Emit shared-port fusion and bound its free five-target completion (no new κ)

research/block3-shared-port-composition/.gitattributes

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+inputs/* -text

research/block3-shared-port-composition/HANDOFF.md

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+# Handoff: finish the explicit fused coupled interface without an extra rank1 child
+
+The actual five-bank word now exists with source phase conventions, a true raw inverse transpose and exact ownership. Four adjacent segments fuse into rank3 children; the paid profile is `{1:2,3:4}`. The endpoint and u_j recurrence are in README/PROOF and WORD.json is executable.
+
+An all5-target consumer must cost zero additional ordinary recursive calls unless it also removes existing paid work or changes the disjoint target census: one extra rank1 call makes the optimistic moment nonpositive for every0<=C<1. The explicit original-input snapshot/reset alternative costs23 rank1 calls before final cleanup, so it is not a profitable repair.
+
+Smallest useful follow-up: derive a free invertible decoder of the actual endpoint, with native routes, source phases and scratch restoration charged, or prove a scoped obstruction for a precisely declared decoder alphabet. Do not repeat dense rank recovery of an ideal observation matrix. If the decoder introduces a new paid operation, rerun the complete profile inequality before expanding the construction.
+
+Source head pins are in ORIGINS.json. Refresh current PRs/discussions before taking this handoff. No new κ is claimed; complete caller, precision, compiler reserve and outer transfer remain later obligations.
+
+```json
+{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"complex-rank-shape-decoder","scope":"Complete the actual fused five-bank coupled endpoint with zero additional recursive calls or a changed complete paid profile","base":"624de9dc66858af0945e5f8a0942488d62280d43","expiry":null,"artifact":null}
+```

research/block3-shared-port-composition/ORIGINS.json

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+[
+  {
+    "pr": 4813,
+    "head": "f982ecc06826e7087e69b9468d3ff52589fd0822",
+    "source_path": "research/complex-block3-five-in-fourteen/verify_schedule.py",
+    "path": "inputs/pr4813-verify_schedule.py",
+    "sha256": "6216fd67f1a762303f0eed0e37b90ea0c72cf8e0cb7db70b1b27b2001ac20069",
+    "git_blob": "17a8439633effba74fff63a8fe4c332b8d709d80",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f982ecc06826e7087e69b9468d3ff52589fd0822/research/complex-block3-five-in-fourteen/verify_schedule.py"
+  },
+  {
+    "pr": 4743,
+    "head": "158048812f4e0aeb132408f4d7cda57ba008b0d5",
+    "source_path": "research/complex-prefix-native-ports/FULL-INPUT-PORT.md",
+    "path": "inputs/pr4743-FULL-INPUT-PORT.md",
+    "sha256": "52b8462e28f9e87925ccfea27872630e2b2da23f19fd3d2265c2654bc016088c",
+    "git_blob": "39a461f2fbf2e009423cd784f56de121d190d842",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/158048812f4e0aeb132408f4d7cda57ba008b0d5/research/complex-prefix-native-ports/FULL-INPUT-PORT.md"
+  },
+  {
+    "pr": 4743,
+    "head": "158048812f4e0aeb132408f4d7cda57ba008b0d5",
+    "source_path": "research/complex-prefix-native-ports/SECTOR-COMPLETION.md",
+    "path": "inputs/pr4743-SECTOR-COMPLETION.md",
+    "sha256": "2e72e19c4733213d1875f60cf87eddb733dde9266cf2581cb56393c3fabf1933",
+    "git_blob": "d3fcedfa0ef8c569810cbfe3b001e509be1274aa",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/158048812f4e0aeb132408f4d7cda57ba008b0d5/research/complex-prefix-native-ports/SECTOR-COMPLETION.md"
+  },
+  {
+    "pr": 4743,
+    "head": "158048812f4e0aeb132408f4d7cda57ba008b0d5",
+    "source_path": "research/complex-prefix-native-ports/NOTICE.md",
+    "path": "inputs/pr4743-NOTICE.md",
+    "sha256": "04a7423af5af1f5c2e9e2772fb1e3bfeb6158abb1464bfe3ffad7f00b7946782",
+    "git_blob": "6f2cac2711e1f6c4c5578b215ae07d700cd60f35",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/158048812f4e0aeb132408f4d7cda57ba008b0d5/research/complex-prefix-native-ports/NOTICE.md"
+  },
+  {
+    "pr": 4628,
+    "head": "ee4fd87f064017c23e5a86fc1dcfe0a5237caed3",
+    "source_path": "research/complex-small-m-lower-bounds/README.md",
+    "path": "inputs/pr4628-README.md",
+    "sha256": "565b38d373a333dec701839b71c485d27ec5c1383816a2e816f93f2883763069",
+    "git_blob": "764fe1ea7b6d31e39f802233fdaeb5514f4b4ab4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ee4fd87f064017c23e5a86fc1dcfe0a5237caed3/research/complex-small-m-lower-bounds/README.md"
+  }
+]

research/block3-shared-port-composition/PR-DRAFT.md

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+## Change and mathematical scope
+
+Construct the actual five-bank shared-port word proposed in #4813 using #4743's dirty-input native interface. Four contiguous pure-word segments satisfy `A D=N K` with unit-phase monomial N, so their literal emission changes the local paid profile from14 rank1 children to **two rank1 plus four rank3 children**, with24 monomial passes and10 ADD passes. WORD.json contains both versions and the actual raw inverse transpose.
+
+The endpoint remains coupled:
+
+```text
+u0=x0; u_j=D x_j+B u_(j-1), j=1,...,4
+outputs=(A² x0+F u4, A u1, A u2, A u3, A u4).
+```
+
+No output job is double credited. There is no claimed complete five-target unit or new κ. Granting all five rank3 targets and free finite work gives optimistic moment `3^(1-C)-2`. One additional rank1 completion child makes it `3^(1-C)-3<=0` throughout0<=C<1, strictly forC>0. The handoff therefore requires a zero-recursive-call completion or another change to the complete bill/inventory.
+
+An explicitly emitted original-input snapshot/reset policy instead costs23 rank1 calls,69 monomial passes and23 ADD passes, with five dependent saved fields still requiring final cleanup. Its restricted single-bank reset lower bound is stated separately from general decoder possibilities.
+
+## Task and overlap
+
+Base and latest fetched canonical main: `624de9dc66858af0945e5f8a0942488d62280d43`; priority revision7. Task `complex-rank-shape-decoder`, scope changed by explicit assignment following the missing-chronology audit. Native chronology and actual paid fusion can change a complete-cost decision; ideal observation rank is not repeated.
+
+Exact heads: #4813 `f982ecc06826e7087e69b9468d3ff52589fd0822`; #4743 `158048812f4e0aeb132408f4d7cda57ba008b0d5`; #4628 `ee4fd87f064017c23e5a86fc1dcfe0a5237caed3`. Five retained source files have immutable URLs, Git blobs and exact hashes in ORIGINS.json. Their CRLF bytes are protected by local attributes; replay has no dependency on cached unmerged objects.
+
+Bounded live searches of `4813 chronology`, `"shared" "port"`, and `"block3"` were refreshed. #4828 concerns sharp two-bank conditioning and #4835 finite address-algebra kernels. Newly read #4841 (`6debdcdac8fe1c87958f8cd42ccb7db73c0a0eef`) supplies a general changed-chart compiler and compensated retiming; it does not emit this particular shared-bank word/fusion/completion screen. #4842 supplies the distinct cascade-conditioning and admission audit that motivated this experiment. Ongoing coordination is in Discussion#4843; exhaustive novelty and unpublished work are not claimed.
+
+## Validation
+
+```sh
+python3 -I -B research/block3-shared-port-composition/verify.py
+python3 -I -O -B research/block3-shared-port-composition/verify.py
+python3 -I -B research/block3-shared-port-composition/mutation_check.py
+python3 -B scripts/research_package.py --package research/block3-shared-port-composition
+python3 -B scripts/check_research_commit.py --package research/block3-shared-port-composition --check-source-history
+```
+
+Python3.12.3, Linux. Exact replay covers all40 basis columns and one dirty vector at width1; fourteen basis columns and one dirty vector at width2. It compares raw/fused words with an independent block recurrence, literal reverse, serialized raw inverse transpose and all1,600 bilinear inverse-transpose entries at width1. The snapshot policy's saved outputs and original-input ownership are checked. All scientific checks remain active under optimized Python.
+
+Separate optimized subprocesses reject retained-source corruption, a changed raw-dual ADD sign and a falseκ receipt in a Git-free export. Source arithmetic/letters are reused and disclosed; chronological emission, fusion, owner recurrence and interpreter are new. The all-width statement uses pure-word tensorization and block substitution, not finite-width extrapolation. No Lean, original complete native suite, complete caller/compiler/outer replay, hosted CI or independent human review is claimed. Native scalar/routing/storage/precision remain explicit separate obligations, with the source native contract cited.
+
+## Credit
+
+Prepared for Chris R / Clear1nsight with substantial OpenAI Codex assistance, Apache-2.0. Credit Dugongue #4743 for actual dirty-input ports and native/precision theorem; Yiyang/Lyy-iiis #4710 and lee-phys #4688 for phase/residual lineage; hexapode #4813 for the proposed cascade; Jacob Alan Sussman #4628 for the scoped small-unit model/bounds. Notices and exact source bytes are retained.
+
+## Open next questions
+
+See HANDOFF.md. Complete the actual fused endpoint with zero additional recursive calls, restored owners and charged native work, or remove an existing child/change disjoint target inventory. A paid completion must pass the complete moment screen before further expansion. A profitable complete caller must then fund precision, compiler reserve and outer transfer before any κ claim.

research/block3-shared-port-composition/PROOF.md

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+# Chronology, fusion, ownership and complete-cost screen
+
+## Formal all-input identities
+
+Write U3(a,b)=(Aa, D b+B a), U2(a,b)=(Aa, A b+F a), where B=D L A, F=A L A, L=P+2Q and all products refer to the source's separately tensorized letters. The exact base pure-word identities `D P A=M C2` and `D Q A=K a` are checked separately; tensorizing each pure identity gives `D_f(P_f+2Q_f)A_f=M_f C2_f+2K_f a_f` at every width. Each port is a finite chronological reversible word on two arbitrary banks. The source implements a monomial-weighted ADD by mapping/restoring its source, so no original input is silently copied or destroyed. The exact inverse of U3 is `(A^-1 t, D^-1 u-L t)` and of U2 is `(A^-1 t, A^-1 s-L t)`.
+
+Composition U3(0,1) followed by U3(1,2) gives
+
+    b0=A x0,
+    b1=A D x1+A B x0,
+    b2=D x2+B D x1+B² x0.
+
+The second port therefore acts on `D x1+B x0`. It does not have the original x1 as its source. This is a literal substitution calculation, valid over any ring of compatible operators. Repeated substitution gives the u_j recurrence and five-bank endpoint in README. All five original inputs remain independent and present; no extra productive input or helper reward is introduced. The final ownership inventory is one original input per x_j, with an invertible but coupled output map. No output is credited as an autonomous job merely because its diagonal coefficient has a useful rank.
+
+## Exact emitted fusion
+
+Between each three-call port and the next port's first call, the shared bank undergoes the adjacent chronological sequence
+
+    C0, W, C2, V, Z1, C0.
+
+Its total operator is A D. The exact base identity `A D=N K`, with N a monomial whose entries are unit phases, gives the f-fold tensor identity `(AD)^(tensor f)=N_f K_f`. It involves no sum, so it does not make the invalid substitution `(P+2Q)^(tensor f)=P_f+2Q_f`. This replacement is therefore a rank3 Gaussian child followed by one actual monomial pass. The source per-column monomial odometer realizes N_f as an ordinary finite native pass, with owned workspace.
+
+All four matches are present in the literal five-port word. They replace12 rank1 children by4 rank3 children. The first A on bank0 and closing A on bank0 have intervening cross-bank contacts and are retained. Raw profile `{1:14}` becomes `{1:2,3:4}`. The rank mass stays14; the nonlinear recursive moment changes. The all-rank1 small-unit model of #4628 is not silently changed to count a rank3 child as one rank1 call.
+
+The emitted finite bill is6 child invocations (two of rank1, four of rank3),24 monomial passes and10 ADD passes: five with coefficient1 and five with coefficient2. These are array-level primitive counts, not a machine-time or precision certificate. Workspace remains a separately charged native resource. Fusing the Gaussian children also needs the ordinary caller's contract for a rank3 child; no custom arithmetic oracle is supplied by a matrix identity.
+
+## Raw inverse transpose
+
+For chronological gates G1,...,Gr, the primal operator is M=Gr...G1. Then M^-T=Gr^-T...G1^-T, so its chronological gate list has the same order, with each gate replaced by inverse transpose. For a unitary single-bank operator G this replacement is conjugate(G). For `dst += c src`, with real rational c here, it is `src -= c dst`. The raw dual has the same recursive profile `{1:2,3:4}`,24 monomial passes and10 ADD passes (with reversed direction and negated coefficients). The raw dual uses no complex conjugation in its bilinear pairing. Applying inverse primitives in reverse order instead constructs M^-1. The verifier checks these different constructions separately and rejects using the forward word as the raw dual.
+
+## Scoped optimistic bound
+
+Set t=1-C, 0<=C<1. Grant all five independent rank3 jobs, even though their extraction is still unproved, and set every finite bill to zero. This gives the upper bound
+
+    legitimate reward <= 5*3^t,
+    recursive cost >= 4*3^t+2,
+    moment <= 3^t-2.
+
+This upper bound is positive only for `C < 1-log(2)/log(3)`. It is a relaxation, not a κ value or evidence of a free consumer. If the same target census and paid profile require one additional ordinary rank1 child, the upper bound becomes `3^t-3<=0`, strictly negative for C>0. Hence there is no funded positive moment anywhere in this declared interval for that completion model, before compiler reserve and finite bills. The proof is interval-wide because 0<t<=1 implies 3^t<=3. A changed recursive profile, additional disjoint independent outputs or another consumer lies outside the bound.
+
+## Explicit original-input reset policy
+
+The alternative in WORD.json, `snapshot_restore`, saves each first-port output in an owned zero work field, applies D^-1 to the shared bank and subtracts L times the preceding retained A x. This restores the original input for the next port. Before the closing port it saves A x0 and restores x0 with A^-1. It has five original inputs and five zero-initialized dependent work fields; none of the work fields is a productive independent input.
+
+Its emitted bill is23 rank1 calls,69 monomial passes and23 ADD passes, before returning the five saved outputs/work fields to the caller's required state. The checker verifies the exact original-input observations, not just their rank. Four D^-1 reset paths cost2 calls each; A^-1 costs1. In the restricted single-bank path model with only monomial maps between rank1 Gaussian calls, a column's support is at most2^s after s calls. D^-1 has support4 and A^-1 support2 at width1, so these reset counts are minimal within that path model. This does not constrain split-register free decoders, alternative storage protocols or changed heterogeneous recursive children.
+
+The policy already exceeds the desired14 rank1 calls before full target recovery or work-field cleanup. No further attempt to optimize that unchanged policy is justified by its complete-cost screen. The retained-interface fusion above changes the premise and is the separate constructive lever; its free completion remains open.