{"paper":{"title":"Quantum mechanics on the line with two origins","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GN","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Abhiram Sripat","submitted_at":"2026-07-24T16:53:14Z","abstract_excerpt":"We study scalar and spinorial quantum dynamics on the standard line with two origins, \\[\n  \\Ltwo=(\\R_1\\sqcup\\R_2)/\\!\\sim,\n  \\qquad\n  (x,1)\\sim(x,2)\\quad\\text{for }x\\neq0, \\] equipped with its identity-glued smooth structure and flat metric. We first show that the ordinary scalar theory is insensitive to the doubled origin: every continuous map from \\(\\Ltwo\\) to a Hausdorff space factors through the quotient \\(q:\\Ltwo\\to\\R\\), while, for the natural measure, \\[\n  C^\\infty(\\Ltwo)\\cong C^\\infty(\\R),\n  \\qquad\n  L^2(\\Ltwo)\\cong L^2(\\R). \\] Accordingly, the natural scalar free Hamiltonian is unitaril"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26080","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/2607.26080/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"}