{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GKLNCZBF64HTTA5KRB2FLNWGSW","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":"3f2cd089d0a6f04ac793cd8a87408c38804d67f145a90b0406877920429ed18f","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-31T11:54:30Z","title_canon_sha256":"34c9f81fb1f6660e65015d9388fe7993ae76e914e0d5762a614f1f68b968f1de"},"schema_version":"1.0","source":{"id":"1508.07768","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07768","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07768v2","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07768","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"GKLNCZBF64HT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GKLNCZBF64HTTA5K","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GKLNCZBF","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:7c44e7564222aa9aa72ca43ae3f170c41e63fe8609e13b13c0d26ddc331e54db","target":"graph","created_at":"2026-05-18T01:15:58Z","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":"We consider tessellations of the Euclidean $(d-1)$-sphere by $(d-2)$-dimensional great subspheres or, equivalently, tessellations of Euclidean $d$-space by hyperplanes through the origin; these we call conical tessellations. For random polyhedral cones defined as typical cones in a conical tessellation by random hyperplanes, and for random cones which are dual to these in distribution, we study expectations for a general class of geometric functionals. They include combinatorial quantities, such as face numbers, as well as, for example, conical intrinsic volumes. For isotropic conical tessella","authors_text":"Daniel Hug, Rolf Schneider","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-31T11:54:30Z","title":"Random conical tessellations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07768","kind":"arxiv","version":2},"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":"sha256:56b4606587f1dacfe2fbc400dbac40dc957fb26752d29cde6af8197ebb6c7d72","target":"record","created_at":"2026-05-18T01:15:58Z","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":"3f2cd089d0a6f04ac793cd8a87408c38804d67f145a90b0406877920429ed18f","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-31T11:54:30Z","title_canon_sha256":"34c9f81fb1f6660e65015d9388fe7993ae76e914e0d5762a614f1f68b968f1de"},"schema_version":"1.0","source":{"id":"1508.07768","kind":"arxiv","version":2}},"canonical_sha256":"3296d16425f70f3983aa887455b6c695b8697270281e1c7ed5dff7ec076cd247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3296d16425f70f3983aa887455b6c695b8697270281e1c7ed5dff7ec076cd247","first_computed_at":"2026-05-18T01:15:58.287340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:58.287340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gTS3Gzuoyil4iK6912bsdaoWkUsdsLOeAfnRBNMNNMxB6PW1Y84xo4eXejMDw5gCtQId8vUueBXbj6l0fZNkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:58.288005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07768","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56b4606587f1dacfe2fbc400dbac40dc957fb26752d29cde6af8197ebb6c7d72","sha256:7c44e7564222aa9aa72ca43ae3f170c41e63fe8609e13b13c0d26ddc331e54db"],"state_sha256":"8350a6d745793a322f9611beeb0b0a6fdb64c0db2484a09f8ae21871d3f79070"}