QF Solver 0.2.8 WP03 — BEAM2 and DISCRETE V&V

This record closes the WP03 technical V&V campaign for four narrowly bounded routes selected by the WP01 maturity baseline. It does not rewrite 0.2.7 evidence and does not claim universal validation, certification, or a general BEAM2/DISCRETE maturity promotion.

The machine-readable record is wp03_beam2_discrete_vnv.json. The WP03 decision delta is maintained separately in wp03_maturity_matrix.json; the WP01 baseline remains unchanged. The executable campaign is test_028_beam2_discrete_vnv.py.

Frozen campaign contract

The baseline is 598704c834b4642f7c2a9a1fdc7595895f9e4130. Before execution, the campaign froze the scope, hypotheses, analytical oracle and tolerance for each case in the JSON record. Each case was executed twice and the replay digests were identical. The test also reruns both replays, so the committed observations are checked against the current implementation rather than being treated as unchecked narrative.

Case	WP01 state	Oracle	Decision	Public maturity action
BEAM2 static	NEEDS_MINOR_VNV	Timoshenko cantilever closed form	QUALIFIED_BOUNDED	Owner confirmation pending
BEAM2 modal	NEEDS_MINOR_VNV	slender cantilever first two bending frequencies	QUALIFIED_BOUNDED	Owner confirmation pending
DISCRETE static	NEEDS_MINOR_VNV	scalar spring solutions and assembly invariants	QUALIFIED_BOUNDED	Owner confirmation pending
DISCRETE modal	NEEDS_MINOR_VNV	closed-form uncoupled mass-spring frequencies	QUALIFIED_BOUNDED	Owner confirmation pending

QUALIFIED_BOUNDED is the technical V&V decision recorded by WP03. The technical evidence record retains promotion_applied: false; the separate final WP03 Owner gate applies the approved bounded maturity action without rewriting this campaign record.

BEAM2 static

The campaign covers a straight, constant-section, isotropic BEAM2 cantilever in small displacement linear statics. It exercises axial traction, transverse flexion in both planes and torsion on one-, two- and four-element meshes.

The oracle is the closed-form Timoshenko cantilever tip displacement. The checks also require reaction balance, strain-energy identity, solver residual and six rigid-body modes in the unconstrained element stiffness. The maximum observed relative displacement error is 2.32e-15; the maximum reaction equilibrium error is 2.40e-14; the maximum relative residual is 4.97e-14. All are below the predeclared 1e-10 limits.

The qualified scope excludes releases, offsets, variable sections, plasticity, contact, large rotations and distributed dynamic loading.

BEAM2 modal

The modal case is a straight slender cantilever with coherent mass, positive density, fixed root and no damping. The first two bending frequencies on one-, two- and four-element meshes are compared with the Euler-Bernoulli slender reference. This oracle is deliberately bounded: it does not qualify thick-beam shear behavior.

The maximum frequency error is 0.4333 %, below the frozen 1 % limit. The maximum eigen-residual is 5.26e-12, and the maximum mass-orthogonality error is 2.38e-16, both below 1e-8. The declared fixed-root model has two positive frequencies in the requested first-two-mode replay; rigid-body and rank behavior is checked separately by the static stiffness invariant.

The qualified scope excludes damping, nonlinear dynamics, joints, offsets, multi-body coupling and thick-beam extrapolation.

DISCRETE static

The static campaign uses three uncoupled translational ground springs with k = (1000, 4000, 9000) N/m, a concentrated mass of 10 kg, and loads (25, -20, 45) N. The closed-form oracle is u = F/k. It additionally checks static equilibrium, energy identity, a two-node rigid translation null mode, and equal/opposite spring forces.

All observed scalar errors are zero at the recorded precision and are below the frozen 1e-12 limits. The scope excludes coupled multi-DOF systems, rotational inertia, local orientations, nonlinear laws, gaps and damping.

DISCRETE modal

The modal campaign uses the same three uncoupled translational spring directions and mass. The oracle is f_i = sqrt(k_i/m)/(2 pi), producing 1.5915494309, 3.1830988618 and 4.7746482928 Hz.

The replay matches all three frequencies at recorded precision. The maximum eigen-residual is 1.80e-16 and mass-orthogonality error is zero, below the frozen 1e-12 limits. The scope excludes rotational inertia, coupled mass, multi-node coupling, damping and transient extrapolation.

Routes not closed by WP03

BEAM2 Newmark, BEAM2 harmonic, DISCRETE Newmark and DISCRETE harmonic remain EXPERIMENTAL. Their required independent time-history or frequency-response oracles, phase/amplitude conventions and route-specific tolerances were not executed in this WP. Existing historical references are not substituted for the absent reproducible 0.2.8 evidence.

Decision and next gate

WP03 establishes four technical QUALIFIED_BOUNDED decisions and its historical route list remains unchanged. The final Owner gate is recorded separately after WP03B, so the frozen evidence is not rewritten.