{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AA33ML6AQXMNF5SUVA3WF2KWNP","short_pith_number":"pith:AA33ML6A","canonical_record":{"source":{"id":"1212.0570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-12-03T21:48:35Z","cross_cats_sorted":[],"title_canon_sha256":"ba3065adc992c29c0d92c7f0f9bd1b0a6cad55b85218b7bda8582690da8242c5","abstract_canon_sha256":"a69360330d82045d8d8bfc3f56a689505817098b4ddca9a422ee3007b34767b0"},"schema_version":"1.0"},"canonical_sha256":"0037b62fc085d8d2f654a83762e9566bd7e816a5a31ebca63422494196e19070","source":{"kind":"arxiv","id":"1212.0570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0570","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0570v2","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0570","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"AA33ML6AQXMN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AA33ML6AQXMNF5SU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AA33ML6A","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AA33ML6AQXMNF5SUVA3WF2KWNP","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-12-03T21:48:35Z","cross_cats_sorted":[],"title_canon_sha256":"ba3065adc992c29c0d92c7f0f9bd1b0a6cad55b85218b7bda8582690da8242c5","abstract_canon_sha256":"a69360330d82045d8d8bfc3f56a689505817098b4ddca9a422ee3007b34767b0"},"schema_version":"1.0"},"canonical_sha256":"0037b62fc085d8d2f654a83762e9566bd7e816a5a31ebca63422494196e19070","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:49.434202Z","signature_b64":"sVPbYi/hNw2960VdK+R25OWzjuva3uHm7JX3lBqowrzP2cd4B7udEHC9jnJzVXZxXp7JBzrGAIebwjoDFlioAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0037b62fc085d8d2f654a83762e9566bd7e816a5a31ebca63422494196e19070","last_reissued_at":"2026-05-18T01:33:49.433725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:49.433725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0570","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QhE9zNjw2SDZCeb49S3Wiw+cdrZJZviTDuvtAGJeWdu6C+E+I92LwZm55EmLpC61eSR49aBc7r2dMebHQiy+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:13:27.906811Z"},"content_sha256":"1157f3db2b37bd9e4856c27c3ceb593cd6ff51183b24d73b3bb145a515e869b7","schema_version":"1.0","event_id":"sha256:1157f3db2b37bd9e4856c27c3ceb593cd6ff51183b24d73b3bb145a515e869b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AA33ML6AQXMNF5SUVA3WF2KWNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $\\theta_5$-graph is a spanner","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andr\\'e van Renssen, Pat Morin, Prosenjit Bose, Sander Verdonschot","submitted_at":"2012-12-03T21:48:35Z","abstract_excerpt":"Given a set of points in the plane, we show that the $\\theta$-graph with 5 cones is a geometric spanner with spanning ratio at most $\\sqrt{50 + 22 \\sqrt{5}} \\approx 9.960$. This is the first constant upper bound on the spanning ratio of this graph. The upper bound uses a constructive argument that gives a (possibly self-intersecting) path between any two vertices, of length at most $\\sqrt{50 + 22 \\sqrt{5}}$ times the Euclidean distance between the vertices. We also give a lower bound on the spanning ratio of $\\frac{1}{2}(11\\sqrt{5} -17) \\approx 3.798$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0570","kind":"arxiv","version":2},"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":"2026-05-18T01:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gP5Y5Rni1mAJ9T6vc+Fh2n3gBB8KfjOpFTuPizKduCMrGs0e15rgsKst/ph9IFex0iEYziaagwqvKs4INbGzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:13:27.907511Z"},"content_sha256":"cbc8caddcf7ef59b461b02d520d48cfb7b9fd19893ea27baa6eec6c166595266","schema_version":"1.0","event_id":"sha256:cbc8caddcf7ef59b461b02d520d48cfb7b9fd19893ea27baa6eec6c166595266"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AA33ML6AQXMNF5SUVA3WF2KWNP/bundle.json","state_url":"https://pith.science/pith/AA33ML6AQXMNF5SUVA3WF2KWNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AA33ML6AQXMNF5SUVA3WF2KWNP/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":"2026-05-25T23:13:27Z","links":{"resolver":"https://pith.science/pith/AA33ML6AQXMNF5SUVA3WF2KWNP","bundle":"https://pith.science/pith/AA33ML6AQXMNF5SUVA3WF2KWNP/bundle.json","state":"https://pith.science/pith/AA33ML6AQXMNF5SUVA3WF2KWNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AA33ML6AQXMNF5SUVA3WF2KWNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AA33ML6AQXMNF5SUVA3WF2KWNP","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":"a69360330d82045d8d8bfc3f56a689505817098b4ddca9a422ee3007b34767b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-12-03T21:48:35Z","title_canon_sha256":"ba3065adc992c29c0d92c7f0f9bd1b0a6cad55b85218b7bda8582690da8242c5"},"schema_version":"1.0","source":{"id":"1212.0570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0570","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0570v2","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0570","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"AA33ML6AQXMN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AA33ML6AQXMNF5SU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AA33ML6A","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:cbc8caddcf7ef59b461b02d520d48cfb7b9fd19893ea27baa6eec6c166595266","target":"graph","created_at":"2026-05-18T01:33:49Z","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":"Given a set of points in the plane, we show that the $\\theta$-graph with 5 cones is a geometric spanner with spanning ratio at most $\\sqrt{50 + 22 \\sqrt{5}} \\approx 9.960$. This is the first constant upper bound on the spanning ratio of this graph. The upper bound uses a constructive argument that gives a (possibly self-intersecting) path between any two vertices, of length at most $\\sqrt{50 + 22 \\sqrt{5}}$ times the Euclidean distance between the vertices. We also give a lower bound on the spanning ratio of $\\frac{1}{2}(11\\sqrt{5} -17) \\approx 3.798$.","authors_text":"Andr\\'e van Renssen, Pat Morin, Prosenjit Bose, Sander Verdonschot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-12-03T21:48:35Z","title":"The $\\theta_5$-graph is a spanner"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0570","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":"sha256:1157f3db2b37bd9e4856c27c3ceb593cd6ff51183b24d73b3bb145a515e869b7","target":"record","created_at":"2026-05-18T01:33:49Z","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":"a69360330d82045d8d8bfc3f56a689505817098b4ddca9a422ee3007b34767b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-12-03T21:48:35Z","title_canon_sha256":"ba3065adc992c29c0d92c7f0f9bd1b0a6cad55b85218b7bda8582690da8242c5"},"schema_version":"1.0","source":{"id":"1212.0570","kind":"arxiv","version":2}},"canonical_sha256":"0037b62fc085d8d2f654a83762e9566bd7e816a5a31ebca63422494196e19070","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0037b62fc085d8d2f654a83762e9566bd7e816a5a31ebca63422494196e19070","first_computed_at":"2026-05-18T01:33:49.433725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:49.433725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sVPbYi/hNw2960VdK+R25OWzjuva3uHm7JX3lBqowrzP2cd4B7udEHC9jnJzVXZxXp7JBzrGAIebwjoDFlioAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:49.434202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1157f3db2b37bd9e4856c27c3ceb593cd6ff51183b24d73b3bb145a515e869b7","sha256:cbc8caddcf7ef59b461b02d520d48cfb7b9fd19893ea27baa6eec6c166595266"],"state_sha256":"04943f80ef6691d30cfab37f3ea0d8f8067c48005ed246ee55755f52b15f0422"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvTpsnm1xkgOeQOohpt/uSXx7uyD4AgywxWgNty+EisNOiOotoEWQY7x47kSfGmtTSxGzJzlmwUSotFShu0FAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:13:27.911083Z","bundle_sha256":"eb802532720e182e09e9f647a3840ca12dc9b83676fe31f34b14bb55e03d199f"}}