{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JOIL2FTG333V4J7RBX57AR3SIH","short_pith_number":"pith:JOIL2FTG","canonical_record":{"source":{"id":"1402.3816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-16T16:58:55Z","cross_cats_sorted":["math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"0caab98893b7a7d99cd487415b5c900b10273e44ce78da25dfa44506c1373128","abstract_canon_sha256":"a43fbb3a77e6c79dd60aca09bf4ddb3a13ada92ce7882c53b787c2d3ac5e3979"},"schema_version":"1.0"},"canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","source":{"kind":"arxiv","id":"1402.3816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3816","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3816v1","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3816","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"JOIL2FTG333V","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JOIL2FTG333V4J7R","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JOIL2FTG","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JOIL2FTG333V4J7RBX57AR3SIH","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-16T16:58:55Z","cross_cats_sorted":["math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"0caab98893b7a7d99cd487415b5c900b10273e44ce78da25dfa44506c1373128","abstract_canon_sha256":"a43fbb3a77e6c79dd60aca09bf4ddb3a13ada92ce7882c53b787c2d3ac5e3979"},"schema_version":"1.0"},"canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:43.996351Z","signature_b64":"EZ+EUbkRK1+RC2YfhfNnvEDMNuk1pBC30daH+ioybYyXDzCb6BM2+XOhZy0ks7ghjv2KnaBFfFkO28ttsej5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","last_reissued_at":"2026-05-18T01:11:43.995891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:43.995891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3816","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tz0dHaJEroOW1lqP44jvNWkcZtoUn2IpRnHOtBXWNbRjF0nOqvi5/XICkOvKecfknPzgLRlZh+yHnU26SZjlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:15:33.616770Z"},"content_sha256":"eab1d4042caad73d2edbf7ae707a4eb0ffbb95243eb9a6e12ca21d1aab5f09f9","schema_version":"1.0","event_id":"sha256:eab1d4042caad73d2edbf7ae707a4eb0ffbb95243eb9a6e12ca21d1aab5f09f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JOIL2FTG333V4J7RBX57AR3SIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander V Turbiner, jr, Willard Miller","submitted_at":"2014-02-16T16:58:55Z","abstract_excerpt":"We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We give the details of the Hamiltonian reduction of the 3D system to a 2D system with modified potential that is separable in elliptic coordinates. The potentials for which there is double-periodicity of the Schr\\\"odinger operator in the space of prolate spheroidal coordinates, including one for the H$_2^+$ molecular ion, are indicated. We study possible potentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3816","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z89CUZer8V8PQnB+QvcrB5+kZLM7HN6FeZyJMiA23vRA2JXS58ijpDk3VVszCY2HtKHLLsm+Ehq1r+PUlaiyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:15:33.617469Z"},"content_sha256":"29fb1733abd214a016afbfac46ae137dc5ae29db16dd461f84f69a43a0841c4d","schema_version":"1.0","event_id":"sha256:29fb1733abd214a016afbfac46ae137dc5ae29db16dd461f84f69a43a0841c4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/bundle.json","state_url":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOIL2FTG333V4J7RBX57AR3SIH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T17:15:33Z","links":{"resolver":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH","bundle":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/bundle.json","state":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOIL2FTG333V4J7RBX57AR3SIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JOIL2FTG333V4J7RBX57AR3SIH","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":"a43fbb3a77e6c79dd60aca09bf4ddb3a13ada92ce7882c53b787c2d3ac5e3979","cross_cats_sorted":["math.MP","nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-16T16:58:55Z","title_canon_sha256":"0caab98893b7a7d99cd487415b5c900b10273e44ce78da25dfa44506c1373128"},"schema_version":"1.0","source":{"id":"1402.3816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3816","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3816v1","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3816","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"JOIL2FTG333V","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JOIL2FTG333V4J7R","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JOIL2FTG","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:29fb1733abd214a016afbfac46ae137dc5ae29db16dd461f84f69a43a0841c4d","target":"graph","created_at":"2026-05-18T01:11:43Z","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"},"paper":{"abstract_excerpt":"We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We give the details of the Hamiltonian reduction of the 3D system to a 2D system with modified potential that is separable in elliptic coordinates. The potentials for which there is double-periodicity of the Schr\\\"odinger operator in the space of prolate spheroidal coordinates, including one for the H$_2^+$ molecular ion, are indicated. We study possible potentia","authors_text":"Alexander V Turbiner, jr, Willard Miller","cross_cats":["math.MP","nlin.SI","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-16T16:58:55Z","title":"Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3816","kind":"arxiv","version":1},"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:eab1d4042caad73d2edbf7ae707a4eb0ffbb95243eb9a6e12ca21d1aab5f09f9","target":"record","created_at":"2026-05-18T01:11:43Z","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":"a43fbb3a77e6c79dd60aca09bf4ddb3a13ada92ce7882c53b787c2d3ac5e3979","cross_cats_sorted":["math.MP","nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-16T16:58:55Z","title_canon_sha256":"0caab98893b7a7d99cd487415b5c900b10273e44ce78da25dfa44506c1373128"},"schema_version":"1.0","source":{"id":"1402.3816","kind":"arxiv","version":1}},"canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","first_computed_at":"2026-05-18T01:11:43.995891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:43.995891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZ+EUbkRK1+RC2YfhfNnvEDMNuk1pBC30daH+ioybYyXDzCb6BM2+XOhZy0ks7ghjv2KnaBFfFkO28ttsej5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:43.996351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eab1d4042caad73d2edbf7ae707a4eb0ffbb95243eb9a6e12ca21d1aab5f09f9","sha256:29fb1733abd214a016afbfac46ae137dc5ae29db16dd461f84f69a43a0841c4d"],"state_sha256":"d96aaac4940f46d39d570d4dd596eee40824d0f9aaf5d3dc66ef1a52e91cd851"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vD2vOgNusVbQJScSApkelBC0nEV63bCt4HQc/F1xClr0wVqxLnf8bouKTD6oqBYEwWCTKnB22zxeTHaRa8KVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:15:33.621307Z","bundle_sha256":"647d323de2e468e3024af8f28844df287cec5e2fa44529d952d507329fbad969"}}