{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XGFSTXCABSA4YADWKW57VB7WNN","short_pith_number":"pith:XGFSTXCA","schema_version":"1.0","canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","source":{"kind":"arxiv","id":"1106.2355","version":1},"attestation_state":"computed","paper":{"title":"Stabilization of Betti Tables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Gwyneth Whieldon","submitted_at":"2011-06-12T22:57:07Z","abstract_excerpt":"Let $I\\subseteq R=\\kk[x_1,...,x_n]$ be a homogeneous equigenerated ideal of degree $r$. We show here that the shapes of the Betti tables of the ideals $I^d$ stabilize, in the sense that there exists some $D$ such that for all $d\\geq D$, $\\betti{i}{j+rd}(I^d)\\neq 0\\Leftrightarrow \\betti{i}{j+rD}(I^D)\\neq 0$. We also produce upper bounds for the stabilization index $\\Stab(I)$. This strengthens the result of Cutkosky, Herzog, and Trung that the Castelnuovo-Mumford regularity $\\reg(I^d)$ is eventually a linear function in $d$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.2355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-12T22:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"87abb0443cfe46ba8ec223a6c1a506e3c6c1797e19f7252271f57707824661f1","abstract_canon_sha256":"7249035023ff6b576e09b727178ce6bbc9712e1137395fe39469820e6bfe827a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:05.930219Z","signature_b64":"XxrW7aa05bIFVfmM8Fu4wkmOn8V+vc8kDw3zBTcMKnAcjgzRjW7DV7rGQmM+/JNSHfV7rtu2gXZcsChJgLMYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","last_reissued_at":"2026-05-18T04:20:05.929739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:05.929739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilization of Betti Tables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Gwyneth Whieldon","submitted_at":"2011-06-12T22:57:07Z","abstract_excerpt":"Let $I\\subseteq R=\\kk[x_1,...,x_n]$ be a homogeneous equigenerated ideal of degree $r$. We show here that the shapes of the Betti tables of the ideals $I^d$ stabilize, in the sense that there exists some $D$ such that for all $d\\geq D$, $\\betti{i}{j+rd}(I^d)\\neq 0\\Leftrightarrow \\betti{i}{j+rD}(I^D)\\neq 0$. We also produce upper bounds for the stabilization index $\\Stab(I)$. This strengthens the result of Cutkosky, Herzog, and Trung that the Castelnuovo-Mumford regularity $\\reg(I^d)$ is eventually a linear function in $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2355","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.2355","created_at":"2026-05-18T04:20:05.929814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.2355v1","created_at":"2026-05-18T04:20:05.929814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2355","created_at":"2026-05-18T04:20:05.929814+00:00"},{"alias_kind":"pith_short_12","alias_value":"XGFSTXCABSA4","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XGFSTXCABSA4YADW","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XGFSTXCA","created_at":"2026-05-18T12:26:44.992195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN","json":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN.json","graph_json":"https://pith.science/api/pith-number/XGFSTXCABSA4YADWKW57VB7WNN/graph.json","events_json":"https://pith.science/api/pith-number/XGFSTXCABSA4YADWKW57VB7WNN/events.json","paper":"https://pith.science/paper/XGFSTXCA"},"agent_actions":{"view_html":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN","download_json":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN.json","view_paper":"https://pith.science/paper/XGFSTXCA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.2355&json=true","fetch_graph":"https://pith.science/api/pith-number/XGFSTXCABSA4YADWKW57VB7WNN/graph.json","fetch_events":"https://pith.science/api/pith-number/XGFSTXCABSA4YADWKW57VB7WNN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/action/storage_attestation","attest_author":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/action/author_attestation","sign_citation":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/action/citation_signature","submit_replication":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/action/replication_record"}},"created_at":"2026-05-18T04:20:05.929814+00:00","updated_at":"2026-05-18T04:20:05.929814+00:00"}