{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WWIEBJGVGUVSUH5OG7DCXPIFTH","short_pith_number":"pith:WWIEBJGV","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"},"canonical_sha256":"b59040a4d5352b2a1fae37c62bbd0599eda6f4aa3d2b2e270a277ea5f55b3f92","source":{"kind":"arxiv","id":"1304.8033","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8033","created_at":"2026-05-18T01:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8033v4","created_at":"2026-05-18T01:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8033","created_at":"2026-05-18T01:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"WWIEBJGVGUVS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWIEBJGVGUVSUH5O","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWIEBJGV","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WWIEBJGVGUVSUH5OG7DCXPIFTH","target":"record","payload":{"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"},"canonical_sha256":"b59040a4d5352b2a1fae37c62bbd0599eda6f4aa3d2b2e270a277ea5f55b3f92","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"},"source_kind":"arxiv","source_id":"1304.8033","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+B04yW80WtyqrEPNnK5VgpK4fnCDuZW+5qv7Uw4ka6fkJsvoc3JD75+NWt98T9w8nMY1jsR1sZuO+oYrLIVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:12:45.353038Z"},"content_sha256":"b609e15785dc236aff7464b6dbc51e33e9a1813cdfe68151e90173eb38200899","schema_version":"1.0","event_id":"sha256:b609e15785dc236aff7464b6dbc51e33e9a1813cdfe68151e90173eb38200899"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WWIEBJGVGUVSUH5OG7DCXPIFTH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xS1EdzB4LKIwRzCp2KCrtCaei4Th5fj5vweNluRCKs3ThdY/mbrvM1fIKQFq831jZjaY/wFDnDQIDRuUV0naAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:12:45.353700Z"},"content_sha256":"a22c37d17bcc082c62bffd31b03a045cd13f57b996e8723abc32e668d80237e6","schema_version":"1.0","event_id":"sha256:a22c37d17bcc082c62bffd31b03a045cd13f57b996e8723abc32e668d80237e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/bundle.json","state_url":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T20:12:45Z","links":{"resolver":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH","bundle":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/bundle.json","state":"https://pith.science/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWIEBJGVGUVSUH5OG7DCXPIFTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WWIEBJGVGUVSUH5OG7DCXPIFTH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c1aff8a2e7ed8eee0cd9eb0db871075d404870c976117ca069311ea29afef93f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T15:30:40Z","title_canon_sha256":"ba211ee7fa663c8582b4265a920c5bd3c55c46df1255d57092f72106a67b8ff3"},"schema_version":"1.0","source":{"id":"1304.8033","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8033","created_at":"2026-05-18T01:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8033v4","created_at":"2026-05-18T01:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8033","created_at":"2026-05-18T01:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"WWIEBJGVGUVS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWIEBJGVGUVSUH5O","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWIEBJGV","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:a22c37d17bcc082c62bffd31b03a045cd13f57b996e8723abc32e668d80237e6","target":"graph","created_at":"2026-05-18T01:16:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Hiroaki Terao, Michael Cuntz, Mohamed Barakat, Takuro Abe, Torsten Hoge","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T15:30:40Z","title":"The freeness of ideal subarrangements of Weyl arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8033","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b609e15785dc236aff7464b6dbc51e33e9a1813cdfe68151e90173eb38200899","target":"record","created_at":"2026-05-18T01:16:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c1aff8a2e7ed8eee0cd9eb0db871075d404870c976117ca069311ea29afef93f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T15:30:40Z","title_canon_sha256":"ba211ee7fa663c8582b4265a920c5bd3c55c46df1255d57092f72106a67b8ff3"},"schema_version":"1.0","source":{"id":"1304.8033","kind":"arxiv","version":4}},"canonical_sha256":"b59040a4d5352b2a1fae37c62bbd0599eda6f4aa3d2b2e270a277ea5f55b3f92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b59040a4d5352b2a1fae37c62bbd0599eda6f4aa3d2b2e270a277ea5f55b3f92","first_computed_at":"2026-05-18T01:16:21.952778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:21.952778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YwKTQagvTnC/J1sepBcGoHARW+jwHssF08gPF8s4WqgHzfeNYIXS4DnrOw7+DQvJRLXEVrhiVM6MwzQ1E3SQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:21.953340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.8033","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b609e15785dc236aff7464b6dbc51e33e9a1813cdfe68151e90173eb38200899","sha256:a22c37d17bcc082c62bffd31b03a045cd13f57b996e8723abc32e668d80237e6"],"state_sha256":"c21434836be0bebded01111689fd6011cc91fb821bad37e8091c933739fe135b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XJVehRvZkgfwQf8BDs7E+Ir1r9nS9oC9HLcpCusv75l32Zaly8wOFe2FUG0jJ6xLIWLAz0X8NLcpCuGc568cDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:12:45.357003Z","bundle_sha256":"9fd746e8aaeed4fc8345354c4565f5385a11b2b93e92c3c1c3b71df6013b62e3"}}