{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PFHC32U5BH2Z4XIVWHGREFDUM5","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":"6616358db23dd30c78de4d989c1999dcd75511e248a0bbe2023a62c088a2ce1a","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-18T16:49:30Z","title_canon_sha256":"b66ae769653d2da9a0a40b9179eca1a4bc6f3da539a74c8a7c61c1ebb111fbe0"},"schema_version":"1.0","source":{"id":"1011.4228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4228","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4228v1","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4228","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"PFHC32U5BH2Z","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PFHC32U5BH2Z4XIV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PFHC32U5","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:18e6dbe35491b32cb2903b433752142f22e04b3934fda18e5ec9839033c68d23","target":"graph","created_at":"2026-05-18T00:55:58Z","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":"Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type $E_8$. With little extra work we prove that also all Coxeter arrangements are inductively free.","authors_text":"Michael Cuntz, Mohamed Barakat","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-18T16:49:30Z","title":"Coxeter and crystallographic arrangements are inductively free"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4228","kind":"arxiv","version":1},"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":"sha256:88d96384b5b5fa88a1bda99a59ec8733dd598ee7d9feca923ae174f4ce6dea93","target":"record","created_at":"2026-05-18T00:55:58Z","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":"6616358db23dd30c78de4d989c1999dcd75511e248a0bbe2023a62c088a2ce1a","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-18T16:49:30Z","title_canon_sha256":"b66ae769653d2da9a0a40b9179eca1a4bc6f3da539a74c8a7c61c1ebb111fbe0"},"schema_version":"1.0","source":{"id":"1011.4228","kind":"arxiv","version":1}},"canonical_sha256":"794e2dea9d09f59e5d15b1cd121474676568656b3f64839b8937a64ec137db9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"794e2dea9d09f59e5d15b1cd121474676568656b3f64839b8937a64ec137db9c","first_computed_at":"2026-05-18T00:55:58.932583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:58.932583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XWOvbzoy2bm+0O2pbGGi26wUjfId0flmZ4++cRh6K5w9FPbXotMMnZTAUVEujawNUI6ms4/BPZ3nc/PRrrn+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:58.933060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88d96384b5b5fa88a1bda99a59ec8733dd598ee7d9feca923ae174f4ce6dea93","sha256:18e6dbe35491b32cb2903b433752142f22e04b3934fda18e5ec9839033c68d23"],"state_sha256":"26d42cd1debfe36f899a13a27eabbdb60a9337c11a319d66367f0bba7d2c6b85"}