LatticeToContDict
plain-language theorem explainer
A two-field record that pairs one discrete lattice notion with its continuum counterpart as plain strings. Anyone documenting the RS discrete-to-smooth dictionary cites it. There is no proof: it is a pure data carrier used to populate the continuum dictionary list.
Claim. A dictionary entry is a pair $(L, C)$ of strings, where $L$ names a lattice (discrete RS) concept and $C$ names the corresponding continuum concept.
background
Module F-014 treats the continuum limit of Recognition Science: discrete J-cost dynamics on the lattice $\mathbb{Z}^3$ should yield, at long wavelength, a second-order diffusion structure matching Klein–Gordon. The J-cost $J(e^t)=\cosh(t)-1$ expands as $t^2/2+O(t^4)$; the quadratic piece produces a lattice Laplacian, which scales to $\nabla^2$.
That story needs an explicit map from ledger language (voxels, log-ratio perturbations, neighbor costs, ticks) to field language (spacetime points, scalar fields, continuum Laplacians). This structure is the typed row of that map: one lattice label and one continuum label.
It sits beside lattice-field and Laplacian scaffolding in the same module and is only a naming device, not a dynamical claim.
proof idea
No proof body. The declaration is a structure with two String fields (lattice_concept, continuum_concept). Instantiation is by providing the two strings; downstream code builds a list of such rows.
why it matters
Fills the documentation half of registry item F-014 (how continuum physics emerges from the discrete ledger). Downstream, continuum_dictionary is a concrete list of these rows (voxel $\mapsto$ spacetime point, log-ratio $t(x)\mapsto$ scalar field, J-cost $\mapsto$ continuum energy density, and so on).
It does not itself force $D=3$, the eight-tick octave, or the Klein–Gordon form; those live in the forcing chain and the analytic continuum-limit theorems. It makes the intended discrete/continuum glossary machine-checkable as data so later results can cite a fixed correspondence table rather than ad hoc prose.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.