{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5TKG4BW2CWU5PNOG6NPE47LGSI","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":"d553cfd82c552cba190f636f3fd205faaf20ae5a2f80f371d0f2b25723b600c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-12T15:15:56Z","title_canon_sha256":"864eac7fb701bae1bc1fcdd9cd939b02128ec7e76bb34cd38a3a4a47aa887050"},"schema_version":"1.0","source":{"id":"1604.03439","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03439","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03439v2","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03439","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"5TKG4BW2CWU5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5TKG4BW2CWU5PNOG","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5TKG4BW2","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:91d40983dd0ae1f4569b58785e91bf39d7a0976eea6dd93592e5ed441e5fed62","target":"graph","created_at":"2026-05-18T00:53:45Z","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"},"paper":{"abstract_excerpt":"In this paper we explore Kruyswijk's method and show how to obtain congruences for cubic partition. That apart we also examine inequalities for a(n) and provide upper bound for it in the fashion of the classic partition function p(n).","authors_text":"Koustav Banerjee, Manosij Ghosh Dastidar, Prabir Das Adhikary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-12T15:15:56Z","title":"Some results on the cubic partition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03439","kind":"arxiv","version":2},"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:f6d063b249075511550f66876ea16c667d0b3bc0c5de4df37df705b612291763","target":"record","created_at":"2026-05-18T00:53:45Z","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":"d553cfd82c552cba190f636f3fd205faaf20ae5a2f80f371d0f2b25723b600c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-12T15:15:56Z","title_canon_sha256":"864eac7fb701bae1bc1fcdd9cd939b02128ec7e76bb34cd38a3a4a47aa887050"},"schema_version":"1.0","source":{"id":"1604.03439","kind":"arxiv","version":2}},"canonical_sha256":"ecd46e06da15a9d7b5c6f35e4e7d669228c45e6742946d8e27b54809cd2f493e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecd46e06da15a9d7b5c6f35e4e7d669228c45e6742946d8e27b54809cd2f493e","first_computed_at":"2026-05-18T00:53:45.396493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:45.396493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fnjw6oVyB0tHaUQl0pgjlaNRshXh3GY0K4iz0vHiaJqk7rblJRZswHUxHQyK2iSPaX7Fof0E649Q6sKuCWkMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:45.397147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03439","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6d063b249075511550f66876ea16c667d0b3bc0c5de4df37df705b612291763","sha256:91d40983dd0ae1f4569b58785e91bf39d7a0976eea6dd93592e5ed441e5fed62"],"state_sha256":"b165967e92ee00ceab48e40f1435d72b24e3b965df9ade26a8f0b8ab1c1f56cd"}