{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZYXRJOTDGIXR6XFU7U5CGXEJTE","short_pith_number":"pith:ZYXRJOTD","schema_version":"1.0","canonical_sha256":"ce2f14ba63322f1f5cb4fd3a235c89992cba9934657c3373f912ce1001aa0d43","source":{"kind":"arxiv","id":"1407.5552","version":2},"attestation_state":"computed","paper":{"title":"Inequalities involving the generating function for the number of partitions into odd parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Cristina Ballantine, Mircea Merca","submitted_at":"2014-07-21T16:27:22Z","abstract_excerpt":"Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of partitions into odd parts and the generating function for the number of odd divisors."},"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":"1407.5552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-21T16:27:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a170119fcbac6070f7529c5dcc5cc869ecd139512096b3a2ff64a447ad6a5cb3","abstract_canon_sha256":"87d11cd714471a2d55212c273f284f73fd86ae0bd05e28905d7525f75788b033"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:48.300494Z","signature_b64":"wLc+yiHk1w05nGv0Zvz6Oe9D1hhdbgD7JonEQz3+ndENaR7PpqxaDbeLM//byov2KAKWKM65GI9Lfns3NZvbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2f14ba63322f1f5cb4fd3a235c89992cba9934657c3373f912ce1001aa0d43","last_reissued_at":"2026-05-18T02:45:48.299932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:48.299932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inequalities involving the generating function for the number of partitions into odd parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Cristina Ballantine, Mircea Merca","submitted_at":"2014-07-21T16:27:22Z","abstract_excerpt":"Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of partitions into odd parts and the generating function for the number of odd divisors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5552","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.5552","created_at":"2026-05-18T02:45:48.300012+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5552v2","created_at":"2026-05-18T02:45:48.300012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5552","created_at":"2026-05-18T02:45:48.300012+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYXRJOTDGIXR","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYXRJOTDGIXR6XFU","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYXRJOTD","created_at":"2026-05-18T12:28:59.999130+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/ZYXRJOTDGIXR6XFU7U5CGXEJTE","json":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE.json","graph_json":"https://pith.science/api/pith-number/ZYXRJOTDGIXR6XFU7U5CGXEJTE/graph.json","events_json":"https://pith.science/api/pith-number/ZYXRJOTDGIXR6XFU7U5CGXEJTE/events.json","paper":"https://pith.science/paper/ZYXRJOTD"},"agent_actions":{"view_html":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE","download_json":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE.json","view_paper":"https://pith.science/paper/ZYXRJOTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5552&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYXRJOTDGIXR6XFU7U5CGXEJTE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYXRJOTDGIXR6XFU7U5CGXEJTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE/action/storage_attestation","attest_author":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE/action/author_attestation","sign_citation":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE/action/citation_signature","submit_replication":"https://pith.science/pith/ZYXRJOTDGIXR6XFU7U5CGXEJTE/action/replication_record"}},"created_at":"2026-05-18T02:45:48.300012+00:00","updated_at":"2026-05-18T02:45:48.300012+00:00"}