Independent

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c3_13_unreviewed: Archived unreviewed argument for thirteen points with 120-degree symmetry; its full case analysis has not been independently checked.

large_distance_graph_and_convex_extension: Archived unverified input; the 2-core improvement and circular-hull extension were checked, while its convex and twelve-point gaps are superseded.

largest_distance_ranks_and_small_orders: Archived independent input, not a canonical proof record; selected claims were checked and incorporated into the linked topical notes.

layer_bound_and_circular_majority: Archived unverified input; the elementary additive and circle bounds were checked, while its layer, finite, and convex scopes are superseded.

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The archived body is retained as supplied. Its claims are not accepted solely because they are called proved in that record. The review checked the promising arguments and compared them with the existing wiki:

• Layers and obstructions retains the angular rank improvement, quantitative layer and separation bounds, abstract coloring obstruction, and source corrections. A literal minimum-distance identification in the cited two-ring construction fails; using its actual radial minimum repairs the needed asymptotic obstruction to choosing the shortest and second-largest classes. The depth lemma and qualitative sparse-layer result repeat existing work; the input's exponential sampling proof is weaker than the old wiki bound.
• Affine deformations proves the coordinate criterion and improves the input's bound to $\lceil n/4\rceil$ by a midpoint-fiber argument. Generic deformation remains invalid.
• Small orders proves the first assertion through ten points using checked source classifications and exact model counts. It records why the eleven- through thirteen-point restrictions do not complete the next orders. The input's eleven-point example is congruent to the existing motif; its extension obstruction has a direct certificate independent of the grid enumeration.
• Circular configurations strengthens the input's warning about the two-polygon rich-distance constructions: the existing positive-circle theorem already forces linearly many rare distances in those families.

These additions do not resolve either unrestricted assertion. The macroscopic-layer obstruction remains.

Review of the second independent input

The body of second independent input is archived unchanged, apart from added metadata. It remains unverified input as a whole; the checked arguments are recorded in canonical topical notes. Its references to companion files are not additional available evidence in this research folder.

• Layers and obstructions incorporates the balanced-circle 2-core proof of $m_A(r_k)\le(2k-1)|B_k|$ and the sharpened floor bounds. The depth lemma, sparse-layer divergence, aspect-ratio criterion, and source corrections repeat established work.
• Circular configurations proves the two-nonvertex/cocircular-hull claim with a shorter argument using the unique-diameter theorem. It also allows the last point anywhere when the other added point is noncentral and in the circular subset's hull. Nearly convex explains why the existing all-but-one convex theorem is stronger than the input's hull version.
• Small orders records the rechecked spectra and equivalent nine-point models. The input's twelve-point six-distance gap is already excluded by the unique-diameter theorem; arbitrary eleven-point five-distance sets remain unclassified here.
• Unrestricted frontier distinguishes the input's unresolved convex asymptotic branch from the established short-edge inverse proof. Its subset-restoration warning and the unrestricted interior-support gap remain valid.

The new geometric proofs were checked by the author and are author-recorded; the finite classifications were checked in the supplied full sources after their digests. No unrestricted solution results.

Review of the third independent input

The body of third independent input is retained unchanged apart from metadata. Its assertions were compared with the indexed topical notes rather than accepted wholesale. None of its linked standalone companion files is present in this research folder.

• Regular cores incorporates a checked elementary small-difference lemma, including the finite-group exterior argument. It replaces Kneser's theorem in that note's majority proof and gives the explicit bound $R(A)\ge h-n/2-10n^{6/7}$. The shifted-grid incidence estimate and strict $t+1$ new-pair budget were reconstructed and checked. This is an elementary alternative with an explicit constant, not an improvement of the established positive-fraction circle scope, its asymptotic bound, or the $q^{7/8}$ threshold.
• Layers and obstructions retains the valid disk-core argument and its local exterior-neighbor bound. Its $(6k-5)|B_k|$ estimate is weaker than the existing $(2k-1)|B_k|$ bound; the existing $O(n)$ aspect-ratio criterion is stronger too. The unused Ramsey constant remains unverified, with the geometric-versus-vertex-disjoint distinction recorded explicitly.
• Small orders records exact isometries identifying the report's two lattice models with the existing nine-point types. Its finite spectra were rechecked, but its undisplayed coordinate reference was not certified. The present twelve-point theorem does not require classifying eleven-point deletions. Nearly convex records that both hull arguments are valid but weaker than the current one- and two-exception results.
• Unrestricted frontier distinguishes the report's historical convex-asymptotic gap from the established short-edge inverse theorem. It also preserves the subset-restoration warning and limits the perturbation warning to what it actually proves; equality-preserving methods remain available.

The author checked the new elementary proofs and their constants; they are author-recorded. The source classifications were checked after their digests, and finite computation was limited to the explicit models. Both unrestricted assertions remain unresolved.