{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6BEOKNVUKQ6FVUM3CZ3N7TR3UP","short_pith_number":"pith:6BEOKNVU","canonical_record":{"source":{"id":"1306.0715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-04T10:01:30Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"bd141f08b17f6301d4e2a9bc38ca78c9c6b3a9ec41b6bf5735c2b6a5a80fa86a","abstract_canon_sha256":"f3a4fa5bf2bb85ce2a52ad5bc285024096297544695c489b7c047cfbd03e9815"},"schema_version":"1.0"},"canonical_sha256":"f048e536b4543c5ad19b1676dfce3ba3db574f3800d347d0c8bbe40e28336ad9","source":{"kind":"arxiv","id":"1306.0715","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0715","created_at":"2026-05-18T01:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0715v1","created_at":"2026-05-18T01:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0715","created_at":"2026-05-18T01:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"6BEOKNVUKQ6F","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6BEOKNVUKQ6FVUM3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6BEOKNVU","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6BEOKNVUKQ6FVUM3CZ3N7TR3UP","target":"record","payload":{"canonical_record":{"source":{"id":"1306.0715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-04T10:01:30Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"bd141f08b17f6301d4e2a9bc38ca78c9c6b3a9ec41b6bf5735c2b6a5a80fa86a","abstract_canon_sha256":"f3a4fa5bf2bb85ce2a52ad5bc285024096297544695c489b7c047cfbd03e9815"},"schema_version":"1.0"},"canonical_sha256":"f048e536b4543c5ad19b1676dfce3ba3db574f3800d347d0c8bbe40e28336ad9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:33.119067Z","signature_b64":"s/rHmh9SmsEVH+/IFJ95EppFN+NkJvg3QaswE9p6DuanoLJVHabjGUB2g8WdLfz9BwNgqNMQqrgZiEdUlfXrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f048e536b4543c5ad19b1676dfce3ba3db574f3800d347d0c8bbe40e28336ad9","last_reissued_at":"2026-05-18T01:49:33.118653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:33.118653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.0715","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":"2026-05-18T01:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AEmLfjfMoHDdsUDQl++RY1lyW8i/rhbYHreoJfNNalHkYsh8NDYyDVdei6WEkU3Xq6PrbjqfPD0mkgkVloLHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:05:37.706125Z"},"content_sha256":"b81ddedd12e7a92110b69cae04129d506883109ae40c603cd196592186d39361","schema_version":"1.0","event_id":"sha256:b81ddedd12e7a92110b69cae04129d506883109ae40c603cd196592186d39361"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6BEOKNVUKQ6FVUM3CZ3N7TR3UP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Walks on Stochastic Temporal Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Mason A. Porter, Renaud Lambiotte, Till Hoffmann","submitted_at":"2013-06-04T10:01:30Z","abstract_excerpt":"In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0715","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":"2026-05-18T01:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXLiQtiAUqSjqEqdisa/U/rXE0GwE/S7FcA/I/XTG1Ax4317MkDE5jQuL58/ChYFXJ6tPwxPmWfAHDaQRAP2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:05:37.706885Z"},"content_sha256":"26e4476f16e218b55c92c4dff324523c213ff67ee5ed29a46e12543bc3afdca0","schema_version":"1.0","event_id":"sha256:26e4476f16e218b55c92c4dff324523c213ff67ee5ed29a46e12543bc3afdca0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP/bundle.json","state_url":"https://pith.science/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP/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":"2026-06-10T11:05:37Z","links":{"resolver":"https://pith.science/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP","bundle":"https://pith.science/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP/bundle.json","state":"https://pith.science/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BEOKNVUKQ6FVUM3CZ3N7TR3UP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6BEOKNVUKQ6FVUM3CZ3N7TR3UP","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":"f3a4fa5bf2bb85ce2a52ad5bc285024096297544695c489b7c047cfbd03e9815","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-04T10:01:30Z","title_canon_sha256":"bd141f08b17f6301d4e2a9bc38ca78c9c6b3a9ec41b6bf5735c2b6a5a80fa86a"},"schema_version":"1.0","source":{"id":"1306.0715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0715","created_at":"2026-05-18T01:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0715v1","created_at":"2026-05-18T01:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0715","created_at":"2026-05-18T01:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"6BEOKNVUKQ6F","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6BEOKNVUKQ6FVUM3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6BEOKNVU","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:26e4476f16e218b55c92c4dff324523c213ff67ee5ed29a46e12543bc3afdca0","target":"graph","created_at":"2026-05-18T01:49:33Z","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 the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a","authors_text":"Mason A. Porter, Renaud Lambiotte, Till Hoffmann","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-04T10:01:30Z","title":"Random Walks on Stochastic Temporal Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0715","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:b81ddedd12e7a92110b69cae04129d506883109ae40c603cd196592186d39361","target":"record","created_at":"2026-05-18T01:49:33Z","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":"f3a4fa5bf2bb85ce2a52ad5bc285024096297544695c489b7c047cfbd03e9815","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-04T10:01:30Z","title_canon_sha256":"bd141f08b17f6301d4e2a9bc38ca78c9c6b3a9ec41b6bf5735c2b6a5a80fa86a"},"schema_version":"1.0","source":{"id":"1306.0715","kind":"arxiv","version":1}},"canonical_sha256":"f048e536b4543c5ad19b1676dfce3ba3db574f3800d347d0c8bbe40e28336ad9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f048e536b4543c5ad19b1676dfce3ba3db574f3800d347d0c8bbe40e28336ad9","first_computed_at":"2026-05-18T01:49:33.118653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:33.118653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/rHmh9SmsEVH+/IFJ95EppFN+NkJvg3QaswE9p6DuanoLJVHabjGUB2g8WdLfz9BwNgqNMQqrgZiEdUlfXrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:33.119067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b81ddedd12e7a92110b69cae04129d506883109ae40c603cd196592186d39361","sha256:26e4476f16e218b55c92c4dff324523c213ff67ee5ed29a46e12543bc3afdca0"],"state_sha256":"906f766134022a0023775ddf044a4732f26fdc0fc527ea176295ecf42db2e38c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/hml8z1fwHSQZptlYXW0mUIgZtcz4Wg9+if52Zze2zP1nkaTzDIGUDCkxSsXlsKZ0iVbpKQJ+88gOjDQGJcfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:05:37.710893Z","bundle_sha256":"ae99854adfdcc308686ec26ecc2d35fffadd9d9a03146f4702051a383559a6f9"}}