{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4XUP7OIL2BO7Y6YLV6M4W32IQX","short_pith_number":"pith:4XUP7OIL","canonical_record":{"source":{"id":"1203.4863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-22T00:46:00Z","cross_cats_sorted":["cs.CG","cs.NI","math.CO"],"title_canon_sha256":"5535239a609d3c79921a3df3340432e503e8fb130ded32b85eccbbb412d2975b","abstract_canon_sha256":"02b39db5b04ff503c127865f57c2061dfec195c4c49096fbf7959338eb8efc4d"},"schema_version":"1.0"},"canonical_sha256":"e5e8ffb90bd05dfc7b0baf99cb6f4885e205f4a39c94445c83d0175215c94268","source":{"kind":"arxiv","id":"1203.4863","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4863","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4863v1","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4863","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"4XUP7OIL2BO7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4XUP7OIL2BO7Y6YL","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4XUP7OIL","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4XUP7OIL2BO7Y6YLV6M4W32IQX","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-22T00:46:00Z","cross_cats_sorted":["cs.CG","cs.NI","math.CO"],"title_canon_sha256":"5535239a609d3c79921a3df3340432e503e8fb130ded32b85eccbbb412d2975b","abstract_canon_sha256":"02b39db5b04ff503c127865f57c2061dfec195c4c49096fbf7959338eb8efc4d"},"schema_version":"1.0"},"canonical_sha256":"e5e8ffb90bd05dfc7b0baf99cb6f4885e205f4a39c94445c83d0175215c94268","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:28.534552Z","signature_b64":"XW2Pkc/oXl1XG0GKTbcZzlYn25VtouLz42nq9ciYHqC966xpzdoEhSHs6ASn8+tSaGsnCGjvCa1O5k6B/5WXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5e8ffb90bd05dfc7b0baf99cb6f4885e205f4a39c94445c83d0175215c94268","last_reissued_at":"2026-05-18T03:59:28.533833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:28.533833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4863","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":"2026-05-18T03:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8bzifcWvrW6r0rZ2Kjw8aNmyiP5KxB6borzzKzYclpJCsmztvs/zrnLOqTbQEQ/gRdRV2sy/X4QZxrE7QonCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:06:28.332561Z"},"content_sha256":"f0ad5115ac4bb638898ce283d97b001cae0b2708869b3c3358e0fbc5c77d7ec8","schema_version":"1.0","event_id":"sha256:f0ad5115ac4bb638898ce283d97b001cae0b2708869b3c3358e0fbc5c77d7ec8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4XUP7OIL2BO7Y6YLV6M4W32IQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Traffic Analysis in Random Delaunay Tessellations and Other Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.NI","math.CO"],"primary_cat":"math.DG","authors_text":"Gabriel H. Tucci, John D. Hobby","submitted_at":"2012-03-22T00:46:00Z","abstract_excerpt":"In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\\\"os-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the maximum vertex flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4863","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":"2026-05-18T03:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDOLc2+GJ1w+hIdP5TeIQSaEEbWd1zFlT5NPnQ3Y1Db4HuY9cOEpkysoncWhB6AE0IkbpNIWZdlNXO6U4YceCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:06:28.332908Z"},"content_sha256":"8f32c89dd5d60849414bba26581dac88793145d978610c53e3e3b5f149ab37f9","schema_version":"1.0","event_id":"sha256:8f32c89dd5d60849414bba26581dac88793145d978610c53e3e3b5f149ab37f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX/bundle.json","state_url":"https://pith.science/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX/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":"2026-06-24T22:06:28Z","links":{"resolver":"https://pith.science/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX","bundle":"https://pith.science/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX/bundle.json","state":"https://pith.science/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XUP7OIL2BO7Y6YLV6M4W32IQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4XUP7OIL2BO7Y6YLV6M4W32IQX","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":"02b39db5b04ff503c127865f57c2061dfec195c4c49096fbf7959338eb8efc4d","cross_cats_sorted":["cs.CG","cs.NI","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-22T00:46:00Z","title_canon_sha256":"5535239a609d3c79921a3df3340432e503e8fb130ded32b85eccbbb412d2975b"},"schema_version":"1.0","source":{"id":"1203.4863","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4863","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4863v1","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4863","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"4XUP7OIL2BO7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4XUP7OIL2BO7Y6YL","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4XUP7OIL","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:8f32c89dd5d60849414bba26581dac88793145d978610c53e3e3b5f149ab37f9","target":"graph","created_at":"2026-05-18T03:59:28Z","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":"In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\\\"os-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the maximum vertex flow.","authors_text":"Gabriel H. Tucci, John D. Hobby","cross_cats":["cs.CG","cs.NI","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-22T00:46:00Z","title":"Traffic Analysis in Random Delaunay Tessellations and Other Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4863","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:f0ad5115ac4bb638898ce283d97b001cae0b2708869b3c3358e0fbc5c77d7ec8","target":"record","created_at":"2026-05-18T03:59:28Z","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":"02b39db5b04ff503c127865f57c2061dfec195c4c49096fbf7959338eb8efc4d","cross_cats_sorted":["cs.CG","cs.NI","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-22T00:46:00Z","title_canon_sha256":"5535239a609d3c79921a3df3340432e503e8fb130ded32b85eccbbb412d2975b"},"schema_version":"1.0","source":{"id":"1203.4863","kind":"arxiv","version":1}},"canonical_sha256":"e5e8ffb90bd05dfc7b0baf99cb6f4885e205f4a39c94445c83d0175215c94268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5e8ffb90bd05dfc7b0baf99cb6f4885e205f4a39c94445c83d0175215c94268","first_computed_at":"2026-05-18T03:59:28.533833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:28.533833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XW2Pkc/oXl1XG0GKTbcZzlYn25VtouLz42nq9ciYHqC966xpzdoEhSHs6ASn8+tSaGsnCGjvCa1O5k6B/5WXCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:28.534552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4863","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0ad5115ac4bb638898ce283d97b001cae0b2708869b3c3358e0fbc5c77d7ec8","sha256:8f32c89dd5d60849414bba26581dac88793145d978610c53e3e3b5f149ab37f9"],"state_sha256":"27f97ac92af375f559245f2180c5f77804c2948e153ebe28cb419bf7268b8105"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsXCuidGkCz52gaswp+2ElnwKgbG+JbnsvDiUf9wFwUmSYBAMj4ZZqrnbDazgXWIqVcgt6PQKR1n4Dv+gyWdCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:06:28.334843Z","bundle_sha256":"6cfcf50624a0cd1d2fcbd0d4c56a0af04e76b1252599fdab7fe53fd17428c81b"}}