AlgorithmAlgorithm: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Algebraic gauge for a rigid-body stiffness nullspace

Definition

Let $K \in R^{N \times N}$ be symmetric positive semidefinite, let $R \in R^{N \times r}$ have full column rank and satisfy $\ker K = range R$ , and let $f \in R^{N}$ be compatible in the sense $R^{T} f = 0$ . Define the gauge solve as the procedure:

Form the square augmented matrix and right-hand side

[\begin{array}{cc} K & R \\ R^{T} & 0 \end{array}], [\begin{array}{c} f \\ 0 \end{array}] .

Solve for $(u, γ) \in R^{N} \times R^{r}$ .
Return $u$ , which is the representative satisfying $R^{T} u = 0$ .

The input hypotheses must be checked for the particular stiffness matrix. The procedure does not identify an omitted nullspace or assert a load is compatible.

Used by

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Long Chen, Introduction to Linear Elasticity and Its Finite Element Approximation (complete 13-page notes) (standard reference, not scraped)
Daniele Boffi, Franco Brezzi, Michel Fortin, Mixed Finite Element Methods and Applications (complete 691-page text) (standard reference, not scraped)