Close the CM5 autorouting verdict's last unknowns (0 unknown, per-connection certificates)

[ecto]

Every connection on the best CM5 board now ends ROUTED or PROVED-INFEASIBLE — no unknowns — and every certificate names the copper forming its cut.

Result

run	verdict
before (same input, same driver contract)	routed 43 / proved 21 / unknown 31
after	routed 44 / proved 51 / unknown 0
second pass over the output	routed 0 / proved 45 / unknown 0 (fixed point)

The 31 unknowns were 28 cluster-level budget trips, 1 singleton budget trip, and 2 paths the fail-closed oracle rejected — budget and discretization artifacts, as expected.

What closes them

• k = 1 is decided by reachability, not the exhaustive DFS. A lone connection cannot trip a budget: BFS returns a shortest path, or an exhausted reachable component that is the proof. This is what makes splitting a cluster terminate.
• A sequential-BFS witness pass runs before the DFS for joint instances. The DFS's first descent is a greedy walk, not a shortest path, so on a wide window it could wander for millions of expansions before its first completion — the dominant source of unknowns. Success is a witness (node-disjoint by construction); failure proves nothing and falls through, so completeness is untouched.
• WindowBudget couples the expansion budget to a cells-per-axis cap, so a wider window keeps its pitch at the width + separation floor instead of coarsening until unrelated terminals collide in one cell. (Lever 2, done the right way: cap raised with the cell budget.)
• The driver escalates instead of accepting an unknown: joint at 1x/5x/25x budget, then per connection in its own 2 / 8 / 20 mm window. A joint infeasibility is no longer charged to the individual connections — it says only that the k cannot all be routed at once, so each connection earns its own verdict.
• Pair-aware pitch: twins in one window are spaced by their declared gap, restoring "distinct cells ⇒ mutually legal" for pairs (lever 3).

Certificates got sharper, not weaker. The severed case reports whichever terminal's pocket is smaller, with the enclosing cut's node count, extent, and the nets holding it; the walled-in case names the pad's own layers and its blockers. All 51 name real copper:

net /LPDDR4 RAM/CK_C_B is severed inside the window: breadth-first search from its from terminal at (128.65, 77.15) exhausted every reachable node — 5 of the 50108 clearance-free (cell, layer) nodes on the 10-layer stack — without touching the other terminal at (133.55, 66.42) (layer FCu); the enclosing cut is 14 blocked nodes spanning x=128.22..129.41, y=76.08..77.57, held by /LPDDR4 RAM/CA5_B (10), /LPDDR4 RAM/CK_T_B (10), /LPDDR4 RAM/CA2_B (8). With k = 1 reachability is exact, so no path exists on the canonical grid at pitch 0.297 mm

Three legality gaps closed in the session oracle

Routing more connections surfaced three ways "routed" copper could still fail the board. Fixing them is what keeps the new copper DRC-clean:

• probe_drill / commit_drill — hole-to-hole across layer spans and nets. Two vias on disjoint spans share no copper layer, so no layer-scoped probe ever compared them; they landed as drill collisions (the durable fix for a known open item). A via barrel is also now probed on every layer it spans, and consecutive transitions at one point merge into one barrel instead of stacking drills at zero spacing.
• TerminalLayers — terminals can be pinned to the layers their net actually has copper on, with a probed dog-bone escape (stub on the pad's layer, barrel checked across its span) when the search wants a different layer. Previously a stub took the first free layer, which on a 10-layer board is usually not the pad's: 142 of 162 new pad-touching stub ends were electrically dangling.
• set_strict_pair_coupling — scores the intra-pair gap the way the DRC does, pads and via annuli included, with the DRC's 1.5 mm pad-breakout exemption mirrored. Opt-in, because it is stricter than the geometry the pair router realizes today (its dog-bone offsets and jogs are sized to base clearance); the verdict driver turns it on and pays for it in routability. Flipping the default needs the pair router's geometry fixed first — noted below.

DRC (same input board, drc_json)

rule	base	after
Clearance	74	74 (baseline floor, exactly)
Short	1315	1315
MinTraceWidth	69	69
HoleToHole	0	0
UnconnectedNet	252	223
NetIslands	18	30
total	1813	1796

No new route-attributable violations. NetIslands +12 is an accounting shift: all 19 newly-listed nets had zero copper on the base board (they were UnconnectedNet entries) and now carry partial copper — some MST edges routed, the rest proved infeasible. An independent connectivity check over all 41 touched nets finds zero floating groups: every committed path is galvanically attached to its net's pads or pre-existing copper, with no zero-length traces and no coincident vias.

Verification

• cargo test -p vcad-ecad-pcb — 252 passed, 0 failed (4 new tests: lone connection never unknown, severed connection proved with a named cut, pinned terminals attach on their own layer, drill probe sees holes no copper probe could).
• cargo clippy -p vcad-ecad-pcb --features gpu -- -D warnings — clean. (--all-targets reports two items after a test module lints in router/auto.rs and router/si_claims.rs; both are pre-existing on main, confirmed by stashing.)
• cargo fmt --all --check — clean.

Follow-up (not in this PR)

The pair router emits dog-bone offsets and jogs that come a gap-width short of the DRC's pair rule (a leg trace 0.175 mm from its twin's via, where the DRC requires 0.245 mm mid-board). Repro: router::pair::tests::pair_layer_transition_keeps_twin_clearance with set_strict_pair_coupling(true). Fixing that geometry is what would let strict coupling become the default.

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