{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:WV66WEQVC3TQHVC7DVJL2SRYFZ","short_pith_number":"pith:WV66WEQV","canonical_record":{"source":{"id":"2110.14526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-10-25T20:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"fee9ad6172e0d6dfeb906d3868a884d80888297b84912b659eb286bc2a8c1849","abstract_canon_sha256":"0984e289643e5e7a029fa28e5290fb8630830287ce5ee2e45ab0827e656dd02e"},"schema_version":"1.0"},"canonical_sha256":"b57deb121516e703d45f1d52bd4a382e413496e253641d5259679926415710c1","source":{"kind":"arxiv","id":"2110.14526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14526","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14526v1","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14526","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"WV66WEQVC3TQ","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"pith_short_16","alias_value":"WV66WEQVC3TQHVC7","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"pith_short_8","alias_value":"WV66WEQV","created_at":"2026-07-05T09:48:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:WV66WEQVC3TQHVC7DVJL2SRYFZ","target":"record","payload":{"canonical_record":{"source":{"id":"2110.14526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-10-25T20:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"fee9ad6172e0d6dfeb906d3868a884d80888297b84912b659eb286bc2a8c1849","abstract_canon_sha256":"0984e289643e5e7a029fa28e5290fb8630830287ce5ee2e45ab0827e656dd02e"},"schema_version":"1.0"},"canonical_sha256":"b57deb121516e703d45f1d52bd4a382e413496e253641d5259679926415710c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:48:58.037794Z","signature_b64":"Ms9oTXT/z2UdeUemv6V5VdSTDkWlhnkShN8BBhd4lIhMHYh59k0NbKNduPtGpvndUW3UhRLcqTrQWbMsIrjCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b57deb121516e703d45f1d52bd4a382e413496e253641d5259679926415710c1","last_reissued_at":"2026-07-05T09:48:58.037228Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:48:58.037228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.14526","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":"2026-07-05T09:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jr/z5EPRjkoAp7OrNmU/x1YmQL59V23tBy1moYJNdjxnWMnKEPfOmU0LloOlFPd+c9u8gieDDW0c4GUYmRSZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:34:26.908033Z"},"content_sha256":"8239dd82c03294c2a9aef5a076c8d18aaf8314513e0843cf6148e5ec30b95502","schema_version":"1.0","event_id":"sha256:8239dd82c03294c2a9aef5a076c8d18aaf8314513e0843cf6148e5ec30b95502"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:WV66WEQVC3TQHVC7DVJL2SRYFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An ubiquitous three-term recurrence relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Francisco M. Fern\\'andez, Paolo Amore","submitted_at":"2021-10-25T20:00:31Z","abstract_excerpt":"We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation, yields exact analytical eigenvalues and eigenfunctions for particular values of a model parameter. From these solutions some researchers have derived a variety of predictions like allowed angular frequencies, allowed field intensities and the like. We also solve the eigenvalue equation numerically by means of the variational Rayleigh-Ritz method and compare"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14526","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14526/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0dbVEZoHXezYH7P6Lm1gnQTLwlekzomcZpVEIaP9OpGZWcxdIIFIyP9HPDxn8/LkvZfSsP8KONLVD3eSr4OBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:34:26.908632Z"},"content_sha256":"6351e9e87404fbdff96e55985020e7aaa5d559105232931055b21385461d4540","schema_version":"1.0","event_id":"sha256:6351e9e87404fbdff96e55985020e7aaa5d559105232931055b21385461d4540"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ/bundle.json","state_url":"https://pith.science/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ/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":"2026-08-08T09:34:26Z","links":{"resolver":"https://pith.science/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ","bundle":"https://pith.science/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ/bundle.json","state":"https://pith.science/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WV66WEQVC3TQHVC7DVJL2SRYFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:WV66WEQVC3TQHVC7DVJL2SRYFZ","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":"0984e289643e5e7a029fa28e5290fb8630830287ce5ee2e45ab0827e656dd02e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-10-25T20:00:31Z","title_canon_sha256":"fee9ad6172e0d6dfeb906d3868a884d80888297b84912b659eb286bc2a8c1849"},"schema_version":"1.0","source":{"id":"2110.14526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14526","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14526v1","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14526","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"WV66WEQVC3TQ","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"pith_short_16","alias_value":"WV66WEQVC3TQHVC7","created_at":"2026-07-05T09:48:58Z"},{"alias_kind":"pith_short_8","alias_value":"WV66WEQV","created_at":"2026-07-05T09:48:58Z"}],"graph_snapshots":[{"event_id":"sha256:6351e9e87404fbdff96e55985020e7aaa5d559105232931055b21385461d4540","target":"graph","created_at":"2026-07-05T09:48:58Z","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/2110.14526/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation, yields exact analytical eigenvalues and eigenfunctions for particular values of a model parameter. From these solutions some researchers have derived a variety of predictions like allowed angular frequencies, allowed field intensities and the like. We also solve the eigenvalue equation numerically by means of the variational Rayleigh-Ritz method and compare","authors_text":"Francisco M. Fern\\'andez, Paolo Amore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-10-25T20:00:31Z","title":"An ubiquitous three-term recurrence relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14526","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":"sha256:8239dd82c03294c2a9aef5a076c8d18aaf8314513e0843cf6148e5ec30b95502","target":"record","created_at":"2026-07-05T09:48:58Z","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":"0984e289643e5e7a029fa28e5290fb8630830287ce5ee2e45ab0827e656dd02e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-10-25T20:00:31Z","title_canon_sha256":"fee9ad6172e0d6dfeb906d3868a884d80888297b84912b659eb286bc2a8c1849"},"schema_version":"1.0","source":{"id":"2110.14526","kind":"arxiv","version":1}},"canonical_sha256":"b57deb121516e703d45f1d52bd4a382e413496e253641d5259679926415710c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b57deb121516e703d45f1d52bd4a382e413496e253641d5259679926415710c1","first_computed_at":"2026-07-05T09:48:58.037228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:48:58.037228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ms9oTXT/z2UdeUemv6V5VdSTDkWlhnkShN8BBhd4lIhMHYh59k0NbKNduPtGpvndUW3UhRLcqTrQWbMsIrjCCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:48:58.037794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.14526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8239dd82c03294c2a9aef5a076c8d18aaf8314513e0843cf6148e5ec30b95502","sha256:6351e9e87404fbdff96e55985020e7aaa5d559105232931055b21385461d4540"],"state_sha256":"0aee44b83b5e739f8b4aafb43f19f0a3dd25fb6b672208a17b98580deed878c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vk5FYMokdEabvuNB8T6VTsTmF1vkjNLiV0Tr6fNk5TkTo4w1TjzGKZxp4u0BBoocGZ/V0PPxjUNHmiQFFMjVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:34:26.913801Z","bundle_sha256":"9b169997fa66eb09b072e4b77a80105da58dd13dc999f1ce685b10854cc0e9f8"}}