verification: Euler columns and Bryan's plate in buckling steps

buckle-euler-pinned and buckle-euler-cantilever (hex20 columns, −0.18 % from Euler with
Engesser's shear correction) and buckle-plate-square (a simply supported square plate, b/t =
100, −0.39 % from k = 4; the support and thickness choices in its README). ROADMAP and parity
updated, docs/oracle.md regenerated.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

docs/parity.md

@@ -63,7 +63,7 @@ products are run, no documentation text is copied). Status: **done**, **started*
 | Decks | LS-DYNA keyword writer (implicit; explicit in M8) | M3 | | done (implicit static and eigenvalue; beam sections planned) |
 | Decks | Readers keeping unknown keywords | M9 | | planned |
 | Solve | Own linear static and modal solver, verified against analytic solutions | M4 | yes | started (solid elements: tet4, tet10, wedge6, hex8, hex20; 2D plane stress, plane strain and axisymmetric tri3, tri6, quad4 (full, incompatible modes), quad8 (full, reduced); quad4/tri3 MITC shells and Timoshenko beams with profiles, mixed with solids; reference points, kinematic and distributing couplings, moments; centrifugal loads) |
-| Solve | Own nonlinear implicit solver: Newton–Raphson with line search and automatic increments, total Lagrangian solids and 2D elements, mixed u–p at finite strain, follower pressure | M15 | yes | started (solids, plane strain, axisymmetric; St Venant–Kirchhoff, neo-Hookean and J2 plasticity (Simo's exponential return map at finite strain, radial return at small strain, consistent tangents, the return shared with explicit dynamics); verified by the elastica, tube inflation, patch and objectivity tests, uniaxial tension to large strain, Hill's thick cylinder, a cantilever's collapse and the Bauschinger effect; Mooney–Rivlin and Yeoh; thermal strain at finite and small strain; a symmetric indefinite LDLᵀ factorization with inertia, Newton through indefinite tangents (hybrid elements at ν = 0.4999 under prescribed displacement); shells, contact, buckling, arc-length next) |
+| Solve | Own nonlinear implicit solver: Newton–Raphson with line search and automatic increments, total Lagrangian solids and 2D elements, mixed u–p at finite strain, follower pressure | M15 | yes | started (solids, plane strain, axisymmetric; St Venant–Kirchhoff, neo-Hookean and J2 plasticity (Simo's exponential return map at finite strain, radial return at small strain, consistent tangents, the return shared with explicit dynamics); verified by the elastica, tube inflation, patch and objectivity tests, uniaxial tension to large strain, Hill's thick cylinder, a cantilever's collapse and the Bauschinger effect; Mooney–Rivlin and Yeoh; thermal strain at finite and small strain; a symmetric indefinite LDLᵀ factorization with inertia, Newton through indefinite tangents (hybrid elements at ν = 0.4999 under prescribed displacement); linear buckling of solids (Euler columns, Bryan's plate); shells, contact, arc-length next) |
 | Solve | Own explicit dynamics solver (central differences, one-point hex8 with hourglass control, nodal-pressure tet4, bulk viscosity, energy balance), verified against analytic wave and impact solutions | M10 | yes | started (X1 core and X2: large deformation, objective rates, J2 and Johnson–Cook plasticity, damage, erosion; X3: deformable contact and friction, verified by bar collision, sliding blocks, the contact patch test and Hertz) |
 | Results | Deformed shape, contours, mode shapes, probes, reaction sums | M4 | | started (results in the session, `solve.probe`, reaction sums; display planned) |
 | Results | XY and path plots, cuts, display groups, free-body forces, animation | M9 | | planned |