{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FVVA36JGLOSQXKIUVLBLLN6MXR","short_pith_number":"pith:FVVA36JG","canonical_record":{"source":{"id":"1012.3664","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-12-16T16:35:48Z","cross_cats_sorted":[],"title_canon_sha256":"e3306f2e853bfad99798ffde14455a7333dd3d75f906098ca3799455ee108252","abstract_canon_sha256":"1aa8cb69b6e9363276736cd9d8b42bcadcc2d3f0d8b29f90e40d9b5cd5b10964"},"schema_version":"1.0"},"canonical_sha256":"2d6a0df9265ba50ba914aac2b5b7ccbc6fc251ff46e1c4eb870571ad36a891ff","source":{"kind":"arxiv","id":"1012.3664","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3664","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3664v6","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3664","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVVA36JGLOSQ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FVVA36JGLOSQXKIU","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FVVA36JG","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FVVA36JGLOSQXKIUVLBLLN6MXR","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3664","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-12-16T16:35:48Z","cross_cats_sorted":[],"title_canon_sha256":"e3306f2e853bfad99798ffde14455a7333dd3d75f906098ca3799455ee108252","abstract_canon_sha256":"1aa8cb69b6e9363276736cd9d8b42bcadcc2d3f0d8b29f90e40d9b5cd5b10964"},"schema_version":"1.0"},"canonical_sha256":"2d6a0df9265ba50ba914aac2b5b7ccbc6fc251ff46e1c4eb870571ad36a891ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:00.725578Z","signature_b64":"QuJ/x5sofU/eF3wei5+OKYl7HCcIqOt/oGvKu+vqPZuE0YpOnVGeKc/dveiu0bCCAwhqi3/n6iLnLflEC/LiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d6a0df9265ba50ba914aac2b5b7ccbc6fc251ff46e1c4eb870571ad36a891ff","last_reissued_at":"2026-05-18T01:19:00.725155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:00.725155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3664","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"67oA8eBGT2Hbvx9GwYyVeeTq9+v8uhrYkfGQ04Yo8yEhGHcJ1k3yidOc3WM8tOJzTvv++cvTyqZIHSzKSxhFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:31:01.927549Z"},"content_sha256":"f627cf6f5296d6a14030d1b8fc74f179a7e98b6bad0f59ffc79670429034d7c1","schema_version":"1.0","event_id":"sha256:f627cf6f5296d6a14030d1b8fc74f179a7e98b6bad0f59ffc79670429034d7c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FVVA36JGLOSQXKIUVLBLLN6MXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The F5 Criterion revised","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alberto Arri, John Perry","submitted_at":"2010-12-16T16:35:48Z","abstract_excerpt":"The purpose of this work is to generalize part of the theory behind Faugere's \"F5\" algorithm. This is one of the fastest known algorithms to compute a Groebner basis of a polynomial ideal I generated by polynomials f_{1},...,f_{m}. A major reason for this is what Faugere called the algorithm's \"new\" criterion, and we call \"the F5 criterion\"; it provides a sufficient condition for a set of polynomials G to be a Groebner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination.\n  This paper introduces some new concepts that place the cr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3664","kind":"arxiv","version":6},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qiuOCMUtbps36BD7mNtCdld0LUeyKJcuardarfGJ84aIIbosUCX5cxWgURFLw+IsNxIsBsAUsIuobv1Uv1xHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:31:01.927902Z"},"content_sha256":"6065a16ec94e6f9d7d5d22766c4961c19e71d5f76d2bc5933a49c0ae56617bae","schema_version":"1.0","event_id":"sha256:6065a16ec94e6f9d7d5d22766c4961c19e71d5f76d2bc5933a49c0ae56617bae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVVA36JGLOSQXKIUVLBLLN6MXR/bundle.json","state_url":"https://pith.science/pith/FVVA36JGLOSQXKIUVLBLLN6MXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVVA36JGLOSQXKIUVLBLLN6MXR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T03:31:01Z","links":{"resolver":"https://pith.science/pith/FVVA36JGLOSQXKIUVLBLLN6MXR","bundle":"https://pith.science/pith/FVVA36JGLOSQXKIUVLBLLN6MXR/bundle.json","state":"https://pith.science/pith/FVVA36JGLOSQXKIUVLBLLN6MXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVVA36JGLOSQXKIUVLBLLN6MXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FVVA36JGLOSQXKIUVLBLLN6MXR","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":"1aa8cb69b6e9363276736cd9d8b42bcadcc2d3f0d8b29f90e40d9b5cd5b10964","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-12-16T16:35:48Z","title_canon_sha256":"e3306f2e853bfad99798ffde14455a7333dd3d75f906098ca3799455ee108252"},"schema_version":"1.0","source":{"id":"1012.3664","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3664","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3664v6","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3664","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"FVVA36JGLOSQ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FVVA36JGLOSQXKIU","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FVVA36JG","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:6065a16ec94e6f9d7d5d22766c4961c19e71d5f76d2bc5933a49c0ae56617bae","target":"graph","created_at":"2026-05-18T01:19:00Z","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":"The purpose of this work is to generalize part of the theory behind Faugere's \"F5\" algorithm. This is one of the fastest known algorithms to compute a Groebner basis of a polynomial ideal I generated by polynomials f_{1},...,f_{m}. A major reason for this is what Faugere called the algorithm's \"new\" criterion, and we call \"the F5 criterion\"; it provides a sufficient condition for a set of polynomials G to be a Groebner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination.\n  This paper introduces some new concepts that place the cr","authors_text":"Alberto Arri, John Perry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-12-16T16:35:48Z","title":"The F5 Criterion revised"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3664","kind":"arxiv","version":6},"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:f627cf6f5296d6a14030d1b8fc74f179a7e98b6bad0f59ffc79670429034d7c1","target":"record","created_at":"2026-05-18T01:19:00Z","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":"1aa8cb69b6e9363276736cd9d8b42bcadcc2d3f0d8b29f90e40d9b5cd5b10964","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-12-16T16:35:48Z","title_canon_sha256":"e3306f2e853bfad99798ffde14455a7333dd3d75f906098ca3799455ee108252"},"schema_version":"1.0","source":{"id":"1012.3664","kind":"arxiv","version":6}},"canonical_sha256":"2d6a0df9265ba50ba914aac2b5b7ccbc6fc251ff46e1c4eb870571ad36a891ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d6a0df9265ba50ba914aac2b5b7ccbc6fc251ff46e1c4eb870571ad36a891ff","first_computed_at":"2026-05-18T01:19:00.725155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:00.725155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuJ/x5sofU/eF3wei5+OKYl7HCcIqOt/oGvKu+vqPZuE0YpOnVGeKc/dveiu0bCCAwhqi3/n6iLnLflEC/LiDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:00.725578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3664","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f627cf6f5296d6a14030d1b8fc74f179a7e98b6bad0f59ffc79670429034d7c1","sha256:6065a16ec94e6f9d7d5d22766c4961c19e71d5f76d2bc5933a49c0ae56617bae"],"state_sha256":"f643777ba63177d8d40495289c734fcc1009d8ba175ac91a566b6aa5e982ebfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I3h9fCkt9Cq8XdWWc27MOT4TwRvPlJEbxTirnqd0hqbV+QzxlSorJfT9o107Xuf1MQLmJuDRQXVV63l8J3hDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T03:31:01.930175Z","bundle_sha256":"5672256bcbc69f322821ee87e662eb5df57d1c27e6bc2fde9cc62f08d1ba318e"}}