minkowskiMatrix
The declaration supplies a direct definition of the four-dimensional Minkowski metric matrix with diagonal entries -1, 1, 1, 1. Workers on matrix representations inside the Recognition Science relativity scaffolding would reference this placeholder. Construction proceeds by a single application of the diagonal matrix constructor with an index-dependent sign flip.
claimThe Minkowski metric matrix is defined by $η = diag(-1, 1, 1, 1)$.
background
This module is explicitly labeled a scaffold placeholder for matrix bridge infrastructure and is excluded from the verified certificate chain. The local setting supplies only a minimal noncomputable definition without any supporting lemmas or derivations. Upstream references consist of interface structures such as ledger bridges and collision-free classes that remain disconnected from any concrete matrix construction.
proof idea
The definition is realized by a direct call to Matrix.diagonal that applies a conditional sign: -1 on the zeroth index and +1 on the remaining three indices.
why it matters in Recognition Science
As a scaffold definition the entry supplies a conventional Minkowski matrix but carries no verified status and feeds no downstream theorems. It occupies a placeholder slot in the relativity geometry bridge without touching any core chain steps such as the forcing sequence or Recognition Composition Law.
scope and limits
- Does not constitute a verified theorem or lemma.
- Does not participate in the certificate chain.
- Does not derive the metric from any Recognition Science axiom or forcing step.
- Does not supply usage sites or downstream applications.
formal statement (Lean)
23noncomputable def minkowskiMatrix : Matrix (Fin 4) (Fin 4) ℝ :=
proof body
Definition body.
24 Matrix.diagonal fun i => if i.val = 0 then -1 else 1
25
26/-- Bridge is accepted if the matrix is invertible (non-zero determinant). -/