{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HQAEAMEJMGLBHPMH7BGC2RCYJU","short_pith_number":"pith:HQAEAMEJ","schema_version":"1.0","canonical_sha256":"3c00403089619613bd87f84c2d44584d350489c7f6af1420416b117b0efc10a9","source":{"kind":"arxiv","id":"1901.04842","version":1},"attestation_state":"computed","paper":{"title":"An Identity Motivated by an Amazing Identity of Ramanujan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2019-01-04T23:57:52Z","abstract_excerpt":"Ramanujan stated an identity to the effect that if three sequences $\\{a_n\\}$, $\\{b_n\\}$ and $\\{c_n\\}$ are defined by $r_1(x)=:\\sum_{n=0}^{\\infty}a_nx^n$, $r_2(x)=:\\sum_{n=0}^{\\infty}b_nx^n$ and $r_3(x)=:\\sum_{n=0}^{\\infty}c_nx^n$ (here each $r_i(x)$ is a certain rational function in $x$), then \\[ a_n^3+b_n^3-c_n^3=(-1)^n, \\hspace{25pt} \\forall \\,n \\geq 0. \\] Motivated by this amazing identity, we state and prove a more general identity involving eleven sequences, the new identity being \"more general\" in the sense that equality holds not just for the power 3 (as in Ramanujan's identity), but fo"},"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":"1901.04842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-04T23:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"609c9b871bf96e623ef46fce55211e913d9290ffcd10167ed8d5b7010572ceb6","abstract_canon_sha256":"c054bc6d4dc1b664113fcbe9fdd6787c8ee607082ef692313d144449c40c4480"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:21.547276Z","signature_b64":"3zacSfSxurQAJucYvpQtfo/my/CiXpbkGavOX7TLGEydknx+FQMWfu3DWpMHMCHxQcOTNmsqNocWehX2gJoFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c00403089619613bd87f84c2d44584d350489c7f6af1420416b117b0efc10a9","last_reissued_at":"2026-05-17T23:56:21.546730Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:21.546730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Identity Motivated by an Amazing Identity of Ramanujan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2019-01-04T23:57:52Z","abstract_excerpt":"Ramanujan stated an identity to the effect that if three sequences $\\{a_n\\}$, $\\{b_n\\}$ and $\\{c_n\\}$ are defined by $r_1(x)=:\\sum_{n=0}^{\\infty}a_nx^n$, $r_2(x)=:\\sum_{n=0}^{\\infty}b_nx^n$ and $r_3(x)=:\\sum_{n=0}^{\\infty}c_nx^n$ (here each $r_i(x)$ is a certain rational function in $x$), then \\[ a_n^3+b_n^3-c_n^3=(-1)^n, \\hspace{25pt} \\forall \\,n \\geq 0. \\] Motivated by this amazing identity, we state and prove a more general identity involving eleven sequences, the new identity being \"more general\" in the sense that equality holds not just for the power 3 (as in Ramanujan's identity), but fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04842","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.04842","created_at":"2026-05-17T23:56:21.546805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.04842v1","created_at":"2026-05-17T23:56:21.546805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04842","created_at":"2026-05-17T23:56:21.546805+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQAEAMEJMGLB","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQAEAMEJMGLBHPMH","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQAEAMEJ","created_at":"2026-05-18T12:33:18.533446+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/HQAEAMEJMGLBHPMH7BGC2RCYJU","json":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU.json","graph_json":"https://pith.science/api/pith-number/HQAEAMEJMGLBHPMH7BGC2RCYJU/graph.json","events_json":"https://pith.science/api/pith-number/HQAEAMEJMGLBHPMH7BGC2RCYJU/events.json","paper":"https://pith.science/paper/HQAEAMEJ"},"agent_actions":{"view_html":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU","download_json":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU.json","view_paper":"https://pith.science/paper/HQAEAMEJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.04842&json=true","fetch_graph":"https://pith.science/api/pith-number/HQAEAMEJMGLBHPMH7BGC2RCYJU/graph.json","fetch_events":"https://pith.science/api/pith-number/HQAEAMEJMGLBHPMH7BGC2RCYJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU/action/storage_attestation","attest_author":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU/action/author_attestation","sign_citation":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU/action/citation_signature","submit_replication":"https://pith.science/pith/HQAEAMEJMGLBHPMH7BGC2RCYJU/action/replication_record"}},"created_at":"2026-05-17T23:56:21.546805+00:00","updated_at":"2026-05-17T23:56:21.546805+00:00"}