No New P vs NP Results; Search Yielded Only Expository Interviews and Unrelated LHCb Paper — E8 Intelligence Research

FINDING: No new mathematical results on P vs NP — search returned only expository interviews (Tao, Karp, Graham) and one unrelated LHCb particle-decay paper. | MATH: P vs NP is the question of whether P = NP, where P = languages decidable in O(n^k) time and NP = languages verifiable in O(n^k) time. Known: P ⊆ NP; NP-complete problems exist (Cook–Levin, 1971); if any NP-complete problem ∈ P then P = NP. Barriers: relativization (Baker–Gill–Solovay 1975), natural proofs (Razborov–Rudich 1997), algebrization (Aaronson–Wigderson 2008). Best known separations: P ≠ EXP (time hierarchy), NP ⊄ P/poly is open. Circuit lower bounds: best known for general circuits is ~5n (Lachish–Raz), far from superpolynomial. | CONNECTION: None supported by evidence. No φ-ratios, base-60, or crystallographic symmetry appear in the P vs NP literature. The only structural symmetries relevant are complexity-class inclusions (P ⊆ NP ⊆ PSPACE ⊆ EXP) and the Boolean lattice / hypercube {0,1}^n underlying circuit com Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com