Audit QQ16 integer consumer incidence and conditional budget

research/qq16-consumer-incidence/PREDECESSORS.json

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+{
+  "retained_data": [
+    {
+      "pr": 3952,
+      "head": "996ff698d3efd0bdce606e240f3b00e6ab91e7fc",
+      "source_path": "research/qq16-f17-demand-projection/WORD.json",
+      "local_path": "vendor/pr3952/WORD.json",
+      "sha256": "f513d235b8206211a4716d013a6dacf34aaebda6839da721b0231981cb8b905e",
+      "git_blob": "c23da2f205170b11f40299c5ec1dcab45b134861"
+    },
+    {
+      "pr": 3952,
+      "head": "996ff698d3efd0bdce606e240f3b00e6ab91e7fc",
+      "source_path": "research/qq16-f17-demand-projection/PROOF.md",
+      "local_path": "vendor/pr3952/PROOF.md",
+      "sha256": "9d674364ef3d9d9dbba6ab32805851cc08b222135f6fc2f18e8f5a230d0764a5",
+      "git_blob": "97c66df9a9f1730c0b2b53da492a304c4ea2edb2"
+    }
+  ],
+  "credit": [
+    {
+      "pr": 3339,
+      "author": "Nick Petalas",
+      "head": "123079bef40faf6949ebac7dfc2859c715acea80",
+      "use": "Nine-word occurrence136H1 ledger and missing idle-credit caution. This package adds full hosted144/16 incidence and site-rate correction, not a new nine-word count."
+    },
+    {
+      "pr": 3963,
+      "author": "Clear1nsight",
+      "head": "82c812c45fbc2bc2751e5a0d02a3631af25c3cba",
+      "use": "Centre absence and interface-gap background. Exact atanh arithmetic adapted locally, no imported executable."
+    },
+    {
+      "pr": 3952,
+      "author": "Clear1nsight",
+      "use": "112-line projection local contract/invoice; frozen data retained."
+    },
+    {
+      "pr": 2512,
+      "author": "ywz65",
+      "use": "Actual local96-output F17 demand."
+    },
+    {
+      "pr": 1969,
+      "author": "Ali Romman",
+      "use": "QQ16 literal local words and source lineage."
+    },
+    {
+      "source": "gauge44/T16/frontier1042",
+      "credit": "Retained supplier, owner and coverage lineage; original notices preserved."
+    }
+  ],
+  "license": "Apache-2.0; new work Chris R / Clear1nsight with substantial OpenAI assistance."
+}

research/qq16-consumer-incidence/PROOF.md

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+# Integer incidence changes the conditional screen
+
+This is a finite source ledger and a conditional arithmetic result. It supplies
+neither a complete QQ16 global consumer nor an admitted new supplier.
+
+## Exact source and the first missing connection
+
+The frozen frontier1042-lineage hosted template is member
+`t16/global/hosted/GLOBAL-TEMPLATE.json.gz` of the canonical selected-replay
+archive. Its compressed member SHA256 is recorded in RESULT. This is the actual
+retained template used here, not a new execution or proof of the current
+frontier1094 global assembly. The selected kappa is used only as the target in
+the explicitly conditional screen below.
+
+The template contains 144 local invocations, exactly one for each of 16 replicas
+and nine stages. Its complete physical schedule has 482 entries:144 local
+sweeps,160 idle sweeps,144 bridges,16 terminal translations,16 terminals and
+two final sweeps. The checker binds each call to the physical schedule, its
+asynchronous order, orientation, active pair, family identifiers and stage
+window. All calls still name the original `gauge44` provider.
+
+The proposed QQ16 sequence on each replica is
+
+    F0, B1_2, F2, B3_4, F4, B5_6, F6, B7_8, F8.
+
+The pair indices are0,0,0,1,1,2,2,3,3. There is one stage1 cut per replica,
+hence **16 proposed module insertion sites /144 local calls=1/9**. There are
+64 backward sites, but the others have completed window dimensions33,49,65,
+rather than stage1's17. PR3952's literal source-bound F17 demand is established
+at the first B1 cut; a transported contract at another stage is an additional
+obligation. Counting all backward calls or72 pair-amortized consumers is not
+an interpretation of this exact one-stage1-module proposal.
+
+There are **zero literal PR3952 invocations in the frozen source**. A source
+site is not a proved demand. The first missing provider binding is already
+schedule index0:the source names gauge44, not QQ16 F0. After the proposed B1
+cut, replica0's next entries are idle pair1 at index5 and bridge1→0 at index6;
+F2 is at index18. These are indices in the full 482-entry `execution_schedule`,
+not the replica-local `source_event` labels. All16 records are enumerated in RESULT. The bridge reads
+current bank families `896*r+112+p` for ordinary ports p, not new owned earlier
+y1_U outputs. PR3963 gives the explicit non-factorization witness; this package
+does not reprove it or claim no richer continuation can work. The ledger closes
+the incidence question for this precisely stated insertion proposal, while
+recording the exact provider/read binding required before it becomes a consumer.
+
+## Complete proposed local incidence
+
+The frozen QQ16 certificate has five forward and four backward words per
+replica. Every core profile is
+`{1:2412,2:418,3:432,4:142,5:82}`, with no H8. Counting actual native-line
+recipes gives8 extra H1 for each F and24 for each B, totaling136 per replica.
+This occurrence count is inherited from Nick Petalas's PR3339 and independently
+recounted here for the source-to-schedule binding. It is not a new discovery.
+
+Thus the complete nine-word producer mean is
+
+    n1=2412+136/9=21844/9,
+    n2=418,n3=432,n4=142,n5=82.
+
+The earlier F0/B1 average2428 is different. A hypothetical d-H1 module placed
+once at every stage1 cut adds16d H1 globally, or d/9 per local call. This is an
+integer16-invocation proposal, not4.5 invocations per nine-call replica.
+
+The retained PR3952 word borrows all112 current Y fields and no X. Each of its
+112 owned W slots is cleared before use, so arbitrary initial owned dirt is
+erased. Its per-invocation invoice is112 H1,224 native wrappers,208 maps,
+560 unit ADDs,384 quarter ADDs and144 CLEARs, scalar allowance9376. Sixteen
+instances therefore add1792 H1,3584 wrappers,3328 maps and150016 scalar
+allowance. These are local occurrences, not a globally admitted paid delta.
+No old idle work is certified displaced.
+
+The output-lifetime ledger is also conditional on a specified consumer horizon.
+Retaining96 outputs per instance until the next F2 gives peak384 logical output
+fields in the actual interleaving; retaining until the corresponding terminal
+gives peak1536. Both have1536 output-bank instances. Sixteen owned temporaries
+and eight private scratch arrays are additional per-invocation requirements.
+These are logical liveness counts, not claims of free allocation, minimal
+storage, or a lower bound on physical families: recomputation, encodings and
+other release points change the contract.
+
+## Family coverage cannot be inferred from output count
+
+The source's productive interval is[0,14336),16*896 arbitrary data families;
+its physical capacity is14826 including work. RESULT binds the exact active
+X/Y family intervals and next bridge readset at every proposed cut. No source
+instruction allocates or reads the new output bank as a productive family.
+
+A concrete control varies the arbitrary initial dirt in an owned W output slot.
+Its first operation is CLEAR, so both dirty states yield the same result.
+Therefore appending this slot does not preserve that slot as an arbitrary
+productive input under the selected family contract. It cannot merely be
+counted as an additional independent source data family in the existing proof.
+This does not exclude a different zero-input/encoded supplier theorem; its
+coverage and denominator would need to be derived separately.
+
+Similarly, the actual incidence ledger does not prove that14336 productive
+families, centre64, or the selected idle completion survive substitution of
+QQ16 locals and a module. PR3339 already warns that unchanged idle additivity
+is not an unconditional inference. This package assigns no displaced-idle
+credit and does not strengthen that earlier result into an obstruction.
+
+## Source-rate conditional moment and sharp integer cap
+
+Assume, only for this screen, m=73,W_global=14336,N=144, fixed mass
+T=72W_global+64N, and the inherited halving guard. Every idle rank is at most51.
+For a≥0 the cost per rank-mass unit decreases with rank, so replacing all
+remaining mass by fractional rank51 idle work is favorable. With the exact
+nine-word producer histogram H and sixteen d-H1 modules, use
+
+    H_d=H+16d*{rank1},
+    G(d)=[sum_r H_d(r)(r/73)^(1-a)
+          +(T-sum_r r H_d(r))/51*(51/73)^(1-a)]/14336.
+
+All maps, wrappers, scalar, movement, precision, storage and placement costs
+are favorably zero in this numerical screen. Their local invoices are not
+zero-cost implementations. At the selected target
+`a=836330098538459/499163669901461541`, exact outward bounds are:
+
+|H1 per stage1 module|G(d)|
+|---:|---|
+|112|[0.999955316227494515,0.999955316227494516]|
+|208|[0.999965022703802474,0.999965022703802475]|
+|224|[0.999966640449853800,0.999966640449853801]|
+|304|[0.999974729180110433,0.999974729180110434]|
+|336|[0.999977964672213086,0.999977964672213087]|
+|553|[0.999999905353034202,0.999999905353034203]|
+|554|[1.000000006462162410,1.000000006462162411]|
+
+The208/224/304 rows are parameter values only, not admissions of contemporaneous
+candidates. The112 and336 rows correspond to predecessor local child invoices;
+this package does not claim they satisfy the same whole output contract.
+The strict integer cap in this fixed model is553 because replacing idle rank
+mass by rank1 has strictly positive excess price when a>0; G(d) is affine and
+strictly increasing. Both threshold sides are verified using exact Fractions.
+
+The same implementation independently checks the earlier paired336 model,
+whose moment exceeds1.000097677880011248. Its failure therefore **cannot be
+transported** to one module per stage1 cut:the336 one-stage1-module screen
+passes. Passing supplies no consumer, compatible family stock, idle placement,
+physical cost allowance or multiplication theorem. This is a correction of
+budget applicability, not evidence that the original full decoder globally fits.
+
+Arithmetic uses40 positive atanh terms for log, exact geometric remainder,
+and degree14 exponential bounds. No predecessor executable is imported.
+The helper is locally adapted from Clear1nsight PR3963 and credited there.
+
+## Decision and next test
+
+Do not reject a once-per-stage1 module using the older one-per-two-call screen.
+The exact cut rate and full nine-word mean leave a favorable conditional margin,
+including for336 native children. The next decision is the first real provider
+and read binding:choose a complete continuation which consumes the projected
+or reconstructed values at one enumerated site, then map its owned/borrowed
+lifetimes and native children to displaced old work. Recompute coverage and
+both complete supplier bills before claiming a gain. No additional observation,
+retention, endpoint tariff or lower bound is justified by arithmetic alone.

research/qq16-consumer-incidence/README.md

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+# QQ16 integer cut incidence and conditional consumer budget
+
+**One proposed module at each first B1 cut means16 invocations per144 calls,
+not one invocation per two calls.** The exact frozen hosted schedule has
+16 replicas and nine stages. Its corresponding nine-word QQ16 producer mean
+is `n1=2412+136/9`, rather than the F0/B1 pair mean2428.
+
+This changes the conditional budget decision. With the same assumed W=896/9,
+centre64 and ideal rank51 idle completion, a336-H1 module at that rate gives
+**G in[0.999977964672213086,0.999977964672213087]**, below one. The strict
+integer native-module cap is553 H1;554 fails. The earlier paired336 rejection
+cannot be carried over to this placement proposal.
+
+**There is no admitted consumer schedule here.** All144 source calls still
+name gauge44. The source contains zero PR3952 invocations. Sixteen is the number
+of source-aligned *proposed insertion sites* for its first-cut F17 contract,
+not sixteen proved consumer demands. The first missing provider connection is
+schedule index0. Each first-cut record then identifies its exact idle sweep,
+current-Y bridge read and subsequent F2/terminal boundaries. The48 other
+backward sites have different stage windows and need transported contracts.
+
+The package adds a source-bound complete482-event/144-call ledger, exact
+family/readset and logical-retention counts, local invoice multiplication and
+a new source-rate conditional screen. It does not repeat the earlier centre
+retirement result or claim productive-family growth from extra outputs.
+Retaining all96 outputs until next F2 gives384 peak logical fields; until each
+replica terminal gives1536. These are explicit horizon sensitivities, not
+physical allocation or storage lower bounds.
+
+[PROOF.md](PROOF.md) states the source distinction, arithmetic and limits.
+RESULT.json retains all16 cut records and complete checks. The frozen template
+is frontier1042 lineage, while current selected kappa1094 is only the target
+parameter. No claim of a fresh current-global-schedule replay is made.
+
+## Reproduce
+
+Python3.12, standard library, from repository root:
+
+```
+python3 -I -Werror -B research/qq16-consumer-incidence/verify.py
+python3 -I -O -Werror -B research/qq16-consumer-incidence/test_verify.py
+python3 -B scripts/research_package.py --package research/qq16-consumer-incidence
+```
+
+Default replay is read-only and compares the complete typed RESULT. All runtime
+canonical inputs are in SOURCES/VERIFY; PR3952 WORD and PROOF are retained as
+hash-pinned data with source head/blob in PREDECESSORS. No pending executable,
+Git object, network, third-party dependency or selected cold replay is needed.
+
+## Open next questions
+
+Pin one actual provider/consumer replacement at one of the16 enumerated cuts.
+Show which current-bank reads or complete recovery operations disappear, and
+supply exact frames, field lifetimes, restoration and a displaced-idle map.
+Only then recompute productive-family coverage and the whole physical bill.
+The positive553-H1 conditional allowance is a screening cap, not a procurement
+budget for an unspecified module. The source has no remaining QQ16 H8 centres
+to retire. TASK.json records this bounded next step and stop rule.
+
+## Workflow and credit
+
+Explicit user assignment following PR3952 and PR3963; canonical main
+20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority6. The investigation is coordinated
+at https://github.com/CrocSwap/integer-mult-bounds/pull/3963#issuecomment-6262031944.
+Live targeted PR search and the repository overlap helper have bounded coverage;
+missing gh prevents a full remote snapshot. PR3339 already reports the136-H1
+nine-word count and missing idle-credit problem; the new contribution is the
+actual hosted cut/family incidence and resulting source-rate budget distinction.
+
+Credit Nick Petalas/PR3339; Ali Romman and the retained QQ16/source lineage;
+ywz65/PR2512/2707; Arham Tahir/PR2681; the gauge44,T16,frontier1042 supplier and
+owner/coverage lineage; and Clear1nsight PR3952/3963. Exact source pins and reuse
+are in PREDECESSORS. New work Chris R / Clear1nsight with substantial OpenAI
+assistance as a separately assigned parallel agent. Apache-2.0; frozen sources,
+selected frontier and predecessor notices unchanged. AI cross-review is distinct
+from human or formal verification.