{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:4CA5NBH6C3DZOT2ODA35JX6P67","short_pith_number":"pith:4CA5NBH6","schema_version":"1.0","canonical_sha256":"e081d684fe16c7974f4e1837d4dfcff7c7544dca448c0b64d44690d1802361fe","source":{"kind":"arxiv","id":"2411.12819","version":2},"attestation_state":"computed","paper":{"title":"Regular subdivisions, bounds on initial ideals, and categorical limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Daniel Corey, George Balla, Igor Makhlin, Victoria Schleis","submitted_at":"2024-11-19T19:13:47Z","abstract_excerpt":"Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a general framework which allows for partial generalizations of these constructions to arbitrary projective schemes (as well as their very affine parts). We associate a point configuration $A$ with any homogeneous ideal $I$. We obtain upper and lower bounds on every initial ideal of $I$, defining them in terms of the regular subdivision of $A$ given by the same weight. Furthermore, both bounds are interpreted categorical"},"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":"2411.12819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-19T19:13:47Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"27a78277663a993d1554a17a052fc5163c0965db79f535659950994d293b1617","abstract_canon_sha256":"d74e8011dd04b0e1f0b320cbe6652f86aa2c6e0e36ed6565c69f99745e641141"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:36.453783Z","signature_b64":"s1gLunmcLpPrXCTcDIjky5DnTTLHtsE013uGmjH+L1rbdFUxxpb07GqUPl/kxwkG6GPKyxOdgNJRlnCkBCjSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e081d684fe16c7974f4e1837d4dfcff7c7544dca448c0b64d44690d1802361fe","last_reissued_at":"2026-07-05T11:05:36.453231Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:36.453231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular subdivisions, bounds on initial ideals, and categorical limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Daniel Corey, George Balla, Igor Makhlin, Victoria Schleis","submitted_at":"2024-11-19T19:13:47Z","abstract_excerpt":"Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a general framework which allows for partial generalizations of these constructions to arbitrary projective schemes (as well as their very affine parts). We associate a point configuration $A$ with any homogeneous ideal $I$. We obtain upper and lower bounds on every initial ideal of $I$, defining them in terms of the regular subdivision of $A$ given by the same weight. Furthermore, both bounds are interpreted categorical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12819","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/2411.12819/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":"2411.12819","created_at":"2026-07-05T11:05:36.453297+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.12819v2","created_at":"2026-07-05T11:05:36.453297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12819","created_at":"2026-07-05T11:05:36.453297+00:00"},{"alias_kind":"pith_short_12","alias_value":"4CA5NBH6C3DZ","created_at":"2026-07-05T11:05:36.453297+00:00"},{"alias_kind":"pith_short_16","alias_value":"4CA5NBH6C3DZOT2O","created_at":"2026-07-05T11:05:36.453297+00:00"},{"alias_kind":"pith_short_8","alias_value":"4CA5NBH6","created_at":"2026-07-05T11:05:36.453297+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/4CA5NBH6C3DZOT2ODA35JX6P67","json":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67.json","graph_json":"https://pith.science/api/pith-number/4CA5NBH6C3DZOT2ODA35JX6P67/graph.json","events_json":"https://pith.science/api/pith-number/4CA5NBH6C3DZOT2ODA35JX6P67/events.json","paper":"https://pith.science/paper/4CA5NBH6"},"agent_actions":{"view_html":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67","download_json":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67.json","view_paper":"https://pith.science/paper/4CA5NBH6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.12819&json=true","fetch_graph":"https://pith.science/api/pith-number/4CA5NBH6C3DZOT2ODA35JX6P67/graph.json","fetch_events":"https://pith.science/api/pith-number/4CA5NBH6C3DZOT2ODA35JX6P67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67/action/storage_attestation","attest_author":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67/action/author_attestation","sign_citation":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67/action/citation_signature","submit_replication":"https://pith.science/pith/4CA5NBH6C3DZOT2ODA35JX6P67/action/replication_record"}},"created_at":"2026-07-05T11:05:36.453297+00:00","updated_at":"2026-07-05T11:05:36.453297+00:00"}