{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FL4IZ4RMR4RLT2R4XPR7NZL3P3","short_pith_number":"pith:FL4IZ4RM","schema_version":"1.0","canonical_sha256":"2af88cf22c8f22b9ea3cbbe3f6e57b7ed83583a8ab54e3ccd6fb925ec3bed20f","source":{"kind":"arxiv","id":"1804.00686","version":2},"attestation_state":"computed","paper":{"title":"Newton complementary duals of $f$-ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Samuel Budd","submitted_at":"2018-04-02T18:28:10Z","abstract_excerpt":"A square-free monomial ideal $I$ of $k[x_1,\\ldots,x_n]$ is said to be an $f$-ideal if the facet complex and non-face complex associated with $I$ have the same $f$-vector. We show that $I$ is an $f$-ideal if and only if its Newton complementary dual $\\widehat{I}$ is also an $f$-ideal. Because of this duality, previous results about some classes of $f$-ideals can be extended to a much larger class of $f$-ideals. An interesting by-product of our work is an alternative formulation of the Kruskal-Katona theorem for $f$-vectors of simplicial complexes."},"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":"1804.00686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-04-02T18:28:10Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b15e4dca81fafb450052fa4ce1d55bdb475448fd887294881bfc65c5573226b0","abstract_canon_sha256":"0dfea57d02a48e6c6ba297b322970926b511245bf293e59569f9bba20c9ee66b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:56:34.367802Z","signature_b64":"oT16PA1T5V5uIu9SmNk1VruHg5p3V/4QFWTxcx1kUEPhu0JzE0dyla4nooFFyX/rck1Ie93kgviIl/YneYdZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2af88cf22c8f22b9ea3cbbe3f6e57b7ed83583a8ab54e3ccd6fb925ec3bed20f","last_reissued_at":"2026-07-04T23:56:34.367440Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:56:34.367440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Newton complementary duals of $f$-ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Samuel Budd","submitted_at":"2018-04-02T18:28:10Z","abstract_excerpt":"A square-free monomial ideal $I$ of $k[x_1,\\ldots,x_n]$ is said to be an $f$-ideal if the facet complex and non-face complex associated with $I$ have the same $f$-vector. We show that $I$ is an $f$-ideal if and only if its Newton complementary dual $\\widehat{I}$ is also an $f$-ideal. Because of this duality, previous results about some classes of $f$-ideals can be extended to a much larger class of $f$-ideals. An interesting by-product of our work is an alternative formulation of the Kruskal-Katona theorem for $f$-vectors of simplicial complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00686","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1804.00686/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1804.00686","created_at":"2026-07-04T23:56:34.367494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.00686v2","created_at":"2026-07-04T23:56:34.367494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00686","created_at":"2026-07-04T23:56:34.367494+00:00"},{"alias_kind":"pith_short_12","alias_value":"FL4IZ4RMR4RL","created_at":"2026-07-04T23:56:34.367494+00:00"},{"alias_kind":"pith_short_16","alias_value":"FL4IZ4RMR4RLT2R4","created_at":"2026-07-04T23:56:34.367494+00:00"},{"alias_kind":"pith_short_8","alias_value":"FL4IZ4RM","created_at":"2026-07-04T23:56:34.367494+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/FL4IZ4RMR4RLT2R4XPR7NZL3P3","json":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3.json","graph_json":"https://pith.science/api/pith-number/FL4IZ4RMR4RLT2R4XPR7NZL3P3/graph.json","events_json":"https://pith.science/api/pith-number/FL4IZ4RMR4RLT2R4XPR7NZL3P3/events.json","paper":"https://pith.science/paper/FL4IZ4RM"},"agent_actions":{"view_html":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3","download_json":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3.json","view_paper":"https://pith.science/paper/FL4IZ4RM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.00686&json=true","fetch_graph":"https://pith.science/api/pith-number/FL4IZ4RMR4RLT2R4XPR7NZL3P3/graph.json","fetch_events":"https://pith.science/api/pith-number/FL4IZ4RMR4RLT2R4XPR7NZL3P3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3/action/storage_attestation","attest_author":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3/action/author_attestation","sign_citation":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3/action/citation_signature","submit_replication":"https://pith.science/pith/FL4IZ4RMR4RLT2R4XPR7NZL3P3/action/replication_record"}},"created_at":"2026-07-04T23:56:34.367494+00:00","updated_at":"2026-07-04T23:56:34.367494+00:00"}