{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y2W52X4ZES5WSHXORAQHLAWCGL","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":"934bc9430ee9129b15ce8c01a9240e364d3212d9b127ff817eabbc2c727de93c","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-02T16:41:54Z","title_canon_sha256":"b9378dee8acc277291d500ec53e075d6e4ac2b56f051ed14b220cbca32e1079d"},"schema_version":"1.0","source":{"id":"1103.0483","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0483","created_at":"2026-05-18T02:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0483v3","created_at":"2026-05-18T02:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0483","created_at":"2026-05-18T02:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"Y2W52X4ZES5W","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y2W52X4ZES5WSHXO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y2W52X4Z","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:04da9b274be6d7f51260f1cd7cdd3a92243abc22c76dc4fea1d876b10bb8a065","target":"graph","created_at":"2026-05-18T02:03:00Z","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":"This paper studies the asymptotic behavior of the syzygies of a smooth projective variety X as the positivity of the embedding line bundle grows. We prove that as least as far as grading is concerned, the minimal resolution of the ideal of X has a surprisingly uniform asymptotic shape: roughly speaking, generators eventually appear in almost all degrees permitted by Castelnuovo-Mumford regularity. This suggests in particular that a widely-accepted intuition derived from the case of curves -- namely that syzygies become simpler as the degree of the embedding increases -- may have been misleadin","authors_text":"Lawrence Ein, Robert Lazarsfeld","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-02T16:41:54Z","title":"Asymptotic syzygies of algebraic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0483","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":"sha256:4617b2886019f72c12c9ec3259b7d23151d7b27b48baecfe0ffec4431f9fe95a","target":"record","created_at":"2026-05-18T02:03:00Z","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":"934bc9430ee9129b15ce8c01a9240e364d3212d9b127ff817eabbc2c727de93c","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-02T16:41:54Z","title_canon_sha256":"b9378dee8acc277291d500ec53e075d6e4ac2b56f051ed14b220cbca32e1079d"},"schema_version":"1.0","source":{"id":"1103.0483","kind":"arxiv","version":3}},"canonical_sha256":"c6addd5f9924bb691eee88207582c232e1d83c696c7057e63856108f97fc9fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6addd5f9924bb691eee88207582c232e1d83c696c7057e63856108f97fc9fcc","first_computed_at":"2026-05-18T02:03:00.934137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:00.934137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yBLx8jAL0m6eUmd5UvyHs9v4JGUgHPWy4d95ditLP/SCSKlxU/HvhjXnrfozAOyt01EHk8hS9odGaGcj7UmvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:00.935143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0483","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4617b2886019f72c12c9ec3259b7d23151d7b27b48baecfe0ffec4431f9fe95a","sha256:04da9b274be6d7f51260f1cd7cdd3a92243abc22c76dc4fea1d876b10bb8a065"],"state_sha256":"771c239174eb77f9dea06fbf8ccc491d70830c8285bf5da7ec64259d5dec2a3e"}