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
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-14 13:30:59 -04:00
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{
"title": "Euler buckling of a pinned column of solids",
"kind": "theory",
"source": "Euler's column with Engesser's shear correction P = P_e/(1 + P_e/(κ G A)), κ = 5/6 (S. P. Timoshenko, J. M. Gere, Theory of Elastic Stability, 2nd ed., McGraw-Hill 1961, §2.1, §2.17): square section 1 × 1, E = 1000, ν = 0, effective length 20, P_e = π² E I/20², so σ_cr = P/A = 2.046071",
"quantities": [
{
"id": "lambda",
"quantity": "first buckling stress (load factor of a unit end pressure)",
"measure": {
"from": "solve",
"pointer": "/modes/0/load_factor"
},
"value": 2.046070629714299,
"tolerance": {
"relative": 0.005
},
"reason": "hex20, 2 × 2 across and 10 along: the 3D solid's bending and shear against beam theory, and the preload concentrated at the held face"
}
]
}