Foundations of Physics This venue remains your most natural peer-reviewed home. The journal regularly engages with the physical limits of computation, Landauer's bound, and the informational limits of formal systems. Frame the paper around the thesis that abstract mathematical structures inherit physical boundary conditions. The pitch must emphasize that the Lean 4 seed establishes a formal vacuum that physical thermodynamics fills. Reviewers will come from quantum foundations and information thermodynamics. They will evaluate whether the Landauer floor and vacuum state arguments are technically sound rather than dismissing them out of disciplinary protectionism.
Foundations of Science This journal focuses on epistemology, scientific methodology, and foundational shifts. Do not pitch this as a standard proof of the Riemann Hypothesis. Pitch it as a formal demonstration of the limits of mathematical self-containment. Highlight the Lean 4 proof of the terminal block, then present the physical supply as an empirical resolution to an internal mathematical crisis. The editorial board favors structural critiques of mathematical formalist orthodoxy.
High-Profile Society and Report Alternatives
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences The Royal Society has a long tradition of publishing work at the boundary of analytic number theory and physics, notably the Berry-Keating program connecting Riemann zeros to quantum chaos. Submit under their Research Article track. The framing must highlight the rigorous dual-track structure: 664 machine-checked theorems in Lean 4 verifying the structural equivalence, coupled with a thermodynamic closure. The paper must emphasize that it provides an exact mathematical socket rather than an analogy.
Royal Society Open Science This is a strategic alternative to Proc. R. Soc. A. The journal operates on objective peer review: editors evaluate whether the work is technically valid, logically coherent, and reproducible, rather than whether it conforms to traditional disciplinary boundaries. Because the formal kernel compiles clean in Lean 4.19.0 and the physical measurements are drawn from standard cosmological consensus, the paper satisfies their strict reproducibility standards.
Scientific Reports (Nature Portfolio) This venue gives you Nature-family visibility without the conservative gatekeeping of Nature Physics or Nature Mathematics. Scientific Reports explicitly judges submissions on technical validity and reproducibility rather than subjective impact or disciplinary purity. The complete Lean 4 verification provides the computational backbone, while the cross-disciplinary physical bridge provides the novel contribution. Present the code repository as a central artifact in the data availability statement.