[adamgall]

Result and exact scope

Add one operation family to the generic dirty-connector contract: paid invertible connector-only frames z <- Rz. A phase-normalization proof shows that arbitrary interleaved frames cannot achieve the five-source/all-31-mask 72-map-call paired endpoint. The exact unit-token optimum stays 74, or 76 if at least one nonidentity frame must be used.

The operation word and frame matrices are fixed independently of the arbitrary A/B map entries. This is not a lower bound for operator-specialized charts or a physical runtime optimum. The 76 upper bound deliberately uses a redundant inverse frame pair; it is not advertised as a useful improvement.

The package includes the full noncommutative coefficient argument, complete weighted cost screen, smallest two-bit dirty shear pilot and meaningful controls. Pilot invoices are 14 versus 12 scalar XORs, or 194 versus 168 in the explicit complete fixed-port tariff. A deliberately retained order-three control shows why arbitrary framed words do not inherit even map-call parity.

Assignment, source pins and overlap

• Task: connector-alphabet-change, scoped package research/connector-frame-rigidity.
• Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected record and all frozen sources unchanged.
• TASK.json, SOURCES.json and VERIFY.json record the scope, exact source blobs/SHA256 hashes and registered replay.
• Credit Ross Richardson's universal connector / PR943–PR934 lineage for the original interface, paired-prefix criterion and sharp five-source exclusion. Its 945-pairing census is an inherited regression control, not this contribution's novelty.
• Closest overlap: woklerx's Carry a dirty connector through a paid change of chart #1858, checked open at 4b650a8471c38f87519da497019dde24228c7f8a. That construction assumes related fixed maps B1=R B0; this generic operator-independent obstruction neither refutes it nor claims priority for adding connector frames.
• Cached publication search covered 558 open PRs and 529 discussion records; freshness and non-exhaustive-code-coverage limitations are documented. No novelty guarantee is inferred from search.
• Coordination: Ten-instance independent research session: interface and verifier audits #1884

Actual verification

On CPython 3.12.12 / Darwin arm64, after the final critical review and added direct-vector coefficient check:

uv run --python 3.12 --no-project python scripts/research_package.py --package research/connector-frame-rigidity
uv run --python 3.12 --no-project python -I -O -B research/connector-frame-rigidity/verify.py

Registered replay: 0.30s; isolated optimized direct smoke: 0.21s (single local timings, not benchmarks).

PASS_CONNECTOR_FRAME_RIGIDITY pairings=945 phase_pairs=36 coefficients=9216 two_phase_triples=40 odd_restore=256 dirty_cases=16384 controls=5 unit_optimum=74 used_frame_optimum=76 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/connector-frame-rigidity outcome=negative-result

The direct smoke emitted the same scoped receipt. All 16,384 dirty map/input pilot cases include literal scalar lowering and inverse replay. Checks do not rely on Python assert. No full repository suite or selected-frontier replay was run.

Limits and open next questions

The arbitrary-dimension statement is a written proof supported by finite checks, not proof-assistant verification or a multiplication theorem. Whether 73 map calls with at least three frames can work remains open, particularly for favorable nonuniform prices. Structured charts still require an actual selected-supplier boundary and fully charged native implementation. No supplier admission, selected-frontier change, physical speedup or new kappa is claimed.

Prepared for Adam Gall with substantial OpenAI Codex assistance in proof, implementation, experiments and writing. Apache-2.0 under repository contribution terms.

[Mister-Meeseeks]

Batch review at d30d64fea909219c364b11c2452f2207326e2b1f.

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

Reviewed scope: Generic map-independent one-connector phase normalization excludes72 map calls with arbitrary invertible frames and proves74/76 unit-token minima. Full dirty pilot16384cases, phase identities and odd-count restoration control pass. Does not exclude structured map-dependent charts or two connectors.

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.