[theon199]

An exact reader can satisfy RP=QR while its rounded replacement fails the identity needed to carry an infinite-order shear. This package proves a scoped obstruction for every fixed coupled grid rounder with a global absolute-error bound, using Q=[[1,1],[0,1]] and half-grid reader outputs. No linearity or coordinatewise rounding is assumed.

Status: adversarial mathematical audit and scoped negative result; no new kappa. PR1537 explicitly uses exact arithmetic and integer readers and is not refuted. This examines a possible numerical extension of its broader rational child contract, with R=I/2; it does not change the selected supplier.

The written orbit proof establishes the all-horizon obstruction. The sharp allowance on one finite orbit is delta*max(1/2,K/4+dist(K/4,Z)), giving 18 grid units at K=70. Two complete rounded dirty echoes demonstrate different carried/eager outputs despite exact scratch restoration; all loads, unloads, frame returns and literal inverse operations are included. The note gives compatible restricted-grid and finite-order controls and states the viable ways to change the hypotheses.

Only research/shear-equivariant-rounding-seed70/ is added, containing the proof, deterministic certificate, exact source pins, verifier, eight focused tests and local claim/result. The finite certificate checks 161 horizons, 357,522 candidate integer seed outputs, 15,288 defect cases, 5,000 rounded echoes (2,344 output differences), 5,000 exact echoes and 10,000 literal inverse cases. These are finite corroborations of the written proof, not a formal multiplication theorem or an impossibility extrapolated from failed search.

Reproduce from the repository root:

python3.12 -B scripts/research_package.py --package research/shear-equivariant-rounding-seed70

Expected final marker: PASS_REGISTERED_RESEARCH_PACKAGE research/shear-equivariant-rounding-seed70 outcome=negative-result.

The registered CPython 3.12.13 replay and all eight tests pass, including source/certificate corruption, a false source head, duplicate JSON and read-only optimized relocation. Optimized CPython 3.14.5 agrees on the complete certificate. All 12 repository research-workflow tests, five selected-record tests, baseline source bindings and staged whitespace checks pass. Hosted CI and full selected cold replay are unclaimed; physical/numerical child admission and complete precision/tape/cost/analytic recurrences remain outside this scope.

Base: 1f327c6f3e3a35271c5c141d381b540bab8ad005. OS assignment seed 70, adversarial audit. PR1537 is pinned at 407f00df6ca0bf86b455b5640f18ec2f62ee77b9; its unchanged README is retained with Git-blob and SHA256 pins. No predecessor executable is imported. Final complete overlap refresh covered 741 open PRs and 245 Discussion/comment/reply records, with no warnings or matching rounding-orbit audit found. Refreshed main 81e81af67714bdc8d1693b0bf5c29468b92f62ff has identical selected-result bytes. This is not a priority guarantee.

Credit Sagar Thakrar/PR1537, Ross Richardson/PR1287 and the retained PR1227/889/1203 interface lineage. PR1466 supplies nearby coordinatewise truncation work; PR1135 studies another rounded borrowing boundary. PR1552/1563/1575 concern exact reset/cost schedules; PR1490/1566 round helper-gauge exponents, not data. These distinctions and open next questions are documented. The selected PR1094 and PR589/555 lineage retain their credit.

Prepared by Sricharan Vagvala (@theon199) with substantial OpenAI Codex assistance in derivation, implementation, verification and writing. One parent agent; no subagents or independent human review. New work is Apache-2.0. upstream/, frozen packages, review ledger and selected frontier are unchanged.

[Mister-Meeseeks]

Batch review at 1c8878b702ee74d21f8a17737c44c6474143cedd.

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

Reviewed scope: No globally bounded grid rounder can be exactly equivariant under the infinite-order shear on all half-grid outputs. Sharp single-orbit finite-horizon allowance and literal restored rounded-echo counterexamples; does not refute PR1537 exact-rational construction.

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.