{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SXO2XMBTPPADNDK73GFVOLUW3I","short_pith_number":"pith:SXO2XMBT","schema_version":"1.0","canonical_sha256":"95ddabb0337bc0368d5fd98b572e96da1664fb1e42ea2ff1d7968da53a9eab35","source":{"kind":"arxiv","id":"1908.05123","version":1},"attestation_state":"computed","paper":{"title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jes\\'us Guillera","submitted_at":"2019-08-14T13:44:01Z","abstract_excerpt":"We prove a kind of bilateral semi-terminating series related to Ramanujan-like series for negative powers of $\\pi$, and conjecture a type of supercongruences associated to them. We support this conjecture by checking all the cases for many primes. In addition we are able to prove a few of them from some terminating hypergeometric identities. Finally, we make an intriguing observation."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.05123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-14T13:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"88b3bbfe92a68aa6d2d99deb688e2bae37b404ef294dc183663415ddde6a3c5c","abstract_canon_sha256":"02c04fc15ca4ff012a1bb6c91aea65d1bbd5d60e05702632a44a6658cca0efbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:56:36.499956Z","signature_b64":"lRml3HGpo6gdKBf1KLFXnF+d1iS31MdhUapb4JlgRPKiw4/AzEztMYFx4fjMiX7/Ti/F7jCRnffJWzg/7fkABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95ddabb0337bc0368d5fd98b572e96da1664fb1e42ea2ff1d7968da53a9eab35","last_reissued_at":"2026-07-04T23:56:36.499551Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:56:36.499551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jes\\'us Guillera","submitted_at":"2019-08-14T13:44:01Z","abstract_excerpt":"We prove a kind of bilateral semi-terminating series related to Ramanujan-like series for negative powers of $\\pi$, and conjecture a type of supercongruences associated to them. We support this conjecture by checking all the cases for many primes. In addition we are able to prove a few of them from some terminating hypergeometric identities. Finally, we make an intriguing observation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05123","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/1908.05123/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.05123","created_at":"2026-07-04T23:56:36.499614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05123v1","created_at":"2026-07-04T23:56:36.499614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05123","created_at":"2026-07-04T23:56:36.499614+00:00"},{"alias_kind":"pith_short_12","alias_value":"SXO2XMBTPPAD","created_at":"2026-07-04T23:56:36.499614+00:00"},{"alias_kind":"pith_short_16","alias_value":"SXO2XMBTPPADNDK7","created_at":"2026-07-04T23:56:36.499614+00:00"},{"alias_kind":"pith_short_8","alias_value":"SXO2XMBT","created_at":"2026-07-04T23:56:36.499614+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I","json":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I.json","graph_json":"https://pith.science/api/pith-number/SXO2XMBTPPADNDK73GFVOLUW3I/graph.json","events_json":"https://pith.science/api/pith-number/SXO2XMBTPPADNDK73GFVOLUW3I/events.json","paper":"https://pith.science/paper/SXO2XMBT"},"agent_actions":{"view_html":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I","download_json":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I.json","view_paper":"https://pith.science/paper/SXO2XMBT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05123&json=true","fetch_graph":"https://pith.science/api/pith-number/SXO2XMBTPPADNDK73GFVOLUW3I/graph.json","fetch_events":"https://pith.science/api/pith-number/SXO2XMBTPPADNDK73GFVOLUW3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I/action/storage_attestation","attest_author":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I/action/author_attestation","sign_citation":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I/action/citation_signature","submit_replication":"https://pith.science/pith/SXO2XMBTPPADNDK73GFVOLUW3I/action/replication_record"}},"created_at":"2026-07-04T23:56:36.499614+00:00","updated_at":"2026-07-04T23:56:36.499614+00:00"}