skills: parallel adapt engines, band pinning, and FMG on adapt children

[lmoresi]

Skills documentation for the adapt-on-top work. Split out of #488 for
reviewability.

Merge after #488 — this documents API that only exists on that branch
(engine="edge_split", repair=True, relax(pin_bands=...)). Based on
development rather than stacked on #488, because deleting a base branch
auto-closes stacked PRs.

adapt-on-top-faults

• Engines: nvb vs edge_split, both parallel in 2-D and 3-D and bit-confluent.
  edge_split has no conforming closure so refinement cannot escape the marked
  region, and marks on the DIAMETER — the volume proxy reported the target met
  while the mesh was 3.2x coarser across the feature.
• repair=True: why it gates on reducing the largest angle and not on Delaunay
  (Delaunay maximises the minimum angle; flipping a gmsh mesh toward it raised
  the 99th-percentile maximum), when it is worth it, and the bit-confluence it
  gives up.
• Relaxing an adapted fault mesh: relax() alone makes it worse (+77% leak);
  pin_bands is the fix.
• New section on sizing the band and representing the fault margin — the
  -2 Cov(eta, edot) leak metric, why a within-cell marking rule loses to the
  plain distance size field, why the optimal band width depends on which objective
  you pick, and what a step-edged margin buys and costs.
• Corrects the stale "NVB at np>1" gotcha, and adds five new ones including
  Mesh(dm) taking the DM over (a bare SIGSEGV if you keep the old handle) and
  Mesh(dm) without boundaries= losing the boundary enum.

adaptive-meshing

"Pin the interface" section for relax(pin_bands=...), since this is a mover
capability — including the signed-vs-unsigned distance rule and the
pinned_labels merge trap (passing it replaces the "pin every named boundary"
default and silently frees the domain edge).

nonlinear-solver

New section: FMG on an adapt-on-top child. The child carries its own graded
custom-P tail and solvers pick it up automatically; the base needs
refinement>=1; a base-only tail triples the V-cycle count; V-cycle counts are
insensitive to element quality, which is a pass and not a failed measurement, so
use GAMG as the quality probe; relax can trip #424 into the dense RBF fallback.
Cross-referenced to both meshing skills, and they to it.

Underworld development team with AI support from Claude Code

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[lmoresi]

Adversarial review

Every command/API/flag the skills teach exists in #488's diff or on development — engine="edge_split", repair=True refusal semantics, relax(pin_bands=[fault] / [(fault, 0.02)], pin_halo=), label_interface_band(surface, offset, halo), child._custom_mg_coarse_meshes auto-pickup, influence_function(profile="step"), the custom_mg barycentric→rbf retry warning text, set_custom_fmg(..., field_id=0), the Mesh(dm, boundaries=...) gotcha. No invented parameters, no stale-API teaching.

Two doc-level overclaims, both tied to #488 defects:

• "raises rather than silently doing nothing otherwise" is false for the adapter="mmg", repair=True corner (Adapt-on-top: closure-free edge_split engine, reconnection repair, and interface-pinned relaxation #488 finding 6).
• The skill teaches child.relax(pin_bands=[fault]) for parallel fault models with no caveat, while Adapt-on-top: closure-free edge_split engine, reconnection repair, and interface-pinned relaxation #488's label_interface_band hangs whenever a rank's subdomain misses the band (Adapt-on-top: closure-free edge_split engine, reconnection repair, and interface-pinned relaxation #488 finding 1). Carry the warning until that is fixed.

Merge strictly after #488 (else the skills document nonexistent features). Holding with it.