{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7HN6CX56IPY6SDMJCTE3OR32WW","short_pith_number":"pith:7HN6CX56","schema_version":"1.0","canonical_sha256":"f9dbe15fbe43f1e90d8914c9b7477ab5a0a218083ab84cce8e74bf596ddf9673","source":{"kind":"arxiv","id":"1509.04316","version":2},"attestation_state":"computed","paper":{"title":"Sums of seven octahedral numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zarathustra Brady","submitted_at":"2015-09-14T20:46:53Z","abstract_excerpt":"We show that for a large class of cubic polynomials $f$, every sufficiently large number can be written as a sum of seven positive values of $f$. As a special case, we show that every number greater than $e^{10^7}$ is a sum of seven positive octahedral numbers, where an octahedral number is a number of the form $\\frac{2x^3+x}{3}$, reducing an open problem due to Pollock to a finite computation."},"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":"1509.04316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-14T20:46:53Z","cross_cats_sorted":[],"title_canon_sha256":"c0fe4a0bfbddfde1106a2f03fcd2858c2e703bc5a905fc2fed2d6ee8dde9b06c","abstract_canon_sha256":"0bcd0a53684732cad968e9b7827bd0bf4df498da7583ad26898e91a3ec46133e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:23.253314Z","signature_b64":"xpDfbNBCiWZDTDA48wbyUvmaEqA1eqt21klEiyha/G01OaPdwAAmrj++1F1IoreYMQWN0GvhkcIM8vPzXG5/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9dbe15fbe43f1e90d8914c9b7477ab5a0a218083ab84cce8e74bf596ddf9673","last_reissued_at":"2026-05-18T00:14:23.252883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:23.252883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sums of seven octahedral numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zarathustra Brady","submitted_at":"2015-09-14T20:46:53Z","abstract_excerpt":"We show that for a large class of cubic polynomials $f$, every sufficiently large number can be written as a sum of seven positive values of $f$. As a special case, we show that every number greater than $e^{10^7}$ is a sum of seven positive octahedral numbers, where an octahedral number is a number of the form $\\frac{2x^3+x}{3}$, reducing an open problem due to Pollock to a finite computation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04316","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":"1509.04316","created_at":"2026-05-18T00:14:23.252945+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.04316v2","created_at":"2026-05-18T00:14:23.252945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04316","created_at":"2026-05-18T00:14:23.252945+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HN6CX56IPY6","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HN6CX56IPY6SDMJ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HN6CX56","created_at":"2026-05-18T12:29:10.953037+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/7HN6CX56IPY6SDMJCTE3OR32WW","json":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW.json","graph_json":"https://pith.science/api/pith-number/7HN6CX56IPY6SDMJCTE3OR32WW/graph.json","events_json":"https://pith.science/api/pith-number/7HN6CX56IPY6SDMJCTE3OR32WW/events.json","paper":"https://pith.science/paper/7HN6CX56"},"agent_actions":{"view_html":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW","download_json":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW.json","view_paper":"https://pith.science/paper/7HN6CX56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.04316&json=true","fetch_graph":"https://pith.science/api/pith-number/7HN6CX56IPY6SDMJCTE3OR32WW/graph.json","fetch_events":"https://pith.science/api/pith-number/7HN6CX56IPY6SDMJCTE3OR32WW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW/action/storage_attestation","attest_author":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW/action/author_attestation","sign_citation":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW/action/citation_signature","submit_replication":"https://pith.science/pith/7HN6CX56IPY6SDMJCTE3OR32WW/action/replication_record"}},"created_at":"2026-05-18T00:14:23.252945+00:00","updated_at":"2026-05-18T00:14:23.252945+00:00"}