minkowski_christoffel_zero
plain-language theorem explainer
The Minkowski metric yields vanishing Christoffel symbols everywhere in flat four-dimensional spacetime. Researchers embedding special relativity inside the Recognition Science framework would cite this to confirm the connection reduces to the flat case. The proof is a direct reflexivity reduction on the placeholder definition of Christoffel symbols from the Minkowski tensor.
Claim. For the Minkowski metric tensor $g = eta$ on $x : Fin 4 → ℝ$, the associated Christoffel symbols satisfy $Γ^ρ_{μν}(x) = 0$ for all indices $ρ, μ, ν ∈ Fin 4$.
background
This module supplies placeholder definitions for Christoffel symbols and covariant derivatives as structural scaffolding outside the verified certificate chain. The Minkowski tensor is instantiated as the standard eta metric with the expected symmetry property. The upstream construction in Gravity.Connection.christoffel_from_metric builds the symbols via the standard formula (1/2) ginv (dg + dg - dg) from the inverse metric and partial derivatives of the metric components.
proof idea
The proof is a one-line wrapper that applies reflexivity to the trivial placeholder definition of christoffel_from_metric applied to minkowski_tensor, which directly evaluates to the zero structure.
why it matters
This declaration confirms the expected zero connection for the flat Minkowski metric, consistent with the flat-space limit in the Recognition framework. It aligns with the overall geometry layer but feeds no downstream theorems, as the module is explicitly marked scaffolding and not part of the certificate chain. The result touches the boundary between the core forcing chain (T0-T8) and the relativity placeholders.
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