2 commits

Author	SHA1	Message	Date
Brandon Schneider	4965029758	feat: integrate May 2026 math papers into Research Stack ... 1. Singer Sidon Sets (2605.03274): - New SidonSets.lean: IsSidon, IsSidonMod, IsIntervalSidon, h(N) - 5 fully proved lemmas, 13 sorry with TODO(lean-port) - GoldenRatioSeparation.lean: singer_density_lt_golden (proved) - lake build: 3303 jobs, 0 errors 2. Hexagonal lattice + RG (2605.09974): - New test_hexagonal_lattice_rg() in unified_rg_tests.py - Avila's global theory exact phase diagram - RG confirms localized/extended regimes - Fractal dimension: extended→1, critical→0.5, localized→0 - 7 tests, all pass 3. Burgers + Hopf-Cole + Fokas (2605.11788): - Added solve_heat_fokas() — unified transform method - Added solve_burgers_fokas() — full Burgers via Hopf-Cole + Fokas - Added solve_heat_fourier_series() — comparison solver - Fokas converges in ~64 quadrature points vs Fourier 2000 terms - Hopf-Cole FFT: 8-208x faster than finite differences	2026-05-30 18:16:57 -05:00
Brandon Schneider	a53e023cbe	feat: Hopf-Cole exact solver for 1D Burgers — 151x speedup ... Hopf-Cole transformation maps Burgers to heat equation: u = -2v * d(ln ψ)/dx dψ/dt = v * d²ψ/dx² (exact via FFT) Benchmark results: N=512, v=0.01: 1.45x speedup N=1024, v=0.01: 83.4x speedup N=2048, v=0.01: 151.3x speedup Key insight from adversarial review: - RG assumption (nonlinear term vanishes) is FALSE - But 1D Burgers IS integrable via Hopf-Cole - Exact solution in O(N log N), no time stepping - The 'insultingly easy' regime exists — just not via RG This is the exact solution the agents found when they broke the RG fixed point assumption.	2026-05-30 17:36:12 -05:00