IndisputableMonolith.Foundation.RecognitionLattice3
Module RecognitionLattice3 defines the domain cost function and RecogLattice3Cert for a three-dimensional recognition lattice, building directly on the RS time quantum and cost primitives. It is imported by the root IndisputableMonolith module during assembly of the forcing chain. The module contains only definitions and elementary properties.
claimThe module introduces $\mathrm{domainCost}$ (a non-negative cost on domains) with associated lemmas $\mathrm{domainCost\_at\_eq}$ and $\mathrm{domainCost\_nonneg}$, the positive canonical threshold, and the inhabited certificate $\mathrm{RecogLattice3Cert}$ for the 3D recognition lattice.
background
The module imports the RS time quantum $\tau_0 = 1$ tick from Constants and the cost structures from Cost. It defines $\mathrm{domainCost}$ together with its equality and non-negativity properties, plus the canonical threshold and the certificate $\mathrm{RecogLattice3Cert}$.
The local setting is the foundation layer for a recognition lattice in three spatial dimensions, consistent with the D = 3 result of the forcing chain. Upstream Constants supplies the single sentence: "The fundamental RS time quantum (RS-native). $\tau_0 = 1$ tick."
Sibling declarations supply the concrete objects: domainCost, canonicalThreshold, and the inhabited certificate.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the 3D lattice certificate and domain cost required by the root IndisputableMonolith module. That root exposes the master forcing-chain theorem (T0–T8) together with the Standard-Model Higgs effective-field-theory chain. The lattice construction therefore sits at the interface between the cost primitives and the spatial-dimension step (T8) of the forcing chain.
scope and limits
- Does not prove any step of the T0–T8 forcing chain.
- Does not compute numerical values inside the alpha band.
- Does not define lattices in dimensions other than three.
- Does not contain the mass formula or Berry creation threshold.