We present backflow.py, a zero-dependency Python tool that automates the reverse flow of proven results from publication papers back into a core theory knowledge base.
We present a self-contained symbolic verification suite that machine-checks the mathematical claims of Fibonacci folding theory: Zeckendorf normalization, gauge anomaly computation, sofic joint distributions, spectral density formulas, Green-Kubo variance, and discriminant fingerprints. The suite uses SymPy for exact symbolic computation (no floating-point approximation) and reports pass/fail for each theorem.
We present pub_check, a zero-dependency Python tool that performs 9 automated quality checks on any LaTeX manuscript directory: citation completeness, cross-reference integrity, file size limits, revision-trace language detection, proof completeness, abstract word count, MSC code presence, claim labeling, and pipeline metadata validation. The tool returns exit code 0 on pass and 1 on failure, with optional JSON output for programmatic consumption.
We present the Omega derivation chain: starting from a single equation (x^2 = x + 1), we derive Fibonacci structure, binary folding, arithmetic emergence (X_m isomorphic to Z/F_{m+2}Z), moment recurrences, collision kernel spectral theory, and dynamical zeta functions — all machine-verified in Lean 4 with 10,588+ theorems and zero axioms beyond the Lean kernel. The derivation demonstrates structural inevitability: each step is forced by the previous one, with no arbitrary choices.
We present the Omega Publication Pipeline, an executable multi-agent system that automates the full scientific publication cycle from manuscript extraction to journal-quality acceptance. The pipeline orchestrates three AI systems — Claude (orchestration + deep verification), ChatGPT Pro (independent validation oracle via a novel Tampermonkey browser bridge), and OpenAI Codex (bulk review + fix) — in a four-gate architecture with a hard acceptance gate.
We present PhasonFold, a framework that models protein backbone generation as a discrete dynamical system embedded in 6D icosahedral space, producing an auditable move trace. Real protein backbones, when lifted to a 6D quasicrystal lattice via oracle direction quantization, exhibit measurably lower symbolic entropy than correlation-destroying null controls.