{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:ZD77ARVVCROAGQ565P4PIVTVMT","short_pith_number":"pith:ZD77ARVV","canonical_record":{"source":{"id":"quant-ph/9905011","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1999-05-05T05:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"c18713620eb89feb5cc5cd4ec8590c8bf38823a316a5e95337866c8b19a1d80f","abstract_canon_sha256":"167fa5565337295e41f427702b3e6b0625ec3b18785cc79efe865a8fad63ff87"},"schema_version":"1.0"},"canonical_sha256":"c8fff046b5145c0343beebf8f4567564c46e7a52048a135a4a8ee83fc001d66e","source":{"kind":"arxiv","id":"quant-ph/9905011","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9905011","created_at":"2026-05-18T04:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9905011v1","created_at":"2026-05-18T04:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9905011","created_at":"2026-05-18T04:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZD77ARVVCROA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ZD77ARVVCROAGQ56","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ZD77ARVV","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:ZD77ARVVCROAGQ565P4PIVTVMT","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9905011","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1999-05-05T05:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"c18713620eb89feb5cc5cd4ec8590c8bf38823a316a5e95337866c8b19a1d80f","abstract_canon_sha256":"167fa5565337295e41f427702b3e6b0625ec3b18785cc79efe865a8fad63ff87"},"schema_version":"1.0"},"canonical_sha256":"c8fff046b5145c0343beebf8f4567564c46e7a52048a135a4a8ee83fc001d66e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:25.652477Z","signature_b64":"FY51c/wDoXGO65Lb80V6i5MjxX8EsgxGRfwtXvjbXLptViRFo9dfPpaO4SkwwSSfc2Grq2TayiqdrgVpMe4nAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8fff046b5145c0343beebf8f4567564c46e7a52048a135a4a8ee83fc001d66e","last_reissued_at":"2026-05-18T04:17:25.651909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:25.651909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9905011","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":"2026-05-18T04:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27TRZDc3/1VtVnxBeVZAhusQJspg5PBemZr7bh0AHSt0tbuJDzJJodDOr9WRZHXETHeerObzfsRq0xlfR8FLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:03:46.240000Z"},"content_sha256":"d57ba46cc5248cebd5772e26b6a31bdcbe924f5f875687954e804891f319f45e","schema_version":"1.0","event_id":"sha256:d57ba46cc5248cebd5772e26b6a31bdcbe924f5f875687954e804891f319f45e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:ZD77ARVVCROAGQ565P4PIVTVMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum equivalent of the Bertrand's theorem","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"N. Gurappa, Prasanta K. Panigrahi, T. Soloman Raju","submitted_at":"1999-05-05T05:12:32Z","abstract_excerpt":"A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have infinite number of energy eigenvalues, are the Coulomb and harmonic oscillator potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9905011","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":"2026-05-18T04:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+FLiW5nU2h05Ke+lAD89OaVmw0WXxM7p3fL2s93lMJFIkGJ11Vg6VPyCAnl7S8Mb8z5oR0D+sk8OdgdPT1/FAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:03:46.240876Z"},"content_sha256":"6861447906b15439c9f867395bef965750d3f0af265856214730725aafdcf190","schema_version":"1.0","event_id":"sha256:6861447906b15439c9f867395bef965750d3f0af265856214730725aafdcf190"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZD77ARVVCROAGQ565P4PIVTVMT/bundle.json","state_url":"https://pith.science/pith/ZD77ARVVCROAGQ565P4PIVTVMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZD77ARVVCROAGQ565P4PIVTVMT/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":"2026-05-26T02:03:46Z","links":{"resolver":"https://pith.science/pith/ZD77ARVVCROAGQ565P4PIVTVMT","bundle":"https://pith.science/pith/ZD77ARVVCROAGQ565P4PIVTVMT/bundle.json","state":"https://pith.science/pith/ZD77ARVVCROAGQ565P4PIVTVMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZD77ARVVCROAGQ565P4PIVTVMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:ZD77ARVVCROAGQ565P4PIVTVMT","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":"167fa5565337295e41f427702b3e6b0625ec3b18785cc79efe865a8fad63ff87","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-05-05T05:12:32Z","title_canon_sha256":"c18713620eb89feb5cc5cd4ec8590c8bf38823a316a5e95337866c8b19a1d80f"},"schema_version":"1.0","source":{"id":"quant-ph/9905011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9905011","created_at":"2026-05-18T04:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9905011v1","created_at":"2026-05-18T04:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9905011","created_at":"2026-05-18T04:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZD77ARVVCROA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ZD77ARVVCROAGQ56","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ZD77ARVV","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:6861447906b15439c9f867395bef965750d3f0af265856214730725aafdcf190","target":"graph","created_at":"2026-05-18T04:17:25Z","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":"A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have infinite number of energy eigenvalues, are the Coulomb and harmonic oscillator potentials.","authors_text":"N. Gurappa, Prasanta K. Panigrahi, T. Soloman Raju","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1999-05-05T05:12:32Z","title":"Quantum equivalent of the Bertrand's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9905011","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:d57ba46cc5248cebd5772e26b6a31bdcbe924f5f875687954e804891f319f45e","target":"record","created_at":"2026-05-18T04:17:25Z","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":"167fa5565337295e41f427702b3e6b0625ec3b18785cc79efe865a8fad63ff87","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-05-05T05:12:32Z","title_canon_sha256":"c18713620eb89feb5cc5cd4ec8590c8bf38823a316a5e95337866c8b19a1d80f"},"schema_version":"1.0","source":{"id":"quant-ph/9905011","kind":"arxiv","version":1}},"canonical_sha256":"c8fff046b5145c0343beebf8f4567564c46e7a52048a135a4a8ee83fc001d66e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8fff046b5145c0343beebf8f4567564c46e7a52048a135a4a8ee83fc001d66e","first_computed_at":"2026-05-18T04:17:25.651909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:25.651909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FY51c/wDoXGO65Lb80V6i5MjxX8EsgxGRfwtXvjbXLptViRFo9dfPpaO4SkwwSSfc2Grq2TayiqdrgVpMe4nAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:25.652477Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9905011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d57ba46cc5248cebd5772e26b6a31bdcbe924f5f875687954e804891f319f45e","sha256:6861447906b15439c9f867395bef965750d3f0af265856214730725aafdcf190"],"state_sha256":"10a33af4dec3d0ed6e8947ade3f6e4a2fdb8985f988a62acff417e9017d93848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4gJyP7bI44+JEqo60ykKI82tdJZYq8UCebOD8ctBVzejVqHnZ6cwWcj3As6lcKRcdGc3vmGSEw/jGe5+3BuHAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:03:46.244551Z","bundle_sha256":"d6611b9f868c795f3ce321ef12951f6f79fa8b44d84c7fcd6f1324cee051f418"}}