Five working tools, each built out of research that was already sitting in this account as a paper, a C++ build or a folder of CSVs — and was therefore impossible to look at without checking something out and compiling it. Everything below opens in a browser.
Mines inequalities between graph invariants from every connected graph up to eight vertices, then attacks the survivors with graphs it never saw. It rediscovers Wilf's theorem. It also proposes χ ≤ ω + 1, which is false — and finds the Grötzsch graph that kills it.
Colour a sparse matrix's bipartite graph and watch the number of matrix–vector products fall. On a 183×183 Jacobian: 183 products uncompressed, 72 one-sided, 20 with star bicolouring, 11 if you only need the band. Every count is verified against the definition before it is shown.
191 book reviews placed where the books are set rather than where they were published, as a map and as a timeline of how far back each author reached. Median reach is 14 years; The Name of the Rose reaches back 653.
The same graph algorithms in Python, JavaScript, C++, Rust and Java, run against one contract pinned tightly enough that any disagreement is a bug. 1,100 comparisons, zero disagreements — except the spectral radius, which differs by 3.6 × 10−15 and always will.
Twenty magnetic observatories as one correlation graph, rewired every day for thirteen years. On a quiet day the network splits into geographic communities; during the March 2015 storm the communities stop existing and modularity hits zero.