{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NY2FTARPCSDREVEUHXKGKG53EZ","short_pith_number":"pith:NY2FTARP","canonical_record":{"source":{"id":"1305.1295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-06T18:19:17Z","cross_cats_sorted":["cs.CC","cs.NI","cs.SI"],"title_canon_sha256":"c1d6e9c4b9d2db00eb77ba7e4bc184ef253dc088a7602609e7e2696d9b0a622f","abstract_canon_sha256":"0421edcc73bfe34133cf1e4c98bb36edc0383ee2993e4340704f4ac988db4e69"},"schema_version":"1.0"},"canonical_sha256":"6e3459822f14871254943dd4651bbb26465ff64a2658b51199d4b2dadaeeabff","source":{"kind":"arxiv","id":"1305.1295","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1295","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1295v1","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1295","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"NY2FTARPCSDR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NY2FTARPCSDREVEU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NY2FTARP","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NY2FTARPCSDREVEUHXKGKG53EZ","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-06T18:19:17Z","cross_cats_sorted":["cs.CC","cs.NI","cs.SI"],"title_canon_sha256":"c1d6e9c4b9d2db00eb77ba7e4bc184ef253dc088a7602609e7e2696d9b0a622f","abstract_canon_sha256":"0421edcc73bfe34133cf1e4c98bb36edc0383ee2993e4340704f4ac988db4e69"},"schema_version":"1.0"},"canonical_sha256":"6e3459822f14871254943dd4651bbb26465ff64a2658b51199d4b2dadaeeabff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:22.079065Z","signature_b64":"VB7SZl8Ck4f2ynMZdV2P2xhLNTk4yG/u+0QlEx6CGH56rK/FCDy+16RSOol51qkAWMSKKkA+l4zVdBdEga/1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e3459822f14871254943dd4651bbb26465ff64a2658b51199d4b2dadaeeabff","last_reissued_at":"2026-05-18T03:26:22.078328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:22.078328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1295","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":"2026-05-18T03:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8jBZm6XETxS3yWRQYWk6Ghml7EJywCcYaPYMP1arT44Fz1rnt1YqrV84N+pQ+qYlQ9dnpb1wn6jelNRSdNuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:44:01.220885Z"},"content_sha256":"28cb2299d451263d3484225eec4b676defd79930f883940da3cd96243dae899b","schema_version":"1.0","event_id":"sha256:28cb2299d451263d3484225eec4b676defd79930f883940da3cd96243dae899b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NY2FTARPCSDREVEUHXKGKG53EZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World Grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.NI","cs.SI"],"primary_cat":"cs.DS","authors_text":"Martin Dietzfelbinger, Philipp Woelfel","submitted_at":"2013-05-06T18:19:17Z","abstract_excerpt":"We consider Kleinberg's celebrated small world graph model (Kleinberg, 2000), in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number of additional unidirectional edges leaving each node. These long range edges are determined at random according to a probability distribution (the augmenting distribution), which is the same for each node. Kleinberg suggested using the inverse D-th power distribution, in which node v is the long range contact of node u with a probability proportional to ||u-v||^(-D). He showed that such an augmenting distribution allows to route a message"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1295","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":"2026-05-18T03:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8AgNdORdXV8OZBAR/AN4Uem+Hpzre9+ECOoFCC8znlX34QH6lEMaaUeIHfDrN/pQwKk2qBs6tnfJVngVN+FyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:44:01.221235Z"},"content_sha256":"09ffd6b6a605684703db203ab1624e543f48f8f128b5d20192507b21f798e4fb","schema_version":"1.0","event_id":"sha256:09ffd6b6a605684703db203ab1624e543f48f8f128b5d20192507b21f798e4fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NY2FTARPCSDREVEUHXKGKG53EZ/bundle.json","state_url":"https://pith.science/pith/NY2FTARPCSDREVEUHXKGKG53EZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NY2FTARPCSDREVEUHXKGKG53EZ/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":"2026-06-25T23:44:01Z","links":{"resolver":"https://pith.science/pith/NY2FTARPCSDREVEUHXKGKG53EZ","bundle":"https://pith.science/pith/NY2FTARPCSDREVEUHXKGKG53EZ/bundle.json","state":"https://pith.science/pith/NY2FTARPCSDREVEUHXKGKG53EZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NY2FTARPCSDREVEUHXKGKG53EZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NY2FTARPCSDREVEUHXKGKG53EZ","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":"0421edcc73bfe34133cf1e4c98bb36edc0383ee2993e4340704f4ac988db4e69","cross_cats_sorted":["cs.CC","cs.NI","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-06T18:19:17Z","title_canon_sha256":"c1d6e9c4b9d2db00eb77ba7e4bc184ef253dc088a7602609e7e2696d9b0a622f"},"schema_version":"1.0","source":{"id":"1305.1295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1295","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1295v1","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1295","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"NY2FTARPCSDR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NY2FTARPCSDREVEU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NY2FTARP","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:09ffd6b6a605684703db203ab1624e543f48f8f128b5d20192507b21f798e4fb","target":"graph","created_at":"2026-05-18T03:26:22Z","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 Kleinberg's celebrated small world graph model (Kleinberg, 2000), in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number of additional unidirectional edges leaving each node. These long range edges are determined at random according to a probability distribution (the augmenting distribution), which is the same for each node. Kleinberg suggested using the inverse D-th power distribution, in which node v is the long range contact of node u with a probability proportional to ||u-v||^(-D). He showed that such an augmenting distribution allows to route a message","authors_text":"Martin Dietzfelbinger, Philipp Woelfel","cross_cats":["cs.CC","cs.NI","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-06T18:19:17Z","title":"Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World Grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1295","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":"sha256:28cb2299d451263d3484225eec4b676defd79930f883940da3cd96243dae899b","target":"record","created_at":"2026-05-18T03:26:22Z","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":"0421edcc73bfe34133cf1e4c98bb36edc0383ee2993e4340704f4ac988db4e69","cross_cats_sorted":["cs.CC","cs.NI","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-06T18:19:17Z","title_canon_sha256":"c1d6e9c4b9d2db00eb77ba7e4bc184ef253dc088a7602609e7e2696d9b0a622f"},"schema_version":"1.0","source":{"id":"1305.1295","kind":"arxiv","version":1}},"canonical_sha256":"6e3459822f14871254943dd4651bbb26465ff64a2658b51199d4b2dadaeeabff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e3459822f14871254943dd4651bbb26465ff64a2658b51199d4b2dadaeeabff","first_computed_at":"2026-05-18T03:26:22.078328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:22.078328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VB7SZl8Ck4f2ynMZdV2P2xhLNTk4yG/u+0QlEx6CGH56rK/FCDy+16RSOol51qkAWMSKKkA+l4zVdBdEga/1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:22.079065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28cb2299d451263d3484225eec4b676defd79930f883940da3cd96243dae899b","sha256:09ffd6b6a605684703db203ab1624e543f48f8f128b5d20192507b21f798e4fb"],"state_sha256":"36032784d6bb091f391344ca1ce89412fde89ab2b92309e9015f4c3d3a0eb1ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7pAMy75Fs7nY9HHOZZmeBsGpAHHxq+doiGPNexbR3VmpuxqoD4t5tJpdIspEUHLaQBzB4k5ubiAj8MQukdJTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:44:01.223506Z","bundle_sha256":"8b6a2f442066efef00252d5acad448718b7f635b840b225437a4b9db43e15541"}}