Clear1nsight · Oct 19, 2026 · Oct 19, 2026
diff --git a/research/qq16-recovery-fusion/PREDECESSORS.json b/research/qq16-recovery-fusion/PREDECESSORS.json
@@ -0,0 +1,111 @@
+{
+  "license": "Apache-2.0",
+  "new_author": "Chris R / Clear1nsight with substantial OpenAI assistance",
+  "dependencies": [
+    {
+      "source": "ywz65 PR2707",
+      "role": "FullF17word,phasebridge,replayinterpreter adapted; native input module authenticated beforeexec.",
+      "canonical_path": "research/qq16-line-normalized-decoder",
+      "canonical_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+      "head": "efa51a6c7ffec6edd556a98deedfe9deeba65809"
+    },
+    {
+      "source": "Arham Tahir PR2681",
+      "role": "Retained canonicalvendor source reconstruction, ordered row algebra, inverseformula andnativechecks reusedthroughauthenticatedPR2707 loader.",
+      "canonical_path": "research/qq16-line-normalized-decoder/vendor/pr2681",
+      "head": "ea96706295631be10d92ae149b63c3e24acaeabc"
+    }
+  ],
+  "context_only": [
+    {
+      "pr": 3952,
+      "head": "996ff698d3efd0bdce606e240f3b00e6ab91e7fc",
+      "role": "reduced96output demand; no bytes or code imported"
+    },
+    {
+      "pr": 3963,
+      "head": "82c812c45fbc2bc2751e5a0d02a3631af25c3cba",
+      "role": "full recovery boundary; no bytes or code imported"
+    },
+    {
+      "pr": 3339,
+      "role": "Separate consumer accounting caveat; no source bytes/code or quantitative claim imported",
+      "head": "123079bef40faf6949ebac7dfc2859c715acea80"
+    }
+  ],
+  "adaptations": {
+    "replay.py": "Copied PR2707 bridge/replay functions, renamed need calls to P.need, extended owned set byD0..D111 andzero/I finalcheck.",
+    "budget.py": "Exact rational atanh/exp interval method reused from authors earlier independent audit; no pending executable imports.",
+    "verify.py": "New sourceauthentication,rectanglewordgenerator,completeinvoice,pairedsymbolicreplays,mutants andreceipt.",
+    "native.py": "Copied PR2707 signedkernelchecker, adapted occurrenceinventory to positive2onA/1onU+T andnegative0onA/1onU+T;224total112*2signedrecipes."
+  },
+  "upstream_retained_manifest": {
+    "schema_version": 1,
+    "files": [
+      {
+        "local": "vendor/pr2681/verify.py",
+        "source_path": "research/qq16-zero-retention-comparison/verify.py",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "71f9a010553691e892703e3ec8d5eedf3e48d72b7f6af24b954a5442f4a52ccf",
+        "git_blob": "99bd60a9139b4d7ef070b69f38a954e64e0f8aa1"
+      },
+      {
+        "local": "vendor/pr2681/WORD.json",
+        "source_path": "research/qq16-zero-retention-comparison/WORD.json",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "f02e57d238f127c8fd195dc6a4a9dce6db6bee9f6050bd9d5b9c14cf6e1946d0",
+        "git_blob": "80de97cf168441a888e7d05fc2c3cace919f31ec"
+      },
+      {
+        "local": "vendor/pr2681/RESULT.json",
+        "source_path": "research/qq16-zero-retention-comparison/RESULT.json",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "e4f3ff28be27f96c341b225a62a2ba84d3907ed3466122d18bcaaf5a60da740e",
+        "git_blob": "a16a8f9a23cd00c9030f9b03cf0ae52c0ff4b526"
+      },
+      {
+        "local": "vendor/pr2681/SOURCES.json",
+        "source_path": "research/qq16-zero-retention-comparison/SOURCES.json",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "30a88d8bf33c603836fffdcab3c3dabf663b98f2deda95893685e394c60ea95c",
+        "git_blob": "1db7201ed145d1ef3707ab24bb599d341439050d"
+      },
+      {
+        "local": "vendor/pr2681/README.md",
+        "source_path": "research/qq16-zero-retention-comparison/README.md",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "b658e00db095f1097b9ae7ec49d8dd465c1a317cdc84da4251cbdd3e0af597d3",
+        "git_blob": "c3d4d76b28fa47b86da37cc7428d5da362c7bf9a"
+      },
+      {
+        "local": "vendor/pr2681/PROOF.md",
+        "source_path": "research/qq16-zero-retention-comparison/PROOF.md",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "471f6360cdac94d9e1054c6c9530ace1822b11942f7e141dfd344864d2357862",
+        "git_blob": "38cd38aa1d342f3bfe0d6d7f3c388aff0352f370"
+      },
+      {
+        "local": "vendor/pr2681/references/PR2540-PROOF.md",
+        "source_path": "research/qq16-zero-retention-comparison/references/PR2540-PROOF.md",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
+        "sha256": "09d587f1d6bc250e90e29fa8751a40f45be79f1a8a56af0b645c144cefaefa46",
+        "git_blob": "6ae136c8baef4793f4f7ae630720afff6c23a953"
+      },
+      {
+        "local": "vendor/pr2681/references/PR2540-README.md",
+        "source_path": "research/qq16-zero-retention-comparison/references/PR2540-README.md",
+        "head_commit": "ea96706295631be10d92ae149b63c3e24acaeabc",
+        "pull_request": 2681,
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+      }
+    ]
+  }
+}
diff --git a/research/qq16-recovery-fusion/PROOF.md b/research/qq16-recovery-fusion/PROOF.md
@@ -0,0 +1,167 @@
+# A rectangular future-logger correction for complete QQ16 recovery
+
+## Contract and source
+
+This transforms the exact full decoder in canonical
+`research/qq16-line-normalized-decoder/WORD.json` (ywz65 / PR2707, built on
+Arham Tahir / PR2681). It keeps all224 original x0/y0 outputs in F17, all224
+current X2/Y2 fields borrowed and unchanged, and no early retention. It adds
+112 exclusively owned full-cover temporary arrays D_p, initially arbitrary,
+which return to zero in identity frame. Peak owner-private scratch remains16.
+
+The complete inverse and native source algebra are inherited and rerun after
+byte authentication. The new statement is a same-output transformation of the
+future-logger inverse, not a new global inverse theorem or physical supplier.
+PR3952's96-output projection and PR3963's missing-boundary audit motivate this
+full-recovery repair but are not executable dependencies.
+
+## Exact rectangular operator
+
+Let A_p be the actual stage2 alignment, on a physical field:
+
+    A_p = C_qp^(-1) M_p.
+
+The source's full modulo-four phase identity states
+
+    A_p F17 = F16 D_p,
+
+where D_p is the actual ordered owner action and F16 is the coordinate product
+on axes9 through24. M_p includes its source-derived affine payload translation.
+Its inverse is M_p^(-1) C_qp, with the inverse translation transported by the
+owner matrix. These are arbitrary-payload operator identities; the checker
+compares all73 linear/quadratic phase coefficients at every ADD.
+
+At the entry to the future-logger block, W_p has logical u_p in F17. The original
+block conjugates every112 field by A_p, forms
+
+    q_k = sum_(p in U+T) R[k,p] D_p u_p,
+
+and updates only A ports by
+
+    y1_p = u_p - D_p^(-1) (sum_k R[k,p] q_k / 4), p in A.
+
+All U+T ports remain u_p. The disjoint query and response supports are the
+reason the all-field return conjugations can be replaced by a rectangular
+correction. There is no commutation of distinct owner actions.
+
+The new block is:
+
+1. For p in U+T (104 ports), clear owned D_p in F17, copy W_p into it,
+   apply M_p and then C_qp^(-1). These query copies have F16 and logical D_p u_p.
+2. Clear D_p at the8 A ports in F16. At each owner form all8 private q_k from
+   the104 query copies, then write `-sum_k R[k,p] q_k/4` into D_p at A ports.
+   Every query is complete before the response fields are updated. Clear all8
+   private q fields in identity frame and finish the entire owner body before
+   visiting another owner.
+3. For p in A apply C_qp and M_p^(-1) to the correction D_p. It now has F17
+   and the required ordered negative correction. Add it to original W_p.
+4. Clear all112 D fields in identity frame. The original104 query-source W
+   fields have remained untouched in F17 throughout.
+
+This produces exactly the original future-logger boundary. Therefore its
+unchanged predecessor and unchanged F0-inverse suffix produce the same224
+original outputs. Temporary clearing is legal because every D is owned;
+no inverse operation is needed to erase a disposable owned query copy.
+Clears are charged, not treated as free native inverses.
+
+## Native legality and verification scope
+
+The stage2 maps and positive/inverse line operators are the exact source
+operations. Every native event occurs outside an owner-private body. The
+complete physical source row convention and affine map order are retained.
+The new interpreter extends the source checker only with the112 owned D fields
+and their required zero/identity return. Existing Z/W output dirt and private
+F/G dirt remain adversarial. Borrowed X/Y are compared at exit with their
+original content and frames; all224 outputs are checked in F17.
+
+The verifier executes the whole fused word twice: on224 independent current
+X/Y symbols against the source's separate inverse formula, and on224 original
+x0/y0 symbols forwarded through F0/B1. It checks the intermediate inverse-B1
+checkpoint and all final outputs using exact rational coefficients with
+ordered owner matrices. The adapted predecessor signed-kernel checker verifies both signs for all112
+ports on all512 columns (114688 columns), binds every224 occurrence to its
+recipe, and rejects a missing negative-wrapper translation. This is explicit source reuse, not a code-disjoint native proof.
+
+The inherited phase identities plus linearity and ordered cover action extend
+the local result to arbitrary arrays and positive tensor lengths under the
+same native-child contracts. Finite symbolic replay alone is not a physical
+tape implementation, numerical stability analysis or all-depth admission.
+In particular the addition path changes, so predecessor rounded-error bounds
+must not be transferred without a fresh error and dirty-range argument.
+
+## Complete local invoice and actual deletions
+
+| Charge | Complete PR2707 | Fused complete recovery | Change |
+|---|---:|---:|---:|
+| H1 children |336|224|−112|
+| Native wrappers |672|448|−224|
+| Full-cover maps |464|352|−112|
+| Unit ADDs |1808|1920|+112|
+| Quarter ADDs |896|896|0|
+| CLEARs |312|536|+224|
+| Scalar primitive allowance |25840|27184|+1344|
+| Owned output arrays |224|224|0|
+| Additional owned full-cover temporaries |0|112|+112|
+| Peak owner-private arrays |16|16|0|
+
+Scalar allowance is8 times unit ADDs plus12 times quarter ADDs plus2 times
+CLEARs. The changed future block uses104 negative query lines and8 positive
+response lines, rather than112 negative plus112 positive lines. It removes
+104 query-source return lines/maps and8 response-entry lines/maps, while
+adding104 source-copy ADDs,8 correction ADDs and224 temporary CLEARs.
+
+All336 owned output/temporary arrays are individually identified. The112
+new temporary lifetimes span only this future-correction block, ending before
+the inverse-B1 checkpoint. The private16 peak occurs later in the unchanged
+F0 inverse. No alias with borrowed storage or free full-cover allocation is
+assumed. Physical storage, access, movement and allocation remain unpriced.
+
+## Budget interpretation and stopping point
+
+With the older hypothetical one-consumer-per-F/B-pair rate, unchanged m73,
+W896/9, centre64 total mass and ideal rank51 idle relaxation, the224-H1
+consumer gives the exact outward enclosure
+
+    1.000046718879394463 <= G <= 1.000046718879394464.
+
+It fails that model even when H8 and all physical overhead are absent. The
+same model's integer threshold is121 passing /122 failing. This is not a
+lower bound of224, a proof that every full inverse fails, or rejection of an
+actual global caller. The pair incidence is not established by the local
+word; the first F0/B1 cut occurs at a different frequency in the retained
+nine-stage schedule. Rebuilding that incidence and coverage can change the
+numerical conclusion. The sibling contribution handles that separate ledger;
+this package does not import its pending result.
+
+The session stops at this complete local identity and invoice. A physical or
+global construction needs an actual caller, integer invocation count, live
+family stock, coverage, physical movement/storage, precision, dirty-state
+bounds, and both all-depth supplier caps. Existing QQ16 core centre removal
+is not claimed again as credit. A passing relaxation under another incidence
+would still not discharge these obligations.
+
+## Open next questions
+
+1. Bind this full-recovery invocation to an actual outer caller and its exact
+   frequency. Recompute productive families and idle coverage from that schedule;
+   keep all112 temporary lifetimes and full physical overhead visible.
+2. Determine whether any of those112 new temporary lifetimes can be hosted in
+   genuinely dead owned storage, with a source-bound alias/return proof. Existing
+   Z outputs, borrowed X/Y and owner-private arrays are not free aliases.
+3. If the resulting physical budget permits further work, bound intermediate
+   magnitudes and rounding defects for this changed additive correction. Exact
+   equality does not preserve a former rounded execution trace.
+
+## Attribution
+
+Credit ywz65 / PR2707 for F17 line normalization and its complete native word;
+Arham Tahir / PR2681 for the ordered inverse and source reconstruction; ywz65
+/ PR2512, PR2492 and PR2468, thakrarsagar / PR2470, starship-s / PR2443,
+Ali Romman and the retained QQ16/native/geometry lineage. PR3952 and PR3963
+supply the motivating reduced-demand and actual-boundary audits; PR3908 and
+PR3946 the earlier conditional budget question. The separate consumer work
+by Nick Petalas / PR3339 records why a fixed idle bill cannot be transported
+unconditionally. Exact canonical input pins and modification credit are
+retained in SOURCES.json/PREDECESSORS.json. New work: Chris R / Clear1nsight
+with substantial OpenAI Codex assistance. Apache-2.0; no independent human
+or proof-assistant review is claimed.
diff --git a/research/qq16-recovery-fusion/README.md b/research/qq16-recovery-fusion/README.md
@@ -0,0 +1,68 @@
+# Full QQ16 recovery with a rectangular future correction
+
+This keeps PR2707's full224 original F17 outputs and reduces its native child
+bill from336H1 to224H1. The future logger reads104 ports but changes only8;
+owned query/correction temporaries let the unchanged104 fields avoid their
+return conjugations and let the8 response fields avoid entry conjugations.
+
+The complete local invoice is224H1,448 native wrappers,352 cover maps,
+1920 unit ADDs,896 quarter ADDs and536 CLEARs: scalar allowance27184.
+Relative to PR2707 this removes112H1,224 wrappers and112 maps, while adding
+1344 scalar allowance and112 owned full-cover temporary arrays. All temporaries
+return zero/identity, all224 current X/Y inputs remain borrowed and unchanged,
+and owner-private peak remains16. No early retention is used.
+
+[PROOF.md](PROOF.md) proves the rectangular operator identity and gives the
+literal schedule, all ownership/frame/cleanup requirements and exact scope.
+`WORD.json` is deterministically regenerated; `RESULT.json` is compared in
+full with type-sensitive equality. The verifier authenticates all canonical
+source bytes before executing reused predecessor helpers, then checks the
+whole new word on independent current and original routed symbols.
+
+The old one-consumer-per-pair fixed-coverage relaxation rejects224H1 at
+G in[1.000046718879394463,1.000046718879394464]. That rate is hypothetical,
+and differs from the actual first-cut frequency in the nine-stage schedule.
+This is not a global rejection. Productive-family stock, invocation incidence,
+coverage, temporary hosting, movement, numerical defects and all-depth supplier
+obligations remain open. No frontier or selected science changes.
+
+## Reproduce
+
+```sh
+python3 -I -Werror -B research/qq16-recovery-fusion/verify.py
+python3 -I -O -Werror -B research/qq16-recovery-fusion/test_verify.py
+python3 -B scripts/research_package.py --package research/qq16-recovery-fusion
+```
+
+Standard-library Python3.12. Normal replay is read-only and refuses modified
+source/word/receipt bytes. `--write` is only initial generation and refuses
+existing artifacts. Source reuse and exact checks are disclosed in
+PREDECESSORS.json and VERIFICATION.json.
+
+## Scope, coordination and overlap
+
+Explicit assigned follow-up of PR3963, canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90,
+priority6; no task reroll. [Canonical investigation](https://github.com/CrocSwap/integer-mult-bounds/pull/3963#issuecomment-6262031944).
+The nearest scopes are the full PR2707 decoder, PR3952's changed96-output
+endpoint, PR3963's missing full-recovery boundary, and PR2651's distinct early
+output-bank retention. This result keeps the full output endpoint and no early
+records, changing the future correction's native sweeps and temporary contract.
+Targeted searches for QQ16 future fusion/correction and224 inverse, plus the
+shared board/overlap check, have partial coverage: no complete remote snapshot
+or guarantee of novelty. TASK.json records the source checks and bounded stop.
+
+## Open next questions
+
+See the three bounded questions in [PROOF.md](PROOF.md#open-next-questions) and
+TASK.json: exact outer incidence/coverage, legal hosting of112 temporary
+lifetimes, and changed intermediate error bounds if a complete budget permits
+further construction. None is discharged by the local native savings.
+
+## Credit
+
+The new interpreter adapts ywz65 PR2707 and uses its authenticated Arham Tahir
+PR2681 algebra. Exact heads and reuse are in PREDECESSORS.json. Preserve credit
+to the current-frame demand, retained QQ16/native/supplier lineage, motivating
+PR3952/3963 audits and the conditional-budget sources named in PROOF.md.
+By Chris R / Clear1nsight with substantial OpenAI Codex assistance, Apache-2.0.
+No independent human, full physical supplier or formal proof claim.