Observation, state, and geometry: building complete suppliers for larger κ

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"
+  ]
+}

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.

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
+  }
+}