{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WWIEBJGVGUVSUH5OG7DCXPIFTH","short_pith_number":"pith:WWIEBJGV","schema_version":"1.0","canonical_sha256":"b59040a4d5352b2a1fae37c62bbd0599eda6f4aa3d2b2e270a277ea5f55b3f92","source":{"kind":"arxiv","id":"1304.8033","version":4},"attestation_state":"computed","paper":{"title":"The freeness of ideal subarrangements of Weyl arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Hiroaki Terao, Michael Cuntz, Mohamed Barakat, Takuro Abe, Torsten Hoge","submitted_at":"2013-04-30T15:30:40Z","abstract_excerpt":"A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers-Tymoczko. In particular, when an ideal subarrangement is equal to the entire Weyl arrangement, our main theorem yields the celebrated formula by Shapiro, Steinberg, Kostant, and Macdonald. Our pr"},"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":"1304.8033","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T15:30:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ba211ee7fa663c8582b4265a920c5bd3c55c46df1255d57092f72106a67b8ff3","abstract_canon_sha256":"c1aff8a2e7ed8eee0cd9eb0db871075d404870c976117ca069311ea29afef93f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:21.953340Z","signature_b64":"YwKTQagvTnC/J1sepBcGoHARW+jwHssF08gPF8s4WqgHzfeNYIXS4DnrOw7+DQvJRLXEVrhiVM6MwzQ1E3SQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b59040a4d5352b2a1fae37c62bbd0599eda6f4aa3d2b2e270a277ea5f55b3f92","last_reissued_at":"2026-05-18T01:16:21.952778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:21.952778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The freeness of ideal subarrangements of Weyl arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Hiroaki Terao, Michael Cuntz, Mohamed Barakat, Takuro Abe, Torsten Hoge","submitted_at":"2013-04-30T15:30:40Z","abstract_excerpt":"A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers-Tymoczko. In particular, when an ideal subarrangement is equal to the entire Weyl arrangement, our main theorem yields the celebrated formula by Shapiro, Steinberg, Kostant, and Macdonald. Our pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8033","kind":"arxiv","version":4},"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":"1304.8033","created_at":"2026-05-18T01:16:21.952866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.8033v4","created_at":"2026-05-18T01:16:21.952866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8033","created_at":"2026-05-18T01:16:21.952866+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWIEBJGVGUVS","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWIEBJGVGUVSUH5O","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWIEBJGV","created_at":"2026-05-18T12:28:06.772260+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/WWIEBJGVGUVSUH5OG7DCXPIFTH","json":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH.json","graph_json":"https://pith.science/api/pith-number/WWIEBJGVGUVSUH5OG7DCXPIFTH/graph.json","events_json":"https://pith.science/api/pith-number/WWIEBJGVGUVSUH5OG7DCXPIFTH/events.json","paper":"https://pith.science/paper/WWIEBJGV"},"agent_actions":{"view_html":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH","download_json":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH.json","view_paper":"https://pith.science/paper/WWIEBJGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.8033&json=true","fetch_graph":"https://pith.science/api/pith-number/WWIEBJGVGUVSUH5OG7DCXPIFTH/graph.json","fetch_events":"https://pith.science/api/pith-number/WWIEBJGVGUVSUH5OG7DCXPIFTH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/action/storage_attestation","attest_author":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/action/author_attestation","sign_citation":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/action/citation_signature","submit_replication":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/action/replication_record"}},"created_at":"2026-05-18T01:16:21.952866+00:00","updated_at":"2026-05-18T01:16:21.952866+00:00"}