Riemann Zeta and Dirichlet L-functions as a Universal Computational Substrate: From Critical-Line Thermodynamics to Applied Cryptography, Genomics, Machine Learning and Code Analysis

We present a unified computational framework that treats the Riemann zetafunction on the critical line Re(s) = 1/2 and the real Dirichlet L-functions L(s, χ)as a single substrate for six families of applied primitives: (i) a thermodynamiclandscape F (σ) = − ln Z whose free-energy minimum at σ = 1/2 reproduces thespectral picture of Connes; (ii) a branchless Q16.16 fixed-point engine (SintMath)that evaluates η(1/2 + it) and L(1/2 + it, χ) in pure integer arithmetic at 5× thespeed of float64 and 50× the speed of mpmath; (iii) a zero-backpropagation classi-fier ZetaSubspaceEngine reaching 97.6% on 8×8 digits (matching Random Forest)and 90.3% on MNIST-784 (matching Logistic Regression), formally equivalentto an RBF classifier on a log-frequency metric; (iv) a DNA screening modulebased on a real Dirichlet character encoding of nucleotides that detects single-point SNPs and outperforms BLAST, Hamming, Levenshtein, and k-mer Jaccardon recombination queries, achieving 100% top-1 retrieval on a 288-query bench-mark against 12 real 256-bp windows from SARS-CoV-2 Wuhan-Hu-1, SARS-CoV-2 Omicron BA.1, Influenza A H1N1 HA, and E. coli K-12; (v) a binary decompilerthat splits a MOS 6502 ROM into WebAssembly capsules along Shannon-entropyseams; (vi) a cryptographically sound key-exchange protocol Z-EXP-256 (thesecure successor to the broken CRM-KE) whose security reduces to the Compu-tational Diffie–Hellman problem over a 2048-bit safe prime, with the L-functionserving as a domain-separating KDF ingredient. We prove formal equivalences,benchmark all six modules against classical baselines including the real-genomeBLAST comparison, and honestly assess which claims are article-worthy andwhich are engineering scaffolding. All modules are released as the open-sourcezeta_applied library under the Apache 2.0 license, with 21/21 unit tests passing.