Station v2 mathematics
Proof and Verification
Thirteen complete mathematical and computational companions to the Station v2 paper. Every page contains the released exposition, equations, code and saved outputs in full.
Headline results
Novel-discovery verification
The six notebooks supporting the reported novel mathematical discoveries.
Book Ramsey numbers
Proofs and computations for three infinite construction families, finite certificates, and coverage through n = 200.
Read the full notebookErdős minimum overlap
The four-row directed-interval certificate for μ > 0.380552, plus upper-bound comparisons and additional analysis.
Read the full notebookFinite-field Kakeya
Exact verification of the new infinite family, the 53-point F₃⁵ set, higher-dimensional constructions, and 25 benchmarks.
Read the full notebookDiscretized Kakeya needle
Verification of the new n = 32, 64 and 128 bounds, exact small-n optima, and the first forced symmetry breaking.
Read the full notebookKissing number in dimension 11
Exact verification of three 604-point configurations, their isometry classes, and explicit algebraic constructions.
Read the full notebookSign uncertainty principle
Verification of the 0.3089 witness, exact coefficient and root data, and analysis of the double-root Laguerre family.
Read the full notebookComplete collection
Additional verification notebooks
Independent reconstructions, computational checks and supporting analysis for seven further research problems.
Difference bases
Verification of the construction, an independent recovery in the Leech–Golay family, and comparison results.
Read the full notebookPrime number theorem
Verification of the 255-term all-x certificate with score 0.980681 and analysis of why a direct Möbius cutoff fails.
Read the full notebookFlat autoconvolution
Verification of the binary-step-function reduction, a 100,000-step construction, and the sharp two-interval ceiling.
Read the full notebookHardy–Littlewood maximal inequality
Exact finite-model analysis of centered and uncentered maximal operators and verification of the 356-atom construction.
Read the full notebookJacobian Conjecture
Exact reconstruction of the announced map, its cuspidal ruling, three-sheeted fibers, and collision certificates.
Read the full notebookOvals problem
Independent recovery of the known Benguria–Loss equality family, plus spectral, symmetry, and polar-moment checks.
Read the full notebookPeak autoconvolution
Exact verification of the 16,384-step construction, two certified local minima, and structural analysis.
Read the full notebook