{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IVK2KRTA2WHORCLCT3NZRHUDWC","short_pith_number":"pith:IVK2KRTA","canonical_record":{"source":{"id":"1503.03462","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-03-11T19:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"5b16fc5ee18a9fc50e8867a12a5e1341b1424eac80e6113ab76d540e4c8cd8aa","abstract_canon_sha256":"d7fed7bb6e991b58fcdf2df2c3fdf9563820368accaa06493083dde1d785da48"},"schema_version":"1.0"},"canonical_sha256":"4555a54660d58ee889629edb989e83b0946c35d211b0f39e6eb40c5fff28f1a1","source":{"kind":"arxiv","id":"1503.03462","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03462","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03462v6","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03462","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"IVK2KRTA2WHO","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IVK2KRTA2WHORCLC","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IVK2KRTA","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IVK2KRTA2WHORCLCT3NZRHUDWC","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03462","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-03-11T19:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"5b16fc5ee18a9fc50e8867a12a5e1341b1424eac80e6113ab76d540e4c8cd8aa","abstract_canon_sha256":"d7fed7bb6e991b58fcdf2df2c3fdf9563820368accaa06493083dde1d785da48"},"schema_version":"1.0"},"canonical_sha256":"4555a54660d58ee889629edb989e83b0946c35d211b0f39e6eb40c5fff28f1a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:58.410031Z","signature_b64":"LPSALaflwFhCQl1+bUa2DXWYiCUkzBUcSVWHjM4U1DGKdZwMGnskKLeoRE56O+u1IA2fEsaVDeUAJhM6iQFBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4555a54660d58ee889629edb989e83b0946c35d211b0f39e6eb40c5fff28f1a1","last_reissued_at":"2026-05-18T00:51:58.409530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:58.409530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03462","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5XJp7TpVYTfT9PFMjw7dVYm1EanXuGaFKIqkUArEAY32b9h4mvDyHvz0v9s62kWa64DPV90FvaSiCuTb5a9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:15:28.612020Z"},"content_sha256":"c6467442b9918b5727250ba9527e3b97a8d0951766672aaf58ec7c78ddb61cf8","schema_version":"1.0","event_id":"sha256:c6467442b9918b5727250ba9527e3b97a8d0951766672aaf58ec7c78ddb61cf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IVK2KRTA2WHORCLCT3NZRHUDWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the zone of a circle in an arrangement of lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Gabriel Nivasch","submitted_at":"2015-03-11T19:36:59Z","abstract_excerpt":"Let $\\mathcal L$ be a set of $n$ lines in the plane, and let $C$ be a convex curve in the plane, like a circle or a parabola. The \"zone\" of $C$ in $\\mathcal L$, denoted $\\mathcal Z(C,\\mathcal L)$, is defined as the set of all cells in the arrangement $\\mathcal A(\\mathcal L)$ that are intersected by $C$. Edelsbrunner et al. (1992) showed that the complexity (total number of edges or vertices) of $\\mathcal Z(C,\\mathcal L)$ is at most $O(n\\alpha(n))$, where $\\alpha$ is the inverse Ackermann function. They did this by translating the sequence of edges of $\\mathcal Z(C,\\mathcal L)$ into a sequence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03462","kind":"arxiv","version":6},"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":"2026-05-18T00:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Giu4xz7MgY7X6smKOSd/4Lf7NYpVqc3lRWBw2AKo7+yRGNiGv8TdlM+iC558jbglVA5+ZqqA3aDB/cECHSYLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:15:28.612383Z"},"content_sha256":"194cd3d2493bfe000fc9cdae1fac8679c8062e3ff99700de2458afea008b27c8","schema_version":"1.0","event_id":"sha256:194cd3d2493bfe000fc9cdae1fac8679c8062e3ff99700de2458afea008b27c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVK2KRTA2WHORCLCT3NZRHUDWC/bundle.json","state_url":"https://pith.science/pith/IVK2KRTA2WHORCLCT3NZRHUDWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVK2KRTA2WHORCLCT3NZRHUDWC/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":"2026-06-02T14:15:28Z","links":{"resolver":"https://pith.science/pith/IVK2KRTA2WHORCLCT3NZRHUDWC","bundle":"https://pith.science/pith/IVK2KRTA2WHORCLCT3NZRHUDWC/bundle.json","state":"https://pith.science/pith/IVK2KRTA2WHORCLCT3NZRHUDWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVK2KRTA2WHORCLCT3NZRHUDWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IVK2KRTA2WHORCLCT3NZRHUDWC","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":"d7fed7bb6e991b58fcdf2df2c3fdf9563820368accaa06493083dde1d785da48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-03-11T19:36:59Z","title_canon_sha256":"5b16fc5ee18a9fc50e8867a12a5e1341b1424eac80e6113ab76d540e4c8cd8aa"},"schema_version":"1.0","source":{"id":"1503.03462","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03462","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03462v6","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03462","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"IVK2KRTA2WHO","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IVK2KRTA2WHORCLC","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IVK2KRTA","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:194cd3d2493bfe000fc9cdae1fac8679c8062e3ff99700de2458afea008b27c8","target":"graph","created_at":"2026-05-18T00:51:58Z","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":"Let $\\mathcal L$ be a set of $n$ lines in the plane, and let $C$ be a convex curve in the plane, like a circle or a parabola. The \"zone\" of $C$ in $\\mathcal L$, denoted $\\mathcal Z(C,\\mathcal L)$, is defined as the set of all cells in the arrangement $\\mathcal A(\\mathcal L)$ that are intersected by $C$. Edelsbrunner et al. (1992) showed that the complexity (total number of edges or vertices) of $\\mathcal Z(C,\\mathcal L)$ is at most $O(n\\alpha(n))$, where $\\alpha$ is the inverse Ackermann function. They did this by translating the sequence of edges of $\\mathcal Z(C,\\mathcal L)$ into a sequence ","authors_text":"Gabriel Nivasch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-03-11T19:36:59Z","title":"On the zone of a circle in an arrangement of lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03462","kind":"arxiv","version":6},"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:c6467442b9918b5727250ba9527e3b97a8d0951766672aaf58ec7c78ddb61cf8","target":"record","created_at":"2026-05-18T00:51:58Z","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":"d7fed7bb6e991b58fcdf2df2c3fdf9563820368accaa06493083dde1d785da48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-03-11T19:36:59Z","title_canon_sha256":"5b16fc5ee18a9fc50e8867a12a5e1341b1424eac80e6113ab76d540e4c8cd8aa"},"schema_version":"1.0","source":{"id":"1503.03462","kind":"arxiv","version":6}},"canonical_sha256":"4555a54660d58ee889629edb989e83b0946c35d211b0f39e6eb40c5fff28f1a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4555a54660d58ee889629edb989e83b0946c35d211b0f39e6eb40c5fff28f1a1","first_computed_at":"2026-05-18T00:51:58.409530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:58.409530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LPSALaflwFhCQl1+bUa2DXWYiCUkzBUcSVWHjM4U1DGKdZwMGnskKLeoRE56O+u1IA2fEsaVDeUAJhM6iQFBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:58.410031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03462","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6467442b9918b5727250ba9527e3b97a8d0951766672aaf58ec7c78ddb61cf8","sha256:194cd3d2493bfe000fc9cdae1fac8679c8062e3ff99700de2458afea008b27c8"],"state_sha256":"3116a60de1fb6eab0ab5008140e82f3f27ad0958eb299c730329fe8fddd32d9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3s7rNimfOmO/wgegjslhvWtf8uvNMFLkibiPUu6xuVp2AfnhzjACa/uEogaUDtwavFzw08Kasu1HSP/DUDIxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:15:28.614287Z","bundle_sha256":"c49be5896d991683d6b381d5ab3865047c85bfe08e5898f28b7373ce8bebc1d7"}}