OpenPatch
plain-language theorem explainer
An open 2D patch is a finite rectangular grid with no periodic wrap, fixed by positive extents nx and ny. Cosmology cell-boundary certificates and the Python cosmogenesis serializers cite it when tagging non-wrapping recognition cells. It is a pure structure: two positivity fields and no proof obligations.
Claim. An open 2D patch is a pair of positive natural numbers $(n_x, n_y)$ giving the extents of a finite rectangular grid without wrap-around identification.
background
The module FiniteCellBoundary is an engineering scaffold for recognition-cell boundary tags. It mirrors the Python exact-cell scripts under cosmogenesis (1D, 2D, 3D, voxel) and supplies certificate targets for periodic rings and open patches. No new axioms are introduced.
Upstream constants fix the ambient geometry: spatial dimension $D = 3$ (forced by T8 in the unified forcing chain) and the voxel as the fundamental length quantum (one voxel per tick at $c = 1$ in RS-native units). Those facts set the larger 3D cell story; this structure itself only packages a 2D open grid.
Sibling tags in the same module cover the periodic ring (wrap in one direction) and the bounded 3D voxel without wrap. OpenPatch is the non-wrapping 2D case.
proof idea
No proof. The declaration is a structure with parameters $n_x, n_y : \mathbb{N}$ and two fields requiring $0 < n_x$ and $0 < n_y$. Inhabiting it is just supplying positive extents.
why it matters
OpenPatch is a boundary-commitment tag in the cosmology scaffold: it names the finite open 2D cell so serialization and certificates can distinguish wrap from no-wrap without ad hoc flags. The module doc frames these tags as certificate targets aligned with the Python cell generators, not as new physics axioms.
It sits beside PeriodicRing and BoundedVoxel so the same pipeline can speak uniformly about 1D rings, open 2D patches, and closed 3D voxels. Downstream use is currently empty in the graph; the intended consumers are cosmogenesis certificates and any later theorem that needs a typed open-grid hypothesis. Framework landmarks in play are only ambient: T8 forcing $D = 3$ and the voxel length quantum. The structure itself does not re-derive those.
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