Independent research notes
Loneorc Research is Francisco Javier Vera Gómez's personal space for technical essays, non-technical explainers, and materials connected to preprints.
Computational complexity — SAT and P versus NP
SAT, proof complexity, and concrete boundaries around P versus NP. Bounded results, reproducible artifacts, and no over-claiming.
The result does not prove P != NP. It builds an explicit SAT family, identifies it exactly as bounded-degree Tseitin, and records where the method stops short of general-resolution size.
axiom-explorer — LLM-assisted mathematical discovery
An LLM-assisted cross-search workflow over modern axiomatic seeds. Claims are falsifiable conjectures, not theorems.
axiom-explorer is a workflow, not an oracle. It picks four modern axioms from distinct branches of mathematics, runs a controlled cross-search, builds dossiers, and surfaces falsifiable candidate observations. The role of the language model is bounded. The human author retains every release decision. The first paper is now on Zenodo with a DOI.
A second preprint, this time the actual case-study output. It registers a falsifiable cardinality bound for a recent invariant (Haine et al.'s condensed fundamental group of a scheme), shows that the same shape appears on two other branches of mathematics, and invites specialists to confirm it as folklore, refute it, or refine it. Open access, DOI 10.5281/zenodo.20184660.
V.E.R.A. — theoretical cosmology
Speculative theoretical cosmology: hypotheses, reduced test benches, and open blockers. Not a finished theory of the observed universe.
A narrative introduction to V.E.R.A., the hypothesis of matter-antimatter segregation across reciprocal branes.