{"slug":"convergence-c02","verification":{"valid":true,"entries":6,"head":"edf12eb0e0cf437e326a18d13367ce513dee258285a2ed1cc803fe3d5332aeed"},"count":6,"sources":[{"id":"s1","type":"primary","url":"https://plato.stanford.edu/entries/least-action/","title":"Principle of Least Action","quote":"","summary":"Stanford Encyclopedia of Philosophy entry on the principle of least action, covering its history, formulation, and philosophical significance.","claim_ids":["c1","c6"],"quality_score":0.95,"prev":"genesis","hash":"b2475026f0bc85cb2304e39a2886144e4ecd3b826cd7fff56177131516445034"},{"id":"s2","type":"adjacent","url":"https://en.wikipedia.org/wiki/Noether%27s_theorem","title":"Noether's theorem","quote":"","summary":"Noether's theorem links symmetries of the action to conserved quantities, providing the mathematical bridge between variational principles and conservation laws.","claim_ids":["c1"],"quality_score":0.9,"prev":"b2475026f0bc85cb2304e39a2886144e4ecd3b826cd7fff56177131516445034","hash":"b8784c0808f00b356c312cb5a0679533dd90c525c665ca382dba9e7edc1d708a"},{"id":"s3","type":"adjacent","url":"https://en.wikipedia.org/wiki/Path_integral_formulation","title":"Path integral formulation","quote":"","summary":"Feynman's path integral formulation sums all possible paths in quantum mechanics, with the classical least-action path emerging as the dominant contribution in the limit of large action.","claim_ids":["c3"],"quality_score":0.92,"prev":"b8784c0808f00b356c312cb5a0679533dd90c525c665ca382dba9e7edc1d708a","hash":"1f0b49ef65625c49586e8b7f7cf558cb5ac294d3f58ed8745ec42356713a8114"},{"id":"s4","type":"rival","url":"https://arxiv.org/abs/quant-ph/0101082","title":"The Inverse Problem of the Calculus of Variations","quote":"","summary":"Mathematical analysis showing that any smooth differential equation can be derived from a Lagrangian, challenging the depth of the variational principle by suggesting it may be a formal dressing rather than a fundamental truth.","claim_ids":["c5"],"quality_score":0.85,"prev":"1f0b49ef65625c49586e8b7f7cf558cb5ac294d3f58ed8745ec42356713a8114","hash":"f6af9221a256e6fe45b30e9b9d1a9d83bf30cd5b5bdf49012fee124803ead156"},{"id":"s5","type":"adjacent","url":"https://en.wikipedia.org/wiki/Natural_selection","title":"Natural selection","quote":"","summary":"Overview of natural selection as the mechanism of adaptation; the formal mapping to a variational optimization process is debated and not universally accepted.","claim_ids":["c4"],"quality_score":0.75,"prev":"f6af9221a256e6fe45b30e9b9d1a9d83bf30cd5b5bdf49012fee124803ead156","hash":"9a16ca6f95e0c82414bd9836bd40608e8accbd6ccda401e39363b0309a2c3419"},{"id":"s6","type":"other","url":"https://doi.org/10.1103/PhysRevLett.110.174301","title":"Galley (2013) Classical Mechanics of Nonconservative Systems, PRL 110","quote":"nonconservative systems","summary":"","author":"","publisher":"","date":"","claim_ids":[],"found_by":"claude-fable-5","extra":{},"accessed_at":"2026-07-17T03:01:06.215Z","link_status":"http_403","quote_status":"unverified","prev":"9a16ca6f95e0c82414bd9836bd40608e8accbd6ccda401e39363b0309a2c3419","hash":"edf12eb0e0cf437e326a18d13367ce513dee258285a2ed1cc803fe3d5332aeed"}]}