Host QQ16 correction temporaries in existing output banks

research/qq16-output-pebbling/PREDECESSORS.json

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+{
+  "schema_version": 1,
+  "canonical_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "retained_data": [
+    {
+      "pr": 3985,
+      "head": "400df7fca8f60c19bf163c77564fe3fbe9154b04",
+      "source_path": "research/qq16-recovery-fusion/WORD.json",
+      "local_path": "vendor/pr3985/WORD.json",
+      "sha256": "a854f516f1d80635fb3414734f9e1c6d1251a5d79ef12e137c143fc6b0b51722",
+      "git_blob": "1518ddc9b61aa6bede045d20f0d5e8cf664863fa",
+      "use": "Full source word authenticated as data and independently regenerated. No pending executable imported."
+    }
+  ],
+  "canonical_reuse": "Authenticated PR2707 verifier and its full transitive retained PR2681/canonical input closure listed in SOURCES. Its inverse and phase algebra are inherited, not code-disjoint.",
+  "adapted_code": [
+    {
+      "source": "PR3985 native.py, itself adapted from ywz65 PR2707",
+      "sha256": "0a53f6df1d5ee88b206547b88a2805d9f7d5db582117baa48c08658d5cd7a4ba",
+      "use": "Ownnative.py signed kernel/occurrence checker, explicit adaptation credit; no runtime dependency onpendingcode."
+    },
+    {
+      "source": "PR3985 verify.py fused()",
+      "use": "Source-word reconstruction independently restated fromcanonical2707 and compared against exact retainedWORD."
+    }
+  ],
+  "credit": [
+    "ywz65 PR2707 and native line-normalization lineage",
+    "Arham Tahir PR2681 orderedinverse/source reconstruction",
+    "Ali Romman and QQ16/source/native/geometry lineage",
+    "commdata2338 PR2651 andDiscussion2617 early-record/output-bank coalescing",
+    "Nick Petalas PR2722 access accounting andPR3339 consumer ledger",
+    "PR3952/3963/3977 demand andactualcaller audits",
+    "Douglas Colkitt andSagarThakrar retainedsupplier/coverage lineage"
+  ],
+  "new_result": "Literal query/response/output lifetime allocation eliminating112 additional full-cover banks and112 clears (224scalar), same224H1/fulloutputcontract.",
+  "license": "Apache-2.0; retained notices unchanged.",
+  "ai_assistance": "Substantial OpenAI Codex assistance; independent agent review only, nohuman/formalkernel claim."
+}

research/qq16-output-pebbling/PROOF.md

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+# Output-bank pebbling for complete QQ16 recovery
+
+## Statement and boundary
+
+At the first post-B1 recovery boundary, PR3985's literal decoder reads all
+224 current X/Y arrays as borrowed inputs and produces all 224 original x/y
+arrays in the owned Z/W output banks, in F17. This package keeps that contract
+and the 224 H1, 448 wrapper and 352 cover-map invoice. It eliminates all 112
+additional full-cover D arrays by scheduling their lifetimes inside eventual
+Z output slots. Peak private scratch remains 16.
+
+The resulting word has 424 CLEARs instead of 536, saving 224 scalar primitive
+allowance: 27,184 becomes **26,960**. No source/input is discarded. The 224
+owned output arrays may enter with arbitrary dirt; all are explicitly
+initialized before their logical values are read. All 224 borrowed current
+arrays retain their exact values and frames. This is a constructive local
+bank allocation, not a minimum-space or global supplier theorem.
+
+The exact source is PR3985 head
+`400df7fca8f60c19bf163c77564fe3fbe9154b04`. Only its WORD data is retained.
+The checker regenerates that full word from the canonical PR2707 decoder,
+then replays the changed whole word against its independent routed inverse
+formula and on independent original inputs propagated through F0/B1.
+Canonical algebra and native contracts are reused with full transitive byte
+and Git-blob authentication before execution.
+
+## The dependency graph that permits deferral
+
+Write A and T for the two eight-port selected sets, and U for the 96 ordinary
+ports. The prefix originally defines every Z_p by `Z_p = X_p`. At A and T
+ports it also adds the normalized initial W_p. Before the future logger:
+
+- Only the eight Z_T values are ever read. They contribute to the current
+  inverse-query correction of W_T and must remain live.
+- Each Z_U is only its initial X_U copy and has no reader yet.
+- Each Z_A is X_A plus initial W_A and has no reader yet. W_A is unchanged
+  through the preceding current-query block and until the future logger's
+  final response additions. The intermediate stage-1 maps on W_A cancel;
+  the complete routed and phase replay checks their return.
+
+Therefore all 104 Z_(U+A) definitions can be deferred. This is dependency
+rescheduling, not destruction of live outputs. The eight Z_T definitions,
+map operations and uses remain at their original positions.
+
+The verifier derives the exact pre-logger Z read set from the retained word,
+checks every removed definition against its complete expected instruction
+sequence, and checks the full W_A write sequence. No generic allocator or
+unverified claim that all Z banks are dead supplies this fact.
+
+## A concrete allocation with zero external banks
+
+The source future logger reads 104 query copies D_(U+T), then writes eight
+response copies D_A. Let z(p) biject the ordered query ports U+T with the
+ordered free output slots U+A. Host each D_p in Z_z(p). Reserve the first
+eight slots in U as the eventual response locations; the explicit mappings
+are recorded in RESULT.json.
+
+The schedule is:
+
+1. Keep the source prefix except the deferred Z_(U+A) definitions.
+2. In each query's assigned output slot, perform the original clear/copy,
+   stage-2 affine map and inverse C_q. The 104 query values now have frame
+   F16, on coordinates 9 through 24. All original W sources remain F17.
+3. Within each owner-private sweep, form **all eight** private F queries
+   from all 104 query copies. Only after the last query read, clear the eight
+   designated response slots in F16 and write their quarter-query response
+   combinations. These eight slots formerly held query copies, whose final
+   use at this owner has passed. Clear the eight private F fields in identity
+   frame before moving to another owner.
+4. All Z_A slots were query-only. After the complete sweep, initialize their
+   deferred values X_A + W_A, in F17, while W_A is still unchanged.
+5. Apply each original positive C_q and inverse affine map to its response
+   slot, returning that correction to F17, and add it into W_A.
+6. After every response has been consumed, initialize all deferred Z_U with
+   X_U in F17. Resume the untouched inverse-B1 checkpoint and F0 suffix.
+
+This is a local last-use reuse inside the owner body: a query value is
+captured in F before the same physical slot is overwritten by a response.
+All native/map events remain outside the private body. Across owner moves,
+only explicit full-cover output banks persist; private F state is returned
+zero/identity. There is no attempt to retain owner-private values through a
+native operation or move.
+
+The response locations are chosen from Z_U, not Z_A. Otherwise recreating
+Z_A before modifying W_A could overwrite a still-live response. The choice
+also means every response has been consumed before its output definition.
+The full replay checks these causal boundaries, values and all 73 linear
+and quadratic modulo-four phase coordinates.
+
+## Why the final clears disappear
+
+In PR3985, each D is separate from every output and must finish zero/identity.
+Here no D allocation exists. Each temporary lifetime ends by the explicit
+initialization of its owned output slot, or by the F16 clear that begins its
+response lifetime. The 112 original final D CLEARs are thus obsolete; they
+would clear actual output storage at the wrong time if retained indiscriminately.
+
+The source's 104 initial query clears and eight initial response clears are
+still paid. The latter move to the query last-use cut inside the private
+body. Every original Z initialization remains paid, merely deferred. Thus
+arbitrary output dirt and all temporary contents are erased by charged
+operations, while every borrowed input survives. Zero/I return remains
+required for private scratch; final output slots are live outputs in F17,
+not promised zero/I temporary outputs.
+
+## Complete local invoice
+
+| Charge | PR3985 | Output-hosted word | Change |
+|---|---:|---:|---:|
+| H1 children |224|224|0|
+| Native wrappers |448|448|0|
+| Full-cover maps |352|352|0|
+| Unit ADDs |1920|1920|0|
+| Quarter ADDs |896|896|0|
+| CLEARs |536|424|−112|
+| Real scalar primitive allowance |27184|26960|−224|
+| Owned output arrays |224|224|0|
+| Additional owned full-cover temporaries |112|0|−112|
+| Peak owner-private fields |16|16|0|
+| Borrowed current X/Y arrays |224|224|0|
+
+Allowance is 8 per unit ADD, 12 per quarter ADD and 2 per CLEAR. The source
+F0/B1 producer is unchanged and additional. This contribution deletes local
+storage obligations and charged clears; it does not lower the recursive
+native count or automatically increase kappa.
+
+## Actual caller and physical limits
+
+The frozen hosted template identifies replica 0's F0 as physical source
+ event 0, B1 as event 1, the other pair's idle preparation as event 2 and
+ordinary bridge as event 3. This recovery insertion is at the cut after B1
+and before the subsequent idle preparation. Current pair-0 X/Y remains
+borrowed. This is the full recovery endpoint, not the reduced bridge-only
+endpoint examined in PR3977.
+
+The bank reuse is real **within the 224 exclusively owned output banks of
+the pinned decoder contract**. It does not identify these output banks with
+borrowed current state, uncleared dirty helpers, or free storage in the
+original gauge44 controller. The actual placement and access of those 224
+owned outputs in a physical caller remain obligations. The local result
+removes the need to supply 112 more fields once that output contract is
+provided; it does not prove a complete six-tape hosting schedule.
+
+| Obligation | Status |
+|---|---|
+| Exact first-B1 source cut and source word | Pinned and checked |
+| Deferred definitions and last-use allocation | Constructively checked |
+| Complete arbitrary-array inverse and output frames | Replayed under authenticated canonical contracts |
+| Borrowed preservation, arbitrary owned dirt and private zero return | Checked |
+| Signed native recipe coverage and primitive invoice | Checked |
+| Physical placement and access of the existing 224 owned outputs | Unknown |
+| Movement, control, output consumption and actual family coverage | Unknown |
+| Changed rounded errors, dirty magnitudes and all-depth supplier admission | Unknown |
+
+No supplier moment or kappa improvement is claimed from the storage delta.
+The bounded next test is physical placement of this existing output bank at
+one actual caller, with all movement and coverage costs; a new local storage
+search without that contract is not justified by this result alone.
+
+## Attribution and overlap
+
+Credit PR3985 for the rectangular correction and its 224-H1 full word; ywz65
+PR2707 for F17 normalization and native checking; Arham Tahir PR2681 for the
+ordered inverse; Ali Romman and the retained QQ16/geometry/native lineage.
+Discussion2617 and commdata2338's PR2651 supplied prior output-bank lifetime
+coalescing for sixteen early records in PR2540. This result concerns the
+104 query and eight response lifetimes in the newer zero-retention PR3985
+word, not a second claim for those early-record savings. Credit Nick Petalas
+PR2722 for explicit storage-layout access accounting and PR3339 for the
+separate consumer/coverage boundary. Source notices remain unchanged.
+
+New contribution: the exact deferral, query/response/output allocation,
+whole-word verification and 112-bank/224-scalar reduction. Chris R /
+Clear1nsight with substantial OpenAI Codex assistance, Apache-2.0. Independent
+agent review is recorded separately; no human or formal proof-kernel review
+is claimed.

research/qq16-output-pebbling/README.md

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+# Host QQ16 correction temporaries in eventual outputs
+
+This is a constructive lifetime allocation for the complete PR3985 recovery
+word. It removes all **112 extra full-cover temporary banks** while preserving
+all 224 original outputs in F17 and all 224 borrowed current X/Y arrays.
+The 224 H1 children, 448 wrappers and 352 cover maps are unchanged.
+Paid CLEARs fall from 536 to 424, reducing scalar allowance from 27,184 to
+**26,960**. Peak owner-private scratch remains 16.
+
+The dependency analysis finds eight live Z_T outputs and 104 deferrable Z_(U+A)
+outputs before the future logger. Those 104 slots hold its query copies.
+After all queries have been captured in private F registers, eight query
+slots become response slots. The deferred Z_A definitions run before W_A
+changes; the deferred Z_U definitions run after response consumption. Every
+clear and frame transition is paid. No borrowed dirty helper is erased and
+no private value crosses a native boundary.
+
+[PROOF.md](PROOF.md) states the complete local contract, operator/phase
+argument, allocation and invoice. RESULT.json records all 104 physical-slot
+lifetimes, exact source-definition indices and the full receipt; WORD.json
+is the complete transformed word. The checker authenticates and regenerates
+the retained PR3985 word as data, then checks the whole new word against the
+canonical routed inverse. It imports no pending executable.
+
+This eliminates temporary allocations **inside the existing 224-owned-output
+contract**. It does not prove those outputs are free in the original gauge44
+physical caller. The first-B1 source cut is pinned, while six-tape placement,
+movement, precision, productive-family coverage and recursive admission
+remain open. No supplier or kappa change is claimed.
+
+## Reproduce
+
+```sh
+python3 -I -Werror -B research/qq16-output-pebbling/verify.py
+python3 -I -O -Werror -B research/qq16-output-pebbling/test_verify.py
+python3 -B scripts/research_package.py --package research/qq16-output-pebbling
+```
+
+Python 3.12, standard library only. Normal replay is read-only; explicit
+regeneration refuses to overwrite either receipt. Tests cover optimized and
+normal execution, Git-free read-only export, source authentication, whole-word
+and type-sensitive receipt corruption, and meaningful lifetime/alias/frame/
+dirty-return controls. Signed native kernels reuse the credited PR2707 method
+through PR3985, cover 114,688 columns and bind all 224 native occurrences.
+The source inverse theorem and native contracts are inherited, not claimed
+as code-disjoint or formal verification.
+
+## Scope, overlap and credit
+
+User-assigned graph-pebbling/register-allocation follow-up of PR3985 at head
+`400df7fca8f60c19bf163c77564fe3fbe9154b04`, on canonical main
+`20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority revision 6.
+The [shared claim](https://github.com/CrocSwap/integer-mult-bounds/pull/3985#issuecomment-6263114494)
+coordinates distinct streaming, lifetime-hosting, reversible-workspace and
+operator-representation investigations. Partial overlap checks include the
+canonical scope map and [Discussion2617](https://github.com/CrocSwap/integer-mult-bounds/discussions/2617),
+which records commdata2338's PR2651 early-record/output-bank coalescing and
+Nick Petalas's PR2722 physical-access work. No novelty guarantee is claimed.
+
+The prior PR2651 result coalesces sixteen early retained records in PR2540;
+this result coalesces the 104 queries and eight responses of the zero-retention
+PR3985 word. The paired streaming investigation uses a different full-cover
+query schedule. Its independently reviewed local construction has 416 CLEARs,
+26,944 scalar allowance, nine deferred output definitions and zero future-logger
+private registers, compared with this construction's 424 CLEARs, 26,960 scalar
+allowance, 104 deferred definitions and eight future private registers. It is
+not an executable or scientific dependency. This owner-private alternative is not asserted
+Pareto optimal. Compare actual movement/access before preferring either.
+
+Credit PR3985, ywz65 / PR2707, Arham Tahir / PR2681, Ali Romman's QQ16 lineage,
+commdata2338 / PR2651, Nick Petalas / PR2722 and PR3339, and all retained
+native/geometry/supplier contributors. Exact source reuse is in
+PREDECESSORS.json and SOURCES.json. New work: Chris R / Clear1nsight with
+substantial OpenAI Codex assistance, Apache-2.0. No independent human or
+proof-assistant review is claimed.
+
+## Open next questions
+
+- Bind the 224 already-owned output slots to an actual first-B1 caller's
+  storage and owner streams. The local alias schedule removes 112 new banks
+  only after that output contract is supplied; unknown placement is not free.
+- Compare this owner-private last-use schedule with the separate streamed
+  query schedule under one explicit physical access model. Count full-cover
+  passes, tape movement, control and endpoint return rather than scalar
+  operations alone.
+- Bound intermediate magnitudes and rounded errors for the changed schedule,
+  then combine exact invocation/family coverage and both supplier caps.
+  Exact operator equality does not establish a new multiplication exponent.