[1337isnot1337]

The 12-query signed 3×3 connector has a four-pass root-transfer construction under one-way shears. This package extends the added operation to paid shears in either direction. A matrix lemma proves that every restoring product of at most three nonzero elementary shears uses the same ordered root pair; the exact source/reader dirt constraints then reduce the connected target to the inherited one-root prefix walk, which fails for all 720 orders.

Status: scoped negative result and independent research note; no new κ or supplier admission. The result rules out the proposed one-pass saving at fixed 12 queries. It does not price or optimize the remaining four-pass bidirectional schedules, higher query counts, free root operations, or native selected-supplier interfaces.

The registered replay checks 127,952 one-to-three-shear words over exact coefficient controls and 2–4 roots. Independent event-order engines cover 6, 90 and 210 short schedules. The 720-path one-root histogram agrees across two enumerators. PR1651's source word expands to 300 factor calls and four transfers, with all 11 dirty columns, literal inverse and removal/sign controls; exact dense integer fixtures at dimensions 2 and 3 pass.

python3.12 -B scripts/research_package.py --package research/bidirectional-root-obstruction-seed50

Expected: PASS_BIDIRECTIONAL_ROOT_OBSTRUCTION monodromy_words=127952 one_root_paths=720 factor_calls=300 transfers=4, then PASS_REGISTERED_RESEARCH_PACKAGE. Selected-record, selected-source inventory, binding-only baseline and diff checks pass; the selected full native cold replay was not run for this scoped note.

Seed 50, recursive interfaces; exact base 2de86c77b4127d2f01f504e0c7c5e4db737caa3c. Final upstream refresh 418e40eb2572d930b58c1cf9b82b41c0fc7ee08d; selected κ remains 836330098538459/500000000000000000, complex binding. Sources pins and retained notices are included.

Credit: Ross Richardson PR1651 (one-way four-pass minimum and witness), Charles Bethin PR1637 (two-root 12-query construction), Ross Richardson PR944 (one-root obstruction), and woklerx PR1438 (source-port argument). Cinna Davis (1337isnot1337), with substantial OpenAI Codex assistance; Apache-2.0.
Claim/result: #1660.

[Mister-Meeseeks]

Batch review at a8d459974abf7ba88316c87396565f7e5fc9656f.

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

Reviewed scope: At most three restored elementary root shears must use one ordered pair, even with bidirectional choices and any number of dirty roots. Combined twelve-query constraints reduce to the credited one-root census; four-transfer witness is fully charged.

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.