Recursive interface: coalesce restoration with cancelling readers

[thakrarsagar]

Change and mathematical scope

Five children can each read and negate a dirty workspace, yet share one final restoration. With reader coefficients [1,1,1,-1,1], both eager and deferred execution add 3W to the data and restore W. The restoration bill falls from five negations to one. Requiring a checkpoint after child two raises the optimum back to five.

This recursive-interface construction and tooling result corrects PR1155's claim that read-free children are necessary. It adds a 73-line planner, a necessary and sufficient interval criterion, a proof of the minimum over checkpoint-correct partitions, and a complete conditional node bill. Every chosen cut must reproduce eager data and workspace. The implemented domain is exact integer diagonal readers and signs with fixed additive restoration prices. No supplier adoption, runtime improvement or new kappa is claimed.

Construction, proof and recurrence. Physical routing/frame admission, whole-call hosting, numerical precision beyond the exact integer model and analytic transfer remain open.

Task and overlap

Base: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe. Assignment seed 53, recursive interfaces. Scope key: restoration-coalescing/diagonal-readers/checkpoint-correct-cuts.

The closest predecessor is PR1155 at 9821c6e9388f3fc097e94b72be9fa7b41a849527. Its original certificate and valid failing-reader example still pass. Its unchanged interpreter also confirms this new counterexample. PR249/309's dirty-response algebra is credited; linear cancellation is not claimed as a new discovery. The new evidence is the applicability correction, observation boundary and independently checked cut planner.

Task card and rejected covered candidates · exact source pins. The final pre-submission check covered 808 open PRs through #1196 and current discussions. No matching correction or planner appeared. Fetched upstream main remained at the investigation base.

Validation

rtk proxy python3 -I -O -B research/reader-restoration-cuts-seed53/verify.py
rtk proxy python3 -I -O -B research/reader-restoration-cuts-seed53/test_package.py

Expected: PASS_READER_RESTORATION_CUTS restoration=5->1 forced_cut=5 exhaustive=2851 seeded=160, then PASS_READER_CUT_PACKAGE with relocation, regeneration and four corruption controls passing.

CPython 3.11.15 and 3.14.8 pass normal and optimized replay. The independent literal-column oracle checks 19,167 partitions across 2,851 exhaustive small batches and 160 seeded longer batches. Checks include the complete dirty state at every cut, literal inversion, a counted scalar invoice, mathematical failure controls, nine invalid inputs and four corrupted files. These finite checks support the written argument; they are not formal verification of the multiplication theorem.

Validation record · exact certificate. Selected-record integrity and 25 related tests pass. Full cold replay, Linux execution, formalization and independent human review were not performed. Only this new research directory is added.

Credit

Aaron Wang / Navinor, with opencode, supplied PR1155's model and retained evidence. Credit also remains with eumemic's PR249/309 and the predecessor lineages listed in NOTICE.md. Prepared for Sagar Thakrar with substantial OpenAI Codex assistance. Apache-2.0; predecessor source attribution is retained.

[Mister-Meeseeks]

100-PR batch review at 85ac2880ea5bda44f28632b71ffa2b4e35ec6b7d.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Nonzero-reader counterexample to read-free necessity, summed-defect criterion and exact diagonal checkpoint planner; observation timing is explicit.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.