Symmetric Exponential Time Requires Near-Maximum Circuit Size: Simplified, Truly Uniform

In a recent breakthrough, Chen, Hirahara and Ren prove that S2E/1 ⊄SIZE2n/n by giving a single-valued FS2P algorithm for the Range Avoidance Problem (Avoid) that works for infinitely many input size n. Building on their work, we present a simple single-valued FS2P algorithm for Avoid that works for all input size n. As a result, we obtain the circuit lower bound S2E ⊄i.o.-SIZE2n/n and many other corollaries: 1. Almost-everywhere near-maximum circuit lower bound for Σ2E ∩ Π2E and ZPENP. 2. Pseudodeterministic FZPPNP constructions for combinatorial objects such as: Ramsey graphs, rigid matrices, pseudorandom generators, two-source extractors, linear codes, hard truth tables, and Kpoly-random strings.