{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PO6WI7YTDSNDYEYIJ4TQHZHLKG","short_pith_number":"pith:PO6WI7YT","canonical_record":{"source":{"id":"1011.2579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-11T07:07:23Z","cross_cats_sorted":["gr-qc","math.MP","quant-ph"],"title_canon_sha256":"b6dc8793a43a626df463cec62f484e81c6dbf6b9a181bb48e962ddbc525cdf40","abstract_canon_sha256":"9dba20ec0e19de10b9ac1775e85e53ab6e817a4e82862ac2d69f3bf311e1b8f4"},"schema_version":"1.0"},"canonical_sha256":"7bbd647f131c9a3c13084f2703e4eb51af395898c35526907dbbf871207dde6b","source":{"kind":"arxiv","id":"1011.2579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2579","created_at":"2026-05-18T04:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2579v1","created_at":"2026-05-18T04:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2579","created_at":"2026-05-18T04:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"PO6WI7YTDSND","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PO6WI7YTDSNDYEYI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PO6WI7YT","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PO6WI7YTDSNDYEYIJ4TQHZHLKG","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-11T07:07:23Z","cross_cats_sorted":["gr-qc","math.MP","quant-ph"],"title_canon_sha256":"b6dc8793a43a626df463cec62f484e81c6dbf6b9a181bb48e962ddbc525cdf40","abstract_canon_sha256":"9dba20ec0e19de10b9ac1775e85e53ab6e817a4e82862ac2d69f3bf311e1b8f4"},"schema_version":"1.0"},"canonical_sha256":"7bbd647f131c9a3c13084f2703e4eb51af395898c35526907dbbf871207dde6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:10.010382Z","signature_b64":"UwZwN7cO0hIlMTjsFm9G1V4npYBxJtoBZib0wed3Glfx5LkBiGseSvCjUn5d1HSOWl+r/SBtLKqEm9pCaRMmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bbd647f131c9a3c13084f2703e4eb51af395898c35526907dbbf871207dde6b","last_reissued_at":"2026-05-18T04:36:10.009711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:10.009711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2579","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":"2026-05-18T04:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tDTq8Sf/dP2ecoTN5zRugCBA4pQ425Qwwd2Xmgex5+W4F3JIXNwlxynQzyJO2DgGCS+op32jEkCto6kRlY9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:58:33.361139Z"},"content_sha256":"6b56f5453e5b5c0ec6299a23563bafedb3a395a8ebe020094f29696de5a57041","schema_version":"1.0","event_id":"sha256:6b56f5453e5b5c0ec6299a23563bafedb3a395a8ebe020094f29696de5a57041"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PO6WI7YTDSNDYEYIJ4TQHZHLKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Spin-weighted Spheroidal Wave functions in the Case of s=1/2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Guihua Tian, Kun Dong, Yue Sun","submitted_at":"2010-11-11T07:07:23Z","abstract_excerpt":"The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-potential in the series of the parameter beta are given. The general form of the nth term of the superpotential is also obtained, which could derived from the previous terms W_{k}, k<n. From the results, it is easy to give the ground eigenfunction of the equation. Furthermore, the shape-invariance property is investigated in the series form of the parameter beta and is proven kept in this series for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2579","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":"2026-05-18T04:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6Ktf5OayLRbmS7JjjGTmMgYcHfbfuEH89ClMrNrzZg5YBZxucJGc8iLqfUAy+zxzyWTr92C+T9oAZHMqZilBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:58:33.361507Z"},"content_sha256":"8ab79bea960fc813378fa4f18cb0645102486f1cea4789c148ae247c664aeb61","schema_version":"1.0","event_id":"sha256:8ab79bea960fc813378fa4f18cb0645102486f1cea4789c148ae247c664aeb61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG/bundle.json","state_url":"https://pith.science/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG/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":"2026-06-02T20:58:33Z","links":{"resolver":"https://pith.science/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG","bundle":"https://pith.science/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG/bundle.json","state":"https://pith.science/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PO6WI7YTDSNDYEYIJ4TQHZHLKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PO6WI7YTDSNDYEYIJ4TQHZHLKG","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":"9dba20ec0e19de10b9ac1775e85e53ab6e817a4e82862ac2d69f3bf311e1b8f4","cross_cats_sorted":["gr-qc","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-11T07:07:23Z","title_canon_sha256":"b6dc8793a43a626df463cec62f484e81c6dbf6b9a181bb48e962ddbc525cdf40"},"schema_version":"1.0","source":{"id":"1011.2579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2579","created_at":"2026-05-18T04:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2579v1","created_at":"2026-05-18T04:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2579","created_at":"2026-05-18T04:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"PO6WI7YTDSND","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PO6WI7YTDSNDYEYI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PO6WI7YT","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:8ab79bea960fc813378fa4f18cb0645102486f1cea4789c148ae247c664aeb61","target":"graph","created_at":"2026-05-18T04:36:10Z","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":"The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-potential in the series of the parameter beta are given. The general form of the nth term of the superpotential is also obtained, which could derived from the previous terms W_{k}, k<n. From the results, it is easy to give the ground eigenfunction of the equation. Furthermore, the shape-invariance property is investigated in the series form of the parameter beta and is proven kept in this series for","authors_text":"Guihua Tian, Kun Dong, Yue Sun","cross_cats":["gr-qc","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-11T07:07:23Z","title":"The Spin-weighted Spheroidal Wave functions in the Case of s=1/2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2579","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":"sha256:6b56f5453e5b5c0ec6299a23563bafedb3a395a8ebe020094f29696de5a57041","target":"record","created_at":"2026-05-18T04:36:10Z","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":"9dba20ec0e19de10b9ac1775e85e53ab6e817a4e82862ac2d69f3bf311e1b8f4","cross_cats_sorted":["gr-qc","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-11T07:07:23Z","title_canon_sha256":"b6dc8793a43a626df463cec62f484e81c6dbf6b9a181bb48e962ddbc525cdf40"},"schema_version":"1.0","source":{"id":"1011.2579","kind":"arxiv","version":1}},"canonical_sha256":"7bbd647f131c9a3c13084f2703e4eb51af395898c35526907dbbf871207dde6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bbd647f131c9a3c13084f2703e4eb51af395898c35526907dbbf871207dde6b","first_computed_at":"2026-05-18T04:36:10.009711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:10.009711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UwZwN7cO0hIlMTjsFm9G1V4npYBxJtoBZib0wed3Glfx5LkBiGseSvCjUn5d1HSOWl+r/SBtLKqEm9pCaRMmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:10.010382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b56f5453e5b5c0ec6299a23563bafedb3a395a8ebe020094f29696de5a57041","sha256:8ab79bea960fc813378fa4f18cb0645102486f1cea4789c148ae247c664aeb61"],"state_sha256":"166eaa6f54d5eb5b5cea9090f54d758b26ec554e7aadf3ecc961dd7f29e894e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DFRJGwhE93Pj0E2E+2SnpwBMp5WxhxfQBWy/WC4TT3WuH4dRFiOUYoRfDsx8Z/VOnmq4/azZlq/pox5acjPLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:58:33.363546Z","bundle_sha256":"46c866dc7b7012aa0732f48755ff152931e9d7ab47fd83755569f2512b5729a8"}}