{"paper":{"title":"The Saddle Point of Everything","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"K. Sravan Kumar","submitted_at":"2026-05-28T08:17:42Z","abstract_excerpt":"The harmonic oscillator is the universal Hamiltonian of stable equilibrium. Its counterpart, the inverted harmonic oscillator (IHO), is the Hamiltonian of unstable equilibrium: the saddle point of physical systems. It appears across disciplines, from condensed matter, quantum optics, and quantum chemistry to the Standard Model Higgs instability and quantum field theory near gravitational horizons. Its mathematical depth is further reflected in its relation to the non-trivial zeros of the Riemann zeta function through the Berry-Keating Hamiltonian. Remarkably, a dual Hamiltonian to the IHO has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30386","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30386/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}