Research: noncommuting reader restoration with a paid dirty-state wrapper

[mightyOil]

Change and mathematical scope

Research note / independent corroboration and exact recursive interface; no new kappa. PR1155's pinned note says any read of drifting workspace prevents deferred restoration. Nonzero readers can instead preserve the observed value: for distinct outputs, the exact all-input condition is H_i(P_(i-1)-I)=0. With one shared output observed only at batch exit, only the sum of defects must vanish. The note proves both statements and gives explicit compatible and incompatible examples.

A noncommuting eight-coordinate, three-child construction includes pre-read cancellation of arbitrary incoming dirt and both complete additive source calls. In the declared fixed borrowing interface, its full emitted word falls from 210 to 150 two-address ADD instructions and 5864 to 4504 data-tape word transitions. The recurrence charges source/coefficient access, both recursive directions, routing, scratch restoration, preparation and dispatch. These are exact online invoices, not a runtime benchmark; extra preparation must be paid before claiming an end-to-end gain. Direct evaluation can be cheaper than either toy wrapper. No supplier, selected frontier, upstream file or review ledger changes.

Task and overlap

The final submission check found Sagar Thakrar's just-opened #1199, pinned
at 85ac2880ea5bda44f28632b71ffa2b4e35ec6b7d. Its README was inspected. It
independently corrects the same claim, implements a diagonal-sign checkpoint
planner and states the general summed-defect identity. No priority is claimed
for the correction or identity. The distinct contribution here is noncommuting
permutation coverage with independent output ports, a wrapper whose outputs are
independent of incoming scratch dirt, and separately implemented symbolic
scalar/tape accounting. This neither repeats nor supersedes its cut planner.

• OS-random assignment seed 50, recursive interfaces; task card: research/invariant-reader-restoration/CLAIM.md.
• Exact base: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe.
• Nearest predecessor: Research note: restoration coalescing across a recursion batch (read-free + composable-family boundary; no new kappa) #1155 at 9821c6e9388f3fc097e94b72be9fa7b41a849527; its original note is retained unchanged with SHA256/Git-blob pins.
• Research: batch common-factor product shears with dirty restoration #889 already supplies shared-B dirty fanout/echo cancellation; no new batching priority is claimed. The additional evidence is noncommuting reader compatibility through intervening permutations and its independently checked invoice.
• Research note: restoration deferral is mass-neutral in the hosted T37 recurrence (no new kappa) #1012/Research: T21/T37 interface budget and bit-binding headroom (no new kappa) #974 price a different hosted-assembly boundary. Research: exact additive echoes with three dirty arrays at any depth (no new kappa) #1057/Recursive interface: four-way port borrowing reduces 56-factor echo from 1568 to 1088 calls #1164 concern dirty-pool allocation and higher-arity echoes. Exact heads are in SOURCE-PINS.json.
• Read the selected Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094 construction/review; refreshed PRs and discussions before submission. No pinned sprint issue existed, so the claim remained local. This does not adopt an unreviewed frontier.

Validation

CPython 3.14.7 on macOS arm64; standard library only:

python3 -I -O -B research/invariant-reader-restoration/verify.py
python3 -I -O -B research/invariant-reader-restoration/test_package.py

Both pass. Evidence includes all 5,832 declared two-coordinate reader instances, all 873 permutations through width six, the full emitted map on 19 arbitrary source/workspace/output coordinates, separate symbolic prefix bounds and invoice reconstruction, explicit mathematical failure witnesses, relocation, deterministic certificate export and eight on-disk corruption controls. CERTIFICATE.json is recomputed and compared field for field. The general theorem is the written algebraic argument, not an extrapolation from finite tests.

No selected cold replay, hosted CI result, physical supplier admission, full multiplication formalization or new exponent is claimed. Inherited compiler, hosting, precision/tape and analytic obligations remain.

Credit

Prepared for mightyOil (Philipp) with substantial OpenAI Codex assistance, including three scoped Codex subagents. Credit Navinor/Aaron Wang (#1155, with opencode), Ross Richardson/CubeJerry (#889), Sagar Thakrar (#1012 and the concurrent #1199 correction/planner), avirazza (#974), Gareth Davidson (#1057), woklerx (#1164), and the retained repository lineage. New files are Apache-2.0; predecessor bytes and notices are retained. AI review is not independent human or proof-assistant review.

[Mister-Meeseeks]

100-PR batch review at 38459854fd5bb93099871a84324413bd0e338d8e.

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

Reviewed scope: Reader-compatible drift invariance with noncommuting examples and paid dirty wrapper; distinct-output and final-sum criteria are separated.

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.