[P2 proof] Write out #675 Lemma A: NN+NNN strip frontier partitions are noncrossing

[LightChainr]

Parent: #650. PR #675 §4 Lemma A: on the square strip with NN+NNN site connectivity, the frontier occupancy partition is always noncrossing, and the reachable class equals the NN-only class (verified w≤6, rows≤4). Proof sketch is a Jordan-curve + face-K4 merge argument. Status there: lemma-with-sketch, not full rigour.

Why

This is the one piece of #675 that is not an obstruction. If the sketch becomes a proof, PR #645's Q2 (crossing states blow #636's cost) is dead as a cost model, without funding #636. If a counterexample exists above width 6, that is also progress.

Questions

1. Write the Jordan-curve argument so that a reader who has not enumerated w≤6 can check it. Both diagonals of a face active ⇒ all four sites occupied ⇒ NN edges merge the would-be crossing.
2. Separate geometric edge-crossings (king-graph diagonals cross at face centres) from partition-crossings on the frontier. The lemma is about the latter.
3. The converse is already recorded as false at cluster level (diagonal footprints that NN cannot make). Keep that. Do not claim the reachable weighted counts equal NN — only the partition classes.
4. Do not enumerate above w=6 on the Mac. If a gap needs w=7+, comment NEED_HUAWEI and stop. Do not start [P1 reserve] Source-visible topology and all-width closure beyond the completed width-four laboratory #636.

Outcomes: proof / sketch-still / counterexample.

No STATUS. Draft PR against main.

Wait for ASSIGNED_MACHINE.

Related: #638, #645, #658, #667, PR #675.

[LightChainr]

In the Go-quota refill queue, not started. ASSIGNED_MACHINE: local when a CLI slot opens after the current six. No w>6 enumeration on the Mac. Do not start #636.

[LightChainr]

ASSIGNED_MACHINE: local

Long-horizon proof. No --max-turns. No w>6 enumeration. Do not start #636. Draft PR against main. No STATUS.

[LightChainr]

Assignment retracted. Wait for the current cluster (#601 #673 #677 #679 #570 #644) to finish before ASSIGNED_MACHINE: local. Do not start this ticket yet.

[LightChainr]

ASSIGNED_MACHINE: local

Current cluster finished. Long-horizon, no --max-turns. No w>6 enum. Do not start #636. Draft PR against main. No STATUS.

[LightChainr]

CLI stopped on request. No PR from this run. ASSIGNED_MACHINE withdrawn. Ticket stays open.