
+        divisions += 1
+    term = total = (Q(1), Q(1))
+    for j in range(1, 65):
+        term = scale(term, x/j)
+        total = rounded(total[0]+term[0], total[1]+term[1])
+    following = scale(term, x/65)
+    # Every remaining ratio is <= 1/132. Twice the next term is safe.
+    result = rounded(total[0], total[1]+2*following[1])
+    for _ in range(divisions):
+        result = mul(result, result)
+    return result
+
+
+def exp_interval(a):
+    return exp_point(a[0])[0], exp_point(a[1])[1]
+
+
+@lru_cache(None)
+def power(n, exponent):
+    return exp_interval(scale(log_bounds(n), exponent))
+
+
+def moment(histogram, exponent):
+    low = high = Q(0)
+    for n, count in histogram.items():
+        a, b = power(n, exponent)
+        low += count*a
+        high += count*b
+    return rounded(low, high)
+
+
+def display(a):
+    unit = 10**30
+
+    def fixed(n):
+        sign = '-' if n < 0 else ''
+        s = str(abs(n)).rjust(31, '0')
+        return sign+s[:-30]+'.'+s[-30:]
+
+    return {'lower': fixed((a[0]*unit).__floor__()),
+            'upper': fixed(-((-a[1]*unit).__floor__()))}
+
+
+def encoded(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): encoded(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [encoded(v) for v in x]
+    return x
+
+
+def source_environment(path):
+    env = {'__file__': str(path), '__name__': 'pinned_source_oracle'}
+    exec(compile(path.read_bytes(), str(path), 'exec'), env)
+    return env
+
+
+def authenticate():
+    result = {}
+    for row in json.loads((HERE/'VENDOR.json').read_text())['files']:
+        path = HERE/'vendor'/Path(row['path']).relative_to(
+            'research/higher-moment-strictification/vendor')
+        digest = sha256(path.read_bytes()).hexdigest()
+        need(digest == row['sha256'], 'changed source: '+row['path'])
+        raw = path.read_bytes()
+        need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()
+             == row['git_blob'], 'changed Git source blob')
+        result[row['path']] = digest
+    return result
+
+
+def invoice_oracle():
+    """Run #4426 unchanged, rebinding only its two file-location globals."""
+    path = HERE/'vendor/invoice-review/verify.py'
+    env = source_environment(path)
+    env.update(ROOT=path.parent, PHASES='DATA-PHASES.json')
+    output = io.StringIO()
+    with redirect_stdout(output):
+        env['main']()
+    result = json.loads(output.getvalue())
+    need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle')
+    need({int(k): v for k, v in result['targets'].items()} == T
+         and {int(k): v for k, v in result['paid'].items()} == P,
+         'exact literal-word invoice')
+    return result
+
+
+def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)):
+    t = 1-C
+    need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks')
+    need(t+u >= 1, 'tail moment exponent at least one')
+    target, paid = moment(T, t), moment(P, t)
+    alpha = divide(paid, target)
+    gamma = divide(moment(P, t+u), mul(power(cutoff, u), target))
+    delta = divide((Q(sum(T.values())*floor),)*2,
+                   mul(power(cutoff, C), target))
+    limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500))
+    for name, bounds, limit in zip(('alpha', 'gamma', 'delta'),
+                                  (alpha, gamma, delta), limits):
+        need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit')
+    a, g, d = limits
+    bound = 1/(1+v*(1-a))+2*g**v+2*d**v
+    need(bound < 1, 'complete charged normalized moment')
+    old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2,
+                       mul(power(cutoff, C), target))
+    old_lower = alpha[0]**v+2*old_gamma[0]**v
+    need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power')
+    return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor,
+            'paid_moment_exponent': t+u, 'tail_offset_u': u,
+            'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma),
+            'delta': display(delta), 'rational_upper_limits': limits,
+            'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2),
+            'old_rank_one_gamma': display(old_gamma),
+            'old_rank_one_bound_lower': display((old_lower, old_lower)),
+            'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v),
+            'maximum_paid': str(cutoff)+'^'+str(v),
+            'productive_fields_before_uniform_compiler': '7688^'+str(v),
+            'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v),
+            'materialized_product_or_uniform_word': False}
+
+
+def uniform_rank(v):
+    t, p, theta = 1-C, 13, Q(6, 7)
+    gap = (C-KAPPA)/7
+    uniform_saving = C-gap
+    need(10**7 < 15**6, 'theta upper bound')
+    need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality')
+    eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t)
+    need(eta[0] > theta**p, 'exit contraction below complement capacity')
+    base = exp_interval(scale(log_bounds(121), v*C))
+    need(base[1] < 2**p, 'entire ordinary base range fits')
+    # Integer grid: gap*H is integral, avoiding enormous rational powers.
+    step = gap.denominator
+    need(gap.numerator == 1, 'chosen rational gap grid')
+
+    def passes(j):
+        H = step*j
+        return (H+1)**p < 2**j
+
+    lo, hi = 1, 2
+    while not passes(hi):
+        lo, hi = hi, 2*hi
+    while hi-lo > 1:
+        mid = (lo+hi)//2
+        if passes(mid):
+            hi = mid
+        else:
+            lo = mid
+    H = step*hi
+    need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison')
+    need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails')
+    return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap,
+            'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta),
+            'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)),
+            'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H),
+            'integer_test': {'left_base': H+1, 'left_exponent': p,
+                             'right_base': 2, 'right_exponent': hi},
+            'grid_step': step, 'previous_grid_point_rejected': True,
+            'smaller_logarithmic_power_rejected': True}
+
+
+def power_majorant_comparison(v, uniform_saving):
+    """Retain #4416's older power proof, changing only the new unit's ranks."""
+    t, z, h = 1-C, 1-uniform_saving, Q(1, 7)
+    z0 = (t+z)/2
+    delta = z0-t
+    B, debt = (4+7*h)*v, 1+7*v*(1-z0)
+    ratio = (delta*B+debt)/(h*delta)
+    H0 = -((-ratio.numerator)//ratio.denominator)
+    ratio = H0*(1-z0)/(z-z0)
+    H1 = ratio.numerator//ratio.denominator+1
+    need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold')
+    need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected')
+    need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0),
+         'strict power-majorant comparison and previous-rank control')
+    return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h,
+            'scope': 'Tail transformation alone, retaining the older power majorant.'}
+
+
+def outer_ledger(uniform_saving):
+    d = (C-KAPPA)/7
+    params = {'kappa': KAPPA, 'tested_saving': C,
+              'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d,
+              'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'),
+              'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10,
+              'stop': d, 'layout': d, 'd': d}
+    env = source_environment(HERE/'vendor/outer_endpoint.py')
+    row = env['ledger'](params)
+    need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3,
+         'complete first outer ledger')
+    need(all(v > 0 for group in ('strict_checks', 'functional_checks')
+             for v in row[group].values()), 'all outer predicates')
+    frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer']
+    need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger')
+    parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes())
+    function = next(n for n in parsed.body
+                    if isinstance(n, ast.FunctionDef) and n.name == 'ledger')
+    constants = [n for n in parsed.body if isinstance(n, ast.Assign)
+                 and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_')
+                         for t in n.targets)]
+    eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a'))
+    grid = 10**10
+    backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA
+    need(backoff > 0, 'strict derived oracle grid backoff')
+    oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8),
+              'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff,
+              'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2),
+              'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16),
+              'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'],
+              'online': Q('0.001730970419199163702738'),
+              'old': Q('0.001730970419199163702738')}
+    code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[]))
+    exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle)
+    second = oracle['ledger']('higher_moment_smaller_ranks')
+    need(second['kappa'] == KAPPA and second['margins'] == row['margins'],
+         'all nine rows match both ledgers')
+    need(len(second['strict_checks']) == 63 and
+         all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates')
+    controls = {}
+    for name, updates in [('closed_epsilon', {'epsilon': Q(1)}),
+                          ('missing_layout', {'layout': Q(0)}),
+                          ('unfunded_kappa', {'kappa': C}),
+                          ('closed_uniform_gap', {'complex_uniform_saving': params['b']}),
+                          ('insufficient_BIT', {'bit_saving': Q('0.0023')})]:
+        bad = env['ledger'](dict(params, **updates))
+        failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0)
+        need(failed, 'outer control rejected: '+name)
+        controls[name] = failed
+    for name, options in [('old_per_axis_scan', {'old_scan': True}),
+                          ('group_equals_dimension', {'beta_': eps})]:
+        bad = oracle['ledger']('reject_'+name, **options)
+        failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0)
+        need(failed, 'legacy control rejected: '+name)
+        controls[name] = failed
+    return {'ledger': row, 'legacy_63_checks': second['strict_checks'],
+            'legacy_grid': grid, 'legacy_backoff': backoff,
+            'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA,
+            'rejected_controls': controls}
+
+
+def finite_controls():
+    def tensor(histogram):
+        out = Counter()
+        for k, n in histogram.items():
+            for h, b in histogram.items():
+                out[k*h] += n*b
+        return out
+
+    def split(histogram, cutoff):
+        out = Counter()
+        for k, n in histogram.items():
+            q, r = divmod(k, cutoff)
+            out[cutoff] += q*n
+            if r:
+                out[r] += n
+        return +out
+
+    target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1})
+    padded, completion = Counter(), Counter()
+    for k, n in target.items():
+        padded[max(k, 9)] += n
+        if k < 9:
+            completion[9-k] += n
+    final = split(paid+completion, 4)
+    mass = lambda x: sum(k*n for k, n in x.items())
+    need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass')
+    need(min(padded) > max(final), 'exact toy separation')
+    need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory')
+    # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension.
+    invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1]
+    need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting')
+    return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13,
+            'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2',
+                                             'sigma': '3/4', 'actual_charge': 100,
+                                             'invalid_upper': display((invalid, invalid))}}
+
+
+def verify():
+    sources = authenticate()
+    invoice = invoice_oracle()
+    tail = tail_certificate()
+    rank = uniform_rank(tail['tensor_power'])
+    endpoint = outer_ledger(rank['uniform_saving'])
+    controls = finite_controls()
+    rejected = []
+    for name, updates, expected in [
+        ('too_short_product', {'v': 100}, 'complete charged normalized moment'),
+        ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'),
+        ('lost_separation', {'floor': 10}, 'strict finite ranks'),
+    ]:
+        try:
+            tail_certificate(**updates)
+        except ValueError as error:
+            need(str(error) == expected, 'wrong rejection: '+name)
+            rejected.append({'mutation': name, 'failed_at': str(error)})
+        else:
+            raise ValueError('accepted mutation: '+name)
+    old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler']
+    return encoded({'schema': 'higher-moment-native-strictification/1',
+                    'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA,
+                    'invoice_oracle': invoice, 'strictification': tail,
+                    'uniform_rank': rank, 'outer': endpoint,
+                    'tail_only_power_majorant': power_majorant_comparison(
+                        tail['tensor_power'], rank['uniform_saving']),
+                    'finite_controls': controls, 'rejected_mutations': rejected,
+                    'predecessor_H': old['H1'],
+                    'rank_exponent_reduction_factor': Q(old['H1'], rank['H']),
+                    'tensor_power_reduction_factor': Q(6240, tail['tensor_power']),
+                    'source_sha256': sources,
+                    'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(),
+                    'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'})
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path)
+    args = parser.parse_args()
+    result = verify()
+    if args.out:
+        need(not args.out.exists(), 'new output path required')
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    else:
+        need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt')
+    print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'],
+                      'uniform_rank': result['uniform_rank']['N'],
+                      'strict_moment_gap': result['strictification']['strict_moment_gap'],
+                      'kappa': result['kappa']}))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/one-terminal-h3-prefix/inputs/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json b/research/one-terminal-h3-prefix/inputs/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json
new file mode 100644
index 0000000000..d9a4f84211
--- /dev/null
+++ b/research/one-terminal-h3-prefix/inputs/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json
@@ -0,0 +1 @@
+{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector."},"global_phase_argument":"Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as 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diff --git a/research/one-terminal-h3-prefix/inputs/research/kappa-function-composition/complex/prune_native.py b/research/one-terminal-h3-prefix/inputs/research/kappa-function-composition/complex/prune_native.py
new file mode 100644
index 0000000000..8c3e11b240
--- /dev/null
+++ b/research/one-terminal-h3-prefix/inputs/research/kappa-function-composition/complex/prune_native.py
@@ -0,0 +1,253 @@
+#!/usr/bin/env python3
+"""Delete exact unconsumed centre-assembly/inverse pairs, including dirty state.
+
+Apache-2.0; substantial OpenAI assistance. The native writer and final verifier
+are reused with attribution from the frozen causal-continuation package. The
+new search checks literal rational perturbations, never numerical similarity.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+import sys
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+RESEARCH = HERE.parents[1]
+BASE = RESEARCH / 'kappa-global-routing/integrated-complex'
+CHECKER = RESEARCH / 'kappa-causal-continuation/buffer-borrowing/verify_buffers.py'
+CHECKER_SHA = '106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7'
+CLIFFORD = RESEARCH / 't74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py'
+TAGS = ('THREE-base', 'THREE-extra', 'FOUR-base', 'FOUR-extra')
+
+
+def need(ok, why):
+    if not ok: raise ValueError(why)
+
+
+def digest(path): return sha256(path.read_bytes()).hexdigest()
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def save(path, value):
+    data = json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+    path.write_bytes(gzip.compress(data, mtime=0))
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    obj = importlib.util.module_from_spec(spec)
+    sys.modules[name] = obj
+    spec.loader.exec_module(obj)
+    return obj
+
+
+def apply(v, rows, event, backward=False):
+    if event[0] == 'warp':
+        r = tuple(event[1]); rows[r] = v.warp(rows[r], event[2], backward)
+    elif event[0] == 'scalar':
+        g = event[1]; r = tuple(g[1])
+        if g[0] == 'add': v.add(rows[r], rows[tuple(g[2])], Q(g[3], g[4]))
+        else:
+            need(g[0] == 'scale', 'No owned field in the clean-J baseline')
+            rows[r] = {k: Q(g[2], g[3])*x for k, x in rows[r].items()}
+
+
+def index_sections(program):
+    phase = None; result = {'A': [], 'full_frame_cleanup': []}
+    for i, e in enumerate(program):
+        if e[0] == 'phase': phase = e[1]
+        if phase in result and e[0] in ('scalar', 'warp'): result[phase].append(i)
+    return result
+
+
+def exact_candidate_screen(v, canonical, program, R):
+    """Test the final 48 assembly gates, with their actual scheduled inverses."""
+    indices = index_sections(program)
+    need(len(indices['A']) == len(canonical['A']), 'Native A gate correspondence')
+    need(len(indices['full_frame_cleanup']) == len(canonical['cleanup']), 'Cleanup gate correspondence')
+    options = []; unmatched = []
+    for j in range(len(canonical['A']) - 48, len(canonical['A'])):
+        g = canonical['A'][j]
+        need(g[0] == 'add' and len(canonical['frames'][g[-1]]) in (7, 8), 'Final centre-assembly grammar')
+        inverse = g[:]; inverse[3] *= -1; inverse[-1] = 1
+        hits = [i for i, h in enumerate(canonical['cleanup']) if h == inverse]
+        if len(hits) == 1:
+            cj = hits[0]
+            options.append((j, cj, indices['A'][j], indices['full_frame_cleanup'][cj]))
+        else: unmatched.append({'A_index': j, 'gate': g, 'matching_inverse_occurrences': hits})
+    sites = {k for option in options for k in option[2:]}
+    effects = {}; rows = {('L', i): v.identity(('L', i)) for i in range(632)}
+    for i, e in enumerate(program):
+        if i in sites:
+            g = e[1]
+            effects[i] = (tuple(g[1]), {k: -Q(g[3], g[4])*x for k, x in rows[tuple(g[2])].items()})
+        apply(v, rows, e)
+    need(all(row == v.expected(r, R, False, True) for r, row in rows.items()), 'Pinned baseline endpoint')
+    accepted = []; rejected = []
+    for aj, cj, ai, ci in options:
+        delta = {('L', i): {} for i in range(632)}
+        live_data_effect = False
+        for i in range(ai, len(program)):
+            if i in (ai, ci):
+                target, effect = effects[i]; v.add(delta[target], effect, Q(1))
+            else: apply(v, delta, program[i])
+            if i < indices['full_frame_cleanup'][0]:
+                e = program[i]
+                if e[0] == 'scalar' and e[1][0] in ('add', 'scale'):
+                    r = tuple(e[1][1])
+                    if r[0] == 'L' and 112 <= r[1] < 224 and delta[r]: live_data_effect = True
+        bad = [(r, row) for r, row in delta.items() if row]
+        item = {'A_index': aj, 'cleanup_index': cj, 'A_gate': canonical['A'][aj],
+                'cleanup_gate': canonical['cleanup'][cj],
+                'native_scalar_sites': [ai, ci], 'Y_difference_before_cleanup': live_data_effect}
+        if not bad:
+            item['all_632_arbitrary_input_columns_exactly_preserved'] = True
+            accepted.append(item)
+        else:
+            r, row = bad[0]; key, value = next(iter(sorted(row.items())))
+            item['first_exact_nonzero_residual'] = {'output': list(r), 'input': list(key[0]),
+                                                   'operator_word': list(key[1]), 'coefficient': str(value)}
+            item['changed_output_fields'] = len(bad)
+            rejected.append(item)
+    need(all(not a['Y_difference_before_cleanup'] for a in accepted), 'No changed data consumer before cleanup')
+    return accepted, rejected, unmatched
+
+
+def prefix_growth(v, program, backward):
+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}
+    maximum_l1 = Q(1); max_coefficient = Q(1); max_numerator = 1; max_denominator = 1
+    witness = {'event': -1, 'register': ['L', 0]}
+    for i, event in enumerate(program):
+        apply(v, rows, event, backward)
+        if event[0] not in ('scalar', 'warp'): continue
+        role = tuple(event[1] if event[0] == 'warp' else event[1][1])
+        values = [abs(x) for x in rows[role].values()]
+        norm = sum(values, Q(0))
+        if norm > maximum_l1:
+            maximum_l1 = norm; witness = {'event': i, 'register': list(role)}
+        if values:
+            max_coefficient = max(max_coefficient, max(values))
+            max_numerator = max(max_numerator, max(x.numerator for x in values))
+            max_denominator = max(max_denominator, max(x.denominator for x in values))
+    return {'max_formal_row_l1': str(maximum_l1), 'max_abs_coefficient': str(max_coefficient),
+            'max_abs_numerator': max_numerator, 'max_denominator': max_denominator,
+            'l1_witness': witness, 'independent_input_columns': 632,
+            'scope': 'Exact logical scalar/monomial prefixes over arbitrary inputs; no rounded child error bound.'}
+
+
+def monomial(ce, recipe, n):
+    result = ce.diag(n, tuple(recipe['quadratic_rows']), tuple(recipe['linear_Z4']))
+    result = result.then(ce.perm(n, tuple(recipe['matrix_rows']))).then(ce.xgate(n, recipe['offset']))
+    return result.then(ce.Op(n, ce.identity(n), [('phase', recipe['phase'])]))
+
+
+def conjugate(ce, op):
+    n = op.n; result = ce.ident(n)
+    for g in op.circuit:
+        if g[0] == 'P': part = ce.perm(n, g[1])
+        elif g[0] == 'X': part = ce.xgate(n, g[1])
+        elif g[0] == 'C': part = ce.cgate(n, g[1], -g[2])
+        elif g[0] == 'D': part = ce.diag(n, g[1], tuple(-x % 4 for x in g[2]))
+        else:
+            need(g[0] == 'phase', 'Known Clifford primitive')
+            part = ce.Op(n, ce.identity(n), [('phase', -g[1] % 4)])
+        result = result.then(part)
+    return result
+
+
+def check_new_edges(canonical, old_program, new_program, cache):
+    ce = load(CLIFFORD, 'function_composition_clifford')
+    old = {(e[3], e[4]) for e in old_program if e[0] == 'climb'}
+    new = {(e[3], e[4]) for e in new_program if e[0] == 'climb'}
+    reports = []
+    for a, b in sorted(new - old):
+        A, B = canonical['frames'][a], canonical['frames'][b]
+        key = tuple(A), tuple(B)
+        if key not in cache:
+            source = ce.canonical_frame(9, A).adjoint().then(ce.canonical_frame(9, B))
+            records = {}
+            for name, op in (('forward', source), ('inverse_transpose', conjugate(ce, source))):
+                recipe, _ = ce.lower_child(op)
+                need(recipe['rank'] == len(B)-len(A), 'Exact new physical child rank')
+                decoded = monomial(ce, recipe['right'], 9).then(ce.fourier(9, range(recipe['rank']))).then(monomial(ce, recipe['left'], 9))
+                need(decoded.tab == op.tab and decoded.zero_state() == op.zero_state(), 'Decoded Clifford equality including global phase')
+                records[name] = recipe
+            cache[key] = records
+        reports.append({'old_frame': a, 'new_frame': b, 'old_basis': A, 'new_basis': B,
+                        'rank': len(B)-len(A), 'exact_physical_recipes': cache[key]})
+    return reports
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path, default=HERE/'pruned-native')
+    args = parser.parse_args(); args.out.mkdir(parents=True, exist_ok=True)
+    need(digest(CHECKER) == CHECKER_SHA, 'Frozen independent checker')
+    v = load(CHECKER, 'function_composition_independent'); v.authenticate()
+    base_receipt = read(BASE/'RESULT.json')
+    R = [{int(k): Q(x) for k, x in row.items()} for row in v.read(v.PACKET)['R_rows']]
+    providers = {}; phase_cache = {}
+    for tag in TAGS:
+        path = BASE/(tag+'-CANONICAL.json.gz')
+        need(digest(path) == base_receipt['providers'][tag]['artifacts'][path.name], 'Pinned baseline canonical')
+        old = read(path); old_native = v.emit_original(old)
+        yes, no, unmatched = exact_candidate_screen(v, old, old_native['forward'], R)
+        candidate = deepcopy(old)
+        a_drop = {r['A_index'] for r in yes}; c_drop = {r['cleanup_index'] for r in yes}
+        candidate['A'] = [g for i, g in enumerate(old['A']) if i not in a_drop]
+        candidate['cleanup'] = [g for i, g in enumerate(old['cleanup']) if i not in c_drop]
+        native = v.emit_original(candidate)
+        histogram = Counter(e[5] for e in native['forward'] if e[0] == 'climb')
+        candidate['local_profile'] = {str(r): n for r, n in sorted(histogram.items())}
+        candidate['edges'] = [list(e) for e in sorted({(e[3], e[4]) for e in native['forward'] if e[0] == 'climb'})]
+        checks = {}
+        for name in ('forward', 'backward'):
+            checks[name] = {'independent_literal_replay': v.replay(native[name], candidate, R, name == 'backward', True),
+                            'baseline_prefix_growth': prefix_growth(v, old_native[name], name == 'backward'),
+                            'new_prefix_growth': prefix_growth(v, native[name], name == 'backward')}
+        phases = check_new_edges(candidate, old_native['forward'], native['forward'], phase_cache)
+        # Removing the computation while retaining its inverse must be rejected.
+        negative = deepcopy(candidate)
+        first = yes[0]
+        negative['cleanup'].insert(0, first['cleanup_gate'])
+        bad_program = v.emit_original(negative)
+        rejected_control = False
+        try: v.replay(bad_program['forward'], negative, R, False, True)
+        except ValueError as error:
+            rejected_control = 'operator mismatch' in str(error)
+        need(rejected_control, 'Unpaired deletion negative control')
+        cp = args.out/(tag+'-CANONICAL.json.gz'); np = args.out/(tag+'-NATIVE-WORD.json.gz')
+        save(cp, candidate); save(np, native)
+        providers[tag] = {'baseline_canonical_sha256': digest(path), 'candidate_pairs_tested': len(yes)+len(no),
+                          'accepted_pairs': yes, 'rejected_pairs': no, 'unmatched_pairs': unmatched,
+                          'old_paid_profile': old['local_profile'], 'new_paid_profile': candidate['local_profile'],
+                          'old_paid_rank_mass': sum(int(r)*n for r, n in old['local_profile'].items()),
+                          'new_paid_rank_mass': sum(int(r)*n for r, n in candidate['local_profile'].items()),
+                          'recursive_calls_removed': sum(old['local_profile'].values())-sum(histogram.values()),
+                          'scalar_ADDs_removed': 2*len(yes), 'checks': checks,
+                          'new_physical_edges': phases, 'unpaired_deletion_negative_control_rejected': True,
+                          'artifacts': {cp.name: digest(cp), np.name: digest(np)}}
+        print('PASS pruned native', tag, len(yes), 'pairs;', dict(sorted(histogram.items())), flush=True)
+    result = {'schema': 'consumer-driven-clean-J-native-pruning/1',
+              'status': 'PASS_ALL_FOUR_BOTH_DIRECTIONS_632_ARBITRARY_FIELDS',
+              'generator_sha256': digest(Path(__file__)), 'baseline_receipt_sha256': digest(BASE/'RESULT.json'),
+              'independent_interpreter_sha256': CHECKER_SHA, 'phase_compiler_path': str(CLIFFORD.relative_to(RESEARCH.parent)),
+              'phase_compiler_sha256': digest(CLIFFORD), 'providers': providers,
+              'native_word_new_children_phase_lowered': True, 'local_data_and_helper_endpoints_unchanged': True,
+              'same_632_field_inventory': True, 'zero_owned_fields': True, 'zero_external_cleanup_fields': True,
+              'no_new_kappa_claimed': True, 'query_producer_contract_preserved': False,
+              'scope': 'Exact ideal clean-J local endpoints only. Final historical query assemblies are partially removed because this local word has no centre consumers. A caller that reads those historical queries cannot substitute this word without reconstructing and pricing its producer interface. The full caller and rounded induction remain open.'}
+    (args.out/'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    print(result['status'], flush=True)
+
+
+if __name__ == '__main__': main()
diff --git a/research/one-terminal-h3-prefix/inputs/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz b/research/one-terminal-h3-prefix/inputs/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz
new file mode 100644
index 0000000000..46d929df83
Binary files /dev/null and b/research/one-terminal-h3-prefix/inputs/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz differ
diff --git a/research/one-terminal-h3-prefix/inputs/research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json b/research/one-terminal-h3-prefix/inputs/research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json
new file mode 100644
index 0000000000..d8a2e0a915
--- /dev/null
+++ b/research/one-terminal-h3-prefix/inputs/research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json
@@ -0,0 +1,142 @@
+{
+  "actual_word_canonical_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "controls": [
+    {
+      "name": "wrong_paid_rank",
+      "rejected": "Paid rank and source frame"
+    }
+  ],
+  "helpers": {
+    "4": 28,
+    "7": 7,
+    "8": 47,
+    "9": 326
+  },
+  "native": {
+    "backward": {
+      "arbitrary_owned_C0_cleared": true,
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "l1_witness": {
+        "event": 6396,
+        "role": [
+          "L",
+          225
+        ]
+      },
+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "paid_profile": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "paid_rank_mass": 5327,
+      "real_scalar_allowance": 158168,
+      "scalar_frames_checked": true,
+      "second_literal": {
+        "all_scalar_frames_checked": true,
+        "clean_J": false,
+        "conservative_real_scalar_primitive_allowance": 158168,
+        "direction": "backward",
+        "dyadic_coefficients_and_unit_scales_checked": true,
+        "event_counts": {
+          "adapter": 448,
+          "center": 8,
+          "climb": 3290,
+          "phase": 10,
+          "scalar": 17453,
+          "warp": 240
+        },
+        "expected_restored_arbitrary_cleanup_buffers": 0,
+        "expected_restored_helpers": 408,
+        "explicitly_owned_C_fields_cleared": 1,
+        "free_warp_operator_endpoint_matches": true,
+        "independent_borrowed_input_fields": 632,
+        "mismatch_examples": [],
+        "negative_control_omitted_last_cleanup_scalar": false,
+        "original_data_fields": 224,
+        "paid_profile": {
+          "1": 2201,
+          "2": 412,
+          "3": 510,
+          "4": 127,
+          "5": 40,
+          "8": 8
+        },
+        "paid_rank_mass": 5327
+      }
+    },
+    "forward": {
+      "arbitrary_owned_C0_cleared": true,
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "l1_witness": {
+        "event": 19036,
+        "role": [
+          "L",
+          224
+        ]
+      },
+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
+      "paid_profile": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "paid_rank_mass": 5327,
+      "real_scalar_allowance": 158120,
+      "scalar_frames_checked": true,
+      "second_literal": {
+        "all_scalar_frames_checked": true,
+        "clean_J": false,
+        "conservative_real_scalar_primitive_allowance": 158120,
+        "direction": "forward",
+        "dyadic_coefficients_and_unit_scales_checked": true,
+        "event_counts": {
+          "adapter": 448,
+          "center": 8,
+          "climb": 3290,
+          "phase": 10,
+          "scalar": 17453,
+          "warp": 240
+        },
+        "expected_restored_arbitrary_cleanup_buffers": 0,
+        "expected_restored_helpers": 408,
+        "explicitly_owned_C_fields_cleared": 1,
+        "free_warp_operator_endpoint_matches": true,
+        "independent_borrowed_input_fields": 632,
+        "mismatch_examples": [],
+        "negative_control_omitted_last_cleanup_scalar": false,
+        "original_data_fields": 224,
+        "paid_profile": {
+          "1": 2201,
+          "2": 412,
+          "3": 510,
+          "4": 127,
+          "5": 40,
+          "8": 8
+        },
+        "paid_rank_mass": 5327
+      }
+    }
+  },
+  "paid": {
+    "1": 2201,
+    "2": 412,
+    "3": 510,
+    "4": 127,
+    "5": 40,
+    "8": 8
+  },
+  "seconds": 4.510284199990565,
+  "status": "PASS_JOINT_HELPER_MAPS_NATIVE_BOTH_632_INTERPRETERS",
+  "verifier_sha256": "785f67e358ac4cff60a64db4b012c43a02a833d90926d72624880040f9648c66"
+}
diff --git a/research/one-terminal-h3-prefix/inputs/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py b/research/one-terminal-h3-prefix/inputs/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/one-terminal-h3-prefix/inputs/research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/one-terminal-h3-prefix/science/PATCH.json b/research/one-terminal-h3-prefix/science/PATCH.json
new file mode 100644
index 0000000000..38526bc8e4
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/PATCH.json
@@ -0,0 +1,68 @@
+{
+  "direction": "backward",
+  "replace_index": 15372,
+  "expected_event": [
+    "climb",
+    "warp_retimed",
+    496,
+    911,
+    1,
+    3
+  ],
+  "initialize_owned": [
+    "scalar",
+    [
+      "clear",
+      [
+        "C",
+        1
+      ]
+    ],
+    181
+  ],
+  "replacement": [
+    [
+      "climb",
+      "one_terminal_h3_split",
+      496,
+      911,
+      181,
+      2
+    ],
+    [
+      "scalar",
+      [
+        "copy",
+        [
+          "C",
+          1
+        ],
+        [
+          "L",
+          496
+        ]
+      ],
+      181
+    ],
+    [
+      "climb",
+      "one_terminal_h3_split",
+      496,
+      181,
+      1,
+      1
+    ]
+  ],
+  "clear_after_new_consumer": [
+    "scalar",
+    [
+      "clear",
+      [
+        "C",
+        1
+      ]
+    ],
+    181
+  ],
+  "owned_entry_zero": true
+}
diff --git a/research/one-terminal-h3-prefix/science/REPORT.md b/research/one-terminal-h3-prefix/science/REPORT.md
new file mode 100644
index 0000000000..7471aabff2
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/REPORT.md
@@ -0,0 +1,118 @@
+# One actual terminal H3 split exposes a clean matching prefix
+
+The phase-bound local offer passes. It replaces one existing paid child
+in the frozen #4610 supplier and exposes an owned clean observation while
+preserving all its original arbitrary-owner outputs. It does not realize
+the hypothetical224H17 two-FULL target bank, a consumer, or a new kappa.
+
+Source:20bb93cd990d2ff683e4d0fc56b87a42cd5d3296. The exact native payload,
+original632-column endpoint receipt, compiler, raw-dual conjugation function,
+and interval library are pinned in SOURCES.json. Nothing is transferred
+to the newer #4929 producer.
+
+## Actual cut and guarded patch
+
+In the actual backward word, helper496 enters empty0 and returns full1.
+Its last scalar write is13182. Event15372 is its terminal paid H3 from
+rank6 frame911 to full1; no later write or warp targets this helper.
+Actual Y151, port39 with q162, has final rank8 chart181. Its last write
+(including Gaussian children) is14597, so it is already in181 at the cut.
+The explicit frame bases are in RESULT.json.
+
+The new patch replaces only event15372 by:
+
+1. H2 climb on496, frame911 to181.
+2. COPY496 into a new owned-zero C1, tagged181.
+3. H1 climb on496, frame181 to full1.
+
+C1 is initialized separately and cleared only after its new consumer
+finishes. No old role is overwritten or initialized; inherited ownedC0
+is untouched. Y151 is not modified inside the old word, so all its future
+reads remain valid. PATCH.json records the guarded old event and exact
+replacement, initialization and eventual reset. This is one resource;
+there is no claim of112 available matching slots.
+
+## Exact operator and arbitrary-owner coverage
+
+Let F_U,F_M,F_V be the canonical frames911,181,full1. The exact identity
+
+    (F_U.adjoint().then(F_M)).then(F_M.adjoint().then(F_V))
+        = F_U.adjoint().then(F_V)
+
+holds as a literal operator with shared middle-frame cancellation.
+The test checks Fourier ranks2,1,3, signed tableaus, zero-column absolute
+phase, and exact monomial/Gaussian lowering. It repeats these checks under
+the actual primitive-wise raw dual, preserving circuit order. Every word
+lifts columnwise to all positive widths; no tensor of an operator sum is
+substituted. The added COPY/CLEAR access words are not automatically
+literal inverse-transposes of one another; forward and raw-dual local
+factor identities are checked separately.
+
+Independent symbolic reverse pullbacks bind the actual clean prefix to
+helper496 alone and Y151 to its own original input. Thus at the new cut
+
+    C1 = bar(F181) h496,
+    Y151 = bar(F181) y151.
+
+The original helper continues to bar(F9)h496. After the two new child
+calls, every old live field is exactly its old value, for every original
+632-input vector. COPY only reads. Every later old operation is unchanged,
+so all old endpoint equations and ownedC0 reset remain valid. C1 returns0
+after its eventual explicit CLEAR. This coverage is an exact local
+replacement proof plus the authenticated old all632-input receipt; a fresh
+whole modified632-column replay was not run.
+
+The actual canonical rank-one tail Gamma=bar(F9)bar(F181)^-1 is **not**
+the bare C162 operator in either sign. The checker rejects those two
+substitutions and records its exact phase-bound lowering. A separate
+source pullback confirms that original Y151 contributes exactly-bar(F9)
+to returned mainX39. Relative to Y151's exit gauge this is-Gamma Y151.
+That binds one actual cross coefficient; it does not supply a free
+arbitrary query, a transverse-only factor, or a completed consumer.
+
+## Paid inventory and finite bills
+
+The exact physical supplier change is
+
+    Delta P = H2+H1-H3,   Delta H = 0.
+
+All408 original helper jobs, including helper496's H9, remain credited
+once. C1 has no independent arbitrary input and earns zero productive
+credit. The old paid rank mass is unchanged; one more ordinary Gaussian
+child is called. The physical change is to one old632-owner supplier.
+
+As a **raw price-only relaxation**, insert that delta into the previously
+hypothetical two-FULL profiles224H17+2H versus2P. Exact rational intervals
+are in RESULT.json. The surcharge is approximately.005758080415496656 at
+C=.0030217758 and.006477091731596653 atC=.0034. The relaxed margins are
+approximately39.05818003438641 and31.96610329180537. The224H17 main targets
+remain unrealized, so these are not complete-caller margins.
+
+Uniformly on the requested interval, t>=.9966 and
+2^t+1-3^t<=3-3^t<=.0306. The old raw relaxation is above31 on that
+interval by its rank5 normalized-moment monotonicity; hence the new raw
+relaxation remains above30.9694. This only clears the necessary price gate.
+
+The added storage is one whole array, of size N=2^(17f) in the proposed
+17-axis embedding. A conservative access bill is one initialization pass,
+one COPY pass and one eventual CLEAR pass. Counting all four new monomial
+boundary blocks at up to four elementary passes each, without subtracting
+old removed normalizers, gives at most19 additional whole-array passes.
+Index/phase work retains the usual columnwise O(f) overhead. The original
+158168 scalar allowance is unchanged except these explicit additions.
+The copied formal prefix has coefficient norm1, below the inherited169
+maximum; copying does not increase the old scalar coefficient growth.
+
+COPY/CLEAR and monomial phases/permutations introduce no arithmetic
+rounding. A precision obligation remains for two recursive unitary child
+approximations replacing one. If each new child has operator error at most
+e/3, their combined error is at most2e/3+e^2/9<e for0<e<=1. This gives an
+explicit local tolerance split; actual source precision allocation, any
+consumer amplification, finite compiler reserves and outer transfer were
+not replayed or funded here.
+
+The next obligation is an exact consumer of this particular copied
+bar(F181)h496 response while returning both independent productive helper
+jobs and all main owners. G owns that algebraic question. The present
+single split should not be expanded into a row bank or a new family
+without another complete endpoint and cost gate.
diff --git a/research/one-terminal-h3-prefix/science/RESULT.json b/research/one-terminal-h3-prefix/science/RESULT.json
new file mode 100644
index 0000000000..078a5708a5
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/RESULT.json
@@ -0,0 +1,2295 @@
+{
+  "status": "PASS_ONE_ACTUAL_H3_SPLIT_CLEAN_PREFIX_NOT_CONSUMER",
+  "source_commit": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296",
+  "source_sha256": {
+    "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "research/kappa-function-composition/complex/prune_native.py": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257",
+    "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326",
+    "research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428"
+  },
+  "source_event": 15372,
+  "helper": 496,
+  "helper_start": 0,
+  "helper_final": 1,
+  "mainY_role": 151,
+  "port": 39,
+  "q": 162,
+  "before_chart": 911,
+  "middle_chart": 181,
+  "after_chart": 1,
+  "chart_bases": {
+    "911": [
+      390,
+      68,
+      34,
+      16,
+      8,
+      1
+    ],
+    "181": [
+      256,
+      130,
+      64,
+      34,
+      16,
+      8,
+      4,
+      1
+    ],
+    "1": [
+      256,
+      128,
+      64,
+      32,
+      16,
+      8,
+      4,
+      2,
+      1
+    ]
+  },
+  "phases": {
+    "forward": {
+      "old_H3": {
+        "rank": 3,
+        "literal_word": [
+          [
+            "D",
+            [
+              0,
+              288,
+              320,
+              0,
+              0,
+              290,
+              324,
+              256,
+              486
+            ],
+            [
+              0,
+              0,
+              0,
+              0,
+              0,
+              3,
+              3,
+              0,
+              3
+            ]
+          ],
+          [
+            "P",
+            [
+              256,
+              64,
+              32,
+              16,
+              8,
+              1,
+              290,
+              324,
+              384
+            ]
+          ],
+          [
+            "C",
+            32,
+            -1
+          ],
+          [
+            "C",
+            16,
+            -1
+          ],
+          [
+            "C",
+            8,
+            -1
+          ],
+          [
+            "C",
+            4,
+            -1
+          ],
+          [
+            "C",
+            2,
+            -1
+          ],
+          [
+            "C",
+            1,
+            -1
+          ],
+          [
+            "P",
+            [
+              32,
+              69,
+              131,
+              16,
+              8,
+              4,
+              2,
+              257,
+              1
+            ]
+          ],
+          [
+            "D",
+            [
+              0,
+              288,
+              320,
+              0,
+              0,
+              290,
+              324,
+              256,
+              486
+            ],
+            [
+              0,
+              0,
+              0,
+              0,
+              0,
+              1,
+              1,
+              0,
+              1
+            ]
+          ],
+          [
+            "C",
+            1,
+            1
+          ],
+          [
+            "C",
+            2,
+            1
+          ],
+          [
+            "C",
+            4,
+            1
+          ],
+          [
+            "C",
+            8,
+            1
+          ],
+          [
+            "C",
+            16,
+            1
+          ],
+          [
+            "C",
+            32,
+            1
+          ],
+          [
+            "C",
+            64,
+            1
+          ],
+          [
+            "C",
+            128,
+            1
+          ],
+          [
+            "C",
+            256,
+            1
+          ]
+        ],
+        "signed_tableau": [
+          [
+            1,
+            0,
+            0
+          ],
+          [
+            290,
+            132,
+            0
+          ],
+          [
+            324,
+            130,
+            0
+          ],
+          [
+            8,
+            0,
+            0
+          ],
+          [
+            16,
+            0,
+            0
+          ],
+          [
+            32,
+            0,
+            0
+          ],
+          [
+            64,
+            0,
+            0
+          ],
+          [
+            384,
+            134,
+            3
+          ],
+          [
+            256,
+            0,
+            0
+          ],
+          [
+            0,
+            1,
+            0
+          ],
+          [
+            290,
+            134,
+            3
+          ],
+          [
+            324,
+            134,
+            3
+          ],
+          [
+            0,
+            8,
+            0
+          ],
+          [
+            0,
+            16,
+            0
+          ],
+          [
+            0,
+            34,
+            2
+          ],
+          [
+            0,
+            68,
+            2
+          ],
+          [
+            384,
+            6,
+            2
+          ],
+          [
+            0,
+            390,
+            0
+          ]
+        ],
+        "recipe": {
+          "rank": 3,
+          "left": {
+            "matrix_rows": [
+              8,
+              17,
+              34,
+              64,
+              128,
+              257,
+              2,
+              4,
+              7
+            ],
+            "offset": 0,
+            "quadratic_rows": [
+              6,
+              5,
+              7,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0
+            ],
+            "linear_Z4": [
+              2,
+              2,
+              3,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0
+            ],
+            "phase": 0
+          },
+          "right": {
+            "matrix_rows": [
+              258,
+              260,
+              384,
+              1,
+              320,
+              64,
+              8,
+              16,
+              352
+            ],
+            "offset": 51,
+            "quadratic_rows": [
+              0,
+              64,
+              320,
+              0,
+              0,
+              0,
+              6,
+              256,
+              132
+            ],
+            "linear_Z4": [
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              2
+            ],
+            "phase": 0
+          }
+        }
+      },
+      "new_H2": {
+        "rank": 2,
+        "literal_word": [
+          [
+            "D",
+            [
+              0,
+              288,
+              320,
+              0,
+              0,
+              290,
+              324,
+              256,
+              486
+            ],
+            [
+              0,
+              0,
+              0,
+              0,
+              0,
+              3,
+              3,
+              0,
+              3
+            ]
+          ],
+          [
+            "P",
+            [
+              256,
+              64,
+              32,
+              16,
+              8,
+              1,
+              290,
+              324,
+              384
+            ]
+          ],
+          [
+            "C",
+            32,
+            -1
+          ],
+          [
+            "C",
+            16,
+            -1
+          ],
+          [
+            "C",
+            8,
+            -1
+          ],
+          [
+            "C",
+            4,
+            -1
+          ],
+          [
+            "C",
+            2,
+            -1
+          ],
+          [
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+          [
+            "D",
+            [
+              0,
+              160,
+              0,
+              0,
+              0,
+              162,
+              0,
+              162,
+              0
+            ],
+            [
+              0,
+              0,
+              0,
+              0,
+              0,
+              1,
+              0,
+              1,
+              0
+            ]
+          ],
+          [
+            "P",
+            [
+              256,
+              128,
+              64,
+              32,
+              16,
+              8,
+              4,
+              1,
+              162
+            ]
+          ],
+          [
+            "C",
+            128,
+            1
+          ],
+          [
+            "C",
+            64,
+            1
+          ],
+          [
+            "C",
+            32,
+            1
+          ],
+          [
+            "C",
+            16,
+            1
+          ],
+          [
+            "C",
+            8,
+            1
+          ],
+          [
+            "C",
+            4,
+            1
+          ],
+          [
+            "C",
+            2,
+            1
+          ],
+          [
+            "C",
+            1,
+            1
+          ],
+          [
+            "P",
+            [
+              128,
+              266,
+              64,
+              32,
+              16,
+              8,
+              4,
+              2,
+              1
+            ]
+          ],
+          [
+            "D",
+            [
+              0,
+              160,
+              0,
+              0,
+              0,
+              162,
+              0,
+              162,
+              0
+            ],
+            [
+              0,
+              0,
+              0,
+              0,
+              0,
+              3,
+              0,
+              3,
+              0
+            ]
+          ],
+          [
+            "C",
+            1,
+            -1
+          ],
+          [
+            "C",
+            2,
+            -1
+          ],
+          [
+            "C",
+            4,
+            -1
+          ],
+          [
+            "C",
+            8,
+            -1
+          ],
+          [
+            "C",
+            16,
+            -1
+          ],
+          [
+            "C",
+            32,
+            -1
+          ],
+          [
+            "C",
+            64,
+            -1
+          ],
+          [
+            "C",
+            128,
+            -1
+          ],
+          [
+            "C",
+            256,
+            -1
+          ]
+        ],
+        "signed_tableau": [
+          [
+            1,
+            0,
+            0
+          ],
+          [
+            162,
+            0,
+            2
+          ],
+          [
+            4,
+            0,
+            0
+          ],
+          [
+            8,
+            0,
+            0
+          ],
+          [
+            16,
+            0,
+            0
+          ],
+          [
+            32,
+            0,
+            0
+          ],
+          [
+            64,
+            0,
+            0
+          ],
+          [
+            128,
+            0,
+            0
+          ],
+          [
+            256,
+            0,
+            0
+          ],
+          [
+            0,
+            1,
+            0
+          ],
+          [
+            162,
+            2,
+            3
+          ],
+          [
+            0,
+            4,
+            0
+          ],
+          [
+            0,
+            8,
+            0
+          ],
+          [
+            0,
+            16,
+            0
+          ],
+          [
+            0,
+            34,
+            2
+          ],
+          [
+            0,
+            64,
+            0
+          ],
+          [
+            0,
+            130,
+            2
+          ],
+          [
+            0,
+            256,
+            0
+          ]
+        ],
+        "recipe": {
+          "rank": 1,
+          "left": {
+            "matrix_rows": [
+              2,
+              5,
+              8,
+              16,
+              32,
+              65,
+              128,
+              1,
+              256
+            ],
+            "offset": 0,
+            "quadratic_rows": [
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0
+            ],
+            "linear_Z4": [
+              2,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0
+            ],
+            "phase": 0
+          },
+          "right": {
+            "matrix_rows": [
+              130,
+              1,
+              128,
+              4,
+              8,
+              16,
+              160,
+              64,
+              256
+            ],
+            "offset": 4,
+            "quadratic_rows": [
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0
+            ],
+            "linear_Z4": [
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              2,
+              0
+            ],
+            "phase": 0
+          }
+        }
+      }
+    }
+  },
+  "allwidth": "literal columnwise identities with exact shared canonical-frame cancellation, not a tensor of sums",
+  "new_observation": "C1=bar(F181) h496; Y151=bar(F181) y151 at simultaneous cut",
+  "actual_main_cross": {
+    "source_X_role": 39,
+    "source_Y_role": 151,
+    "logical_coefficient": -1,
+    "physical_coefficient": "-bar(F9)",
+    "relative_to_Y_exit": "-Gamma Y151, Gamma=bar(F9)bar(F181)^-1",
+    "phase_identity": "Exact same canonical endpoint frames as retained raw-dual H1 tail; no bareQ substitution.",
+    "limitation": "One source cross coefficient, not proof of a free arbitrary query or a whole multi-input consumer."
+  },
+  "helper_original_return": "bar(F9) h496",
+  "other_original_owners_unchanged": true,
+  "all_owner_equations": "For every old632-input vector, after the two child calls the old live state equals the oldH3 state exactly; COPY reads only; all later old events are identical. C1 retains observation until consumer, then CLEAR returns0.",
+  "inherited_owned_C0_unchanged": true,
+  "new_owned_C1": {
+    "initial": 0,
+    "at_cut": "bar(F181)h496",
+    "after_clear": 0
+  },
+  "actual_paid_delta": {
+    "1": 1,
+    "2": 1,
+    "3": -1
+  },
+  "productive_delta": {},
+  "paid_profile": {
+    "1": 4403,
+    "3": 1019,
+    "2": 825,
+    "4": 254,
+    "5": 80,
+    "8": 16
+  },
+  "target_profile": {
+    "9": 652,
+    "4": 56,
+    "8": 94,
+    "7": 14,
+    "17": 224
+  },
+  "original_supplier_paid_profile": {
+    "1": 2201,
+    "3": 510,
+    "2": 412,
+    "4": 127,
+    "5": 40,
+    "8": 8
+  },
+  "changed_supplier_paid_profile": {
+    "1": 2202,
+    "3": 509,
+    "2": 413,
+    "4": 127,
+    "5": 40,
+    "8": 8
+  },
+  "original_supplier_scalar_allowance": 158168,
+  "inherited_formal_prefix_l1": "169",
+  "cost_comparisons": {
+    "15108879/5000000000": {
+      "split_surcharge": [
+        "1129501767769066118585551753595867257196834648284478447/196159429230833773869868419475239575503198607639501078528",
+        "36144056568610115794737656115067752230298708745103311131/6277101735386680763835789423207666416102355444464034512896"
+      ],
+      "new_margin": [
+        "245172169674892321129884497959629355207660137413098584118543/6277101735386680763835789423207666416102355444464034512896",
+        "61293042418723080282471124489907338801915034353274647374837/1569275433846670190958947355801916604025588861116008628224"
+      ]
+    },
+    "17/5000": {
+      "split_surcharge": [
+        "5082170468583009128146019405279791806065041739004148127/784637716923335095479473677900958302012794430558004314112",
+        "40657363748664073025168155242238334448520333912033185823/6277101735386680763835789423207666416102355444464034512896"
+      ],
+      "new_margin": [
+        "100327241223270688530832851381177730983727478699910933434925/3138550867693340381917894711603833208051177722232017256448",
+        "200654482446541377061665702762355461967454957399821872177199/6277101735386680763835789423207666416102355444464034512896"
+      ]
+    }
+  },
+  "whole_C_interval": [
+    ".0030217758",
+    ".0034"
+  ],
+  "cost_scope": "Raw price-only relaxation:224H17 main targets remain unrealized. The exact physical achievement changes one old632-input supplier paid child; it is not a complete two-FULL caller.",
+  "uniform_positive_bound": "splitdelta<=3-3^t<=.0306; oldmargin>31 oninterval, hence newmargin>30.9694",
+  "finite_bill": {
+    "extra_storage_fields": 1,
+    "ambient": 17,
+    "N": "2^(17f)",
+    "initialize_passes": 1,
+    "COPY_passes": 1,
+    "CLEAR_passes": 1,
+    "conservative_new_monomial_passes_ignoring_old_removed_normalizers": 16,
+    "conservative_total_extra_full_array_passes": 19,
+    "COPY_and_CLEAR_exact": true,
+    "precision": "COPY adds no arithmetic rounding. Allocate each new unitary child error<=oldchild_error/3: combined<=2e/3+e^2/9<e for0<e<=1. Concrete source precision/compiler/outer reserves not replayed."
+  },
+  "tail_is_not_bare_Q": true,
+  "productive_H9_not_subtracted": true,
+  "raw_duality_scope": "Each forward/raw-dual local child split is checked separately. Added owned COPY/CLEAR access words are not asserted to be literal inverse-transposes of one another.",
+  "proof_coverage": "Exact local9-axis signed tableau plus absolute phase, prefix pullbacks and authenticated retained632-input endpoint receipt. No fresh full632-column replay or complete mixed-target consumer.",
+  "one_resource_only": true,
+  "capacity112_claim": false,
+  "consumer_constructed": false,
+  "compiler_funded": false,
+  "no_transfer_to_4929": true,
+  "new_kappa": false
+}
diff --git a/research/one-terminal-h3-prefix/science/SOURCES.json b/research/one-terminal-h3-prefix/science/SOURCES.json
new file mode 100644
index 0000000000..cf8e20ea93
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/SOURCES.json
@@ -0,0 +1,36 @@
+{
+  "source_commit": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296",
+  "source_sha256": {
+    "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "research/kappa-function-composition/complex/prune_native.py": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257",
+    "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326",
+    "research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428"
+  },
+  "own_files": [
+    {
+      "path": "PATCH.json",
+      "sha256": "9935b03b917f97cee5cd18089b7f57383386e68d48d4511343215467cf0fd63e"
+    },
+    {
+      "path": "REPORT.md",
+      "sha256": "5105dca9d8f2f69593d1d8cff4f8ccd005d8356c1043eaabe91472b33ed973a5"
+    },
+    {
+      "path": "RESULT.json",
+      "sha256": "f62b9ca79788407dba125c1f612c4b245c2685cfd63256dbebbd677481337b8e"
+    },
+    {
+      "path": "check.py",
+      "sha256": "cd9821de2e6cce4cd89e83ef1b1b8ceb5b4603e637d85ee5168c2706464e64a1"
+    },
+    {
+      "path": "normal.log",
+      "sha256": "81596cc9409c479b1b39f20ca08bfa893a961ed1b19bb2d08d90544adf6e3621"
+    },
+    {
+      "path": "optimized.log",
+      "sha256": "81596cc9409c479b1b39f20ca08bfa893a961ed1b19bb2d08d90544adf6e3621"
+    }
+  ]
+}
diff --git a/research/one-terminal-h3-prefix/science/check.py b/research/one-terminal-h3-prefix/science/check.py
new file mode 100644
index 0000000000..ae0a3c1c57
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/check.py
@@ -0,0 +1,138 @@
+#!/usr/bin/env python3
+"""One actual paid H3 split and owned clean prefix, source20bb only.
+Apache-2.0; substantial OpenAI Codex assistance. Credits native #4610,
+#4712 arbitrary-owner protocols and the retained exact phase compiler.
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+import ast,gzip,json,os,subprocess,sys,types
+HERE=Path(__file__).resolve().parent
+PIN='20bb93cd990d2ff683e4d0fc56b87a42cd5d3296'
+WORD='research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'
+CE='research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py'
+PRUNE='research/kappa-function-composition/complex/prune_native.py'
+IV='research/higher-moment-strictification/verify.py'
+VAL='research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json'
+def need(x,m):
+    if not x:raise ValueError(m)
+def read(p):return subprocess.check_output(['git','show',PIN+':'+p],env={**os.environ,'GIT_NO_REPLACE_OBJECTS':'1'})
+raw={p:read(p)for p in(WORD,CE,PRUNE,IV,VAL)}
+need(sha256(raw[WORD]).hexdigest()=='7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05','frozen4610 word')
+p=json.loads(gzip.decompress(raw[WORD]));c=p['canonical'];w=p['programs']['backward'];f=c['frames']
+old_validation=json.loads(raw[VAL])
+need(old_validation['actual_word_canonical_sha256']==sha256(gzip.decompress(raw[WORD])).hexdigest(),
+    'retained original632-column endpoint receipt binds exact payload')
+need(old_validation['native']['backward']['independent_persistent_columns']==632
+    and old_validation['native']['backward']['arbitrary_owned_C0_cleared'],
+    'authenticated retained all-owner original endpoint coverage')
+old=['climb','warp_retimed',496,911,1,3]
+need(w[15372]==old and c['start'][496]==0 and c['final'][496]==1,'one actual H3 primitive and wholeH9 helper')
+need(c['ports'][39]==162 and c['final'][151]==181,'actual selected mainY interface')
+def writes(e,r):return(e[0]=='scalar'and e[1][1]==['L',r])or(e[0]=='warp'and e[1]==['L',r])
+need(max(i for i,e in enumerate(w)if writes(e,496))==13182,'helper clean before terminal child')
+need(max(i for i,e in enumerate(w)if writes(e,151)or(e[0]=='climb'and e[2]==151))==14597,'Y already final and never written again')
+need(all(r[1]==0 for e in w if e[0]=='scalar'for r in e[1][1:3]if isinstance(r,list)and r[0]=='C'),'new ownedC1 does not alias oldC0')
+ce=types.ModuleType('actual_h3_split');sys.modules[ce.__name__]=ce
+exec(compile(raw[CE],CE,'exec'),ce.__dict__)
+defs=[n for n in ast.parse(raw[PRUNE]).body if isinstance(n,ast.FunctionDef)and n.name=='conjugate'];env={'need':need}
+exec(compile(ast.Module(body=defs,type_ignores=[]),PRUNE,'exec'),env)
+def bar(op):return env['conjugate'](ce,op)
+def grade(op):return ce.rank([x for x,z,p in op.tab[op.n:]])
+def same(a,b):return a.tab==b.tab and a.zero_state()==b.zero_state()
+FU,FM,FV=[ce.canonical_frame(9,f[j])for j in(911,181,1)]
+records={}
+for direction,conv in [('forward',lambda x:x),('backward_raw_dual',bar)]:
+    original=conv(FU.adjoint().then(FV));first=conv(FU.adjoint().then(FM));second=conv(FM.adjoint().then(FV))
+    need([grade(z)for z in(original,first,second)]==[3,2,1],'actual physical child ranks')
+    need(same(first.then(second),original),'all-input signed-tableau and absolute-phase replacement')
+    lowered={}
+    for tag,z in [('old_H3',original),('new_H2',first),('new_H1',second)]:
+        recipe,reconstructed=ce.lower_child(z);need(same(z,reconstructed),'literal child decomposition phase')
+        lowered[tag]=dict(rank=grade(z),literal_word=z.circuit,signed_tableau=z.tab,recipe=recipe)
+    records[direction]=lowered
+need(not same(FM.adjoint().then(FV),ce.cgate(9,162))and not same(FM.adjoint().then(FV),ce.cgate(9,162,-1)),
+    'do not replace actual tail by bare rootQ in either sign')
+
+# Independent reverse pullbacks bind the prefix to actual arbitrary owners.
+def pullback(role,cut):
+    state={('L',role):{():Q(1)}}
+    def add(t,b,k):
+        a=state.setdefault(t,{})
+        for u,v in b.items():
+            a[u]=a.get(u,Q(0))+k*v
+            if not a[u]:del a[u]
+        if not a:state.pop(t,None)
+    for e in reversed(w[:cut]):
+        if e[0]=='scalar':
+            g=e[1];t=tuple(g[1]);v=dict(state.get(t,{}))
+            if not v:continue
+            if g[0]=='add':add(tuple(g[2]),v,Q(g[3],g[4]))
+            elif g[0]=='scale':state[t]={u:k*Q(g[2],g[3])for u,k in v.items()}
+            elif g[0]=='copy':state.pop(t,None);add(tuple(g[2]),v,Q(1))
+            elif g[0]=='clear':state.pop(t,None)
+        elif e[0]=='warp':
+            t=tuple(e[1]);v=state.get(t,{})
+            state[t]={(u[1:]if u and u[0]==-e[2]else(e[2],)+u):k for u,k in v.items()}
+            if not state[t]:state.pop(t,None)
+    return state
+need(pullback(496,15372)=={('L',496):{():Q(1)}},'clean arbitrary helper prefix before old child')
+need(pullback(151,15372)=={('L',151):{():Q(1)}},'simultaneous clean arbitrary Y field')
+xrow=pullback(39,len(w))
+need(xrow.get(('L',151))=={():Q(-1)},'actual backward mainX39 cross coefficient from originalY151')
+patch=dict(direction='backward',replace_index=15372,expected_event=old,
+    initialize_owned=['scalar',['clear',['C',1]],181],
+    replacement=[['climb','one_terminal_h3_split',496,911,181,2],
+        ['scalar',['copy',['C',1],['L',496]],181],
+        ['climb','one_terminal_h3_split',496,181,1,1]],
+    clear_after_new_consumer=['scalar',['clear',['C',1]],181],owned_entry_zero=True)
+(HERE/'PATCH.json').write_text(json.dumps(patch,indent=2)+'\n')
+P=Counter(e[5]for e in p['programs']['forward']if e[0]=='climb');P.update(e[4]for e in p['programs']['forward']if e[0]=='center')
+supplier_new=P.copy();supplier_new[3]-=1;supplier_new[2]+=1;supplier_new[1]+=1
+H=Counter(len(f[c['final'][r]])-len(f[c['start'][r]])for r in range(224,632))
+paid=Counter({r:2*n for r,n in P.items()});newpaid=paid.copy();newpaid[3]-=1;newpaid[2]+=1;newpaid[1]+=1
+targets=Counter({r:2*n for r,n in H.items()});targets[17]=224
+coeff={r:targets.get(r,0)-paid.get(r,0)for r in set(targets)|set(paid)if targets.get(r,0)!=paid.get(r,0)}
+need(all((v<0 and r<=5)or(v>0 and r>5)for r,v in coeff.items()),
+    'old raw relaxation normalized by5^t increases throughout the interval')
+iv={'__name__':'one_child_split_intervals','__file__':str(HERE/'pinned_iv.py')};exec(compile(raw[IV],IV,'exec'),iv)
+def sub(a,b):return a[0]-b[1],a[1]-b[0]
+comparisons={}
+for C in(Q('.0030217758'),Q('.0034')):
+    t=1-C;two=iv['power'](2,t);delta=sub((two[0]+1,two[1]+1),iv['power'](3,t))
+    margin=sub(iv['moment'](dict(targets),t),iv['moment'](dict(newpaid),t))
+    need(delta[0]>0 and margin[0]>31,'positive small split cost with complete raw profile still positive')
+    comparisons[str(C)]=dict(split_surcharge=list(map(str,delta)),new_margin=list(map(str,margin)))
+out=dict(status='PASS_ONE_ACTUAL_H3_SPLIT_CLEAN_PREFIX_NOT_CONSUMER',source_commit=PIN,
+    source_sha256={k:sha256(v).hexdigest()for k,v in raw.items()},source_event=15372,
+    helper=496,helper_start=0,helper_final=1,mainY_role=151,port=39,q=162,
+    before_chart=911,middle_chart=181,after_chart=1,chart_bases={j:f[j]for j in(911,181,1)},
+    phases=records,allwidth='literal columnwise identities with exact shared canonical-frame cancellation, not a tensor of sums',
+    new_observation='C1=bar(F181) h496; Y151=bar(F181) y151 at simultaneous cut',
+    actual_main_cross=dict(source_X_role=39,source_Y_role=151,logical_coefficient=-1,
+        physical_coefficient='-bar(F9)',relative_to_Y_exit='-Gamma Y151, Gamma=bar(F9)bar(F181)^-1',
+        phase_identity='Exact same canonical endpoint frames as retained raw-dual H1 tail; no bareQ substitution.',
+        limitation='One source cross coefficient, not proof of a free arbitrary query or a whole multi-input consumer.'),
+    helper_original_return='bar(F9) h496',other_original_owners_unchanged=True,
+    all_owner_equations='For every old632-input vector, after the two child calls the old live state equals the oldH3 state exactly; COPY reads only; all later old events are identical. C1 retains observation until consumer, then CLEAR returns0.',
+    inherited_owned_C0_unchanged=True,new_owned_C1=dict(initial=0,at_cut='bar(F181)h496',after_clear=0),
+    actual_paid_delta={1:1,2:1,3:-1},productive_delta={},paid_profile=dict(newpaid),target_profile=dict(targets),
+    original_supplier_paid_profile=dict(P),changed_supplier_paid_profile=dict(supplier_new),
+    original_supplier_scalar_allowance=old_validation['native']['backward']['real_scalar_allowance'],
+    inherited_formal_prefix_l1=old_validation['native']['backward']['max_formal_prefix_l1'],
+    cost_comparisons=comparisons,whole_C_interval=['.0030217758','.0034'],
+    cost_scope='Raw price-only relaxation:224H17 main targets remain unrealized. The exact physical achievement changes one old632-input supplier paid child; it is not a complete two-FULL caller.',
+    uniform_positive_bound='splitdelta<=3-3^t<=.0306; oldmargin>31 oninterval, hence newmargin>30.9694',
+    finite_bill=dict(extra_storage_fields=1,ambient=17,N='2^(17f)',
+        initialize_passes=1,COPY_passes=1,CLEAR_passes=1,
+        conservative_new_monomial_passes_ignoring_old_removed_normalizers=16,
+        conservative_total_extra_full_array_passes=19,
+        COPY_and_CLEAR_exact=True,precision='COPY adds no arithmetic rounding. Allocate each new unitary child error<=oldchild_error/3: combined<=2e/3+e^2/9<e for0<e<=1. Concrete source precision/compiler/outer reserves not replayed.'),
+    tail_is_not_bare_Q=True,productive_H9_not_subtracted=True,
+    raw_duality_scope='Each forward/raw-dual local child split is checked separately. Added owned COPY/CLEAR access words are not asserted to be literal inverse-transposes of one another.',
+    proof_coverage='Exact local9-axis signed tableau plus absolute phase, prefix pullbacks and authenticated retained632-input endpoint receipt. No fresh full632-column replay or complete mixed-target consumer.',
+    one_resource_only=True,capacity112_claim=False,consumer_constructed=False,compiler_funded=False,
+    no_transfer_to_4929=True,new_kappa=False)
+(HERE/'RESULT.json').write_text(json.dumps(out,indent=2)+'\n')
+print(json.dumps({k:v for k,v in out.items()if k not in('phases','chart_bases')},sort_keys=True))
diff --git a/research/one-terminal-h3-prefix/science/normal.log b/research/one-terminal-h3-prefix/science/normal.log
new file mode 100644
index 0000000000..0908a052ce
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/normal.log
@@ -0,0 +1 @@
+{"actual_main_cross": {"limitation": "One source cross coefficient, not proof of a free arbitrary query or a whole multi-input consumer.", "logical_coefficient": -1, "phase_identity": "Exact same canonical endpoint frames as retained raw-dual H1 tail; no bareQ substitution.", "physical_coefficient": "-bar(F9)", "relative_to_Y_exit": "-Gamma Y151, Gamma=bar(F9)bar(F181)^-1", "source_X_role": 39, "source_Y_role": 151}, "actual_paid_delta": {"1": 1, "2": 1, "3": -1}, "after_chart": 1, "all_owner_equations": "For every old632-input vector, after the two child calls the old live state equals the oldH3 state exactly; COPY reads only; all later old events are identical. C1 retains observation until consumer, then CLEAR returns0.", "allwidth": "literal columnwise identities with exact shared canonical-frame cancellation, not a tensor of sums", "before_chart": 911, "capacity112_claim": false, "changed_supplier_paid_profile": {"1": 2202, "2": 413, "3": 509, "4": 127, "5": 40, "8": 8}, "compiler_funded": false, "consumer_constructed": false, "cost_comparisons": {"15108879/5000000000": {"new_margin": ["245172169674892321129884497959629355207660137413098584118543/6277101735386680763835789423207666416102355444464034512896", "61293042418723080282471124489907338801915034353274647374837/1569275433846670190958947355801916604025588861116008628224"], "split_surcharge": ["1129501767769066118585551753595867257196834648284478447/196159429230833773869868419475239575503198607639501078528", "36144056568610115794737656115067752230298708745103311131/6277101735386680763835789423207666416102355444464034512896"]}, "17/5000": {"new_margin": ["100327241223270688530832851381177730983727478699910933434925/3138550867693340381917894711603833208051177722232017256448", "200654482446541377061665702762355461967454957399821872177199/6277101735386680763835789423207666416102355444464034512896"], "split_surcharge": ["5082170468583009128146019405279791806065041739004148127/784637716923335095479473677900958302012794430558004314112", "40657363748664073025168155242238334448520333912033185823/6277101735386680763835789423207666416102355444464034512896"]}}, "cost_scope": "Raw price-only relaxation:224H17 main targets remain unrealized. The exact physical achievement changes one old632-input supplier paid child; it is not a complete two-FULL caller.", "finite_bill": {"CLEAR_passes": 1, "COPY_and_CLEAR_exact": true, "COPY_passes": 1, "N": "2^(17f)", "ambient": 17, "conservative_new_monomial_passes_ignoring_old_removed_normalizers": 16, "conservative_total_extra_full_array_passes": 19, "extra_storage_fields": 1, "initialize_passes": 1, "precision": "COPY adds no arithmetic rounding. Allocate each new unitary child error<=oldchild_error/3: combined<=2e/3+e^2/9<e for0<e<=1. Concrete source precision/compiler/outer reserves not replayed."}, "helper": 496, "helper_final": 1, "helper_original_return": "bar(F9) h496", "helper_start": 0, "inherited_formal_prefix_l1": "169", "inherited_owned_C0_unchanged": true, "mainY_role": 151, "middle_chart": 181, "new_kappa": false, "new_observation": "C1=bar(F181) h496; Y151=bar(F181) y151 at simultaneous cut", "new_owned_C1": {"after_clear": 0, "at_cut": "bar(F181)h496", "initial": 0}, "no_transfer_to_4929": true, "one_resource_only": true, "original_supplier_paid_profile": {"1": 2201, "2": 412, "3": 510, "4": 127, "5": 40, "8": 8}, "original_supplier_scalar_allowance": 158168, "other_original_owners_unchanged": true, "paid_profile": {"1": 4403, "2": 825, "3": 1019, "4": 254, "5": 80, "8": 16}, "port": 39, "productive_H9_not_subtracted": true, "productive_delta": {}, "proof_coverage": "Exact local9-axis signed tableau plus absolute phase, prefix pullbacks and authenticated retained632-input endpoint receipt. No fresh full632-column replay or complete mixed-target consumer.", "q": 162, "raw_duality_scope": "Each forward/raw-dual local child split is checked separately. Added owned COPY/CLEAR access words are not asserted to be literal inverse-transposes of one another.", "source_commit": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296", "source_event": 15372, "source_sha256": {"research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", "research/kappa-function-composition/complex/prune_native.py": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257", "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", "research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428", "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"}, "status": "PASS_ONE_ACTUAL_H3_SPLIT_CLEAN_PREFIX_NOT_CONSUMER", "tail_is_not_bare_Q": true, "target_profile": {"4": 56, "7": 14, "8": 94, "9": 652, "17": 224}, "uniform_positive_bound": "splitdelta<=3-3^t<=.0306; oldmargin>31 oninterval, hence newmargin>30.9694", "whole_C_interval": [".0030217758", ".0034"]}
diff --git a/research/one-terminal-h3-prefix/science/optimized.log b/research/one-terminal-h3-prefix/science/optimized.log
new file mode 100644
index 0000000000..0908a052ce
--- /dev/null
+++ b/research/one-terminal-h3-prefix/science/optimized.log
@@ -0,0 +1 @@
+{"actual_main_cross": {"limitation": "One source cross coefficient, not proof of a free arbitrary query or a whole multi-input consumer.", "logical_coefficient": -1, "phase_identity": "Exact same canonical endpoint frames as retained raw-dual H1 tail; no bareQ substitution.", "physical_coefficient": "-bar(F9)", "relative_to_Y_exit": "-Gamma Y151, Gamma=bar(F9)bar(F181)^-1", "source_X_role": 39, "source_Y_role": 151}, "actual_paid_delta": {"1": 1, "2": 1, "3": -1}, "after_chart": 1, "all_owner_equations": "For every old632-input vector, after the two child calls the old live state equals the oldH3 state exactly; COPY reads only; all later old events are identical. C1 retains observation until consumer, then CLEAR returns0.", "allwidth": "literal columnwise identities with exact shared canonical-frame cancellation, not a tensor of sums", "before_chart": 911, "capacity112_claim": false, "changed_supplier_paid_profile": {"1": 2202, "2": 413, "3": 509, "4": 127, "5": 40, "8": 8}, "compiler_funded": false, "consumer_constructed": false, "cost_comparisons": {"15108879/5000000000": {"new_margin": ["245172169674892321129884497959629355207660137413098584118543/6277101735386680763835789423207666416102355444464034512896", "61293042418723080282471124489907338801915034353274647374837/1569275433846670190958947355801916604025588861116008628224"], "split_surcharge": ["1129501767769066118585551753595867257196834648284478447/196159429230833773869868419475239575503198607639501078528", "36144056568610115794737656115067752230298708745103311131/6277101735386680763835789423207666416102355444464034512896"]}, "17/5000": {"new_margin": ["100327241223270688530832851381177730983727478699910933434925/3138550867693340381917894711603833208051177722232017256448", "200654482446541377061665702762355461967454957399821872177199/6277101735386680763835789423207666416102355444464034512896"], "split_surcharge": ["5082170468583009128146019405279791806065041739004148127/784637716923335095479473677900958302012794430558004314112", "40657363748664073025168155242238334448520333912033185823/6277101735386680763835789423207666416102355444464034512896"]}}, "cost_scope": "Raw price-only relaxation:224H17 main targets remain unrealized. The exact physical achievement changes one old632-input supplier paid child; it is not a complete two-FULL caller.", "finite_bill": {"CLEAR_passes": 1, "COPY_and_CLEAR_exact": true, "COPY_passes": 1, "N": "2^(17f)", "ambient": 17, "conservative_new_monomial_passes_ignoring_old_removed_normalizers": 16, "conservative_total_extra_full_array_passes": 19, "extra_storage_fields": 1, "initialize_passes": 1, "precision": "COPY adds no arithmetic rounding. Allocate each new unitary child error<=oldchild_error/3: combined<=2e/3+e^2/9<e for0<e<=1. Concrete source precision/compiler/outer reserves not replayed."}, "helper": 496, "helper_final": 1, "helper_original_return": "bar(F9) h496", "helper_start": 0, "inherited_formal_prefix_l1": "169", "inherited_owned_C0_unchanged": true, "mainY_role": 151, "middle_chart": 181, "new_kappa": false, "new_observation": "C1=bar(F181) h496; Y151=bar(F181) y151 at simultaneous cut", "new_owned_C1": {"after_clear": 0, "at_cut": "bar(F181)h496", "initial": 0}, "no_transfer_to_4929": true, "one_resource_only": true, "original_supplier_paid_profile": {"1": 2201, "2": 412, "3": 510, "4": 127, "5": 40, "8": 8}, "original_supplier_scalar_allowance": 158168, "other_original_owners_unchanged": true, "paid_profile": {"1": 4403, "2": 825, "3": 1019, "4": 254, "5": 80, "8": 16}, "port": 39, "productive_H9_not_subtracted": true, "productive_delta": {}, "proof_coverage": "Exact local9-axis signed tableau plus absolute phase, prefix pullbacks and authenticated retained632-input endpoint receipt. No fresh full632-column replay or complete mixed-target consumer.", "q": 162, "raw_duality_scope": "Each forward/raw-dual local child split is checked separately. Added owned COPY/CLEAR access words are not asserted to be literal inverse-transposes of one another.", "source_commit": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296", "source_event": 15372, "source_sha256": {"research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", "research/kappa-function-composition/complex/prune_native.py": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257", "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", "research/kappa-round3-warp-20261022/NATIVE-VALIDATION.json": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428", "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"}, "status": "PASS_ONE_ACTUAL_H3_SPLIT_CLEAN_PREFIX_NOT_CONSUMER", "tail_is_not_bare_Q": true, "target_profile": {"4": 56, "7": 14, "8": 94, "9": 652, "17": 224}, "uniform_positive_bound": "splitdelta<=3-3^t<=.0306; oldmargin>31 oninterval, hence newmargin>30.9694", "whole_C_interval": [".0030217758", ".0034"]}
diff --git a/research/one-terminal-h3-prefix/verify.py b/research/one-terminal-h3-prefix/verify.py
new file mode 100644
index 0000000000..549ed5919c
--- /dev/null
+++ b/research/one-terminal-h3-prefix/verify.py
@@ -0,0 +1,76 @@
+#!/usr/bin/env python3
+"""Read-only vendored-source replay of unchanged one-H3 prefix science.
+
+Only the Git source-loader function is rebound in an in-memory AST. Emitted
+receipts are regenerated in private scratch and compared byte-for-byte.
+Apache-2.0; substantial OpenAI Codex assistance; source credit in README.
+"""
+import ast
+from contextlib import redirect_stdout
+from hashlib import sha256
+import io
+import json
+from pathlib import Path
+import sys
+from tempfile import TemporaryDirectory
+
+HERE = Path(__file__).resolve().parent
+SCIENCE = HERE / 'science'
+MANIFEST_SHA256 = '3e0eaff1f992b59f9cce72523311bcc2b70897ed5765fc40dacaccb70f3c8aa3'
+ORIGINAL_READ = "def read(p):return subprocess.check_output(['git','show',PIN+':'+p],env={**os.environ,'GIT_NO_REPLACE_OBJECTS':'1'})"
+
+
+def need(test, why):
+    if not test:
+        raise ValueError(why)
+
+
+def authenticate():
+    raw = (SCIENCE / 'SOURCES.json').read_bytes()
+    need(sha256(raw).hexdigest() == MANIFEST_SHA256, 'Exact science source manifest')
+    manifest = json.loads(raw)
+    expected = {r['path'] for r in manifest['own_files']} | {'SOURCES.json'}
+    need(expected == {p.name for p in SCIENCE.iterdir() if p.is_file()}, 'Exact seven-file science archive')
+    for row in manifest['own_files']:
+        need(sha256((SCIENCE / row['path']).read_bytes()).hexdigest() == row['sha256'],
+             'Frozen science: ' + row['path'])
+    sources = {}
+    for path, digest in manifest['source_sha256'].items():
+        data = (HERE / 'inputs' / path).read_bytes()
+        need(sha256(data).hexdigest() == digest, 'Pinned vendored source: ' + path)
+        sources[path] = data
+    need(len(sources) == 5, 'Five exact source inputs')
+    return sources
+
+
+def adapted_tree(body):
+    tree = ast.parse(body)
+    loaders = [n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name == 'read']
+    need(len(loaders) == 1, 'One source loader')
+    old = loaders[0]
+    need(ast.dump(old) == ast.dump(ast.parse(ORIGINAL_READ).body[0]), 'Exact documented Git loader')
+    replacement = ast.parse('def read(p): return FROZEN_SOURCES[p]').body[0]
+    index = tree.body.index(old)
+    before = [ast.dump(n) for n in tree.body]
+    tree.body[index] = replacement
+    after = [ast.dump(n) for n in tree.body]
+    need([i for i, pair in enumerate(zip(before, after)) if pair[0] != pair[1]] == [index],
+         'Only source-loader AST is changed')
+    return ast.fix_missing_locations(tree)
+
+
+if __name__ == '__main__':
+    need(len(sys.argv) == 1, 'Read-only verifier accepts no generation arguments')
+    sources = authenticate()
+    tree = adapted_tree((SCIENCE / 'check.py').read_bytes())
+    with TemporaryDirectory(prefix='one-terminal-h3-prefix-') as directory:
+        temporary = Path(directory)
+        environment = {'__file__': str(temporary / 'check.py'), '__name__': 'one_h3_private_replay',
+                       'FROZEN_SOURCES': sources}
+        with redirect_stdout(io.StringIO()):
+            exec(compile(tree, 'unchanged_one_h3_science_with_vendored_source_loader', 'exec'), environment)
+        for name in ['PATCH.json', 'RESULT.json']:
+            need((temporary / name).read_bytes() == (SCIENCE / name).read_bytes(),
+                 'Exact regenerated scientific receipt: ' + name)
+    need(authenticate() == sources, 'Read-only replay left all frozen inputs unchanged')
+    print('PASS_PORTABLE_ONE_TERMINAL_H3_PREFIX exact_phase_and_prefix receipts_equal no_consumer no_new_kappa')
diff --git a/research/one-terminal-h3-prefix/verify_homogeneous.py b/research/one-terminal-h3-prefix/verify_homogeneous.py
new file mode 100644
index 0000000000..9b56a83d21
--- /dev/null
+++ b/research/one-terminal-h3-prefix/verify_homogeneous.py
@@ -0,0 +1,74 @@
+#!/usr/bin/env python3
+"""Portable read-only replay of unchanged one-port homogeneous construction.
+
+Only the Git-byte loader assignment is rebound in an in-memory AST. The
+unchanged local interval dependency is staged at its expected relative path
+in private scratch. Apache-2.0; substantial OpenAI Codex assistance.
+"""
+import ast
+from contextlib import redirect_stdout
+from hashlib import sha256
+import io
+import json
+from pathlib import Path
+import sys
+from tempfile import TemporaryDirectory
+
+HERE = Path(__file__).resolve().parent
+FROZEN = HERE / 'homogeneous'
+MANIFEST_SHA = 'dc0cd91a5d4ec4c3e1b19a9c6534cbb0cda7a6ec218b05bc116f08f6b5370e07'
+OLD_LOADER = "raw = {k: subprocess.check_output(['git', '--no-replace-objects', 'show', PIN+':'+v]) for k,v in PATHS.items()}"
+
+
+def need(test, why):
+    if not test:
+        raise ValueError(why)
+
+
+def authenticate():
+    manifest = (FROZEN / 'FILES.json').read_bytes()
+    need(sha256(manifest).hexdigest() == MANIFEST_SHA, 'Exact G science manifest')
+    rows = json.loads(manifest)['files']
+    need({r['path'] for r in rows} | {'FILES.json'} == {p.name for p in FROZEN.iterdir() if p.is_file()}, 'Exact G nine-file archive')
+    for row in rows:
+        need(sha256((FROZEN / row['path']).read_bytes()).hexdigest() == row['sha256'], 'Frozen G file: ' + row['path'])
+    result = json.loads((FROZEN / 'RESULT.json').read_text())
+    sources = {}
+    for path, digest in result['sources'].items():
+        raw = (HERE / 'inputs' / path).read_bytes()
+        need(sha256(raw).hexdigest() == digest, 'Exact G source: ' + path)
+        sources[path] = raw
+    dependency = json.loads((FROZEN / 'DEPENDENCIES.json').read_text())['local_interval_library']
+    interval = (HERE / 'inputs/local/prefix-interval-library.py').read_bytes()
+    need(sha256(interval).hexdigest() == dependency['sha256'], 'Exact retained local interval library')
+    return sources, interval
+
+
+def adapted_tree(body):
+    tree = ast.parse(body)
+    loads = [n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name == 'load']
+    need(len(loads) == 1, 'One G source loader')
+    old = ast.parse(OLD_LOADER).body[0]
+    need(ast.dump(loads[0].body[0]) == ast.dump(old), 'Exact Git-byte loader assignment')
+    original = [ast.dump(n) for n in loads[0].body[1:]]
+    loads[0].body[0] = ast.parse('raw = {k: FROZEN_SOURCES[v] for k,v in PATHS.items()}').body[0]
+    need([ast.dump(n) for n in loads[0].body[1:]] == original, 'Scientific loader body unchanged')
+    return ast.fix_missing_locations(tree)
+
+
+if __name__ == '__main__':
+    need(len(sys.argv) == 1, 'Read-only launcher accepts no generation arguments')
+    sources, interval = authenticate()
+    tree = adapted_tree((FROZEN / 'check.py').read_bytes())
+    with TemporaryDirectory(prefix='one-h3-homogeneous-') as directory:
+        root = Path(directory)
+        (root / 'check.py').write_bytes(interval)
+        local = root / 'actual'
+        local.mkdir()
+        (local / 'RESULT.json').write_bytes((FROZEN / 'RESULT.json').read_bytes())
+        env = {'__file__': str(local / 'check.py'), '__name__': '__main__', 'FROZEN_SOURCES': sources}
+        with redirect_stdout(io.StringIO()):
+            exec(compile(tree, 'unchanged_G_science_with_vendored_byte_loader', 'exec'), env)
+        need((local / 'RESULT.json').read_bytes() == (FROZEN / 'RESULT.json').read_bytes(), 'G replay is read-only')
+    need(authenticate() == (sources, interval), 'Frozen inputs remain unchanged')
+    print('PASS_PORTABLE_ONE_NATIVE_TALL_U three_original_owners dependent_prefix total36passes no_complete_caller no_new_kappa')