data/theorems.csv

theorem_id,name,statement,status,proof_location,dependencies,verifier
T1,Positive-density outlier theorem,"For each fixed integer g>=3, there exist constants c_g, delta_g>0 and infinitely many finite connected simple cubic graphs F of girth at least g such that every edge signing sigma has at least c_g |V(F)| adjacency eigenvalues, counted with algebraic multiplicity, satisfying |lambda_i(A_sigma)| >= 2*sqrt(2)+delta_g.",proved_in_manuscript,main v4 manuscript,"T0, multi-core completion, algebraic gap lemma",code/verify_extensive.py
T2,Linear negative-inertia localizer,"For the same family and every signing, ind_-(8I-A_sigma^2) >= c_g |V(F)|.",proved_corollary,main v4 manuscript,T1,analytic
T3,Exterior-power obstruction,"For k up to the guaranteed outlier multiplicity, ||wedge^k A_sigma|| >= (2*sqrt(2)+delta_g)^k.",proved_corollary,main v4 manuscript,T1,analytic
T4,Finite moment/SOS certificate,"For each fixed g, one finite even moment order m_g suffices to reject every signing in the constructed infinite family: tr(A_sigma^(2m_g))/n > 8^m_g.",proved_in_manuscript,main v4 manuscript,"T1, algebraic gap lemma",code/verify_extensive.py
T0,Arbitrary-girth persistence dependency,For every target girth g>=3 there exist infinitely many finite connected simple cubic graphs of girth at least g for which every signing has norm >2sqrt(2).,proved_in_bundled_v3,bundled v3 manuscript,AMS/HHH root-response construction,code/verify_high_girth_v3.py