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IndisputableMonolith.Relativity.Geometry.DiscreteBridge

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The module supplies the lattice spacing for N sites in a box of side L and the discrete-to-continuum bridge theorems in RS relativity geometry. Researchers modeling discretized spacetime cite it for the RS-native discretization rules. It imports metric unification and curvature results to construct the bridge. The structure proceeds by direct spacing definitions followed by positivity, limit, and chain proofs.

claimLattice spacing $a = L/N$ for $N$ sites in a box of side $L$, with associated positivity, convergence to zero, flat chain, and weak-field bridge statements.

background

The module sits inside the RS relativity geometry stack. It imports the fundamental RS time quantum τ₀ = 1 tick, standard basis vectors e_μ, Christoffel symbols, and the unique torsion-free metric-compatible connection on pseudo-Riemannian manifolds. MetricUnification shows the RS-derived Minkowski metric equals the IM MetricTensor via the chain RCL → J unique (T5) → J''(1)=1 (spatial curvature positive).

proof idea

This module introduces definitions for lattice spacing and related objects. Theorems such as flat chain holding and weak field bridge are established by applying the imported curvature and metric unification results. The overall argument reduces discrete properties to the continuum limit using standard analysis on the lattice.

why it matters in Recognition Science

This module is imported by the Geometry aggregator. It supplies the discrete bridge components that complete the geometry stack in Recognition Science, linking to the forcing chain steps T5 through T8 for dimensions and constants.

scope and limits

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (8)

Lean names referenced from this declaration's body.

declarations in this module (13)