{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PXYFPGZC2UVRDNMXJBIM2J6CMI","short_pith_number":"pith:PXYFPGZC","schema_version":"1.0","canonical_sha256":"7df0579b22d52b11b5974850cd27c26227f21d176026a249030c4f35b71f4c69","source":{"kind":"arxiv","id":"2502.19998","version":1},"attestation_state":"computed","paper":{"title":"Symbolic powers of polymatroidal ideals","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Somayeh Moradi","submitted_at":"2025-02-27T11:23:30Z","abstract_excerpt":"In this paper, we investigate the componentwise linearity and the Castelnuovo-Mumford regularity of symbolic powers of polymatroidal ideals. For a polymatroidal ideal $I$, we conjecture that every symbolic power $I^{(k)}$ is componentwise linear and $$ \\text{reg}\\,I^{(k)}=\\text{reg}\\,I^k $$ for all $k \\ge 1$. We prove that $\\text{reg}\\,I^{(k)}\\ge\\text{reg}\\,I^k$ for all $k \\ge 1$ when $I$ has no embedded associated primes, for instance if $I$ is a matroidal ideal. Moreover, we establish a criterion on the symbolic Rees algebra $\\mathcal{R}_s(I)$ of a monomial ideal of minimal intersection type"},"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":"2502.19998","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2025-02-27T11:23:30Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8ab51fc7d70c4367d7873338c26134b0e79a252c5bf3bb5ff3433ca63fe931df","abstract_canon_sha256":"b8a17307bfb2b48ced3b9aa1eee71f67114235bb1271c54f86cfd61fd58d78f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:56.623815Z","signature_b64":"7Fbsy9a4ZKGTmBBL4Jm2QBTgWNWLUv5/Jk8kI7G5g0t3DV4J75NjJG3l0ALycOSOKatI9x/FFWajGTte4vIFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7df0579b22d52b11b5974850cd27c26227f21d176026a249030c4f35b71f4c69","last_reissued_at":"2026-07-05T10:20:56.623348Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:56.623348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symbolic powers of polymatroidal ideals","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Somayeh Moradi","submitted_at":"2025-02-27T11:23:30Z","abstract_excerpt":"In this paper, we investigate the componentwise linearity and the Castelnuovo-Mumford regularity of symbolic powers of polymatroidal ideals. For a polymatroidal ideal $I$, we conjecture that every symbolic power $I^{(k)}$ is componentwise linear and $$ \\text{reg}\\,I^{(k)}=\\text{reg}\\,I^k $$ for all $k \\ge 1$. We prove that $\\text{reg}\\,I^{(k)}\\ge\\text{reg}\\,I^k$ for all $k \\ge 1$ when $I$ has no embedded associated primes, for instance if $I$ is a matroidal ideal. Moreover, we establish a criterion on the symbolic Rees algebra $\\mathcal{R}_s(I)$ of a monomial ideal of minimal intersection type"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19998","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.19998/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":"2502.19998","created_at":"2026-07-05T10:20:56.623409+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.19998v1","created_at":"2026-07-05T10:20:56.623409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19998","created_at":"2026-07-05T10:20:56.623409+00:00"},{"alias_kind":"pith_short_12","alias_value":"PXYFPGZC2UVR","created_at":"2026-07-05T10:20:56.623409+00:00"},{"alias_kind":"pith_short_16","alias_value":"PXYFPGZC2UVRDNMX","created_at":"2026-07-05T10:20:56.623409+00:00"},{"alias_kind":"pith_short_8","alias_value":"PXYFPGZC","created_at":"2026-07-05T10:20:56.623409+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.07022","citing_title":"Principal vector-spread Borel ideals","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI","json":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI.json","graph_json":"https://pith.science/api/pith-number/PXYFPGZC2UVRDNMXJBIM2J6CMI/graph.json","events_json":"https://pith.science/api/pith-number/PXYFPGZC2UVRDNMXJBIM2J6CMI/events.json","paper":"https://pith.science/paper/PXYFPGZC"},"agent_actions":{"view_html":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI","download_json":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI.json","view_paper":"https://pith.science/paper/PXYFPGZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.19998&json=true","fetch_graph":"https://pith.science/api/pith-number/PXYFPGZC2UVRDNMXJBIM2J6CMI/graph.json","fetch_events":"https://pith.science/api/pith-number/PXYFPGZC2UVRDNMXJBIM2J6CMI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI/action/storage_attestation","attest_author":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI/action/author_attestation","sign_citation":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI/action/citation_signature","submit_replication":"https://pith.science/pith/PXYFPGZC2UVRDNMXJBIM2J6CMI/action/replication_record"}},"created_at":"2026-07-05T10:20:56.623409+00:00","updated_at":"2026-07-05T10:20:56.623409+00:00"}