Geometric configuration interfaces

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areas_and_tilings: Uniform area thresholds, weighted triangle incidences and square-multiple tiling extensions expose distinct unresolved interfaces.

circumradii: Pair counting gives a linear radius bound and a conditional superlinear link; finite algebraic selection tests require exact general position.

colorings: Compactness supplies finite witnesses for fixed forbidden configurations, but equilateral witness sizes cannot stay bounded near equal scales.

convex_subsets: Double counting turns polygon existence thresholds into quadratic-log bounds, while leaving the exact threshold and leading constant open.

cube_dissections: An explicit refinement threshold proves an odd-dimensional sub-n-to-the-n bound; prime-successor dimensions obstruct the same small-grid mechanism.

distance_subsets: Isosceles triples govern bad four-sets; robust multiplicity and deletion estimates retain distinct exponents and dimension conventions.

rich_lines: Separate fixed-cap little-o questions from near-quadratic constructions, abstract incidence systems and maxima of different line counts.

self_avoiding_walks: Finite walk counts provide upper bounds for the connective constant; displacement estimates retain their dimension and uniformity restrictions.

unit_distance_independence: A certified finite ratio below one quarter propagates to all large orders, but the required geometric fractional-coloring certificate is uninspected.

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These notes retain explicit deductions, source specializations and useful obstructions. Each note states the exact remaining hypothesis or test. All original arguments are author-recorded by Plasma AI; source premises keep their stated reading and acceptance limits.