{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QKQFDC2ILUND3MU64EDCMFDI3H","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":"d336f3c6486e0974af29eeb15686a902e247f12d64944a3d93a8fdfb3daae33c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-10T11:49:21Z","title_canon_sha256":"897d1a9e1a74ec138d5990b7b1cd3388907884559e1e8c5254fbbe20091c3bf2"},"schema_version":"1.0","source":{"id":"1101.1780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1780","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1780v1","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1780","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"QKQFDC2ILUND","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QKQFDC2ILUND3MU6","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QKQFDC2I","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:980632cd4fd4b452d6e389551d0aedda7cd46a674cc6754e6eb9528ffc957722","target":"graph","created_at":"2026-05-18T02:22:59Z","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 introduce the concept of f-ideals and discuss its algebraic properties. In particular, we give the characterization of all the f-ideals of degree 2.","authors_text":"G. Q. Abbasi, Imran Anwar, Sarfraz Ahmad, Waqas A. Baig","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-10T11:49:21Z","title":"F-ideals of degree 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1780","kind":"arxiv","version":1},"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:c38387eef197204131674b250292e0bf7abb00909647cfc3abf7f8252832deb8","target":"record","created_at":"2026-05-18T02:22:59Z","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":"d336f3c6486e0974af29eeb15686a902e247f12d64944a3d93a8fdfb3daae33c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-10T11:49:21Z","title_canon_sha256":"897d1a9e1a74ec138d5990b7b1cd3388907884559e1e8c5254fbbe20091c3bf2"},"schema_version":"1.0","source":{"id":"1101.1780","kind":"arxiv","version":1}},"canonical_sha256":"82a0518b485d1a3db29ee106261468d9da8e47a029ed6159ac25fbc709353d9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82a0518b485d1a3db29ee106261468d9da8e47a029ed6159ac25fbc709353d9e","first_computed_at":"2026-05-18T02:22:59.436228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:59.436228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hG4Eqpv6ktCOLCTuCHzySc8iRIuT84UGqJblg6SVTmzst26CGFArYQQ26n9XsegZkNdLPne5d/69TikrQdUIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:59.436910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c38387eef197204131674b250292e0bf7abb00909647cfc3abf7f8252832deb8","sha256:980632cd4fd4b452d6e389551d0aedda7cd46a674cc6754e6eb9528ffc957722"],"state_sha256":"36e5d1c44a75e491209f835a07b1f0847bbd4eb0516876f130ca7d70c4763470"}