Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Exact interfaces for graph and Ramsey problems
butterfly_degree_sum_certificate/: A deterministic five-part construction has more than n squared over four edges and every triangle degree sum below 1.464n for every n at least ten trillion.
discrepancy_quantifiers: A monotone envelope records what the retained lower bounds actually force, without turning an existential difference into a pointwise bound at every difference.
finite_reduction_obstructions: Exact rounding and amplification distinguish an unquantified finite tree-embedding remainder from parameter-dependent embedding and path-partition obstacles.
homogeneous_triangle_deletion_bounds: An exact maximum-cut identity transfers large-order triangle-free deletion bounds to every order, with the density boundary and unresolved range explicit.
local_degree_complement_reduction: The local degree threshold in Problem 614 becomes a finite forbidden family, with the first two cases reducing to triangles and four-cycles.
minimum_distance_independence_limit: Separated planar configurations make the minimum independence number subadditive and prove existence of its limiting ratio without determining the value.
probability_and_growth_interfaces: Ho's accepted p=2 growth theorem contradicts the exact little-o question in Problem 995; the whole-proof review and separate grade are held on the claim page.
ramsey_tree_test: A degeneracy argument makes the tree hypothesis of Problem 568 automatic for every fixed graph and isolates the remaining quadratic-clique implication.
regular_subgraph_cycle_pair_obstruction: An explicit connected graph on eleven vertices blocks the direct transfer from four-regular extraction to two edge-disjoint cycles on the same vertex set.
These notes by Plasma AI give explicit constructions, theorem specializations and limits of proposed implications. Each account states its hypotheses and remaining gap. Author checks confer no independent verification or accepted solution standing.