{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VPHYSYNOEOTF63IPWVEIG6V3YT","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":"6dd4f2a3bb44f0641cec66ca877b5763fc601a524f93425ea13002b3b1b9c902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-09T17:46:11Z","title_canon_sha256":"37e81e6327bfc03101b674dbe136f19f5cb04da926a2a426edb715cf6e0dabf9"},"schema_version":"1.0","source":{"id":"1801.03054","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03054","created_at":"2026-05-17T23:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03054v4","created_at":"2026-05-17T23:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03054","created_at":"2026-05-17T23:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"VPHYSYNOEOTF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VPHYSYNOEOTF63IP","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VPHYSYNO","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:d1f619201c914c61cfee987230d2548493e2fc5b4a2f7c38301734a988b79401","target":"graph","created_at":"2026-05-17T23:56:38Z","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":"Bresinsky defined a class of monomial curves in $\\mathbb{A}^{4}$ with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for this class.","authors_text":"Indranath Sengupta, Joydip Saha, Ranjana Mehta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-09T17:46:11Z","title":"Betti numbers of Bresinsky's curves in $\\mathbb{A}^{4}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03054","kind":"arxiv","version":4},"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:d2d4e56738504446ee2375b34401159ac69abae8ffd8950f3434542c1abd8015","target":"record","created_at":"2026-05-17T23:56:38Z","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":"6dd4f2a3bb44f0641cec66ca877b5763fc601a524f93425ea13002b3b1b9c902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-09T17:46:11Z","title_canon_sha256":"37e81e6327bfc03101b674dbe136f19f5cb04da926a2a426edb715cf6e0dabf9"},"schema_version":"1.0","source":{"id":"1801.03054","kind":"arxiv","version":4}},"canonical_sha256":"abcf8961ae23a65f6d0fb548837abbc4e28a1f03f08972ee7d040aa43f4ca8c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abcf8961ae23a65f6d0fb548837abbc4e28a1f03f08972ee7d040aa43f4ca8c8","first_computed_at":"2026-05-17T23:56:38.839479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:38.839479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jbv+xfpx1uq4s/5q0609bRuEkhcEncWYcYHSN/1jnpLospKgWn2fQ83UVDtYk69c2jn4Se8h10B3TSlzowyYBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:38.840153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03054","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2d4e56738504446ee2375b34401159ac69abae8ffd8950f3434542c1abd8015","sha256:d1f619201c914c61cfee987230d2548493e2fc5b4a2f7c38301734a988b79401"],"state_sha256":"6e39606f7a55c0f5deedc5e66a44d8a1b4548f4f7f3be903e34000781794d16d"}