{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VPKVK4TYKWZHZLIGLBBFJ5H7LE","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":"009c421f2a44ff35dfd348bff525e72801b8d71994d97ec1eae1f5f80b850dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-21T23:46:48Z","title_canon_sha256":"4ff84413c96950ce9b6c62367a928c33f0ff7e3675ef63d53cb7abb2f1f6d6eb"},"schema_version":"1.0","source":{"id":"1610.06976","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06976","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06976v3","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06976","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"VPKVK4TYKWZH","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VPKVK4TYKWZHZLIG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VPKVK4TY","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:9d8b490fd3fca517557af314d357cc96b654c67de546e3ac0b0c84a1af7883e5","target":"graph","created_at":"2026-05-18T00:23:56Z","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 asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi polynomial behavior of graded Betti numbers of powers of homogenous ideals to Z-graded algebra over Notherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.","authors_text":"Kamran Lamei, Siamak Yassemi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-21T23:46:48Z","title":"Graded Betti numbers of good filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06976","kind":"arxiv","version":3},"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:b0ac234b010902b061843ffee46e2170ea4d0883a497b4b0c11b11d53c61a8f9","target":"record","created_at":"2026-05-18T00:23:56Z","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":"009c421f2a44ff35dfd348bff525e72801b8d71994d97ec1eae1f5f80b850dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-21T23:46:48Z","title_canon_sha256":"4ff84413c96950ce9b6c62367a928c33f0ff7e3675ef63d53cb7abb2f1f6d6eb"},"schema_version":"1.0","source":{"id":"1610.06976","kind":"arxiv","version":3}},"canonical_sha256":"abd555727855b27cad06584254f4ff59264bd515ebc27e668ba1a2c3c10f83cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abd555727855b27cad06584254f4ff59264bd515ebc27e668ba1a2c3c10f83cb","first_computed_at":"2026-05-18T00:23:56.978992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:56.978992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cJhHwcltUbO5r1FzeCw6brptDzP7UE7N4fcsaFMswifWMlo+N9GsrL0f3s7O/UVQ3XPOq35LoIu0YNu1eBZTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:56.979502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06976","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0ac234b010902b061843ffee46e2170ea4d0883a497b4b0c11b11d53c61a8f9","sha256:9d8b490fd3fca517557af314d357cc96b654c67de546e3ac0b0c84a1af7883e5"],"state_sha256":"3eb22b3a975b467735fa41f22f90e34c1c90b9d69eb7c9bde77f08be39ede678"}