{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6OS7WOFEU5CQENHRZLQE5GHIKX","short_pith_number":"pith:6OS7WOFE","canonical_record":{"source":{"id":"1811.12663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-11-30T08:12:42Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"29071ac394327233b36987e4c049540a54259cb9c077c9ee4417bce2197d2b47","abstract_canon_sha256":"5d0022e53e0eaa1c510497da69a6fd30ff4f1e47605d0c7762f7ef1ed262df7d"},"schema_version":"1.0"},"canonical_sha256":"f3a5fb38a4a7450234f1cae04e98e855d3829df25afe964fcaf05cbc4808e21a","source":{"kind":"arxiv","id":"1811.12663","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12663","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12663v1","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12663","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"6OS7WOFEU5CQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6OS7WOFEU5CQENHR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6OS7WOFE","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6OS7WOFEU5CQENHRZLQE5GHIKX","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-11-30T08:12:42Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"29071ac394327233b36987e4c049540a54259cb9c077c9ee4417bce2197d2b47","abstract_canon_sha256":"5d0022e53e0eaa1c510497da69a6fd30ff4f1e47605d0c7762f7ef1ed262df7d"},"schema_version":"1.0"},"canonical_sha256":"f3a5fb38a4a7450234f1cae04e98e855d3829df25afe964fcaf05cbc4808e21a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:28.900150Z","signature_b64":"rECBz6EzCwdbN+N2Stzwk3u6u74+wnm8lXi2icdWAoFePe71SkHQNTH72DxjG9mbgDSctoD725IDrpgcoeRvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3a5fb38a4a7450234f1cae04e98e855d3829df25afe964fcaf05cbc4808e21a","last_reissued_at":"2026-05-17T23:59:28.899417Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:28.899417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12663","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTJ697OXip78l1xYh2R+um3+zKrEhqjwDbC3QcoNgv5BqBAGlvabC6+zMPBNzimzGlHMaQJ5XMmjsr3e31T6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:20:02.005780Z"},"content_sha256":"5ab492962594671667481d559cd62cf95094d1bf7b232ad8e762fccb55bd4dc4","schema_version":"1.0","event_id":"sha256:5ab492962594671667481d559cd62cf95094d1bf7b232ad8e762fccb55bd4dc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6OS7WOFEU5CQENHRZLQE5GHIKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient reduction strategy for signature-based algorithms to compute Groebner basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Kosuke Sakata","submitted_at":"2018-11-30T08:12:42Z","abstract_excerpt":"This paper introduces a strategy for signature-based algorithms to compute Groebner basis. The signature-based algorithms generate S-pairs instead of S-polynomials, and use s-reduction instead of the usual reduction used in the Buchberger algorithm. There are two strategies for s-reduction: one is the only-top reduction strategy which is the way that only leading monomials are s-reduced. The other is the full reduction strategy which is the way that all monomials are s-reduced. A new strategy, which we call selective-full strategy, for s-reduction of S-pairs is introduced in this paper. In the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12663","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8kUBqyx6AlOVcyzMkhTImOpzhvt7HyMi9avrGW5PnY7z/ICUXHB11kNa7/ITdFC2kinxzUCo6B7ihOwpxtuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:20:02.006116Z"},"content_sha256":"ab3aab788063e7e8653bb86dac7acd5e962f49116e0ddb1c2e5508bbfb660a78","schema_version":"1.0","event_id":"sha256:ab3aab788063e7e8653bb86dac7acd5e962f49116e0ddb1c2e5508bbfb660a78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OS7WOFEU5CQENHRZLQE5GHIKX/bundle.json","state_url":"https://pith.science/pith/6OS7WOFEU5CQENHRZLQE5GHIKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OS7WOFEU5CQENHRZLQE5GHIKX/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":"2026-06-10T21:20:02Z","links":{"resolver":"https://pith.science/pith/6OS7WOFEU5CQENHRZLQE5GHIKX","bundle":"https://pith.science/pith/6OS7WOFEU5CQENHRZLQE5GHIKX/bundle.json","state":"https://pith.science/pith/6OS7WOFEU5CQENHRZLQE5GHIKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OS7WOFEU5CQENHRZLQE5GHIKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6OS7WOFEU5CQENHRZLQE5GHIKX","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":"5d0022e53e0eaa1c510497da69a6fd30ff4f1e47605d0c7762f7ef1ed262df7d","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-11-30T08:12:42Z","title_canon_sha256":"29071ac394327233b36987e4c049540a54259cb9c077c9ee4417bce2197d2b47"},"schema_version":"1.0","source":{"id":"1811.12663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12663","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12663v1","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12663","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"6OS7WOFEU5CQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6OS7WOFEU5CQENHR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6OS7WOFE","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:ab3aab788063e7e8653bb86dac7acd5e962f49116e0ddb1c2e5508bbfb660a78","target":"graph","created_at":"2026-05-17T23:59:28Z","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":"This paper introduces a strategy for signature-based algorithms to compute Groebner basis. The signature-based algorithms generate S-pairs instead of S-polynomials, and use s-reduction instead of the usual reduction used in the Buchberger algorithm. There are two strategies for s-reduction: one is the only-top reduction strategy which is the way that only leading monomials are s-reduced. The other is the full reduction strategy which is the way that all monomials are s-reduced. A new strategy, which we call selective-full strategy, for s-reduction of S-pairs is introduced in this paper. In the","authors_text":"Kosuke Sakata","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-11-30T08:12:42Z","title":"An efficient reduction strategy for signature-based algorithms to compute Groebner basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12663","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":"sha256:5ab492962594671667481d559cd62cf95094d1bf7b232ad8e762fccb55bd4dc4","target":"record","created_at":"2026-05-17T23:59:28Z","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":"5d0022e53e0eaa1c510497da69a6fd30ff4f1e47605d0c7762f7ef1ed262df7d","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-11-30T08:12:42Z","title_canon_sha256":"29071ac394327233b36987e4c049540a54259cb9c077c9ee4417bce2197d2b47"},"schema_version":"1.0","source":{"id":"1811.12663","kind":"arxiv","version":1}},"canonical_sha256":"f3a5fb38a4a7450234f1cae04e98e855d3829df25afe964fcaf05cbc4808e21a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3a5fb38a4a7450234f1cae04e98e855d3829df25afe964fcaf05cbc4808e21a","first_computed_at":"2026-05-17T23:59:28.899417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:28.899417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rECBz6EzCwdbN+N2Stzwk3u6u74+wnm8lXi2icdWAoFePe71SkHQNTH72DxjG9mbgDSctoD725IDrpgcoeRvCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:28.900150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab492962594671667481d559cd62cf95094d1bf7b232ad8e762fccb55bd4dc4","sha256:ab3aab788063e7e8653bb86dac7acd5e962f49116e0ddb1c2e5508bbfb660a78"],"state_sha256":"76192c45b2082f1fad137d5a881be078982d274f4f31e61917250ae7bc82365a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bRvYNfaZ5jWIAx1lJvEWLSFqhmDM8N89AjsaDW0FKYklFbigA9rOHlx1lEyUhnIWJeC01dRM/SepfzWYRJPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:20:02.008107Z","bundle_sha256":"3d0bf26e9225ca99f6aa84f79a1ed3f218e9661aff87be05c1bfacedd36f459d"}}