{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PJZWIMC7YXFDKN5MSGUHT7A6KV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5c2be2f6bdf885d8457a12782e8d7ff68f234204595bd8b98497131440aa1cdf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2021-08-31T11:26:48Z","title_canon_sha256":"cb1240835093c2279cc144d409c824b1864cec499922fe149331966849c99445"},"schema_version":"1.0","source":{"id":"2108.13762","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.13762","created_at":"2026-07-05T06:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"2108.13762v3","created_at":"2026-07-05T06:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.13762","created_at":"2026-07-05T06:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"PJZWIMC7YXFD","created_at":"2026-07-05T06:36:19Z"},{"alias_kind":"pith_short_16","alias_value":"PJZWIMC7YXFDKN5M","created_at":"2026-07-05T06:36:19Z"},{"alias_kind":"pith_short_8","alias_value":"PJZWIMC7","created_at":"2026-07-05T06:36:19Z"}],"graph_snapshots":[{"event_id":"sha256:5a78eed8e4e28b1988dc55ee1d27e9636571e8cce543ef3706fa6e8e5900e748","target":"graph","created_at":"2026-07-05T06:36:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.13762/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Niels Bohr successfully predicted in 1913 the energy levels for the hydrogen atom by applying certain quantization rules to classically obtained periodic orbits. Many physicists tried to apply similar methods to other atoms. In his well-known 1921 paper, I.~Langmuir established numerically the existence of a periodic orbit in the helium atom considered as a classical three body problem. In this paper we give an analytic proof of the existence of Langmuir's periodic orbit.","authors_text":"Kai Cieliebak, Martin Schwingenheuer, Urs Frauenfelder","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2021-08-31T11:26:48Z","title":"On Langmuir's periodic orbit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.13762","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:91abb60b83d77425c88030843eb12921538ca44e0f363e5ba50054a18c9e6191","target":"record","created_at":"2026-07-05T06:36:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5c2be2f6bdf885d8457a12782e8d7ff68f234204595bd8b98497131440aa1cdf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2021-08-31T11:26:48Z","title_canon_sha256":"cb1240835093c2279cc144d409c824b1864cec499922fe149331966849c99445"},"schema_version":"1.0","source":{"id":"2108.13762","kind":"arxiv","version":3}},"canonical_sha256":"7a7364305fc5ca3537ac91a879fc1e55487bd741f98b2d38a96c8176612de23d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a7364305fc5ca3537ac91a879fc1e55487bd741f98b2d38a96c8176612de23d","first_computed_at":"2026-07-05T06:36:19.576737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:36:19.576737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CyQnKvr293x/q3ruz0A8Qa5egXEEurUGp2A2XQO1YgwKM8VeLfeqTz30g4E3FtxY0UAW9tZ+GF4+MRxBLUppDw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:36:19.577184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.13762","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91abb60b83d77425c88030843eb12921538ca44e0f363e5ba50054a18c9e6191","sha256:5a78eed8e4e28b1988dc55ee1d27e9636571e8cce543ef3706fa6e8e5900e748"],"state_sha256":"161836c2163100db1b2c331e67b3574a36be292ceaaf6daedf96b326fca221f5"}