diff --git a/research/outside-input-research-targets/OVERLAP.json b/research/outside-input-research-targets/OVERLAP.json
new file mode 100644
index 0000000000..7337bf95aa
--- /dev/null
+++ b/research/outside-input-research-targets/OVERLAP.json
@@ -0,0 +1,39 @@
+{
+  "coverage": {
+    "discussions": {
+      "complete_pagination": true,
+      "fetched_at": "2026-10-24T11:07:16.567072+00:00",
+      "records": 4707
+    },
+    "local": {
+      "complete_head_inventory": true,
+      "head": "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700",
+      "head_records": 7376,
+      "records": 7376,
+      "unsearched_head_paths": []
+    },
+    "open_prs": {
+      "complete_pagination": true,
+      "fetched_at": "2026-10-24T11:06:09.656605+00:00",
+      "records": 316
+    }
+  },
+  "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. Local coverage compares searched working-tree notes with regular note paths at coverage.local.head; it does not certify HEAD contents or historical coverage. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+  "matches_total": 1194,
+  "note": "One cached task-shaped search supplements live reading of current PR/discussion text; this report proposes targets and claims neither novelty nor completed investigations.",
+  "searched_at": "2026-10-24T11:07:17.174877+00:00",
+  "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE",
+  "terms": [
+    "complex-rank-shape-decoder",
+    "rank shape",
+    "block climb",
+    "masked decoder",
+    "overcomplete",
+    "effective rank",
+    "complex-local-word-ceiling",
+    "complex-decoder-field-extension-seed44",
+    "complex-frame-pair-decoders",
+    "selected-k8-unrestricted-ends",
+    "eisenstein-reduction-copy-floor"
+  ]
+}
diff --git a/research/outside-input-research-targets/PR-DRAFT.md b/research/outside-input-research-targets/PR-DRAFT.md
new file mode 100644
index 0000000000..4adfee0a72
--- /dev/null
+++ b/research/outside-input-research-targets/PR-DRAFT.md
@@ -0,0 +1,76 @@
+# Observation, state, and geometry: building complete suppliers for larger κ
+
+Local identities and decoders can lose their savings when the caller pays for observation access, restoration, transport or precision. The ten targets below address those boundaries through outside mathematics and reusable search tools. The [detailed assessment](README.md) expands the literature, predecessor work and stopping conditions.
+
+The baseline is canonical commit [`1a3ced6`](https://github.com/CrocSwap/integer-mult-bounds/commit/1a3ced60b2f7a46bc70280a04f2eeb8ca027c700): **conditional κ = 0.003027288235**, ordinary BIT saving **0.0034363538396**, conservatively admitted as **0.0034**. The binding outer row is `main_transform`; the [selected record](https://github.com/CrocSwap/integer-mult-bounds/blob/1a3ced60b2f7a46bc70280a04f2eeb8ca027c700/certificates/selected-result.json) identifies the five retained framework assumptions. This is an exploratory research agenda with diagnostic tooling; no new κ or admitted supplier is established.
+
+## Ten proposed results
+
+| Proposed result | Opportunity and outside input | Main risk or tradeoff | First useful test and stopping rule |
+|---|---|---|---|
+| **1. Encoded outputs with an internally produced observation** | [Observability](https://people.duke.edu/~hpgavin/SystemID/References/Kalman-JSIAM-1963.pdf) and [local index decoding](https://arxiv.org/abs/1910.08745) could let consumers use encoded states, avoiding repeated decoding and restoration. | Deferred restoration creates history and source-version obligations. [#5427](https://github.com/CrocSwap/integer-mult-bounds/pull/5427) reports that the required `ZQY` observation is absent from the frozen words in its grammar; a changed producer or paid interface is necessary. | Extend [#5419](https://github.com/CrocSwap/integer-mult-bounds/pull/5419) at one actual FULL/thin-query cut; preserve independent inputs and close two generations. Stop if an essential read is unavailable or observation plus return costs exhaust the allowance. |
+| **2. An exact query–memory–restoration frontier** | [Reversible compilation](https://arxiv.org/abs/1510.00377) and I/O pebbling suggest an optimizer that emits an attaining dirty-state program and a checkable lower bound. Useful even when the outcome is a scoped exclusion. | Saving queries can increase live state, movement, precision or cleanup. General synthesis may be intractable; stationary fanout bounds do not settle changing sources. | Solve two changing-source contacts with bounded scratch, beyond the [stationary model](../dirty-fanout-cut-certificate/README.md) and [#5425](https://github.com/CrocSwap/integer-mult-bounds/pull/5425). Compare exact synthesis with cut lower bounds; stop if the instance reduces to an already solved grammar. |
+| **3. A physically admissible vector decoder** | [Fractional Haemers methods](https://arxiv.org/abs/1802.00476) permit noncommuting block actions that could escape scalar restrictions and support several geometries. | Transport, copying and restoration can outweigh a block-rank advantage. The [fixed paired-plane mask](../paired-plane-block-rank/README.md) already has an all-field `49d` floor. Dense embeddings can inflate payload volume quadratically. | Change the mask or legal side information; test exact dimension-two blocks with a complete physical invoice. Stop if an O(N) payload requires an N² dense child or the optimistic complete bill loses. |
+| **4. Paid-cost optimal decoder factorizations** | [Operator sparsification](https://arxiv.org/abs/2008.03759) motivates optimizing supports, pairing ranks and endpoints jointly. Overcomplete factors may be cheaper than rank-minimal factors. | Extra terms can worsen preparation or precision. The [product-plane comparison](https://github.com/CrocSwap/integer-mult-bounds/discussions/1587) improved pairing cost but failed its tested serial native screen. PSD restrictions can exclude valid indefinite fits. | Reconstruct the 15,232 versus 15,552 pairing comparison, then price a changed native realization. Stop before expanding the geometry search if a favorable complete relaxation already fails. |
+| **5. A profitable multitype recursive supplier** | Plain, encoded and history-bearing states could form a contracting cycle, certified by an adapter-inclusive `M(C)v < v`. The [positive-vector theorem](../kappa-action-theory/volumes/04-analytic.md) already exists; the opportunity is a physical instance. | Weights do not eliminate conversion, return or volume costs. The [phase accumulator](../phase-accumulator-tensor-closure/README.md) closes two levels but has a critical optimistic bill before wrappers. | Derive real child-size lists and every adapter for one representation pair; require strict contraction and outer admission. Stop if the types merely rename a schedule or only ordinary tolls improve. |
+| **6. Optimal productive BIT helper relations** | [Generalized Hamming weights](https://ieeexplore.ieee.org/abstract/document/133259/), code shortening and matroids suggest systematic relation-space search. BIT progress supports gains beyond the selected admitted .0034 input. | Relations can remove productive directions as well as paid operands. Every lost target needs its debit; characteristic, frames and chronology constrain legal relations. | Calibrate against [aliromman](https://github.com/aliromman)'s nine-relation [#5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421), then enumerate one bounded legal block. Stop if preparation or lost-target costs consume the gain. Its claimed BIT improvement remains predecessor evidence. |
+| **7. Precision composition for approximate suppliers** | [Stable recursive multiplication analysis](https://arxiv.org/abs/math/0603207) could provide sufficient conditions for approximate or alternative-basis suppliers, including dirty state and final exact recovery. | Lower algebraic cost can require more bits and storage. Independent error bounds may be too pessimistic; assumed correlations may be unsound. Matrix-multiplication stability does not automatically transfer to native operators. | Propagate actual magnitudes, correlated errors and rounding through a real producer, consumer and second generation. Stop if precision consumes the saving or exact recovery lacks a proof. A better condition number alone is insufficient. |
+| **8. Compact all-width native identity certificates** | [Noncommutative identity testing](https://arxiv.org/abs/1511.03730) suggests a restricted symbolic language and small checker covering phases, spectators and inverses, potentially discharging part of `native_all_columns`. | Tractable languages may omit needed operations. Free-algebra identities and concrete address operators have different hypotheses; a sound representation/lifting theorem is essential. | Extend one named operation beyond the [four-width class](https://github.com/CrocSwap/integer-mult-bounds/discussions/5354) or [p19 lift](https://github.com/CrocSwap/integer-mult-bounds/pull/5270). Test exponent, order, phase and spectator mutations. Stop at an unsupported lifting implication; additional finite widths do not prove it. |
+| **9. A contract-aware paid-profile superoptimizer** | [Equality saturation](https://arxiv.org/abs/2004.03082) could discover coordinated noncommuting graph changes and emit literal replacements with equivalence certificates. | Local expression costs can reward illegal sharing or omit target, ownership and restoration costs. Search spaces grow quickly; fewer scalar instructions need not improve the recursive invoice. | Extend [commuting rewrites](../paired-swap-normal45/README.md) and [projection cuts](../projection-cut-toolkit/README.md) on one small paid neighborhood. Require a changed complete signed invoice and proof of equivalence; stop if all candidates preserve that invoice. |
+| **10. A uniform fixed-tape mixed-target compiler theorem** | Constructive completion, splitting, normalizer generation, ownership and movement bounds could reduce inherited assumptions for every later supplier. [I/O complexity](https://www.eecs.harvard.edu/~htk/publication/1981-stoc-hong-kung.pdf) helps expose access costs. | A slower foundation project with limited immediate κ upside. RAM lookup or abstract routing can conceal uniform-generation and tape costs; overly general hypotheses may be hard to instantiate. | Extend [#4192](https://github.com/CrocSwap/integer-mult-bounds/pull/4192) through one uncovered completion/splitting pass with metadata, source reads and head returns charged. Stop at a precise unabsorbed cost or uniformity gap. Analytic recovery remains separate. |
+
+## Portfolio tradeoffs
+
+**1, 6 and 4** are the suggested construction starting points: changed complex endpoints, complementary BIT progress and paid-cost geometry. **5** offers a structural alternative when immediate format restoration remains too expensive. These routes have substantial upside and can still fail their complete-cost gates.
+
+**2, 8 and 9** offer reusable optimization or verification results with less dependence on a new profitable geometry. Scoped negative outcomes can retain value, although infrastructure alone does not raise κ. **7** should accompany approximate constructions; **10** merits a separate foundation effort with a named lemma and budget. Existing active scopes should be checked before assignment.
+
+The decisive comparison is the whole caller: a query saving can return as cleanup, a complex gain can expose the BIT bottleneck, and a low-rank factor can require an expensive physical realization. The [detailed assessment](README.md) records these dependencies and the evidence that would justify expanding each family.
+
+## Nearest overlapping work
+
+- [#5419](https://github.com/CrocSwap/integer-mult-bounds/pull/5419): literature-informed coupled consumers and catalytic junctions. Target 1 extends its missing observer/two-generation obligations; another inverse-only result would duplicate covered work.
+- [#5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421), by [aliromman](https://github.com/aliromman): nine owned BIT relations, claiming ordinary saving .0034441226396. Target 6 seeks a general legal relation-selection method; it does not claim this predecessor's improvement.
+- [#5424](https://github.com/CrocSwap/integer-mult-bounds/pull/5424) and [#5425](https://github.com/CrocSwap/integer-mult-bounds/pull/5425), by [Clear1nsight](https://github.com/Clear1nsight): the optimistic Global120 allowance and scoped standalone fanout optimum. Unearned outputs remain unearned, and a standalone bound does not determine incremental cost at a global cut.
+- [#5427](https://github.com/CrocSwap/integer-mult-bounds/pull/5427): frozen-word observation and paid-response reuse exclusions. Target 1 requires a changed contract or producer; a repeat search within the excluded grammar is not proposed.
+
+The [overlap snapshot](OVERLAP.json) covers **316 open PRs, 4,707 discussion records and 7,376 local note records**. Its coverage excludes arbitrary diffs, all historical PR bodies and unpublished work. The contribution is a cross-family assessment with bounded diagnostics; overlapping submissions retain their stated evidence status and have not been independently admitted here.
+
+## Diagnostic evidence
+
+The [probe](probe.py) uses the complete selected histograms: **64,260 paid jobs**, **10,928 productive fields**, and exact rank-mass surplus **752**. For `F(C) = Σ_targets n_r r^(1-C) − Σ_paid n_r r^(1-C)`:
+
+| Candidate saving C | Approximate raw deficit | Isolated H1 deletions for positive raw margin, all else fixed |
+|---|---:|---:|
+| .0033 | 67.256506 | 68 |
+| .0034 | 91.898559 | 92 |
+| .004 | 239.525048 | 240 |
+| .006 | 728.828475 | 729 |
+| .01 | 1694.706712 | 1695 |
+
+These are numerical necessary screens **before compiler reserves, physical feasibility and outer admission**. Decimal powers use 65 significant digits without outward error bounds. The counts exhibit no legal deletions and do not transfer to changed profiles. The selected 144 paid/target H8 pairs cancel; every new target needs a producer and every lost target its full debit.
+
+A second, exact scalar diagnostic computes `rank([S; H]) − rank(S)` for available answers `Sz` and demanded answers `Hz`. It detects missing linear information, including correlated responses, source-version changes and Q/F2 differences. Native frames, oracle legality, acquisition, volume and restoration remain outside this scalar model.
+
+```sh
+python3 -B scripts/research_selected_baseline.py
+python3 -I -B research/outside-input-research-targets/probe.py --check-source-root .
+python3 -O -I -B research/outside-input-research-targets/probe.py --check-source-root .
+```
+
+On **CPython 3.14.5, macOS 26.5.1, arm64**, normal, optimized and portable runs matched byte-for-byte. The custom-cut control passed; an altered histogram with unchanged source pins rejected under optimized Python. [PROFILE.json](PROFILE.json), [RESULT.json](RESULT.json) and [VALIDATION.json](VALIDATION.json) retain source bindings, output and checks. The selected metadata baseline passed. Native engines, the full selected replay, Lean, Docker, SDP, heavy censuses and hosted CI were not run; their obligations remain outside these diagnostics.
+
+## Credit
+
+The selected foundation retains [Chris R / Clear1nsight](https://github.com/Clear1nsight)'s completion and audits ([#5413](https://github.com/CrocSwap/integer-mult-bounds/pull/5413), [#5414](https://github.com/CrocSwap/integer-mult-bounds/pull/5414), [#5407](https://github.com/CrocSwap/integer-mult-bounds/pull/5407)); [Dillon Amburgey / dillona](https://github.com/dillona)'s provider ([#5402](https://github.com/CrocSwap/integer-mult-bounds/pull/5402)); [Ali Romman / aliromman](https://github.com/aliromman)'s controller ([#5398](https://github.com/CrocSwap/integer-mult-bounds/pull/5398)); [Cao Yifan / intqwq](https://github.com/intqwq)'s native construction ([#4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)); [Dugongue](https://github.com/Dugongue)'s completion; [Cinna Davis / 1337isnot1337](https://github.com/1337isnot1337)'s controllers/helpers; [zxv](https://github.com/zxv)'s native/compiler/precision machinery; and [Jacob Alan Sussman / Mister-Meeseeks](https://github.com/Mister-Meeseeks)'s mixed-target recursion. The [contributor map](../../docs/research/community-neutral5413-contributors.md) preserves the cumulative BIT, Clifford, geometry, ownership, analytic and verification lineage.
+
+Literature attribution appears in the linked papers and detailed assessment. New prose and probe code are **Apache-2.0, with substantial OpenAI Codex assistance**. Proposed applications do not claim invention of the underlying theories or independent human/formal verification.
+
+## Open next questions
+
+- Can a changed coupled producer earn its observation and close two generations within the combined allowance?
+- Can relation-space optimization improve [#5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421)'s witness after preparation and target debits?
+- Can the product-plane factorization's pairing advantage survive a changed native implementation?
+- Which missing primitive can extend the all-width certificate class with a sound representation theorem?
+
+The table gives the first test and stopping condition for each direction; the [detailed assessment](README.md) expands their blockers and follow-ups.
diff --git a/research/outside-input-research-targets/PROFILE.json b/research/outside-input-research-targets/PROFILE.json
new file mode 100644
index 0000000000..09a0c3ec69
--- /dev/null
+++ b/research/outside-input-research-targets/PROFILE.json
@@ -0,0 +1,55 @@
+{
+  "attribution": "Selected PR5413 by Chris R / Clear1nsight, Dillon Amburgey PR5402 provider, Ali Romman PR5398 controller, Cao Yifan native, Cinna Davis and retained predecessor/compiler/geometry/BIT lineage. See docs/research/community-neutral5413-contributors.md.",
+  "base_commit": "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700",
+  "paid": {
+    "1": 41154,
+    "16": 448,
+    "2": 7416,
+    "24": 448,
+    "3": 9180,
+    "32": 448,
+    "4": 2286,
+    "40": 448,
+    "48": 448,
+    "5": 720,
+    "56": 448,
+    "64": 448,
+    "72": 224,
+    "8": 144
+  },
+  "schema": "outside-input-diagnostic-profile/1",
+  "scope": "Frozen histogram excerpt only; probe calculations are heuristic numerical diagnostics, not source admission or a theorem replay.",
+  "selected_kappa": "0.003027288235",
+  "sources": [
+    {
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "path": "certificates/selected-result.json",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    },
+    {
+      "git_blob": "d66216ad80b502c4042979269655bacb9f6668b9",
+      "path": "research/coupled-helper-neutral-completion/reports/expected/invoice.json",
+      "sha256": "e7df9fe1a7a00f67bbf35e9b155537fd26a0c05b61788653b878bd84d9006450"
+    },
+    {
+      "git_blob": "ffc2de2792f51111f73500be3a2e4e8f6bf55a57",
+      "path": "research/coupled-helper-neutral-completion/reports/expected/funding.json",
+      "sha256": "70ab7d13548962097ad83ad393b8482f52e827b8996869011ce6d071146bd3eb"
+    }
+  ],
+  "targets": {
+    "145": 224,
+    "17": 448,
+    "25": 448,
+    "33": 448,
+    "4": 504,
+    "41": 448,
+    "49": 448,
+    "57": 448,
+    "65": 448,
+    "7": 126,
+    "73": 224,
+    "8": 990,
+    "9": 5724
+  }
+}
diff --git a/research/outside-input-research-targets/README.md b/research/outside-input-research-targets/README.md
new file mode 100644
index 0000000000..2c54c7010d
--- /dev/null
+++ b/research/outside-input-research-targets/README.md
@@ -0,0 +1,175 @@
+# Ten reusable research targets beyond the selected κ regime
+
+Observation access, restoration, physical realization and precision can prevent a useful local identity from becoming a profitable complete supplier. These ten proposed research results target those recurring boundaries. The ranking emphasizes reuse across searches. New prose and probe code: Apache-2.0, with substantial OpenAI Codex assistance.
+
+The source checkpoint is canonical main **`1a3ced60b2f7a46bc70280a04f2eeb8ca027c700`**, fetched October 24, 2026. Its selected conditional result is **κ = 0.003027288235**, from [Chris R / Clear1nsight](https://github.com/Clear1nsight)'s [PR5413](https://github.com/CrocSwap/integer-mult-bounds/pull/5413) with [Dillon Amburgey](https://github.com/dillona)'s [PR5402](https://github.com/CrocSwap/integer-mult-bounds/pull/5402) provider, [Ali Romman](https://github.com/aliromman)'s [PR5398](https://github.com/CrocSwap/integer-mult-bounds/pull/5398) controller, [Cao Yifan](https://github.com/intqwq)'s native construction, the [PR5407](https://github.com/CrocSwap/integer-mult-bounds/pull/5407) and [PR5414](https://github.com/CrocSwap/integer-mult-bounds/pull/5414) audits and the retained [Cinna Davis](https://github.com/1337isnot1337), [zxv](https://github.com/zxv), [Jacob Alan Sussman](https://github.com/Mister-Meeseeks), BIT, geometry and analytic lineages. The selected ordinary BIT saving is **0.0034363538396**, conservatively admitted as **0.0034**; the binding outer row is `main_transform`. Read the [selected record](../../certificates/selected-result.json) and its linked review for the five retained framework assumptions. Historical fixed-inventory ceilings and the balanced `a/(1+a)` conversion are not bounds on this mixed-target interface.
+
+The fast source-bound baseline passed. No full selected replay was needed for this proposal report. The local probes below are independent arithmetic/information diagnostics, not supplier admission.
+
+**What the probes say.** For the selected complete paid/target histograms, define the raw necessary margin
+
+`F(C) = Σ_targets n_r r^(1-C) − Σ_paid n_r r^(1-C)`.
+
+The exact rank-mass surplus at C=0 is **752**, with **64,260 paid jobs** and **10,928 productive fields**. The numerical raw deficits are approximately:
+
+| Candidate saving C | Selected-profile raw deficit | H1 deletions needed to make this raw margin positive, all else fixed |
+|---|---:|---:|
+| 0.0033 | 67.256506 | 68 |
+| 0.0034 | 91.898559 | 92 |
+| 0.004 | 239.525048 | 240 |
+| 0.006 | 728.828475 | 729 |
+| 0.01 | 1694.706712 | 1695 |
+
+These are numerical necessary screens **before compiler reserves and admission**. They do not show that such deletions exist, and they are not transferable to a changed profile. The current neutral 144 paid/target H8 pairs cancel. A new helper or lost target must be included with its sign. [PR5423](https://github.com/CrocSwap/integer-mult-bounds/pull/5423)'s eight-H1 saving concerns another local interface and is not subtracted here. Reaching C=.004 on the complex side alone would also leave a BIT bottleneck under the selected outer interface.
+
+1. **An encoded-output supplier with an internally produced observer and bounded history.**
+
+   **Target result:** a literal changed provider/caller that produces the current-version observation it needs, consumes encoded rather than immediately decoded outputs, closes at least two recursive generations, and returns every borrowed response and owned field correctly. The complete signed invoice must improve an explicit saving point. A small exact reusable composition theorem should accompany the first instance, stating which downstream observations suffice and how deferred restoration is charged.
+
+   **Outside input:** minimal realization and observability distinguish an internal state from what a consumer must observe. [Kalman's original realization paper](https://people.duke.edu/~hpgavin/SystemID/References/Kalman-JSIAM-1963.pdf) provides that distinction; it provides no native supplier or restoration discount. Locality-aware index coding similarly treats the cost of obtaining the demanded observations rather than assuming access to the entire codeword: [Natarajan, Krishnan, Lalitha and Dau](https://arxiv.org/abs/1910.08745).
+
+   **Why many searches would use it:** it changes the endpoint requirement that currently forces repeated decoding and restoration. This could unlock whole families, whereas another inverse formula would not.
+
+   **Existing work and first gate:** build on [PR5419's 25-paper synthesis](https://github.com/CrocSwap/integer-mult-bounds/pull/5419), [Dugongue](https://github.com/Dugongue)'s completion and [Dillon](https://github.com/dillona)'s coupled provider. The newly read [PR5427](https://github.com/CrocSwap/integer-mult-bounds/pull/5427) reports that `ZQY` and reusable paid responses are absent in the frozen words within its declared free-word grammar. Thus the next experiment must change the producer, paid observation or contract. Start at one actual FULL/thin-query cut; retain all independent original modes and both source versions. Stop if the needed observation has no legal producer or its complete cost exhausts the allowance. The existing Global120 point budget [PR5424](https://github.com/CrocSwap/integer-mult-bounds/pull/5424) is an optimistic bound, not earned outputs.
+
+   **Assessment:** strongest direct complex-side opportunity, with substantial construction risk. It is active predecessor work to extend or independently test, not a newly discovered vacant assignment.
+
+2. **A restoration-aware time–space–query frontier for dirty linear programs.**
+
+   **Target result:** for a useful stated class of source-versioned linear programs, compute a Pareto frontier of paid query moment, peak live state, ordinary operations and precision growth. Emit an attaining program plus a separately checkable lower bound. Distinguish reusable borrowed dirt from owned state that may be erased. The goal is an optimality result beyond a stationary single-oracle fanout grammar, allowing changing sources and legal recomputation.
+
+   **Outside input:** reversible pebbling supplies the compute/uncompute view; I/O pebbling charges obtaining data. [Parent, Roetteler and Svore](https://arxiv.org/abs/1510.00377) demonstrate dependency-aware reversible compilation, and [Hong–Kung](https://www.eecs.harvard.edu/~htk/publication/1981-stoc-hong-kung.pdf) supply a model for data movement. Neither model automatically charges the repository's native frames or recursive oracle tariffs.
+
+   **Why many searches would use it:** useful memory is repeatedly mistaken for free memory, and a shorter local word can create an expensive global return. A frontier would let each candidate choose a feasible space/price tradeoff before implementing a complete caller.
+
+   **Existing work and first gate:** preserve the exact stationary result in [dirty-fanout-cut-certificate](../dirty-fanout-cut-certificate/README.md) and the scoped 112-call bound in [PR5425](https://github.com/CrocSwap/integer-mult-bounds/pull/5425). Start with two actual contacts and a small finite scratch limit, using exact shortest-path synthesis and independent cut lower bounds. Require an example whose source changes between contacts; otherwise this merely repeats stationary fanout. An exponential finite search is acceptable for the first bounded result; no generic polynomial algorithm is assumed.
+
+   **Assessment:** high reuse value even if it yields a scoped negative theorem rather than a new κ.
+
+3. **A physically admissible vector index code with a genuine block advantage.**
+
+   **Target result:** a rational or binary block decoder that improves the complete cost over the best scalar implementation for a **changed, explicitly named** mask, with arbitrary payload columns, legal native frame transport, volume proportional to the actual payload, and full restoration. A block fitting matrix alone is the algebraic certificate; the sought research result includes the physical realization and its favorable invoice.
+
+   **Outside input:** [Bukh and Cox's fractional Haemers framework](https://arxiv.org/abs/1802.00476), crediting Blasiak, searches rank per block dimension rather than scalar minrank. [Vector network coding](https://arxiv.org/abs/1512.06352) gives independent motivation for non-scalar linear actions. Neither guarantees a useful repository instance.
+
+   **Why many searches would use it:** successful block actions could escape scalar or commuting-projection restrictions and provide a reusable decoder backend for new geometries.
+
+   **Existing work and first gate:** [paired-plane-block-rank](../paired-plane-block-rank/README.md) already proves `49d` for every field/block size on its fixed mask; enlarging d there does not help. Odd cycles, unequal payloads and the seven-vertex theta mask have additional completed capacity results. Change the actual mask or source side information and pin it. Test d=2 first with exact noncommuting blocks and a complete volume ledger. Reject dense embeddings requiring a child of volume N² to represent O(N) original data; a sparse service would require a new proved ABI.
+
+   **Assessment:** high structural upside; physical realization is the principal risk, not finding a low-rank numerical matrix.
+
+4. **A decoder factorization theory that minimizes paid cost, including overcomplete factors.**
+
+   **Target result:** characterize or construct `M = Σ_j u_j v_j^T` minimizing the **actual sum of binary pairing ranks and endpoint costs**, with signed target losses, rather than minimizing only `rank(M)` or the number of summands. Produce a reusable optimizer and a scoped lower certificate, then one changed geometry whose complete caller passes.
+
+   **Outside input:** [Beniamini, Cheng, Holtz, Karstadt and Schwartz](https://arxiv.org/abs/2008.03759) study sparsifying operators of fast bilinear algorithms. This motivates searching bases and factors jointly, while their arithmetic objective must be replaced by the repository's paid frame/decoder objective. [Higher-point coding bounds](https://arxiv.org/abs/1812.06045) suggest symmetry-reduced exclusion screens for suitable geometric subclasses. PSD assumptions apply only to the declared real Gram subclass; general fitting matrices can be indefinite or nonsymmetric.
+
+   **Why many searches would use it:** a rank-minimal factor need not have the cheapest support pattern. The October 24 product-plane discussion already reports an overcomplete pairing tariff **15,232** versus **15,552** for its tested rank-minimal factor, followed by a failed serial native cost screen. This is motivation, not an admitted improvement.
+
+   **Existing work and first gate:** retain [line-system-saturation](../line-system-saturation/README.md), existing lattice/polynomial kernels and the [product-plane handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/1587). Calibrate the optimizer against that exact pair of factorizations; then price a changed native realization. Stop if the optimistic **complete** moment already fails. Another rank count, new shell size or better scalar factor alone is not the target result.
+
+   **Assessment:** a strong route for importing geometry and algebra while learning from an already discriminating local example.
+
+5. **A fully charged supplier with genuinely different recursive representation types.**
+
+   **Target result:** an actual two- or three-type recursive construction, such as plain, encoded and history-bearing states, with real child-size lists, complete conversion/return charges and a positive rational vector satisfying `M(C)v < v`. It must improve the admitted result relative to the best applicable one-type implementation and survive the outer reduction.
+
+   **Outside input:** positive-matrix/Lyapunov certificates price different states differently; type weights can make a full cycle contract even when one row sum exceeds one. This is established mathematics, and the repository **already has** A051–A056 in [kappa-action-theory](../kappa-action-theory/volumes/04-analytic.md). The open result is a physical instantiation, not another proof of Perron–Frobenius theory.
+
+   **Why many searches would use it:** it removes the demand that every locally useful representation immediately convert back to one universal format. Several individually losing interfaces could participate in a favorable, correctly priced cycle.
+
+   **Existing work and first gate:** [idea-a-spectral-radius-screen](../idea-a-spectral-radius-screen/README.md) explains why the tested 3|7 macro is only a finite scheduling saving, not a multitype supplier. [phase-accumulator-tensor-closure](../phase-accumulator-tensor-closure/README.md) already supplies a real two-operation, two-level closure whose optimistic bill is critical before wrappers. A successor must change that bill or use another real representation pair. Derive the transition matrix from emitted jobs and include all adapters. Stop if the two proposed types differ only in labels, or if the necessary contraction fails. Never average independently computed seed exponents; [scale-dependent-seed-moment-audit](../scale-dependent-seed-moment-audit/README.md) supplies a counterexample.
+
+   **Assessment:** high upside and high usefulness, conditional on finding real cross-type transitions.
+
+6. **An optimal relation-selection theorem for productive BIT helpers.**
+
+   **Target result:** select a legal subspace of helper relations that makes expensive recursive operands zero or dependent, while preserving independent productive inputs and explicitly debiting every lost target. Optimize the complete signed moment, with per-port frame and ownership constraints. Return the actual reverse word and a certificate of the selected relation space, preferably with a sharp optimum for a useful family.
+
+   **Outside input:** [Wei's generalized Hamming weights](https://ieeexplore.ieee.org/abstract/document/133259/) organize the support obtainable by subspaces of a linear code. Shortening, relative support weights and matroid representations suggest a systematic replacement for independent zero-operand guesses. The repository adaptation has weighted, chronological and physical constraints, so ordinary code weights alone do not solve it.
+
+   **Why many searches would use it:** BIT improvements are necessary for a sustained move past the selected admitted .0034 input, and this turns a successful local idea into a search primitive for many words.
+
+   **Existing work and first gate:** [Ali Romman](https://github.com/aliromman)'s pending [PR5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421) already claims nine owned relations and ordinary BIT saving **0.0034441226396**, admitting .00344412; it is not a complete new multiplication κ. Preserve that credit and use its nine-relation witness as a positive control. Enumerate legal relation spaces on one bounded connected block, separately over F2 and Q as appropriate. Require the saved paid calls and all lost productive directions in the same invoice. A duplicated input basis or a helper set to zero without its target debit is a rejection, not a win.
+
+   **Assessment:** especially useful companion to complex-side exploration; the recent witness makes the first calibration concrete.
+
+7. **A precision composition theorem for approximate recursive suppliers with dirty state.**
+
+   **Target result:** given a typed word, derive internal magnitude bounds, correlated error propagation, rounding points, required bits and storage, and the resulting recursive cost. Include source encoding, borrowed dirt, the consumer and final exact recovery. The useful theorem would state when an approximate, encoded or degenerate local algorithm retains a favorable exponent after these costs.
+
+   **Outside input:** [Demmel, Dumitriu, Holtz and Kleinberg](https://arxiv.org/abs/math/0603207) analyze stable recursive matrix multiplication. The much newer [arbitrary-precision approximate matrix multiplication paper](https://arxiv.org/abs/2610.13905) is another lead, not a checked transplant. Those theorems do not establish stability or cost of this Gaussian/native supplier.
+
+   **Why many searches would use it:** it makes approximate or alternative-basis ideas testable and could replace repeated ad hoc guard arguments with a reusable sufficient criterion. It can also reject a numerically impressive circuit before a large implementation.
+
+   **Existing work and first gate:** [PR5419](https://github.com/CrocSwap/integer-mult-bounds/pull/5419) already covers gauge optimization and warns that the non-nilpotent `ZW=14I` cycle cannot simply be made small by similarity. Do not repeat a condition-number-only scan. Start from one real producer and propagate the **actual correlated** defects through one consumer and then a second generation. Test independent dirty inputs and explicit rounding; compare the complete precision-weighted invoice. Stop if the required precision consumes the saving or the recovery hypothesis is unproved.
+
+   **Assessment:** broad reuse and a possible gateway to a genuinely new regime, with no generic promise that border-rank ideas transfer.
+
+8. **Small symbolic certificates of native identities valid at every column width.**
+
+   **Target result:** a decidable, explicitly restricted operator language with a sound map to the native phase/address operators at every positive column multiplicity. Emit compact identity certificates that a small checker can verify, including spectators, inverse orientation, phases and ownership adapters. A proof for the selected operator class could discharge a meaningful part of the `native_all_columns` assumption.
+
+   **Outside input:** [Garg, Gurvits, Oliveira and Wigderson](https://arxiv.org/abs/1511.03730) give algorithms for noncommutative symbolic invertibility and rational identities. That motivates exact symbolic reasoning, but free-skew-field identities and concrete native representations have different hypotheses. The representation/lifting theorem is essential.
+
+   **Why many searches would use it:** every new word needs reliable all-width validation. A compact proof interface would make searches safer and reduce the cost of independently reviewing their outputs.
+
+   **Existing work and first gate:** [Discussion 5354](https://github.com/CrocSwap/integer-mult-bounds/discussions/5354) already reports four-width sufficiency in its affine-quadratic class, and [PR5270](https://github.com/CrocSwap/integer-mult-bounds/pull/5270) proposes a p19 lifting argument. The next result must cover a named operation or composition missing from those classes. Test exponent two, reversed noncommuting factors, phase/spectator mutations and a word that passes small-width evaluation while failing the proposed symbolic rule. A random small-bank replay is a control, not the all-width proof.
+
+   **Assessment:** one of the strongest infrastructure targets; it improves confidence rather than automatically increasing κ.
+
+9. **A contract-aware superoptimizer that extracts paid-profile improvements.**
+
+   **Target result:** equality saturation or counterexample-guided synthesis over typed noncommuting words, with shared-DAG extraction and an objective containing the full signed recursive invoice, retained targets, ownership, frame transitions and precision. Emit a literal replacement and a checkable equivalence proof. A useful first publication would find one improvement missed by commuting-only rewrites and explain the new rule's exact domain.
+
+   **Outside input:** [Willsey and colleagues' egg](https://arxiv.org/abs/2004.03082) supplies the equality-saturation architecture. Its standard expression costs do not automatically model shared histories, whole-program restoration or nonlinear moment objectives; those are the research work.
+
+   **Why many searches would use it:** it expands the search from seed changes and adjacent swaps to coordinated graph changes, with a common output format for independent validation.
+
+   **Existing work and first gate:** [paired-swap-normal45](../paired-swap-normal45/README.md) already investigated bounded commuting rewrites, and [projection-cut-toolkit](../projection-cut-toolkit/README.md) gives exact joint frame optimization for its fixed graph. Reuse both rather than relabeling them. Start with a small paid neighborhood where a noncommuting identity changes the graph. Optimize the paid profile before ordinary instruction count. Stop if every extracted word retains the same signed invoice; scalar savings alone do not meet this target.
+
+   **Assessment:** high tool reuse; the central risk is a cost model that rewards an illegal or economically neutral rewrite.
+
+10. **A uniform fixed-tape implementation theorem for mixed-target compilation.**
+
+   **Target result:** turn a finite typed, fully priced template into a uniform implementation with constructive completion/splitting, real normalizer generation, owner allocation/erasure, sequential movement, bounded precision and explicit coefficients in the recurrences. Prove the exact sufficient hypotheses, and instantiate them on the selected template or a changed one. This should discharge a specified portion of the selected `compiler`, `owned_erasure` and `precision_tape` premises; analytic recovery remains a separate theorem.
+
+   **Outside input:** uniform circuit compilation, reversible dependency scheduling and communication-cost models suggest the proof structure. [Hong–Kung](https://www.eecs.harvard.edu/~htk/publication/1981-stoc-hong-kung.pdf) is useful for exposing movement obligations, not for proving linear-tape access or granting random lookup. A RAM or I/O upper bound is not a fixed-tape Turing-machine upper bound.
+
+   **Why many searches would use it:** an explicit sufficient interface would let future constructors know exactly what must be supplied and prevent a large class of finite-certificate-to-all-size gaps. Removing an inherited assumption could be more significant than a tiny conditional exponent increase.
+
+   **Existing work and first gate:** this extends the pinned mixed-target and compact-control work, not a claim that no compiler proof exists. [PR4192](https://github.com/CrocSwap/integer-mult-bounds/pull/4192) already audits Beneš compilation with sequential arena scans, and [PR4100](https://github.com/CrocSwap/integer-mult-bounds/pull/4100) has separately tracked unconditional CRT/native/precision/tape claims. Choose one uncovered lemma and its actual caller before expanding. Begin with one chronological completion/splitting pass, including metadata generation, head returns and all source reads. If its cost cannot be absorbed under the declared recurrence, deliver that scoped gap. Do not relaunch the entire historical proof/replay stack.
+
+   **Assessment:** strongest foundational target in this list; slower to complete, but potentially useful to every future construction.
+
+**Suggested starting order.** For immediate exponent exploration, take **1, 6 and 4**, with **5** as the structural alternative to forcing each call back to one format. For reusable results with less dependence on a successful new geometry, take **2, 8 and 9**. Target **7** should accompany any approximate construction, and **10** is a separate foundation project. This is an assessment, not an instruction to change the standing task catalogue or reserve another contributor's active task.
+
+**Probes and reproduction.** [probe.py](probe.py), [PROFILE.json](PROFILE.json) and [RESULT.json](RESULT.json) are local, exploratory artifacts. They use only Python's standard library. The three original source hashes and Git blob IDs are in PROFILE.json; the originating canonical commit is explicit. The frozen histogram excerpt can be used without a Git checkout. `--check-source-root` optionally authenticates it against the three source files at the pinned checkout.
+
+```sh
+python3 -I -B research/outside-input-research-targets/probe.py --check-source-root .
+python3 -O -I -B research/outside-input-research-targets/probe.py --check-source-root .
+```
+
+Normal and optimized output matched byte-for-byte on CPython **3.14.5** on Darwin, including portable temporary-directory runs without repository inputs. A custom-cut CLI control passed, and an altered histogram with unchanged source pins rejected under optimized Python. [VALIDATION.json](VALIDATION.json) records the environment, checks and result hash. Decimal powers use 65 significant digits but are **not** outward-rounded interval proofs. Raw moment sign change is a diagnostic only; more digits of that same profile are not an improved result. The baseline source check is source/metadata orientation only. No native operator engine, full selected replay, Lean, Docker, numerical SDP or heavy census was run.
+
+The second probe is exact row-space algebra. For independent latent coordinates z, already available answers `Sz` and demanded answers `Hz`,
+
+`d = rank([S; H]) − rank(S)`
+
+is the dimension of the missing scalar linear information. Each new scalar linear answer supplies at most one dimension, so d is a lower bound. Arbitrary unconstrained linear queries could attain it; native queries, legal coefficients, source versions, acquisition cost and restoration can make the actual cost larger. Raw untransformed inputs must not be listed as free transformed responses. The probe is deliberately not a group-algebra or all-width verifier.
+
+Synthetic controls need **4** answers with no side information but **2** after two correlated answers are legally available. Two new independent source-version defects still need **2** answers even when all four old outputs are retained. A characteristic control gives rank **2 over Q** and **1 over F2**, preventing a silent cross-field substitution. An even-denominator F2 input rejects. All controls use explicit checks retained under `-O`.
+
+To screen a new scalar cut, provide a JSON file with `width`, `field` (`Q` or `F2`), `available` and `demanded` row arrays, using integers or rational strings, and pass `--cut /absolute/path/to/cut.json`. The output includes an independent demand-row basis for the quotient. Exact row counts do not establish a legal observer or recursive saving.
+
+**Overlap and evidence limits.** The start-here discussion, newest handoffs, mechanism-proposal thread, recent discussions and current PR bodies were read. The cached `complex-rank-shape-decoder` search covered **316 open PRs, 4,707 discussion records and 7,376 local note records**, with complete pagination/head-note inventory at the time shown in [OVERLAP.json](OVERLAP.json). It does not search arbitrary code diffs, all historical PR bodies or unpublished work. Directly read active PRs include 5270, 5418–5421 and 5423–5427. Proposed targets deliberately credit overlap; no priority, novelty or independent mathematical acceptance is claimed. Literature citations support the imported concepts, not the proposed repository applications.
+
+**Open next questions.**
+
+- Can a changed coupled producer earn its observation at an actual first cut and close a second generation? This decides target 1. First derive its full endpoint and legal source versions; observation production, independent modes, target preservation and the combined invoice are blockers.
+- Does relation-space optimization beat the existing nine-relation BIT witness after target debits? This decides target 6. First pin [PR5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421)'s exact word and enumerate one bounded legal block; frame transport, independent columns and complete compiler/outer admission remain separate obligations.
+- Can an overcomplete factor's support advantage survive a changed native realization? This decides target 4. First reconstruct the published product-plane tariff comparison and price its replacement physical path; a favorable rank or scalar identity cannot pay for the missing path.
+- Which new operation can extend the existing all-width certificate class? This decides target 8. First identify one rejected but needed primitive/composition and prove its representation map; arbitrary finite-width testing is not a substitute.
+
+The ten targets are the deliverable of this session. None of their still-open construction or proof obligations has been marked complete.
diff --git a/research/outside-input-research-targets/RESULT.json b/research/outside-input-research-targets/RESULT.json
new file mode 100644
index 0000000000..729d590d87
--- /dev/null
+++ b/research/outside-input-research-targets/RESULT.json
@@ -0,0 +1,154 @@
+{
+  "base_commit": "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700",
+  "moments": {
+    "decimal_precision": 65,
+    "neutral_144_H8_paid_target_cancellation": true,
+    "numerical_raw_sign_change_bracket": [
+      "0.0030272882499395587812724623905386986018790387519973014490357043904",
+      "0.0030272882499395587812724623905544758199834589881055360203413601150"
+    ],
+    "paid_jobs_exact": 64260,
+    "points": [
+      {
+        "C": "0.003027288235",
+        "alternative_extra_targets_equivalent_to_raw_deficit": {
+          "145": "0E+62",
+          "16": "0E+63",
+          "25": "0E+63",
+          "8": "0E+64",
+          "9": "0E+64"
+        },
+        "d_margin_d_C": "-246768.15315353109672903453450177612919620286791774985582970802808",
+        "isolated_H1_deletions_to_cross_zero": 0,
+        "local_dC_per_removed_H1_at_this_point": "0.0000040523867736605080245896575070252766428840649133717442689768178821",
+        "raw_deficit_to_zero_before_reserves": "0",
+        "raw_target_minus_paid": "0.00000368660732926292801723995353114943041602864431062019267"
+      },
+      {
+        "C": "0.0033",
+        "alternative_extra_targets_equivalent_to_raw_deficit": {
+          "145": "0.47151858465757583427150721443885387029269948839244153328321150482",
+          "16": "4.2421685117705233758330028676981275564093921918502919957260508585",
+          "25": "2.7189892847615796818952077901598986145398137087790696860099410974",
+          "8": "8.4649522510722535143855282766595033113207772660139723305292658637",
+          "9": "7.5273271842025412685625044384004893423604830355724704225172366875"
+        },
+        "d_margin_d_C": "-246474.35809443177766591714878504785020857918338345643622187054839",
+        "isolated_H1_deletions_to_cross_zero": 68,
+        "local_dC_per_removed_H1_at_this_point": "0.0000040572171796340362892859599101040360163846789387261906304096946660",
+        "raw_deficit_to_zero_before_reserves": "67.25650614237805738943445737816357345686238284901222256985581",
+        "raw_target_minus_paid": "-67.25650614237805738943445737816357345686238284901222256985581"
+      },
+      {
+        "C": "0.0034",
+        "alternative_extra_targets_equivalent_to_raw_deficit": {
+          "145": "0.64459859221339135297492470730606136207447345015934913122474293603",
+          "16": "5.7980603171410145939340581225118970922036852324626136612746400242",
+          "25": "3.7163934936120267348685144286682404238055457171096333398493195793",
+          "8": "11.568824229341717349521595156299741630306721800944952800928942625",
+          "9": "10.287518253615060102562354670451835514557894291788737164897781481"
+        },
+        "d_margin_d_C": "-246366.71615630039581684723300752441174627437647759871006819626748",
+        "isolated_H1_deletions_to_cross_zero": 92,
+        "local_dC_per_removed_H1_at_this_point": "0.0000040589898489598663156715046231523129051786044997357398529835816209",
+        "raw_deficit_to_zero_before_reserves": "91.89855945693865431851670931173980037757561283060944429956344",
+        "raw_target_minus_paid": "-91.89855945693865431851670931173980037757561283060944429956344"
+      },
+      {
+        "C": "0.004",
+        "alternative_extra_targets_equivalent_to_raw_deficit": {
+          "145": "1.6851105840704049631887410144219404544437065277280176133048999117",
+          "16": "15.137265694508241592987945867075723454467002430586396319458239853",
+          "25": "9.7051597401845515800349023676517094442670497799393024583349722181",
+          "8": "30.190708821166413896765307830322674217979113379792942709886735221",
+          "9": "26.848831987266489920438534052876203201371369826069811445541221172"
+        },
+        "d_margin_d_C": "-245721.86641979476774682191205135428939706532470514294914715884360",
+        "isolated_H1_deletions_to_cross_zero": 240,
+        "local_dC_per_removed_H1_at_this_point": "0.0000040696418864554187841903710783169112153217767138711140926801035945",
+        "raw_deficit_to_zero_before_reserves": "239.52504840639124567689306984589647373409926194445299234920955",
+        "raw_target_minus_paid": "-239.52504840639124567689306984589647373409926194445299234920955"
+      },
+      {
+        "C": "0.006",
+        "alternative_extra_targets_equivalent_to_raw_deficit": {
+          "145": "5.1787570551706037738385018903575618217826470459716389710080004476",
+          "16": "46.315895930335477478987147171026868295554666252989005663067718360",
+          "25": "29.721653278545939723748392596693795586430949062303232679792991796",
+          "8": "92.247347053146405681500070011379074472238129150655711568502936798",
+          "9": "82.055609892596286110037375009742999019235593280102384387500788144"
+        },
+        "d_margin_d_C": "-243584.72004033742732834227071298610161402583538708959202496495245",
+        "isolated_H1_deletions_to_cross_zero": 729,
+        "local_dC_per_removed_H1_at_this_point": "0.0000041053478224512638992885266174103729202392063117101149999236901406",
+        "raw_deficit_to_zero_before_reserves": "728.82847532590106510098039448770237596840011440729421692400134",
+        "raw_target_minus_paid": "-728.82847532590106510098039448770237596840011440729421692400134"
+      },
+      {
+        "C": "0.01",
+        "alternative_extra_targets_equivalent_to_raw_deficit": {
+          "145": "12.284011866948687478078700813275403421531881190419381864352658872",
+          "16": "108.89696267623814551598484944015055535140686859347464705762380789",
+          "25": "70.005786786016716723176418961734379309318591712908412304902327509",
+          "8": "216.28951281931819880416107763183103968204804090253281033518185959",
+          "9": "192.48392467535186215539610549944506514810148110288011056312400894"
+        },
+        "d_margin_d_C": "-239366.86199387759822992459820150317537348685228781988115290445122",
+        "isolated_H1_deletions_to_cross_zero": 1695,
+        "local_dC_per_removed_H1_at_this_point": "0.0000041776877203059857245136281107659177138295578097226354861663596720",
+        "raw_deficit_to_zero_before_reserves": "1694.70671208342451693997939201573354929857451887160862414550428",
+        "raw_target_minus_paid": "-1694.70671208342451693997939201573354929857451887160862414550428"
+      }
+    ],
+    "productive_fields_exact": 10928,
+    "rank_mass_surplus_exact": 752,
+    "scope": "Heuristic Decimal arithmetic; no outward error bounds, uniqueness proof, compiler reserve, physical construction or kappa admission. Equivalent target counts are isolated alternatives, not additive credits. Existing targets cannot be counted again."
+  },
+  "profile_sha256": "3778cc757903c67e1456c56394c2a20a7824707f942425abf4439ae400e8a155",
+  "python": "3.14.5",
+  "status": "PASS_EXPLORATORY_DIAGNOSTICS_NO_NEW_KAPPA",
+  "synthetic_cut_controls": {
+    "all_controls_passed": true,
+    "correlated_available_responses": {
+      "additional_answer_dimension_lower_bound": 2,
+      "available_rank": 2,
+      "field": "Q",
+      "independent_latent_coordinates": 6,
+      "joint_rank": 4,
+      "residual_demand_basis_indices": [
+        0,
+        2
+      ],
+      "scope": "Exact scalar linear information deficit only. All listed available rows must already be legally accessible in the same frame/version. Does not price observation production, copying, maps, volume, approximation or restoration; does not prove a native implementation attaining the bound."
+    },
+    "field_control_F2_rank": 1,
+    "field_control_Q_rank": 2,
+    "source_version_drift": {
+      "additional_answer_dimension_lower_bound": 2,
+      "available_rank": 4,
+      "field": "Q",
+      "independent_latent_coordinates": 6,
+      "joint_rank": 6,
+      "residual_demand_basis_indices": [
+        0,
+        2
+      ],
+      "scope": "Exact scalar linear information deficit only. All listed available rows must already be legally accessible in the same frame/version. Does not price observation production, copying, maps, volume, approximation or restoration; does not prove a native implementation attaining the bound."
+    },
+    "warning": "Synthetic examples only; no selected-caller rows are claimed.",
+    "without_available_responses": {
+      "additional_answer_dimension_lower_bound": 4,
+      "available_rank": 0,
+      "field": "Q",
+      "independent_latent_coordinates": 6,
+      "joint_rank": 4,
+      "residual_demand_basis_indices": [
+        0,
+        1,
+        2,
+        3
+      ],
+      "scope": "Exact scalar linear information deficit only. All listed available rows must already be legally accessible in the same frame/version. Does not price observation production, copying, maps, volume, approximation or restoration; does not prove a native implementation attaining the bound."
+    }
+  }
+}
diff --git a/research/outside-input-research-targets/VALIDATION.json b/research/outside-input-research-targets/VALIDATION.json
new file mode 100644
index 0000000000..7514e3c612
--- /dev/null
+++ b/research/outside-input-research-targets/VALIDATION.json
@@ -0,0 +1,37 @@
+{
+  "checks": [
+    {
+      "check": "portable_normal",
+      "passed": true
+    },
+    {
+      "check": "portable_optimized",
+      "passed": true
+    },
+    {
+      "check": "custom_cut_cli",
+      "passed": true
+    },
+    {
+      "check": "forged_histogram_rejected_optimized",
+      "passed": true
+    },
+    {
+      "check": "source_bound_normal",
+      "passed": true
+    },
+    {
+      "check": "source_bound_optimized",
+      "passed": true
+    },
+    {
+      "check": "text_whitespace",
+      "passed": true
+    }
+  ],
+  "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O",
+  "python": "3.14.5 (main, May 10 2026, 10:21:34) [Clang 21.0.0 (clang-2100.0.123.102)]",
+  "result_sha256": "fe1237554a6b7d077cfc868f8abfe0bb5cf8bcb752f90c8bc0a6672734b6065c",
+  "scope": "Local standard-library diagnostics only; no native, all-width, full selected, compiler, theorem, human or formal acceptance.",
+  "status": "PASS_LOCAL_EXPLORATORY_PROBE_VALIDATION"
+}
diff --git a/research/outside-input-research-targets/probe.py b/research/outside-input-research-targets/probe.py
new file mode 100644
index 0000000000..21c5da1895
--- /dev/null
+++ b/research/outside-input-research-targets/probe.py
@@ -0,0 +1,219 @@
+#!/usr/bin/env python3
+"""Small research diagnostics; no physical, compiler or theorem admission.
+
+Decimal moments are numerical search aids, not directed interval certificates.
+Row-space ranks are exact in the declared scalar model, not native oracle costs.
+New code: OpenAI Codex for the repository user, Apache-2.0.
+"""
+
+import argparse
+from decimal import Decimal, localcontext
+from fractions import Fraction
+import hashlib
+import json
+from pathlib import Path
+import platform
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def rank(rows, width, field="Q"):
+    require(field in ("Q", "F2"), "Only Q and F2 are implemented")
+    require(all(len(row) == width for row in rows), "Inconsistent row widths")
+    a = [[Fraction(x) for x in row] for row in rows]
+    if field == "F2":
+        require(all(x.denominator % 2 for row in a for x in row),
+                "An even denominator cannot be reduced modulo two")
+        a = [[x.numerator % 2 for x in row] for row in a]
+    pivot = 0
+    for column in range(width):
+        found = next((i for i in range(pivot, len(a)) if a[i][column]), None)
+        if found is None:
+            continue
+        a[pivot], a[found] = a[found], a[pivot]
+        if field == "Q":
+            v = a[pivot][column]
+            a[pivot] = [x / v for x in a[pivot]]
+        for i in range(pivot + 1, len(a)):
+            v = a[i][column]
+            if field == "Q":
+                a[i] = [x - v * y for x, y in zip(a[i], a[pivot])]
+            else:
+                a[i] = [(x - v * y) % 2 for x, y in zip(a[i], a[pivot])]
+        pivot += 1
+        if pivot == len(a):
+            break
+    return pivot
+
+
+def cut_probe(data):
+    width, field = data["width"], data.get("field", "Q")
+    require(type(width) is int and width > 0, "width must be a positive integer")
+    available, demanded = data["available"], data["demanded"]
+    old = rank(available, width, field)
+    new = rank(available + demanded, width, field)
+    basis, selected = available[:], []
+    current = old
+    for i, row in enumerate(demanded):
+        after = rank(basis + [row], width, field)
+        if after > current:
+            basis.append(row)
+            selected.append(i)
+            current = after
+    return {
+        "field": field, "independent_latent_coordinates": width,
+        "available_rank": old, "joint_rank": new,
+        "additional_answer_dimension_lower_bound": new - old,
+        "residual_demand_basis_indices": selected,
+        "scope": "Exact scalar linear information deficit only. All listed available rows must already be legally accessible in the same frame/version. Does not price observation production, copying, maps, volume, approximation or restoration; does not prove a native implementation attaining the bound.",
+    }
+
+
+def cut_controls():
+    e = [[int(i == j) for j in range(6)] for i in range(6)]
+    sums = [[x + y for x, y in zip(e[0], e[1])],
+            [x + y for x, y in zip(e[2], e[3])]]
+    correlated = cut_probe({"width": 6, "available": sums, "demanded": e[:4]})
+    require(correlated["additional_answer_dimension_lower_bound"] == 2,
+            "Correlated-side-information positive control failed")
+    none = cut_probe({"width": 6, "available": [], "demanded": e[:4]})
+    require(none["additional_answer_dimension_lower_bound"] == 4,
+            "No-side-information control failed")
+    drift = [[x + y for x, y in zip(e[0], e[4])], e[1],
+             [x + y for x, y in zip(e[2], e[5])], e[3]]
+    versioned = cut_probe({"width": 6, "available": e[:4], "demanded": drift})
+    require(versioned["additional_answer_dimension_lower_bound"] == 2,
+            "Changed-version control failed")
+    require(rank([[1, 1], [1, -1]], 2, "Q") == 2, "Q field control failed")
+    require(rank([[1, 1], [1, -1]], 2, "F2") == 1, "F2 field control failed")
+    try:
+        rank([["1/2"]], 1, "F2")
+    except ValueError:
+        pass
+    else:
+        raise ValueError("Even-denominator control failed")
+    require(rank([], 2) == 0 and rank([[0, 0]], 2) == 0, "Zero control failed")
+    return {"correlated_available_responses": correlated,
+            "without_available_responses": none,
+            "source_version_drift": versioned,
+            "field_control_Q_rank": 2, "field_control_F2_rank": 1,
+            "all_controls_passed": True,
+            "warning": "Synthetic examples only; no selected-caller rows are claimed."}
+
+
+def moments(profile):
+    paid = {int(r): int(n) for r, n in profile["paid"].items()}
+    targets = {int(r): int(n) for r, n in profile["targets"].items()}
+    require(all(r > 0 and n > 0 for d in (paid, targets) for r, n in d.items()),
+            "Histograms require positive ranks and counts")
+    with localcontext() as ctx:
+        ctx.prec = 65
+        logs = {r: Decimal(r).ln() for r in set(paid) | set(targets) | {1, 8, 9, 16, 25, 145}}
+
+        def price(r, c):
+            if c == 0:
+                return Decimal(r)
+            return ((1 - c) * logs[r]).exp()
+
+        def evaluate(p, t, c):
+            return sum(Decimal(n) * price(r, c) for r, n in t.items()) - sum(
+                Decimal(n) * price(r, c) for r, n in p.items())
+
+        def margin(c):
+            return evaluate(paid, targets, c)
+
+        def derivative(c):
+            return sum(Decimal(n) * price(r, c) * logs[r] for r, n in paid.items()) - sum(
+                Decimal(n) * price(r, c) * logs[r] for r, n in targets.items())
+
+        mass = sum(r * n for r, n in targets.items()) - sum(r * n for r, n in paid.items())
+        require(margin(Decimal(0)) == mass, "Rank-mass control failed")
+        # A source-bound control for the selected neutral completion. For a
+        # different exploratory profile, this baseline-specific control is off.
+        selected_profile = profile.get("base_commit") == "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700"
+        neutral_control = None
+        if selected_profile:
+            require(paid.get(8, 0) >= 144 and targets.get(8, 0) >= 144,
+                    "Expected selected neutral H8 cancellation missing")
+            reduced_paid, reduced_targets = paid.copy(), targets.copy()
+            reduced_paid[8] -= 144
+            reduced_targets[8] -= 144
+            neutral_control = True
+        points = []
+        for s in [profile["selected_kappa"], "0.0033", "0.0034", "0.004", "0.006", "0.01"]:
+            c = Decimal(s)
+            m = margin(c)
+            slopes = derivative(c)
+            # Necessary raw-moment change only: compiler reserve/outer costs
+            # would require additional slack. This is not an admission budget.
+            need = max(-m, Decimal(0))
+            points.append({
+                "C": s, "raw_target_minus_paid": str(m),
+                "raw_deficit_to_zero_before_reserves": str(need),
+                "d_margin_d_C": str(slopes),
+                "isolated_H1_deletions_to_cross_zero": int(need) + 1 if m <= 0 else 0,
+                "alternative_extra_targets_equivalent_to_raw_deficit": {
+                    str(r): str(need / price(r, c)) for r in (8, 9, 16, 25, 145)},
+                "local_dC_per_removed_H1_at_this_point": str(-1 / slopes),
+            })
+            if selected_profile:
+                reduced = evaluate(reduced_paid, reduced_targets, c)
+                require(abs(m - reduced) < Decimal("1e-55"),
+                        "Removing the neutral H8 pairs changed the raw margin")
+                missing_target = evaluate(paid, reduced_targets, c)
+                require(missing_target < m - 1000,
+                        "Removing the productive H8 credit was not charged")
+        lo, hi = Decimal(0), Decimal("0.02")
+        require(margin(lo) > 0 and margin(hi) < 0, "No bracket in diagnostic range")
+        for _ in range(100):
+            mid = (lo + hi) / 2
+            if margin(mid) > 0:
+                lo = mid
+            else:
+                hi = mid
+        return {"decimal_precision": ctx.prec,
+                "scope": "Heuristic Decimal arithmetic; no outward error bounds, uniqueness proof, compiler reserve, physical construction or kappa admission. Equivalent target counts are isolated alternatives, not additive credits. Existing targets cannot be counted again.",
+                "rank_mass_surplus_exact": mass,
+                "paid_jobs_exact": sum(paid.values()),
+                "productive_fields_exact": sum(targets.values()),
+                "numerical_raw_sign_change_bracket": [str(lo), str(hi)],
+                "neutral_144_H8_paid_target_cancellation": neutral_control,
+                "points": points}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--profile", type=Path, default=Path(__file__).with_name("PROFILE.json"))
+    parser.add_argument("--cut", type=Path, help="JSON: width, field Q/F2, available rows, demanded rows")
+    parser.add_argument("--check-source-root", type=Path,
+                        help="Optionally check all three frozen source hashes in an existing checkout")
+    args = parser.parse_args()
+    raw = args.profile.read_bytes()
+    profile = json.loads(raw)
+    if args.check_source_root:
+        for source in profile["sources"]:
+            observed = hashlib.sha256((args.check_source_root / source["path"]).read_bytes()).hexdigest()
+            require(observed == source["sha256"], "Source bytes changed: " + source["path"])
+        selected = json.loads((args.check_source_root / "certificates/selected-result.json").read_text())
+        invoice = json.loads((args.check_source_root / "research/coupled-helper-neutral-completion/reports/expected/invoice.json").read_text())
+        require(profile["paid"] == invoice["histograms"]["paid"],
+                "Frozen paid histogram disagrees with its authenticated source")
+        require(profile["targets"] == invoice["histograms"]["productive"],
+                "Frozen target histogram disagrees with its authenticated source")
+        require(profile["selected_kappa"] == selected["decimal"],
+                "Frozen kappa disagrees with its authenticated source")
+    result = {"status": "PASS_EXPLORATORY_DIAGNOSTICS_NO_NEW_KAPPA",
+              "python": platform.python_version(),
+              "base_commit": profile["base_commit"],
+              "profile_sha256": hashlib.sha256(raw).hexdigest(),
+              "moments": moments(profile), "synthetic_cut_controls": cut_controls()}
+    if args.cut:
+        result["user_cut"] = cut_probe(json.loads(args.cut.read_text()))
+    print(json.dumps(result, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()