rs_eta_00
plain-language theorem explainer
rs_eta_00 confirms that the time-time component of the Recognition Science Minkowski metric equals negative one. Researchers bridging RS forcing chains to standard relativity would reference this when confirming the metric signature matches the expected Lorentzian form. The proof proceeds by direct simplification from the piecewise definition of the rs_eta function.
Claim. The (0,0) component of the RS-derived Minkowski metric satisfies $rs_eta(0,0) = -1$.
background
The module establishes that the Minkowski metric derived from Recognition Science's forcing chain matches the IndisputableMonolith stack's standard metric tensor. The function rs_eta defines this metric on Fin 4 indices: zero off-diagonal, -1 for the time component (index 0), and +1 for spatial components. This follows from the T0-T8 chain: RCL to J-uniqueness to eight-tick octave to D=3, yielding diag(-1,1,1,1).
proof idea
The proof is a one-line wrapper that applies the definition of rs_eta and simplifies the case for indices 0 and 0.
why it matters
This theorem supplies one of the diagonal entries needed to establish rs_minkowski_eq, which equates the RS metric to the IM minkowski_tensor. It supports the unification so that GR theorems like Christoffel symbols and geodesics can use the RS-derived metric. It directly instantiates the T8 step where D=3 and the metric signature is fixed by the eight-tick structure.
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