{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5DNRAE6C5CCWDDKCOVZSUTY65B","short_pith_number":"pith:5DNRAE6C","canonical_record":{"source":{"id":"1906.09394","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-06-22T06:10:17Z","cross_cats_sorted":["cond-mat.stat-mech","math.CO","nlin.AO","physics.soc-ph"],"title_canon_sha256":"7d616d71b9c4c140b419cd613515d30f254165865f921e2427fd65ef7032da4d","abstract_canon_sha256":"d06b0b6f2631e6c64d62ef67c39a2bdb9cedeffe5423f816367616cd01e0728e"},"schema_version":"1.0"},"canonical_sha256":"e8db1013c2e885618d4275732a4f1ee87722af397f65ec8e278e7d1d77eca9e3","source":{"kind":"arxiv","id":"1906.09394","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09394","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09394v2","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09394","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"pith_short_12","alias_value":"5DNRAE6C5CCW","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"pith_short_16","alias_value":"5DNRAE6C5CCWDDKC","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"pith_short_8","alias_value":"5DNRAE6C","created_at":"2026-07-05T02:13:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5DNRAE6C5CCWDDKCOVZSUTY65B","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09394","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-06-22T06:10:17Z","cross_cats_sorted":["cond-mat.stat-mech","math.CO","nlin.AO","physics.soc-ph"],"title_canon_sha256":"7d616d71b9c4c140b419cd613515d30f254165865f921e2427fd65ef7032da4d","abstract_canon_sha256":"d06b0b6f2631e6c64d62ef67c39a2bdb9cedeffe5423f816367616cd01e0728e"},"schema_version":"1.0"},"canonical_sha256":"e8db1013c2e885618d4275732a4f1ee87722af397f65ec8e278e7d1d77eca9e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:13:41.964468Z","signature_b64":"zM8GsFEBxHNU9lDVs3r1ZdrFHd8MU+mrERA607GR2WMxdln+5x7gBDqwjzCRWxMZoSdPbz51KslKUhZWb+BHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8db1013c2e885618d4275732a4f1ee87722af397f65ec8e278e7d1d77eca9e3","last_reissued_at":"2026-07-05T02:13:41.964097Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:13:41.964097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09394","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":"2026-07-05T02:13:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRkt0qotZPsflMUJEhXV5PpjHxNoBMc/AqQUl94bfyaMaP8u5w2MYqdLfmogsBr1/rwIS0Oekr8zGxDt/INwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:58:05.872446Z"},"content_sha256":"b2b2ea5f735d1405e7a647b114d5ff2ebec2e8eead7d885e1b3b6473f46a85d8","schema_version":"1.0","event_id":"sha256:b2b2ea5f735d1405e7a647b114d5ff2ebec2e8eead7d885e1b3b6473f46a85d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5DNRAE6C5CCWDDKCOVZSUTY65B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO","nlin.AO","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Mason A Porter, Xinzhe Zuo","submitted_at":"2019-06-22T06:10:17Z","abstract_excerpt":"The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09394","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.09394/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:13:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ioOT1vheshgt3tCPurLDI0Dj9vF9+YDdRzOE6/tOqsfdVVi/QV6FGfa2NfC4B57oboFpjjWnKWvUGpXOkEKlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:58:05.872978Z"},"content_sha256":"840f5818c2be102e514ee41a5c06d03c57e6252fac349f3bdf73ec9cf63fc256","schema_version":"1.0","event_id":"sha256:840f5818c2be102e514ee41a5c06d03c57e6252fac349f3bdf73ec9cf63fc256"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DNRAE6C5CCWDDKCOVZSUTY65B/bundle.json","state_url":"https://pith.science/pith/5DNRAE6C5CCWDDKCOVZSUTY65B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DNRAE6C5CCWDDKCOVZSUTY65B/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":"2026-08-19T22:58:05Z","links":{"resolver":"https://pith.science/pith/5DNRAE6C5CCWDDKCOVZSUTY65B","bundle":"https://pith.science/pith/5DNRAE6C5CCWDDKCOVZSUTY65B/bundle.json","state":"https://pith.science/pith/5DNRAE6C5CCWDDKCOVZSUTY65B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DNRAE6C5CCWDDKCOVZSUTY65B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5DNRAE6C5CCWDDKCOVZSUTY65B","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":"d06b0b6f2631e6c64d62ef67c39a2bdb9cedeffe5423f816367616cd01e0728e","cross_cats_sorted":["cond-mat.stat-mech","math.CO","nlin.AO","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-06-22T06:10:17Z","title_canon_sha256":"7d616d71b9c4c140b419cd613515d30f254165865f921e2427fd65ef7032da4d"},"schema_version":"1.0","source":{"id":"1906.09394","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09394","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09394v2","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09394","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"pith_short_12","alias_value":"5DNRAE6C5CCW","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"pith_short_16","alias_value":"5DNRAE6C5CCWDDKC","created_at":"2026-07-05T02:13:41Z"},{"alias_kind":"pith_short_8","alias_value":"5DNRAE6C","created_at":"2026-07-05T02:13:41Z"}],"graph_snapshots":[{"event_id":"sha256:840f5818c2be102e514ee41a5c06d03c57e6252fac349f3bdf73ec9cf63fc256","target":"graph","created_at":"2026-07-05T02:13:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1906.09394/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays","authors_text":"Mason A Porter, Xinzhe Zuo","cross_cats":["cond-mat.stat-mech","math.CO","nlin.AO","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-06-22T06:10:17Z","title":"Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09394","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:b2b2ea5f735d1405e7a647b114d5ff2ebec2e8eead7d885e1b3b6473f46a85d8","target":"record","created_at":"2026-07-05T02:13:41Z","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":"d06b0b6f2631e6c64d62ef67c39a2bdb9cedeffe5423f816367616cd01e0728e","cross_cats_sorted":["cond-mat.stat-mech","math.CO","nlin.AO","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-06-22T06:10:17Z","title_canon_sha256":"7d616d71b9c4c140b419cd613515d30f254165865f921e2427fd65ef7032da4d"},"schema_version":"1.0","source":{"id":"1906.09394","kind":"arxiv","version":2}},"canonical_sha256":"e8db1013c2e885618d4275732a4f1ee87722af397f65ec8e278e7d1d77eca9e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8db1013c2e885618d4275732a4f1ee87722af397f65ec8e278e7d1d77eca9e3","first_computed_at":"2026-07-05T02:13:41.964097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:41.964097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zM8GsFEBxHNU9lDVs3r1ZdrFHd8MU+mrERA607GR2WMxdln+5x7gBDqwjzCRWxMZoSdPbz51KslKUhZWb+BHDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:41.964468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09394","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b2ea5f735d1405e7a647b114d5ff2ebec2e8eead7d885e1b3b6473f46a85d8","sha256:840f5818c2be102e514ee41a5c06d03c57e6252fac349f3bdf73ec9cf63fc256"],"state_sha256":"2d0a4fa6c61757b3f5aef05fc85b258b79e6d562454a96bc22855ee2818c9364"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edU47kgsSsu2hUG6k2jO7Sh5p5CrqHKnOn0x7ApLt+0fFsXPgtLkjuIkYSX2hw+Da9rVqMMIXkhHNc4szXTzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:58:05.876805Z","bundle_sha256":"7c44096faa42f70e66037c86da392fa7b5d74c203a4e018ace732c154ea341d6"}}