{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TM6QB5XYBQFKXED45Z3XN6YYXF","short_pith_number":"pith:TM6QB5XY","canonical_record":{"source":{"id":"1112.1451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-12-07T01:26:16Z","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"title_canon_sha256":"59af0be8546b2876dea5e2e09da59b68bc97a905447922fde6cbdea66939067f","abstract_canon_sha256":"4141b4f1174fa9e3d85aca594d22e0ca6370a66739a9a77a898e0a5324e20138"},"schema_version":"1.0"},"canonical_sha256":"9b3d00f6f80c0aab907cee7776fb18b9646df55e19923234d9761f19d1baa31b","source":{"kind":"arxiv","id":"1112.1451","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1451","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1451v2","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1451","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"pith_short_12","alias_value":"TM6QB5XYBQFK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TM6QB5XYBQFKXED4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TM6QB5XY","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TM6QB5XYBQFKXED45Z3XN6YYXF","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-12-07T01:26:16Z","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"title_canon_sha256":"59af0be8546b2876dea5e2e09da59b68bc97a905447922fde6cbdea66939067f","abstract_canon_sha256":"4141b4f1174fa9e3d85aca594d22e0ca6370a66739a9a77a898e0a5324e20138"},"schema_version":"1.0"},"canonical_sha256":"9b3d00f6f80c0aab907cee7776fb18b9646df55e19923234d9761f19d1baa31b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:16.005487Z","signature_b64":"yxpBLZ3QVvffdYKvUH48LRzTzD3noMjGo4QS1nX6zezS9UgMVgO2EO41Tp3Pt5G32EbuWVmMgdxQcFPlRNTcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3d00f6f80c0aab907cee7776fb18b9646df55e19923234d9761f19d1baa31b","last_reissued_at":"2026-05-18T01:59:16.004741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:16.004741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1451","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tCEiE+veEdGHZ3Lby4WtzQUvSCLe0LyBxGGm/vBv1hZRXMVvzk77EyZxwOEKkeizJ5xThNNRcPFkMxjvfnV8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:27:23.957803Z"},"content_sha256":"dd02675f0c45d6e189ccd075e91446e7ea6950e26d4491c760dbf734ae9ab962","schema_version":"1.0","event_id":"sha256:dd02675f0c45d6e189ccd075e91446e7ea6950e26d4491c760dbf734ae9ab962"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TM6QB5XYBQFKXED45Z3XN6YYXF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact wave functions of two-electron quantum rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","physics.chem-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos","submitted_at":"2011-12-07T01:26:16Z","abstract_excerpt":"We demonstrate that the Schr\\\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1451","kind":"arxiv","version":2},"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":"2026-05-18T01:59:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+D8SP2XMjJ0LkmHXZaQKWmvJSw+G0+4IN3sZwdu1tvhqEDFWokPyv3QrzrnI8BTEPoOe5mWxpZIFYjh7SB5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:27:23.958526Z"},"content_sha256":"2c980a0385feba090a3635fc1b47049f6ec4eb4f03493dfe0d04f2785e1228bc","schema_version":"1.0","event_id":"sha256:2c980a0385feba090a3635fc1b47049f6ec4eb4f03493dfe0d04f2785e1228bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TM6QB5XYBQFKXED45Z3XN6YYXF/bundle.json","state_url":"https://pith.science/pith/TM6QB5XYBQFKXED45Z3XN6YYXF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TM6QB5XYBQFKXED45Z3XN6YYXF/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":"2026-06-10T01:27:23Z","links":{"resolver":"https://pith.science/pith/TM6QB5XYBQFKXED45Z3XN6YYXF","bundle":"https://pith.science/pith/TM6QB5XYBQFKXED45Z3XN6YYXF/bundle.json","state":"https://pith.science/pith/TM6QB5XYBQFKXED45Z3XN6YYXF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TM6QB5XYBQFKXED45Z3XN6YYXF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TM6QB5XYBQFKXED45Z3XN6YYXF","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":"4141b4f1174fa9e3d85aca594d22e0ca6370a66739a9a77a898e0a5324e20138","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-12-07T01:26:16Z","title_canon_sha256":"59af0be8546b2876dea5e2e09da59b68bc97a905447922fde6cbdea66939067f"},"schema_version":"1.0","source":{"id":"1112.1451","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1451","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1451v2","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1451","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"pith_short_12","alias_value":"TM6QB5XYBQFK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TM6QB5XYBQFKXED4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TM6QB5XY","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:2c980a0385feba090a3635fc1b47049f6ec4eb4f03493dfe0d04f2785e1228bc","target":"graph","created_at":"2026-05-18T01:59:16Z","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 demonstrate that the Schr\\\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states.","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos","cross_cats":["cond-mat.other","physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-12-07T01:26:16Z","title":"Exact wave functions of two-electron quantum rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1451","kind":"arxiv","version":2},"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:dd02675f0c45d6e189ccd075e91446e7ea6950e26d4491c760dbf734ae9ab962","target":"record","created_at":"2026-05-18T01:59:16Z","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":"4141b4f1174fa9e3d85aca594d22e0ca6370a66739a9a77a898e0a5324e20138","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-12-07T01:26:16Z","title_canon_sha256":"59af0be8546b2876dea5e2e09da59b68bc97a905447922fde6cbdea66939067f"},"schema_version":"1.0","source":{"id":"1112.1451","kind":"arxiv","version":2}},"canonical_sha256":"9b3d00f6f80c0aab907cee7776fb18b9646df55e19923234d9761f19d1baa31b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b3d00f6f80c0aab907cee7776fb18b9646df55e19923234d9761f19d1baa31b","first_computed_at":"2026-05-18T01:59:16.004741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:16.004741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxpBLZ3QVvffdYKvUH48LRzTzD3noMjGo4QS1nX6zezS9UgMVgO2EO41Tp3Pt5G32EbuWVmMgdxQcFPlRNTcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:16.005487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1451","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd02675f0c45d6e189ccd075e91446e7ea6950e26d4491c760dbf734ae9ab962","sha256:2c980a0385feba090a3635fc1b47049f6ec4eb4f03493dfe0d04f2785e1228bc"],"state_sha256":"41f1ad2dc3803ee0e2c66b4e31563cba0d9815bfc4b41b02178a1aebac1b1bd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4QEDzK8h/P1gWwG2vdGTW3BuQzXWXWXT65EGY6XHXFVtgFCfGS2PFIJok5VqJ4VR29V3U5OXNj9r8ItiAlmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:27:23.961828Z","bundle_sha256":"1ecc4fa3927300d4b3e448e6099156f260e4770b7446a05ee7625c9bbb8060f7"}}