Expose 112 funded native helper queries in an entrance prologue

research/native-helper-query-bank/ATTRIBUTION.md

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+# Source credit and distinct addition
+
+The fixed source word and all its native/compiler/precision lineage are retained.
+New work is Apache-2.0 with substantial OpenAI Codex assistance for Dillon /
+dillona; no independent human or formal-kernel acceptance is asserted.
+
+- **Cao Yifan / intqwq, PR #4610**: round-three joint-helper/native-map word,
+  retained as `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz` and the
+  source payload consumed here.
+- **Dugongue / mdumitrean, PR #4929**: exact center-free producer, helper-clean
+  pre-compensation, explicit eight-mode code and all-width free-group proof in
+  `research/native-center-free-code/`. This package replays its complete forward
+  word; it does not claim center deletion or helper-clean endpoints as new.
+- **Cinna Davis / 1337isnot1337, PRs #4694 and #4698**, and the **PR #4470**
+  controller/native-helper lineage: center-free cache kernel, cold-helper
+  observations, physical helper normalization and explicit helper-basis methods.
+  The present full first-departure basis is a new application of that lineage,
+  not a claim to invent scalar helper recoding.
+- **Dillon / dillona, PR #4933**: exact real R-centralizing normalizers and their
+  signed phases, literal monomial lowering, physical coded interface and
+  all-width lift conventions in `research/coded-native-caller/`. Those K words
+  and the credited Clifford implementation are pinned and reused here.
+- **Chris R / Clear1nsight, PR #4931**: actual helper496 paid-prefix split and
+  ownership discipline. It supplied the source-history positive control and
+  motivation for using an existing chronological response. This package's
+  selected112 responses need no paid split.
+- **Dillon / dillona, PR #5126**: sharp standalone local-query count; its grammar
+  does not include this internal paid-history interface. We do not present this
+  interface as a counterexample to that scoped result.
+- **zxv, PR #5283**: exact Gaussian cache reuse requires the matching live row,
+  unchanged independent returns and full costs. The present package supplies
+  explicit rows and return decoding for one native interface, while preserving
+  that distinction from a completed caller.
+
+The retained source proofs also credit DaysSky, Nick Petalas, Ryanson Jonathan,
+Jacob Alan Sussman, zxv and the scalar, Clifford, precision, compiler and outer
+construction contributors. Their attribution and notices in the unchanged
+predecessor directories remain applicable. No predecessor archive is copied or
+rewritten by this package.
+
+The distinct result is the invertible **358-by-358 matrix of actual chronological
+first departures**, selecting **112 funded H1 observations of common Q** with
+literal exact phases, together with **26 H5 + 6 H1** cold-return completion,
+full 358-input decoding, unchanged 50-hot-helper return contract, and explicit
+ordinary work and owned observation storage. The entrance-prologue extension
+relocates those same children, using exact first-departure identities and
+whole-field swaps with chart transport. It adds explicit storage and movement,
+with the same Gaussian calls. That interface remains separate from the
+still-unproved main/helper caller.
+
+Submission checkpoint: canonical `1ec1119972c9aefe42525172d07b332fcff81cb4`;
+source-manifest baseline: `7c472563474e60185e6ca101a17622133d047e56`;
+scientific source freeze: `a5df48c55ea806d7952b65acc9c76d878ff09b13`.
+The sources are already retained in canonical history, and exact live file pins
+are in `SOURCES.json`. Coordination and overlap were reviewed by the parent
+paid-history campaign in Discussion #4930 before this package was assigned;
+this subtask did not reroll the research card or take over a concurrent claim.

research/native-helper-query-bank/README.md

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+# 112 common-Q observations inside a paid native helper history
+
+This forward interface exposes **112 common rank-one Gaussian responses on 112
+independent helper inputs**, using 112 existing paid H1 children of the
+center-free native producer. An explicit invertible basis on all 358 cold helper
+inputs removes the other-helper contamination at those chronological cuts. The
+coded main endpoint is unchanged, and every independent helper input is returned.
+An exact rescheduling can expose all 112 responses in an **entrance prologue**,
+before the original native operations, while preserving the same paid inventory.
+
+The observations add no Gaussian child or split. **Return decoding does add
+26 H5 and six H1 children.** It upgrades the 358 cold helper jobs to H9, and leaves
+the other 50 helper jobs unchanged. It does not retain the old helper target
+profile. The full local profiles are:
+
+| Profile | Before | After this interface |
+|---|---|---|
+| Paid children | `{1:2201,2:412,3:510,4:127,5:40}` | `{1:2207,2:412,3:510,4:127,5:66}` |
+| Independent helper targets | `{4:28,7:7,8:47,9:326}` | `{4:2,7:7,8:41,9:358}` |
+| Added paid rank mass | — | 136 |
+| Added productive observation jobs | — | 0 |
+
+The 112 copied responses are dependent observations, not additional productive
+jobs. Their 112 owned storage fields, 112 copies, 224 initial/terminal clears,
+6,828 scalar passes and at most 400 monomial field maps are explicit ordinary
+work, additional to the producer's existing work and 32 new Gaussian children.
+The scalar programs include fixed rational coefficients with odd denominators;
+no free exact-division operation or complete finite-precision tariff is assumed.
+Those counts describe observation at the original cuts. The early version uses
+224 owned fields, 224 copies, 448 clears and 112 whole-field swaps instead;
+its scalar, monomial and paid-child counts are unchanged.
+
+**This is a forward observer ABI, not a complete Gaussian caller or a new κ.**
+In particular, its arguments are independent helper inputs. Substituting main
+inputs for them still requires a caller that restores all displaced helpers.
+No backward observation interface is asserted.
+
+[PROOF.md](PROOF.md) gives the exact input/output contract, chronology, all-width
+argument and bill. [BANK.json](BANK.json) contains both 358-owner scalar programs,
+all query cut indices and literal phase-correct words, and all 32 completion
+recipes. [HOIST.json](HOIST.json) records the entrance prologue and the exact
+112 source-event replacements. [ATTRIBUTION.md](ATTRIBUTION.md) records the
+predecessor work.
+
+## Reproduce
+
+Only Python 3.12 and its standard library are required, in a full Git checkout:
+
+```sh
+python3 scripts/research_package.py --package research/native-helper-query-bank --check-only
+python3.12 scripts/research_package.py --package research/native-helper-query-bank
+```
+
+The bounded registered replay runs the verifier normally and with `-O`. Direct
+replay is `python3.12 -I -B research/native-helper-query-bank/verify.py`.
+It authenticates the source files, regenerates all 632 endpoint rows and 358
+first departures, checks the full scalar basis, checks exact signed Clifford
+tableaux and absolute phases for all 112 responses and 32 completions, and
+rejects four base semantic mutations. A second replay tracks all 632 original
+and 225 arbitrary owned inputs through the hoisted schedule, checks all 112
+replacement cuts and unchanged paid counts, and rejects two rescheduling
+mutations. The observation readout phases are checked separately from their raw
+copied rows. It compares parsed receipts without writing. The explicit authoring
+option `--write` regenerates `BANK.json` and `HOIST.json`.
+
+Local verification on 2026-10-23 passed the metadata check and both registered
+replays under Python 3.12.15 on macOS 27.0.1 arm64. The normal and optimized
+replays, including the entrance-prologue checks, took 13.20 seconds together.
+The independently regenerated T, T inverse and all 112 cut indices also matched
+the discovery witness. No hosted CI or selected-construction cold replay is
+claimed.
+
+Scientific inputs are unchanged from `a5df48c55ea806d7952b65acc9c76d878ff09b13`;
+the source manifest retains provenance baseline
+`7c472563474e60185e6ca101a17622133d047e56`. The submission checkpoint is canonical
+`1ec1119972c9aefe42525172d07b332fcff81cb4`, checked at 21:54 UTC on 2026-10-23.
+Priority revision 7 is unchanged; the selected conditional result is now
+κ = 0.0030217758 after the PR4610/PR5241 admission. All scientific inputs used
+here are unchanged across that selection update. The native decompressed payload is
+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.
+[SOURCES.json](SOURCES.json) pins every live input. The physical native source
+implementation and its all-width evaluation theorem are explicitly inherited,
+not independently re-proved or accepted by a formal kernel here.
+
+## Open next questions
+
+[TASK.json](TASK.json) records the scoped continuation questions: a chronological
+main-input caller that restores all helpers; an independently checked backward
+interface; and a full storage, finite-precision and multiplication budget after
+caller closure. The present package is an intermediate result in the continuing
+[paid-history investigation](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19154057).
+It does not complete that investigation or claim the selected frontier changed.
+
+Prepared for Dillon / dillona with substantial OpenAI Codex assistance.
+Apache-2.0; predecessor credit is retained.

research/native-helper-query-bank/SOURCES.json

@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "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/coded-native-caller/NORMALIZERS.json",
+      "usage": "input",
+      "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f",
+      "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da"
+    },
+    {
+      "path": "research/coded-native-caller/PHYSICAL.md",
+      "usage": "input",
+      "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f",
+      "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078"
+    },
+    {
+      "path": "research/coded-native-caller/clifford_exact.py",
+      "usage": "input",
+      "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    {
+      "path": "research/native-center-free-code/CODE.json",
+      "usage": "input",
+      "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae",
+      "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0"
+    },
+    {
+      "path": "research/native-center-free-code/CODED-PROOF.md",
+      "usage": "input",
+      "git_blob": "1f28d33884ec99b34f8366d022d8f7b9b7653ae2",
+      "sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01"
+    },
+    {
+      "path": "research/native-center-free-code/CODED-WORDS.json.gz",
+      "usage": "input",
+      "git_blob": "935fedd9c9a77f870dd6afbabbf56c8ea6e321d4",
+      "sha256": "797bad53122f84aa0f05b602f2bdceb6b50f95a64023799d4f24560d9c61aad6"
+    },
+    {
+      "path": "research/native-center-free-code/SOURCE-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    },
+    {
+      "path": "research/native-center-free-code/native_core.py",
+      "usage": "input",
+      "git_blob": "5d8a8f0a6382c66449f76b6f57bdd380c057ddc1",
+      "sha256": "178ff80824a012970fc9435f122152da03c7e6bdc3a7de12136fe03e05cf24fe"
+    }
+  ]
+}

research/native-helper-query-bank/TASK.json

@@ -0,0 +1,86 @@
+{
+  "schema_version": 1,
+  "task_id": "centre-path-sharing",
+  "priority_revision": 7,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "original_card": {
+    "id": "centre-path-sharing",
+    "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
+      "Prove a lower bound on copied information per call for the selected decoder contract."
+    ],
+    "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). 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": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
+    "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
+    "allowed_variations": [
+      "One sharing pattern across a fixed number of calls.",
+      "One reduced copied-total contract for the existing decoder.",
+      "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": [
+      "Removing copies without a replacement contract for the decoder's copied totals.",
+      "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": [
+      "centre path",
+      "copied totals",
+      "private temporary",
+      "shared centre",
+      "batching"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Forward paid-history ABI: 112 existing H1 children expose a common Q on 112 independent cold-helper input coordinates, either at their original cuts or in an entrance prologue, with an invertible 358-owner basis and charged completion and decoding of every cold helper return.",
+  "scope_change_reason": "This continues the authorized native-history campaign rather than rerolling the center-sharing card. It isolates an executable information interface needed by a future caller; it does not claim the card acceptance gate or finish the donor objective.",
+  "bottleneck_link": "The center-free producer still has the coded main cross-transfer A. Actual funded native responses may provide the missing caller information, while preserving every original productive helper. This package identifies those responses but does not show that they can receive the necessary main arguments.",
+  "budget_minutes": null,
+  "stop_rule": "This package ends at the exact forward observer ABI, complete local invoice and independently replayable proof. The parent research campaign continues on a full main/helper caller.",
+  "outcome": "partial",
+  "evidence": "verify.py regenerates all 632 endpoint rows and 358 first-departure rows; checks both 358-dimensional basis programs, 112 exact-phase response identities, 32 completion identities and four base mutations. The entrance-prologue replay checks 632 original plus 225 arbitrary owned input columns, 112 physical cut replacements, unchanged paid inventory and two rescheduling mutations. BANK.json and HOIST.json are compared read-only.",
+  "author": "Dillon / dillona",
+  "ai_assistance": "Substantial OpenAI Codex assistance, including separate discovery, package and caller-research agents.",
+  "open_questions": [
+    {
+      "question": "Can required main-caller arguments occupy these helper coordinates while returning all displaced independent helper inputs?",
+      "why_it_matters": "The current query arguments are independent helper inputs; making them main-derived without restoring the original helpers forfeits the productive-job contract.",
+      "first_step": "Use the early responses in one explicit main-entrance recoding, then emit a full chronological caller and prove every original main/helper output row and every owned clear obligation.",
+      "blocked_by": "No complete helper-restoring caller has been proved."
+    },
+    {
+      "question": "Can the same physical interface be supplied for the actual raw-dual backward word?",
+      "why_it_matters": "A multi-stage caller may need both orientations; forward observations alone do not establish backward snapshots or their phases.",
+      "first_step": "Regenerate backward first departures using conjugated physical frames and the X-only Q-squared convention in the credited physical interface; charge any changed children.",
+      "blocked_by": "The present certificate is forward only."
+    },
+    {
+      "question": "Does a complete caller using this bank beat the selected bound after ordinary work, storage and finite precision are charged?",
+      "why_it_matters": "A local response ABI and its paid profile are not a multiplication theorem or an exponent improvement.",
+      "first_step": "After exact caller closure, price all scalar and monomial passes, observation lifetimes and rational rounding in the compiler ABI, then compute the full moment.",
+      "blocked_by": "Complete caller closure and its invocation schedule remain open."
+    }
+  ],
+  "scientific_origin_commit": "a5df48c55ea806d7952b65acc9c76d878ff09b13",
+  "canonical_checkpoint": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19154057",
+  "checkpoint_utc": "2026-10-23T21:54:37Z",
+  "selected_kappa_at_checkpoint": "0.0030217758",
+  "checkpoint_decision": "Canonical main remains1ec111997; priority7 and scientific inputs unchanged. Reviewed newer owned-relation/transposition and observer-limit scopes; this forward helper-query hoist is distinct and does not consume their pending sources. Native caller research continues.",
+  "hoist_extension": "Copy selected D_K xi coordinates before T inverse, relocate their existing adapted children, then replace original child events by whole-field swaps with chart transport and owned clears. No Gaussian or scalar pass is added; ordinary storage/movement increases explicitly."
+}