Price exact dirty-workspace restoration for QQ16 recovery

research/qq16-dirty-commutator/PREDECESSORS.json

@@ -0,0 +1,52 @@
+{
+  "retained_data": [
+    {
+      "pr": 3985,
+      "head": "400df7fca8f60c19bf163c77564fe3fbe9154b04",
+      "path": "research/qq16-recovery-fusion/WORD.json",
+      "local_path": "vendor/pr3985/WORD.json",
+      "sha256": "a854f516f1d80635fb3414734f9e1c6d1251a5d79ef12e137c143fc6b0b51722",
+      "git_blob": "1518ddc9b61aa6bede045d20f0d5e8cf664863fa"
+    },
+    {
+      "pr": 3985,
+      "head": "400df7fca8f60c19bf163c77564fe3fbe9154b04",
+      "path": "research/qq16-recovery-fusion/RESULT.json",
+      "local_path": "vendor/pr3985/RESULT.json",
+      "sha256": "c8667f150380b277dff75bce442880e28cb0b8012fd878e4ab450d6268ba8b97",
+      "git_blob": "e0ab3ecee0fd337c2ddffc001cc2886066e6ba0b"
+    },
+    {
+      "pr": 3985,
+      "head": "400df7fca8f60c19bf163c77564fe3fbe9154b04",
+      "path": "research/qq16-recovery-fusion/PROOF.md",
+      "local_path": "vendor/pr3985/PROOF.md",
+      "sha256": "73d5598a49cf8132cca3250621806fbb82296a9ab077e38cdc6a5706c5c12d53",
+      "git_blob": "94acdd44e22befa40f3bd7f1e9de59ba2b69755d"
+    },
+    {
+      "pr": 3976,
+      "head": "137c557bbd5fb9f2221457fa400e3ed439481922",
+      "path": "research/qq16-consumer-incidence/RESULT.json",
+      "local_path": "vendor/pr3976/RESULT.json",
+      "sha256": "eab730f516cebba863c0182d71259393d9d70344c29c6d0ce8458632ec15d40d",
+      "git_blob": "aaf829118d9569cb99bba8b30a0c7f2278bc88de"
+    },
+    {
+      "pr": 3976,
+      "head": "137c557bbd5fb9f2221457fa400e3ed439481922",
+      "path": "research/qq16-consumer-incidence/PROOF.md",
+      "local_path": "vendor/pr3976/PROOF.md",
+      "sha256": "9902b7349f2c5f27b0a537115aa5caa784a11c072775f3cb1eb6619d944dfb33",
+      "git_blob": "e3d1efbe8e94bff3abdeeb9593318c86ec52b913"
+    }
+  ],
+  "credit": [
+    "ywz65 PR2707 line-normalized decoder; authenticated source primitives and replay adapted locally",
+    "Arham Tahir PR2681 ordered inverse and native/routed algebra",
+    "Clear1nsight PR3985 rectangular104-query/8-response cut and224-native baseline",
+    "Clear1nsight PR3976 conditional553 cap at proposed1/9 incidence; no supplier admission",
+    "Ali Romman and retained QQ16/native/geometry/supplier lineage"
+  ],
+  "new_work": "Chris R / Clear1nsight with substantial OpenAI assistance. Apache-2.0."
+}

research/qq16-dirty-commutator/PROOF.md

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+# Exact borrowed-dirty restoration repays the rectangular saving
+
+This package tests one reversible-computation repair of PR3985's storage
+obligation. It removes the need for 112 additional exclusively owned
+full-cover temporary arrays, but the fixed-query-frame implementation costs
+976 H1 in the complete decoder. That exceeds the conditional 553-H1 screen
+of PR3976. One bounded pivot costs 352 H1 and is dominated in native and
+additional-owned storage counts by the original 336-H1 PR2707 decoder.
+Neither construction improves the known full-recovery implementation.
+This is a scoped stop, not an ancilla lower bound or a global impossibility.
+
+## Source boundary and changed ownership contract
+
+The canonical PR2707 word, credited to ywz65 and Arham Tahir's PR2681,
+recovers all 224 original x0/y0 outputs in F17 from 224 borrowed current X/Y
+arrays. PR3985 replaces its future-logger block with a rectangular correction:
+104 query ports J=U union T are read, and eight disjoint A ports are changed.
+That 224-H1 full decoder uses 112 additional owned arrays, initially arbitrary
+and cleared on entry/exit. We retain its precise rectangular operator.
+
+Write A_p=C_qp^(-1) M_p, including the actual affine map translation, so
+A_p F17=F16 D_p. Here F16 is the coordinate product on axes 9 through 24;
+D_p is the ordered owner action. At entry W_p has logical u_p in F17. Define
+
+    q_k = sum_(p in J) R[k,p] D_p u_p,
+    L_p(q) = sum_k R[k,p] q_k/4.
+
+The required update is W_p <- W_p - D_p^(-1)L_p(q), for p in A, with every
+J output unchanged. Query/response support disjointness permits uncomputing
+q after changing A. No commutation of distinct owner actions is assumed.
+
+We borrow eight full-cover banks Q_k and one S, each with arbitrary independent
+content and entry frame F16. They may be changed temporarily but must return
+with exactly their original content and frame. They are distinct from current
+X/Y, all output W/Z arrays, and private scratch. These nine auxiliaries are mutable borrowed workspace; the original224 current
+X/Y inputs remain frozen. None of the nine may be cleared. This is
+an explicit local availability premise; no actual global provider of these
+nine banks, their alignment, their ranges or physical access is established.
+Private scratch inside unchanged source blocks remains owned and paid under
+the inherited contract, with peak 16. The change removes the 112 D arrays,
+not every owned or private resource in the complete decoder.
+
+## A dirty query increment with fixed query-source frames
+
+Suppose S contains arbitrary s in F16 and W_p stays in F17. To increment
+Q_k by R[k,p]D_p u_p, execute the following for all nonzero R[k,p]:
+
+1. Q_k -= R[k,p] S.
+2. Apply A_p^(-1) to S, then S += W_p, then A_p to S.
+3. Q_k += R[k,p] S.
+4. Apply A_p^(-1) to S, then S -= W_p, then A_p to S.
+
+The two Q updates cancel the old s. At the second update S has logical
+s+D_p u_p in F16. Its last three operations return it to s in F16. W_p
+is never a destination. All additions occur in equal full phase frames.
+There are four native lines and four full-cover maps per query port.
+Replacing both Q-update signs reverses the query increment while again
+restoring S. Query compute and uncompute therefore cost 8*104=832 H1.
+
+This is the reversible dirty-ancilla principle specialized to the literal
+routed native operators: an unknown workspace contribution is subtracted
+before computation and added after it, then the workspace computation is
+undone. The compensation and both inverse paths are paid explicitly.
+
+## Paired dirty responses
+
+For each response port p, a response visit with sign t does:
+
+    S += L_p(Q); A_p^(-1) S; W_p += t S; A_p S; S -= L_p(Q).
+
+It returns S and changes W_p by t D_p^(-1)(s+L_p(Q)). Each visit costs two
+native lines and two maps. Execute a positive visit for all eight A ports
+before computing q, and a negative visit for all A after Q has become Q+q.
+Their difference is exactly -D_p^(-1)L_p(q): both the arbitrary S dirt and
+arbitrary original Q dirt cancel. Then uncompute q using the unchanged J
+sources. This restores every Q and S content and frame. The 16 visits cost
+32 H1. No private query accumulator survives across native recursion; Q/S
+are explicitly borrowed full-cover resources throughout.
+
+The future block thus costs 832+32=864 H1. The unchanged prefix and F0
+inverse suffix contribute 112, for **976 complete-decoder H1**. The frozen
+WORDS and RESULT give every event and the full map/wrapper/scalar invoice.
+No borrowed CLEAR appears anywhere in the replacement block.
+
+Its complete invoice is976 H1,1952 wrappers,1104 cover maps,3488 unit ADDs,
+992 quarter ADDs and296 owned/private CLEARs:40400 scalar allowance under
+the source tariff8/unit ADD,12/quarter ADD,2/CLEAR. The pivot below costs
+352 H1,704 wrappers,480 maps,2240 unit ADDs,992 quarter ADDs and296 CLEARs,
+for30416 scalar allowance. Maps and wrappers still need physical tariffs.
+
+## Bounded pivot and comparison with the original decoder
+
+The fixed-frame query preservation premise is stronger than requiring the
+owned outputs to be correct at return. In one bounded pivot, align each of
+the 104 query W arrays in place, add its contribution to Q, and retain that
+aligned frame until Q is uncomputed. Then return W to F17. This pays only
+two native lines/maps per query port, or 208, while the same paired responses
+cost 32. Its complete decoder costs **352 H1** and restores all nine borrowed
+arrays. It never changes the final output contract.
+
+This is not promoted as a new improvement: the original canonical PR2707
+already costs 336 H1 and needs no additional owned D arrays. The pivot adds
+16 native calls and nine borrowed banks. The primary checker preserves the
+original as an explicit comparator. The 976-H1 failure is restricted to the
+literal fixed-query-frame dirty-copy strategy, not all dirty-workspace
+strategies. The 352-H1 result supplies no optimality or storage lower bound.
+A separate parallel dead-output aliasing construction is outside this package
+and is neither an executable nor a scientific dependency.
+
+## Verification and native scope
+
+Canonical inputs are authenticated before inherited code executes. The
+canonical source word is regenerated. Each proposed complete word is checked
+on 224 independent original inputs forwarded through F0/B1 and on 224
+independent current X/Y symbols against the source's ordered inverse formula.
+The nine borrowed dirt symbols are independent in both executions. The
+intermediate inverse-B1 checkpoint and all final outputs/frames are checked;
+all borrowed X/Y and Q/S content and phase frames must return exactly.
+
+Repeated scratch use would accumulate redundant phase terms. The interpreter
+merges identical parity vectors modulo4, drops zero terms and checks equality
+of the entire phase polynomial before and after each compaction. This is an
+exact representation reduction; the frozen words and their operations do not
+change. The interpreter adapts PR2707's exact routed algebra and complete modulo-four
+phase comparisons on all 73 coordinates. Signed native kernels are checked
+for both signs on all 512 local columns for all 112 ports; every new native
+occurrence is bound to one checked signed recipe. The114688 column tests check
+the recipe basis; they are not976 independently new native kernel proofs. This is credited reuse,
+not a code-disjoint proof of the inherited primitives. The source native
+identities and tensor extension give the same conditional arbitrary-array,
+positive-tensor-length interpretation as the predecessor. No finite replay
+is claimed to establish physical routing, recursive tariffs or precision.
+
+Controls omit the old-dirt response, query uncompute, scratch subtraction,
+affine payload shift, or correct response sign, and attempt an illegal CLEAR
+of a borrowed query bank. They must fail. For a concrete dirty witness, take Q0=constant1, all other Q/S and all J
+inputs zero. Omitting the first response leaves future W0=-1/4 even though
+the desired query is zero; owner permutations fix constants. RESULT pins
+that port and coefficient. These controls distinguish a truly
+restored dirty workspace from a computation that happened to start clean.
+
+## Budget decision and reopening condition
+
+PR3976's retained exact receipt gives a 553-H1 native-only cap for one proposed
+module at each first-B1 cut (16 sites per 144 calls), under unchanged W=896/9,
+centre64 and ideal rank51 remainder completion. This package reuses that
+conditional screen, rather than deriving a new moment or assuming actual
+consumer admission. The fixed-frame word exceeds it by **423 H1**, with all
+physical costs still favorably ignored. The cheaper pivot's native count is
+below that cap but is dominated by the original decoder; passing a screening
+cap would not pay its placement or establish a new supplier.
+
+Stop this exact borrowed-dirty substitution. Reopen only with a named native
+or scalar cancellation, genuinely available workspace, and a complete
+restoration contract that changes this comparison. Dirty ranges and rounded
+cancellation errors need new bounds; exact cancellation does not authorize
+transferring an earlier precision guarantee. The actual global provider
+remains gauge44, and no new kappa, family coverage or centre credit is claimed.
+
+## Credit
+
+The reversible compute/uncompute and dirty-baseline subtraction idea is
+standard reversible linear algebra; the new contribution is its source-pinned
+QQ16 native realization, complete restored-state checks and failed cost
+comparison. Credit ywz65 PR2707; Arham Tahir PR2681; Ali Romman and the retained
+QQ16/native/geometry lineage; PR3985's rectangular cut and owned-copy result;
+and PR3976's conditional incidence/cap. New work Chris R / Clear1nsight with
+substantial OpenAI Codex assistance, Apache-2.0. Source notices are preserved.

research/qq16-dirty-commutator/README.md

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+# A priced dirty-ancilla replacement of the rectangular QQ16 correction
+
+An explicit reversible repair replaces PR3985's112 additional owned full-cover
+temporaries with **nine mutable borrowed banks**, supplied in F16 with arbitrary
+content and returned exactly. All224 current X/Y input fields remain frozen;
+all224 original recovery outputs still finish in F17. No borrowed bank is cleared.
+
+It fails the intended cost screen. Keeping all104 query-source W fields in F17
+throughout the rectangular block costs **976 H1**, not224. The before/after
+response cancels arbitrary query and scratch dirt, but computing and uncomputing
+the query pays832 lines; responses pay32, and the unchanged decoder pays112.
+Against PR3976's explicitly conditional553-H1 native-only allowance, this exact
+strategy exceeds the cap by423. No universal dirty-ancilla lower bound follows.
+
+One bounded pivot temporarily aligns the104 owned query outputs until the query
+has been uncomputed. It costs352 H1 and restores all borrowed state, but the
+original PR2707 decoder already costs336 H1 with no additional D temporaries.
+The pivot is therefore not presented as a new improved decoder. The result is a
+source-pinned stopping decision for this attempted ownership repair.
+
+| Complete word | H1 | Wrappers | Cover maps | Unit ADD | Quarter ADD | CLEAR | Scalar allowance |
+|---|---:|---:|---:|---:|---:|---:|---:|
+| Canonical PR2707 |336|672|464|1808|896|312|25840|
+| PR3985 owned rectangular copy |224|448|352|1920|896|536|27184|
+| Fixed-query-frame dirty repair |976|1952|1104|3488|992|296|40400|
+| Aligned-query dirty pivot |352|704|480|2240|992|296|30416|
+
+The dirty words have zero extra owned D arrays and nine extra borrowed full-cover
+banks; the unchanged owner-private peak is16. Those banks are a required local
+interface, not storage proven available in the actual caller. Maps/wrappers are
+not free physical operations. Precision, dirty ranges, hosting, access, movement,
+actual outer consumption and productive-family coverage remain open.
+
+[PROOF.md](PROOF.md) states the ordered commutator identities and complete scope.
+RESULT records both invoices, a concrete dirty-baseline witness, failure controls
+and source pins. WORDS freezes both complete programs. No new kappa, second centre
+credit, or globally admitted consumer is claimed. The actual global provider
+still names gauge44.
+
+## Reproduce
+
+Python3.12 standard library:
+
+```
+python3 -I -Werror -B research/qq16-dirty-commutator/verify.py
+python3 -I -O -Werror -B research/qq16-dirty-commutator/test_verify.py
+python3 -B scripts/research_package.py --package research/qq16-dirty-commutator
+```
+
+Default replay authenticates source bytes before inherited execution and compares
+both complete words and the typed receipt. It checks arbitrary original and
+current routed inputs, independent dirt in all nine borrowed banks, full73-coordinate
+phase frames and every borrowed return. Six semantic controls reject broken
+dirt cancellation, return, map payload, sign or ownership. Signed kernel basis
+checks cover112 ports with both signs (114688 columns); each976/352 occurrence
+is bound to one such recipe, not described as a new independent kernel proof.
+Boundary tests cover source/manifest/data/word/receipt mutation, generation
+refusal, and normal/optimized Git-free read-only exports.
+
+## Open next questions
+
+Reopen only if an actual typed replacement deletes some of the paid native
+compute/uncompute paths or supplies genuinely dead owned workspace with a
+restoration proof. First name those events and compare against both PR2707 and
+PR3985; a reduction relative to the expensive dirty construction alone is not
+an improved known decoder. Physical availability and a full caller bill must
+precede another parameter or precision round. A separate parallel output-aliasing
+construction is outside this package and is not a dependency.
+
+## Workflow and credit
+
+Explicit user-assigned reversible-computation lane, original
+`joint-query-controller` card, priority6, canonical base20ecf2891d80b5acf18d980b2164fb44ea7faa90.
+Main remained unchanged at round entry and the pre-pivot checkpoint.
+[Canonical claim](https://github.com/CrocSwap/integer-mult-bounds/pull/3985#issuecomment-6263114494).
+Targeted live dirty/commutator overlap and shared Discussion review have partial
+coverage. Adjacent3374 prices widths;3422 records a dirty fault magnitude;
+3985 supplies the rectangular cut. They do not price this restored borrowed-bank
+substitution. No exhaustive novelty claim is made.
+
+Credit ywz65 PR2707, Arham Tahir PR2681, Ali Romman and the retained QQ16/native/
+geometry/supplier lineage, PR3985's owned-copy construction and PR3976's conditional
+cap. Reversible compute/uncompute and dirty-baseline compensation are standard
+linear-algebra techniques; the new result is this literal source-bound realization
+and bounded failure decision. New work Chris R / Clear1nsight with substantial
+OpenAI Codex assistance, Apache-2.0. Independent AI review is not human or formal
+verification. Exact reuse is recorded in PREDECESSORS and SOURCES.