{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JJPPHR2LQM6PLTW6LJWFT7EG46","short_pith_number":"pith:JJPPHR2L","canonical_record":{"source":{"id":"1305.1752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-08T09:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"590fa22c298448c04d98020190e60f1b1fe89ffa3d32652cdd15c5b6265c56dc","abstract_canon_sha256":"e84151e5be73175e5410bccdf95f9eef4645061205a89dd80a37ab907b36ace6"},"schema_version":"1.0"},"canonical_sha256":"4a5ef3c74b833cf5cede5a6c59fc86e7bc1862052490873589bfbd89b09a8140","source":{"kind":"arxiv","id":"1305.1752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1752","created_at":"2026-05-18T02:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1752v1","created_at":"2026-05-18T02:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1752","created_at":"2026-05-18T02:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"JJPPHR2LQM6P","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JJPPHR2LQM6PLTW6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JJPPHR2L","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JJPPHR2LQM6PLTW6LJWFT7EG46","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-08T09:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"590fa22c298448c04d98020190e60f1b1fe89ffa3d32652cdd15c5b6265c56dc","abstract_canon_sha256":"e84151e5be73175e5410bccdf95f9eef4645061205a89dd80a37ab907b36ace6"},"schema_version":"1.0"},"canonical_sha256":"4a5ef3c74b833cf5cede5a6c59fc86e7bc1862052490873589bfbd89b09a8140","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:04.132197Z","signature_b64":"wqYkhF0czUFjK6XvYe3NpjVdboe98L6bhfk6gHMbU5LomBcEWz99LBO/RAHoihaqBeK0isofM2oWB6yvuKRcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a5ef3c74b833cf5cede5a6c59fc86e7bc1862052490873589bfbd89b09a8140","last_reissued_at":"2026-05-18T02:31:04.131715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:04.131715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1752","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWp7ACmpH4n8Uhbs3LwTj3ma3JN016Y4d2c/oC73IhbyEPpNCshvBJ63B655P7RQmNzk10aprGPkaM6GOZmKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:10:46.157718Z"},"content_sha256":"6b43626ae37914f524a7ac5f5d16d28b1c514dc2a5391371cb7b0551b6a3fd04","schema_version":"1.0","event_id":"sha256:6b43626ae37914f524a7ac5f5d16d28b1c514dc2a5391371cb7b0551b6a3fd04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JJPPHR2LQM6PLTW6LJWFT7EG46","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erez Lapid, Tobias Finis","submitted_at":"2013-05-08T09:08:18Z","abstract_excerpt":"We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the $n$-formality of these hyperplane arrangements. As an application, we are able to bound the Castelnouvo-Mumford regularity of certain modules over polynomial rings associated to Coxeter arrangements (real reflection arrangements) and their restrictions. The modules in question are defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1752","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":""},"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":"2026-05-18T02:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bG3KGmgu5xwtTP1VLOsOarO41bfOG0+TCDRgkJmJ5AYDro1iVkhQ8eFkDhgHGMIqmhLMmuyvrPWoncXD7RxaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:10:46.158062Z"},"content_sha256":"25f2eb8904b7915e2913d83cc6b51d9b5c9bf5c0303ffeb83d9e4063ffce23c0","schema_version":"1.0","event_id":"sha256:25f2eb8904b7915e2913d83cc6b51d9b5c9bf5c0303ffeb83d9e4063ffce23c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJPPHR2LQM6PLTW6LJWFT7EG46/bundle.json","state_url":"https://pith.science/pith/JJPPHR2LQM6PLTW6LJWFT7EG46/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJPPHR2LQM6PLTW6LJWFT7EG46/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":"2026-06-21T23:10:46Z","links":{"resolver":"https://pith.science/pith/JJPPHR2LQM6PLTW6LJWFT7EG46","bundle":"https://pith.science/pith/JJPPHR2LQM6PLTW6LJWFT7EG46/bundle.json","state":"https://pith.science/pith/JJPPHR2LQM6PLTW6LJWFT7EG46/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJPPHR2LQM6PLTW6LJWFT7EG46/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JJPPHR2LQM6PLTW6LJWFT7EG46","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":"e84151e5be73175e5410bccdf95f9eef4645061205a89dd80a37ab907b36ace6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-08T09:08:18Z","title_canon_sha256":"590fa22c298448c04d98020190e60f1b1fe89ffa3d32652cdd15c5b6265c56dc"},"schema_version":"1.0","source":{"id":"1305.1752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1752","created_at":"2026-05-18T02:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1752v1","created_at":"2026-05-18T02:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1752","created_at":"2026-05-18T02:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"JJPPHR2LQM6P","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JJPPHR2LQM6PLTW6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JJPPHR2L","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:25f2eb8904b7915e2913d83cc6b51d9b5c9bf5c0303ffeb83d9e4063ffce23c0","target":"graph","created_at":"2026-05-18T02:31:04Z","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":"We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the $n$-formality of these hyperplane arrangements. As an application, we are able to bound the Castelnouvo-Mumford regularity of certain modules over polynomial rings associated to Coxeter arrangements (real reflection arrangements) and their restrictions. The modules in question are defi","authors_text":"Erez Lapid, Tobias Finis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-08T09:08:18Z","title":"Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1752","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":"sha256:6b43626ae37914f524a7ac5f5d16d28b1c514dc2a5391371cb7b0551b6a3fd04","target":"record","created_at":"2026-05-18T02:31:04Z","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":"e84151e5be73175e5410bccdf95f9eef4645061205a89dd80a37ab907b36ace6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-08T09:08:18Z","title_canon_sha256":"590fa22c298448c04d98020190e60f1b1fe89ffa3d32652cdd15c5b6265c56dc"},"schema_version":"1.0","source":{"id":"1305.1752","kind":"arxiv","version":1}},"canonical_sha256":"4a5ef3c74b833cf5cede5a6c59fc86e7bc1862052490873589bfbd89b09a8140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a5ef3c74b833cf5cede5a6c59fc86e7bc1862052490873589bfbd89b09a8140","first_computed_at":"2026-05-18T02:31:04.131715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:04.131715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wqYkhF0czUFjK6XvYe3NpjVdboe98L6bhfk6gHMbU5LomBcEWz99LBO/RAHoihaqBeK0isofM2oWB6yvuKRcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:04.132197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b43626ae37914f524a7ac5f5d16d28b1c514dc2a5391371cb7b0551b6a3fd04","sha256:25f2eb8904b7915e2913d83cc6b51d9b5c9bf5c0303ffeb83d9e4063ffce23c0"],"state_sha256":"a64941a7b8a3af6f6def054d04a22b166f88c0ca4757b428fd68b95080e2af55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"07j/DCQgkQ0BakIzKMncZjSrH0NrmvXhxfKHvEsdyLTCJiS1KPDxcgBSh7myrkkK8Nxzez7N3VDh0m0rQoD1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:10:46.159976Z","bundle_sha256":"1bc175fafcc97700153dbe6cbe2ae538f0b00ae9c0ea1db36450d1fa1bcf2773"}}