{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H2TUCTN3ISEIQR35NUA5WO7FNT","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":"a655b0180845c126163c51c2e49b8cdd08678476f47ea39fe8bf7569666bd718","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-11-14T11:47:05Z","title_canon_sha256":"f0a47cd821f6179bf457b9bd237bec3f96e4e158f26fbd8180b7eb46f26258b4"},"schema_version":"1.0","source":{"id":"1811.05736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05736","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05736v1","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05736","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"H2TUCTN3ISEI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H2TUCTN3ISEIQR35","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H2TUCTN3","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:b49a3d14d7d7d26388ae0582c420c50cdfa2579f092a78c697766e18212c2a46","target":"graph","created_at":"2026-05-18T00:00:42Z","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 state and explain techniques useful for the computation of strong Gr\\\"obner and standard bases over Euclidean domains: First we investigate several strategies for creating the pair set using an idea by Lichtblau. Then we explain methods for avoiding coefficient growth using syzygies. We give an in-depth discussion on normal form computation resp. a generalized reduction process with many optimizations to further avoid large coefficients. These are combined with methods to reach GCD-polynomials at an earlier stage of the computation. Based on various examples we show that our n","authors_text":"Adrian Popescu, Christian Eder, Gerhard Pfister","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-11-14T11:47:05Z","title":"Standard Bases over Euclidean Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05736","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":"sha256:1b90d7de71c69f6106c11e6c0a1004c616d6c2d03836f984ff937e1901b61009","target":"record","created_at":"2026-05-18T00:00:42Z","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":"a655b0180845c126163c51c2e49b8cdd08678476f47ea39fe8bf7569666bd718","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-11-14T11:47:05Z","title_canon_sha256":"f0a47cd821f6179bf457b9bd237bec3f96e4e158f26fbd8180b7eb46f26258b4"},"schema_version":"1.0","source":{"id":"1811.05736","kind":"arxiv","version":1}},"canonical_sha256":"3ea7414dbb448888477d6d01db3be56cd00f0941fdd72f8edc3b1e6c7e6a5ec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ea7414dbb448888477d6d01db3be56cd00f0941fdd72f8edc3b1e6c7e6a5ec7","first_computed_at":"2026-05-18T00:00:42.199242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:42.199242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"67qwCQQkOQq2o+lff19+7v/pU3KNRX2a2iz4IzaaOIuh3LgAKCh5pbkSDZu/dj0e6VVeAfL4wEnwollJl2PFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:42.199627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b90d7de71c69f6106c11e6c0a1004c616d6c2d03836f984ff937e1901b61009","sha256:b49a3d14d7d7d26388ae0582c420c50cdfa2579f092a78c697766e18212c2a46"],"state_sha256":"81e45adaaa5278d0c434e57d1245b277ae2e5fc0253e1571d676cbb4a8f4d9d2"}