Implicit solver: fem kernels (tet4/10, hex8, hex20), sparse Cholesky, block Lanczos, solve.* commands (M4) (#23)

* Renumber the layer table for solver crates: fem at L1, solver at L2, fsi at L3

L0 model -> L1 geometry, mesh, fem, decks, render -> L2 solver (explicit, lbm later)
-> L3 fsi (later) -> L4 doc -> L5 io -> L6 engine -> L7 ui-egui, mcp -> apps.
UI_MIN_LAYER moves to 7, the testkit sits above it.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* modelcraft-fem: element kernels for tet4, tet10, hex8 (full, incompatible modes), hex20 (full, reduced)

Shape functions, Gauss and conical-product quadrature, stiffness, consistent and HRZ-lumped
mass, body forces, consistent pressure loads on faces, integration-point stresses and their
least-squares extrapolation to nodes, isotropic and orthotropic elasticity. The element table is
one row per kind, so wedges, shells and beams are added locally.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* modelcraft-solver: linear static and frequency analysis with an analytic verification suite

Assembly from the resolved model on the node graph, boundary conditions by elimination,
consistent pressure, gravity and body-force loads, nested-dissection ordering, sparse up-looking
Cholesky with a factor-size cap, reactions, integration-point and nodal-averaged stresses, von
Mises; shift-invert block Lanczos with full reorthogonalization for natural modes, participation
and effective mass. ADR 0001 records the own-linear-algebra decision (determinism, wasm).

Verified against closed forms: displacement and traction patch tests for every element, cantilever
tip deflection (Timoshenko) with convergence rates, Lamé cylinder, Kirsch hole (Kt -> 3),
cantilever and free-free beam frequencies with six rigid-body modes.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Engine: solve.static, solve.frequency and solve.probe; results kept in the session

Results are stored per step, restored on a failed command and cleared when the model changes.
Caps (degrees of freedom, factor entries, Lanczos vectors) may only be lowered; hostile parameters
are tested against a solvable session.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* docs: implicit solver architecture, roadmap M4, parity and references

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Simplify the solver: shared face integration, block assembly, cached extrapolation

- model: one face integrator (nodal::face_normal_weights) for tractions and pressures
- fem: mid-side tables from ElementKind::edges, orthotropic via inverse3, symmetric
  accumulation without a symmetrize pass, incompatible-mode recovery without K_uu, model's
  coordinate check, dead table rows removed
- solver: one pattern search per node pair (block, scalar and diagonal adds), extrapolation built
  once per element type, reactions from the prescribed rows only, matrices dropped after
  restriction, the free-body shift keyed on the factorization error, step selection in the solver,
  Error::Element naming the element
- engine: the solver owns the default step and the shift check; the model comparison runs once

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* docs: results are stamped with the session revision

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

---------

Co-authored-by: jyviko <[email protected]>
Co-authored-by: Claude Opus 5.5 <[email protected]>

AGENTS.md

@@ -75,9 +75,9 @@ People trust ModelCraft with their models; a crash loses their work. **This outr
   JSON `run`) + tests. The UI, scripts, CLI and control channel all reach the same commands.
 - **Programmatic calls never open dialogs.**
 - **Layering** is enforced by `cargo xtask layers` (`docs/architecture.md`): L0 `model` → L1
-  `geometry`, `mesh`, `fem`, `decks`, `render` → L2 solvers (`solver`, `explicit`, `lbm`) → L3
-  `fsi` → then `doc`, `io`, `engine`, UI and apps above (the layer table is renumbered when the
-  first solver crate lands). Nothing below L5 depends on egui/eframe/winit/wgpu/rfd. **Only
+  `geometry`, `mesh`, `fem`, `decks`, `render` → L2 solvers (`solver`; `explicit`, `lbm` later) →
+  L3 `fsi` (later) → L4 `doc` → L5 `io` → L6 `engine` → L7 `ui-egui`, `mcp` → apps. Nothing below
+  L7 depends on egui/eframe/winit/wgpu/rfd. **Only
   `crates/geometry` may use `solidcraft-*`.**
 - **Determinism.** The same input gives the same mesh, deck and CPU solver result, bit for bit, on
   every platform: no hash-order iteration into output, no thread-count-dependent results. GPU