research: exact QQ16 consumer budget obstruction under centre-64 law

research/qq16-consumer-cap-audit/README.md

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+# QQ16 decoder consumer charge under the selected coverage law
+
+## Question and scope
+
+This is a narrow independent check of the consumer-price branch in open PR
+[#3181](https://github.com/CrocSwap/integer-mult-bounds/pull/3181), head
+`80fc72d14546088e9fce3c06dc12bc67270da0af`. The audited candidate is one
+`CONSERVED-QQ16` `F0 + B_1_2` two-call pair followed by the pinned #2707
+zero-retention decoder. The specific question is whether its rank-one decoder
+children leave enough recursive budget to reach the selected kappa under the
+unchanged `centre=64` coverage law.
+
+The exact local F and B profiles come from
+`research/joint-query/evidence/CONSERVED-QQ16.json`; the #2707 child count comes
+from `research/qq16-line-normalized-decoder/RESULT.json`. Those source files,
+the selected record, and the selected ceiling model are pinned in
+[`SOURCES.json`](SOURCES.json). The PR #3181 README was retrieved at its exact
+head. Its path, Git blob, and SHA256 are recorded in [`TARGET.json`](TARGET.json).
+The fetched PR README is preserved as [compressed raw PR #3181 README](PR3181-README.md.gz).
+Its bytes are checked against the exact Git blob and SHA256 recorded in
+[`TARGET.json`](TARGET.json), so the numerical premise can be replayed offline.
+The PR head itself remains an external source premise; the package does not
+claim that this unmerged commit is in local Git history.
+
+## Result
+
+The source profiles are
+
+```text
+F0:    {1:2420, 2:418, 3:432, 4:142, 5:82}
+B1_2:  {1:2436, 2:418, 3:432, 4:142, 5:82}
+#2707: 336 rank-one children across the two-call pair
+```
+
+Their per-call average is `{1:2596, 2:418, 3:432, 4:142, 5:82}`. For the
+most favorable test, I omit the PR #3181 profile's eight rank-eight children
+and allow their 64 units of rank mass to move into rank-51 idle children. This
+lowers the relaxed moment. The resulting local mass is 5,706 per call; the
+unchanged coverage law gives 7,232 total units per call and 1,526 idle units.
+
+At the exact selected saving
+`a = kappa/(1-kappa) = 836330098538459/499163669901461541`, an independent
+rational lower bound on the relaxed moment exceeds `100009/100000 = 1.00009`.
+The proof uses a 32-term positive atanh expansion after range reduction for
+each logarithm and a five-term positive exponential sum. Every operation in
+the verifier is exact `Fraction` arithmetic. Since the relaxation is already
+above one at the selected exponent, the cap for this fixed local profile and
+coverage law is strictly below the selected kappa. The reported rank-eight
+profile has an even larger lower bound.
+
+This establishes a scoped recursive-price obstruction for the stated
+two-call profile. It does not establish the exact root reported in #3181, a
+physical consumer bill, storage/retention feasibility, a global barrier, or a
+new kappa. Endpoint adapters, movement, owner placement, routing, cleanup, and
+physical hosting are not charged. The `centre=0` alternative is a changed
+coverage law and is outside this result.
+
+## Reproduce
+
+From the repository root:
+
+```sh
+python3 -B research/qq16-consumer-cap-audit/verify.py
+python3 -B scripts/research_package.py --package research/qq16-consumer-cap-audit --check-only
+python3.12 -B scripts/research_package.py --package research/qq16-consumer-cap-audit
+```
+
+The verifier checks the exact source hashes and Git blob IDs, reconstructs the
+per-call profile, computes the favorable rank-51 relaxation, and checks
+negative controls for an illegal rank-52 child and an uneven two-call split.
+Expected verifier status:
+`PASS_QQ16_CONSUMER_CAP_BELOW_SELECTED no_new_kappa`.
+
+## Open next questions
+
+Can a changed, globally valid coverage law remove the 64-per-call centre cost
+while an actual F17 consumer accepts the decoder output in its produced frame?
+This matters because the fixed centre-64 profile already misses the selected
+threshold before physical costs. The first step is to pin a real downstream
+caller, state its entry frames and owner lifetimes, then derive its coverage
+identity and complete physical bill. The blocker is that the current evidence
+does not bind such a caller; a centre-free local surrogate is not that proof.
+
+## Credit and review status
+
+Credit the #2697 `CONSERVED-QQ16` producer and its retained native lineage,
+ywz65/#2707 for the zero-retention decoder, Nick Petalas/#2965 for the
+completed-output transfer, and dcharb78 for the #3181 profile and cost screen.
+This package adds a separate exact one-sided moment proof. No independent
+human or formal-kernel review is claimed. New work is Apache-2.0.

research/qq16-consumer-cap-audit/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/RESULT.json",
+      "usage": "input",
+      "git_blob": "77f55043a679dd722330f1e2499863e36376d9f9",
+      "sha256": "d91d6c46509875abf1f61de67c2609656d3dc685451299f83caa6f922493692d"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    },
+    {
+      "path": "research/joint-query/evidence/CONSERVED-QQ16.json",
+      "usage": "input",
+      "git_blob": "7a155a27dcf7f1ccd48e40d57a2c5d2724016e9b",
+      "sha256": "b91eb8599c403db55c889bb225a1cd93f46fdb83eb339f101d18843d52b1c920"
+    },
+    {
+      "path": "research/qq16-line-normalized-decoder/RESULT.json",
+      "usage": "input",
+      "git_blob": "ba4167dbf133cff51513bb832802c290edcdffea",
+      "sha256": "58df4ad68e2ff335ee58fa4336a449d0f73f3366d840574e5e30b50f507c358d"
+    }
+  ]
+}

research/qq16-consumer-cap-audit/TARGET.json

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+{
+  "schema_version": 1,
+  "source": {
+    "pr": 3181,
+    "state_at_check": "OPEN",
+    "head": "80fc72d14546088e9fce3c06dc12bc67270da0af",
+    "path": "research/qq16-interior-dynamic-range-and-adjoint-ledger/README.md",
+    "git_blob": "b2408a73cdcf287fbbf274ff68f9a208c2d01bb2",
+    "sha256": "2d2284bcb33cc437a9d3e03eaf93ca1ebfef4ced52fdb5d727a79970eab3b61b",
+    "checked_utc_date": "2026-10-19",
+    "local_archive": "PR3181-README.md.gz"
+  },
+  "audited_claim": {
+    "producer_pair_calls": 2,
+    "decoder_rank_one_children_per_pair": 336,
+    "coverage": {
+      "m": 73,
+      "families_per_nine_stage_replica": 896,
+      "stages": 9,
+      "centre_per_call": 64,
+      "idle_rank_cap": 51
+    },
+    "reported_profile_per_call": {
+      "1": 2596,
+      "2": 418,
+      "3": 432,
+      "4": 142,
+      "5": 82,
+      "8": 8
+    },
+    "reported_kappa_cap": "0.001631159602"
+  }
+}

research/qq16-consumer-cap-audit/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/joint-query/README.md",
+      "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md",
+      "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md",
+      "docs/research/community-efficient1000-review.md",
+      "research/qq16-producer-defect-transfer/README.md"
+    ],
+    "methods": [
+      "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.",
+      "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder."
+    ],
+    "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. 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",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the revision-6 family record and #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.",
+    "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+    "allowed_variations": [
+      "One paid query, one changed first pair, or one precisely specified affine helper state.",
+      "A counterexample or lower bound for that exact proposed repair.",
+      "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+    ],
+    "scope_change_triggers": [
+      "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+      "Treating cover-map counts as zero-cost physical address operations.",
+      "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+      "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate."
+    ],
+    "overlap_terms": [
+      "QQ16",
+      "joint-query",
+      "changing-chart controller",
+      "selected observation",
+      "1969",
+      "2540",
+      "early record",
+      "output-bank retention",
+      "complete native decoder",
+      "2965",
+      "producer defect",
+      "dirty-helper range",
+      "F17 consumer"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Independently test whether the pinned decoder rank-one children of the PR #3181 F0+B1_2 pair fit the exact selected recursive-price budget under the unchanged centre-64 coverage law.",
+  "scope_change_reason": "The full physical consumer invoice is not source-bound. This isolates one exact necessary budget condition using the pinned producer and decoder while retaining the card\u2019s consumer-boundary focus; a failure before physical costs is a scoped obstruction, not a complete supplier or universal barrier.",
+  "bottleneck_link": "Tests whether the proposed local QQ16 consumer profile can reach the selected exponent even under the most favorable allowed idle-rank relaxation.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after an exact one-sided moment bound for the pinned pair and decoder, or if the PR source/profile cannot be bound. Do not optimize a new profile or infer a global barrier.",
+  "outcome": "completed",
+  "evidence": "Reconstructed the per-call profile from pinned F0 and B1_2 native counts plus the decoder\u2019s 336 rank-one children across two calls. An exact Fraction lower bound exceeds 1.00009 after dropping rank-eight children and relaxing all freed mass to rank 51.",
+  "author": "macbook-07",
+  "ai_assistance": "Substantial automated assistance was used for research and implementation. No independent human or formal-kernel review is claimed.",
+  "open_questions": [
+    {
+      "question": "Can a changed globally valid coverage law remove the 64-per-call centre charge while an actual F17 consumer accepts the decoder output in its produced frame?",
+      "why_it_matters": "The fixed centre-64 profile already misses the selected threshold before physical movement, storage, hosting, and consumption costs.",
+      "first_step": "Pin a real downstream caller, its entry frames and owner lifetimes; derive its coverage identity and full physical bill.",
+      "blocked_by": "Current evidence does not bind a physical F17 caller or a globally valid centre-free coverage law."
+    }
+  ],
+  "assignment": {
+    "seed": "dcad28253c4c262b26d8deea86c90cc4",
+    "track": "recursive-interfaces",
+    "task_id": "joint-query-controller"
+  },
+  "overlap": {
+    "searched_at": "2026-10-19T02:37:11.955097+00:00",
+    "terms": [
+      "QQ16",
+      "joint-query",
+      "1969",
+      "2540",
+      "output-bank retention",
+      "2965",
+      "producer defect",
+      "F17 consumer"
+    ],
+    "coverage": {
+      "open_prs": {
+        "fetched_at": "2026-10-19T02:36:30.574262+00:00",
+        "complete_pagination": true,
+        "records": 587
+      },
+      "discussions": {
+        "fetched_at": "2026-10-19T02:37:09.290746+00:00",
+        "complete_pagination": true,
+        "records": 2536
+      }
+    },
+    "warnings": [],
+    "matches_total": 164,
+    "assessment": "The refreshed search found open PR #3181, whose exact-head README supplies the candidate profile, and prior early-record/decoder discussions. Live PR #3652 still states that physical routing, caller admission and F17 consumption remain open. This package adds an exact independent necessary-budget inequality for the fixed centre-64 profile; the search is not a novelty certificate.",
+    "limits": "Open PR and discussion titles/bodies plus local records are searched; code diffs and arbitrary package files are not. PR #3181 and #3652 were checked directly for current state and head."
+  },
+  "freshness": {
+    "checked_at": "2026-10-19T02:37:11.955097+00:00",
+    "main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+    "priority_revision": 6,
+    "relevant_change": "Final canonical-main fetch returned the same commit as the launch pin. PR #3181 remains open at the pinned head; PR #3652 remains open and leaves the physical caller/F17 consumer unresolved. Relevant #1166 and #1163 discussions were re-read."
+  }
+}

research/qq16-consumer-cap-audit/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/complex-local-word-ceiling/RESULT.json",
+    "research/complex-local-word-ceiling/ceiling.py",
+    "research/joint-query/evidence/CONSERVED-QQ16.json",
+    "research/qq16-line-normalized-decoder/RESULT.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact source blob and SHA256 pins; producer/decoder profile reconstruction; favourable rank-51 moment lower bound; centre-free scope control; invalid-rank and uneven-split controls."
+    }
+  ]
+}