{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:UPDHAK5GMQD56TNVLZEERDDHAU","short_pith_number":"pith:UPDHAK5G","schema_version":"1.0","canonical_sha256":"a3c6702ba66407df4db55e48488c6705175908ed00f5e093e427169ac915c176","source":{"kind":"arxiv","id":"1009.1430","version":1},"attestation_state":"computed","paper":{"title":"Finite atomic lattices and resolutions of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Sonja Mapes","submitted_at":"2010-09-08T00:56:29Z","abstract_excerpt":"In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated LCM lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial ideal whose LCM lattice is P, and we give a complete characterization of all such coordinatizations. We prove that all relations in the lattice L(n) of all finite atomic lattices with n ordered atoms can be realized as deformations of exponents of monomial ideals. We also give structural results for L(n). Moreover, we prove that the cellular structure of a min"},"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":"1009.1430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-08T00:56:29Z","cross_cats_sorted":[],"title_canon_sha256":"1f90eff85faaf46be1ff27f4133bd422a1eb45468c7bdbd8fbcc0123e68c612d","abstract_canon_sha256":"e043c998084c30b817a969a97e814760ee315532a86e3cb433c6586d4d9e3bef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:14.806717Z","signature_b64":"6N1Nw4T76kF2DnhM/j2lVGT/BIO0KH0ZvhGncCo6ZSihZsqnRbfUv+tBgHsfyizSLW2jSaIBe3+wCQS4YPuXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3c6702ba66407df4db55e48488c6705175908ed00f5e093e427169ac915c176","last_reissued_at":"2026-05-18T04:41:14.806086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:14.806086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite atomic lattices and resolutions of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Sonja Mapes","submitted_at":"2010-09-08T00:56:29Z","abstract_excerpt":"In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated LCM lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial ideal whose LCM lattice is P, and we give a complete characterization of all such coordinatizations. We prove that all relations in the lattice L(n) of all finite atomic lattices with n ordered atoms can be realized as deformations of exponents of monomial ideals. We also give structural results for L(n). Moreover, we prove that the cellular structure of a min"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1430","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":"1009.1430","created_at":"2026-05-18T04:41:14.806173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.1430v1","created_at":"2026-05-18T04:41:14.806173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1430","created_at":"2026-05-18T04:41:14.806173+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPDHAK5GMQD5","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPDHAK5GMQD56TNV","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPDHAK5G","created_at":"2026-05-18T12:26:15.391820+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/UPDHAK5GMQD56TNVLZEERDDHAU","json":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU.json","graph_json":"https://pith.science/api/pith-number/UPDHAK5GMQD56TNVLZEERDDHAU/graph.json","events_json":"https://pith.science/api/pith-number/UPDHAK5GMQD56TNVLZEERDDHAU/events.json","paper":"https://pith.science/paper/UPDHAK5G"},"agent_actions":{"view_html":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU","download_json":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU.json","view_paper":"https://pith.science/paper/UPDHAK5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.1430&json=true","fetch_graph":"https://pith.science/api/pith-number/UPDHAK5GMQD56TNVLZEERDDHAU/graph.json","fetch_events":"https://pith.science/api/pith-number/UPDHAK5GMQD56TNVLZEERDDHAU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU/action/storage_attestation","attest_author":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU/action/author_attestation","sign_citation":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU/action/citation_signature","submit_replication":"https://pith.science/pith/UPDHAK5GMQD56TNVLZEERDDHAU/action/replication_record"}},"created_at":"2026-05-18T04:41:14.806173+00:00","updated_at":"2026-05-18T04:41:14.806173+00:00"}