[petalas]

Summary

Scoped construction and composition proof: consecutive paid CRT row queries now reuse one supplied 52-role physical ROM bank. The ten-row fixture retains 8,894 work cells instead of the derived equal-capacity distinct-bank baseline of 24,314, saving 15,420 finite-symbol tape cells. No new kappa or selected-frontier change.

- allocate a distinct ROM bank for each active RowQuery
+ lease the same preallocated bank after the previous query retires

This answers the shared-ROM part of Open next question 2 in Ali Romman's merged #5625. The new interface preserves each role's identity, complete historical extent and blank reentry. Numerical workspaces and the three other joined ports remain separate and fully charged. At fixed node, q active rows save exactly (q-1) B(P,H) cells under the declared distinct-bank contract.

The 52-role inventory, B(P,H) formula and within-row extent argument are commdata2338's #5519, with its retained predecessors. The new step is executable reuse across separately constructed rows and the source-update boundary. Their numerical, ROM and caller theorems are cited premises, not audit deliverables. The contribution was produced by Nick Petalas; all source notices and predecessor credit retain their bytes.

Advance CLAIM. Canonical base 19fdb086ea96af9a9f87936a2b888e10af4ed810, priority revision 8. Only research/crt-shared-row-banks/ is added.

Evidence

• Before: the declared contract retains six separate 3,084-cell banks in the complete level fixture. Its other work backing is kept in the baseline.
• After: the changed caller executes ten rows and twelve physical producer calls with one bank. The source round trip, protected dirty bytes and nontrivial heads, numerical retirement, joined retirement and every historical bank-tail cell pass. Exact physical-identity accounting gives the 15,420-cell reduction.
• A two-row control runs a long target followed by a short target within each row and reuses that backing at the next row. Five semantic controls reject overlapping leases, a wrong release object, a nonblank historical tail, a changed extent and source drift.
• RESULT.json is generated, compared on replay and bound to the implementation and source manifest by SHA256. All 36 declared live inputs have exact pins.
• CPython 3.12.15 on macOS 27.0.1 arm64: warning-strict registered normal and optimized commands pass in 24.168s and 23.151s. Both have 240-second timeouts. A separate direct verifier run passes in 22.539s. These are timeout measurements, not speedup claims.
• Metadata/pins, committed bytes and modes, declared source history, the official 44-file export and all 36 input checks pass. Optimized Git-free replay with empty executable PATH passes from the read-only export and preserves all 45 extracted files. No predecessor scientific replay was run.

Exact reproduction from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/crt-shared-row-banks/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -O -B research/crt-shared-row-banks/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/crt-shared-row-banks
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/crt-shared-row-banks --check-source-history --check-modes

Any CPython 3.12 executable can replace the local path. Expected markers: PASS_CRT_SHARED_ROW_BANKS, PASS_REGISTERED_RESEARCH_PACKAGE, PASS_RESEARCH_COMMIT_BYTES.

Limitations and unrun obligations

This is a source-bound scoped proof with finite executable corroboration, conditional on the credited producer and caller contracts. Clean preallocated bank supply is an entry premise. Counts are finite-symbol tape cells; source/protected backing, interpreter metadata and exterior reserves are additional. Numerical banks are still charged separately. The adapter adds fixed ownership control and changes allocation wiring, preserving all runtime tape instructions; no binary transition compiler is supplied.

Arbitrary dirty acquisition, failure rollback, composition with the separate numerical owner, changing-precision node boundaries, whole-tree and exceptional-key execution, full supplier admission and all five selected framework assumptions remain open. The selected cold replay, Lean and a complete multiplication theorem were not run or claimed. Independent human and formal proof-kernel review are unclaimed.

Open next questions

• Compose JoyboyBrian's existing #5505 reusable 63-role numerical owner with the source-update/shared-ROM caller. Start by binding its live-result lease and paid marker reinstatement to this close/reentry boundary.
• Cross one changing-precision node boundary with actual protected-word conversions and source ownership. Monotone bank capacities alone do not prove that caller contract.
• Supply and price clean bank capacity from arbitrary dirty backing, including restoration or allocation.

Related open work

• #4192 gives the sequential Beneš arena compiler/query component inherited by the ROM producer. This package changes its caller's cross-row bank ownership and uses the credited arena footprint; it does not audit that compiler or change its bill.
• #4187 prices the CRT last-K two-slice streaming wrapper. This package addresses the internal row ROM-bank lifecycle; it does not supply that wrapper's complete evaluator or alter its tariff.

Live open-PR, merged-work, main README, cached full-PR/Discussion and batch-claim searches found no matching cross-row ROM-bank interface in their stated coverage. Search coverage does not exclude unpublished work. The adjacent composite-chirp work #6002 concerns a different numerical operator and does not compute this retained-bank quantity.

Completion refresh inspected all 15 other open account PRs created since the advance CLAIM: #6013, #6014, #6015, #6016, #6017, #6019, #6020, #6021, #6022, #6023, #6024, #6025, #6026, #6027 and #6028. Their result scopes cover packed-bit averages, decoder spectra, helper algebra, continuation headers, transpose replay, convolution/routing refinements, precision and lattices. None studies this 52-role CRT ROM-bank reuse interface or computes its retained-bank quantity. No extra computations were run to check their results, and no conflicting shared numerical value was identified.

• #6020 reduces continuation-header storage under a parent/child suspension contract. This package reuses ROM backing between retired row queries; the storage objects and numerical claims differ.
• #6028 reduces XOR-routing tape travel while restoring one dirty scratch record. This package changes bank allocation and leases, preserving its runtime tape instructions; no routing tariff or numerical count is compared.

CI notes

At head 1d63837a18287830a71707f9cd5f21f17a8c8444, run 40592004886 completed successfully. Both hosted checks passed: plan and replay (research/crt-shared-row-banks). The completed checks were read once, and the successful run head matches the PR head. Hosted replay executed the registered normal and optimized commands and confirmed committed inputs remained unchanged. This certifies the bounded automated replay; independent human and formal proof-kernel review remain unclaimed.

Merge danger

Door: two-way.

Blast radius: isolated.

One standalone research package and its opt-in replay are added. No shared code, selected record, frozen evidence or predecessor source is modified.