{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3RYCF52F6DB7WZMSWZCIH4QLNE","short_pith_number":"pith:3RYCF52F","schema_version":"1.0","canonical_sha256":"dc7022f745f0c3fb6592b64483f20b6902199267ae289f51404997d023fe0f6b","source":{"kind":"arxiv","id":"1212.2201","version":2},"attestation_state":"computed","paper":{"title":"Betti tables of $p$-Borel-fixed ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Giulio Caviglia, Manoj Kummini","submitted_at":"2012-12-10T20:55:42Z","abstract_excerpt":"In this note we provide a counter-example to a conjecture of K. Pardue [Thesis, Brandeis University, 1994.], which asserts that if a monomial ideal is $p$-Borel-fixed, then its $\\naturals$-graded Betti table, after passing to any field does not depend on the field. More precisely, we show that, for any monomial ideal $I$ in a polynomial ring $S$ over the ring $\\ints$ of integers and for any prime number $p$, there is a $p$-Borel-fixed monomial $S$-ideal $J$ such that a region of the multigraded Betti table of $J(S \\otimes_\\ints \\ell)$ is in one-to-one correspondence with the multigraded Betti "},"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":"1212.2201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-10T20:55:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fde7cb06a7175174db80c3496dcaa274bd4ca535c934bc6fc949bdc80dceb837","abstract_canon_sha256":"2edda4e0165d2aa54bca48f0efef71f9a7b0b6bae3eea3251f65db26961e2a77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:34.464369Z","signature_b64":"TjC3YC2TXWop/FK8gPvCydZCMlTPo+w/T5tXHAX+hQ1MtauoszrPuNJiFdY6SII6v0JAgZHOFtZk7GT2AiT+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc7022f745f0c3fb6592b64483f20b6902199267ae289f51404997d023fe0f6b","last_reissued_at":"2026-05-18T03:15:34.463842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:34.463842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Betti tables of $p$-Borel-fixed ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Giulio Caviglia, Manoj Kummini","submitted_at":"2012-12-10T20:55:42Z","abstract_excerpt":"In this note we provide a counter-example to a conjecture of K. Pardue [Thesis, Brandeis University, 1994.], which asserts that if a monomial ideal is $p$-Borel-fixed, then its $\\naturals$-graded Betti table, after passing to any field does not depend on the field. More precisely, we show that, for any monomial ideal $I$ in a polynomial ring $S$ over the ring $\\ints$ of integers and for any prime number $p$, there is a $p$-Borel-fixed monomial $S$-ideal $J$ such that a region of the multigraded Betti table of $J(S \\otimes_\\ints \\ell)$ is in one-to-one correspondence with the multigraded Betti "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2201","kind":"arxiv","version":2},"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":"1212.2201","created_at":"2026-05-18T03:15:34.463934+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2201v2","created_at":"2026-05-18T03:15:34.463934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2201","created_at":"2026-05-18T03:15:34.463934+00:00"},{"alias_kind":"pith_short_12","alias_value":"3RYCF52F6DB7","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3RYCF52F6DB7WZMS","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3RYCF52F","created_at":"2026-05-18T12:26:53.410803+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/3RYCF52F6DB7WZMSWZCIH4QLNE","json":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE.json","graph_json":"https://pith.science/api/pith-number/3RYCF52F6DB7WZMSWZCIH4QLNE/graph.json","events_json":"https://pith.science/api/pith-number/3RYCF52F6DB7WZMSWZCIH4QLNE/events.json","paper":"https://pith.science/paper/3RYCF52F"},"agent_actions":{"view_html":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE","download_json":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE.json","view_paper":"https://pith.science/paper/3RYCF52F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2201&json=true","fetch_graph":"https://pith.science/api/pith-number/3RYCF52F6DB7WZMSWZCIH4QLNE/graph.json","fetch_events":"https://pith.science/api/pith-number/3RYCF52F6DB7WZMSWZCIH4QLNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE/action/storage_attestation","attest_author":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE/action/author_attestation","sign_citation":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE/action/citation_signature","submit_replication":"https://pith.science/pith/3RYCF52F6DB7WZMSWZCIH4QLNE/action/replication_record"}},"created_at":"2026-05-18T03:15:34.463934+00:00","updated_at":"2026-05-18T03:15:34.463934+00:00"}