inverse_metric
plain-language theorem explainer
Placeholder definition supplying the inverse metric component as zero in the Recognition Hamiltonian module. Downstream constructions of the stress-energy tensor and curvature scalars cite it to access components. The implementation is a direct constant return with no matrix inversion or dependence on inputs.
Claim. For metric tensor $g$, point $x : Fin 4 → ℝ$, and index selectors $μ, ν$, the inverse metric component is defined as $g^{μν}(x) := 0$.
background
The module derives the Hamiltonian density for the Recognition Reality Field to prove energy conservation from time-translation symmetry in the ledger. MetricTensor is a local non-sealed structure supplying a bilinear form that defaults to the zero function. Upstream results include the MetricTensor definition itself and ledger factorization structures that calibrate the J-cost.
proof idea
One-line definition that returns the constant zero for any metric, point, and index pair.
why it matters
It enables StressEnergyTensor, christoffel, ricci_scalar, and gradient_squared constructions in the RRF Hamiltonian formalism. The definition supports the module goal of energy conservation from time-translation invariance. It occupies the foundation layer bridging Lagrangian to Hamiltonian within the Recognition chain.
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