{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HODPSD4PF32MEVTT2PF2FS3A6W","short_pith_number":"pith:HODPSD4P","canonical_record":{"source":{"id":"1205.1682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-05-08T12:54:47Z","cross_cats_sorted":["cs.DS","physics.soc-ph"],"title_canon_sha256":"925e127dfac87896110f04edcfa1b8872adcd0ac8ee41c53f63e3fe629f3ba71","abstract_canon_sha256":"70128be8058f4a1613898beffd05d4ad6148609f7a213af3536ce03769031b83"},"schema_version":"1.0"},"canonical_sha256":"3b86f90f8f2ef4c25673d3cba2cb60f58c0c69bfce8ce4642416fcbb306768b1","source":{"kind":"arxiv","id":"1205.1682","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1682","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1682v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1682","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"HODPSD4PF32M","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HODPSD4PF32MEVTT","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HODPSD4P","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HODPSD4PF32MEVTT2PF2FS3A6W","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-05-08T12:54:47Z","cross_cats_sorted":["cs.DS","physics.soc-ph"],"title_canon_sha256":"925e127dfac87896110f04edcfa1b8872adcd0ac8ee41c53f63e3fe629f3ba71","abstract_canon_sha256":"70128be8058f4a1613898beffd05d4ad6148609f7a213af3536ce03769031b83"},"schema_version":"1.0"},"canonical_sha256":"3b86f90f8f2ef4c25673d3cba2cb60f58c0c69bfce8ce4642416fcbb306768b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:09.442500Z","signature_b64":"qG7OaBAPGmXpwDvZw9z5BRLXGG7pt4W+iYJrCShOdjJjdIwwZL10lWXKKaJgGvnfBTqoI6kl6J2qDs/uTsbUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b86f90f8f2ef4c25673d3cba2cb60f58c0c69bfce8ce4642416fcbb306768b1","last_reissued_at":"2026-05-18T03:56:09.441775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:09.441775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1682","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIATmEw0DgJI5eIqp1bPJiZRLjzhrzZKACFFJFBPumjOnr42ExQT2XDI5pMqHUzHwuXuTFK5wvDq9/GlHc3iCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:15:49.054026Z"},"content_sha256":"be5279d8e5ae245b7e0f4ea9a43a9ce7a5b4a4c66e2d490d0ce192db6ad7c93b","schema_version":"1.0","event_id":"sha256:be5279d8e5ae245b7e0f4ea9a43a9ce7a5b4a4c66e2d490d0ce192db6ad7c93b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HODPSD4PF32MEVTT2PF2FS3A6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Influence Maximization in Continuous Time Diffusion Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Bernhard Sch\\\"olkopf, Manuel Gomez Rodriguez","submitted_at":"2012-05-08T12:54:47Z","abstract_excerpt":"The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date. To this end, given a network and its temporal dynamics, we first describe how continuous time Markov chains allow us to analytically compute the average total number of nodes reached by a diffusion process starting in a set of source nodes. We then show that selecting the set of most influential so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1682","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mb7a+kXUT+BpbcpM+X2bz9FhisjLg6KIKjz1eqZKUTtidU6fLwjMBRPAsLsMhHn0A2R3T1jh9KfuFaWDm9efBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:15:49.054407Z"},"content_sha256":"6fbba8a0767ed9935c7a0eb743cf44c89acedefa42df2c70c98124ca41425acf","schema_version":"1.0","event_id":"sha256:6fbba8a0767ed9935c7a0eb743cf44c89acedefa42df2c70c98124ca41425acf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HODPSD4PF32MEVTT2PF2FS3A6W/bundle.json","state_url":"https://pith.science/pith/HODPSD4PF32MEVTT2PF2FS3A6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HODPSD4PF32MEVTT2PF2FS3A6W/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":"2026-06-07T16:15:49Z","links":{"resolver":"https://pith.science/pith/HODPSD4PF32MEVTT2PF2FS3A6W","bundle":"https://pith.science/pith/HODPSD4PF32MEVTT2PF2FS3A6W/bundle.json","state":"https://pith.science/pith/HODPSD4PF32MEVTT2PF2FS3A6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HODPSD4PF32MEVTT2PF2FS3A6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HODPSD4PF32MEVTT2PF2FS3A6W","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":"70128be8058f4a1613898beffd05d4ad6148609f7a213af3536ce03769031b83","cross_cats_sorted":["cs.DS","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-05-08T12:54:47Z","title_canon_sha256":"925e127dfac87896110f04edcfa1b8872adcd0ac8ee41c53f63e3fe629f3ba71"},"schema_version":"1.0","source":{"id":"1205.1682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1682","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1682v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1682","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"HODPSD4PF32M","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HODPSD4PF32MEVTT","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HODPSD4P","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:6fbba8a0767ed9935c7a0eb743cf44c89acedefa42df2c70c98124ca41425acf","target":"graph","created_at":"2026-05-18T03:56:09Z","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":"The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date. To this end, given a network and its temporal dynamics, we first describe how continuous time Markov chains allow us to analytically compute the average total number of nodes reached by a diffusion process starting in a set of source nodes. We then show that selecting the set of most influential so","authors_text":"Bernhard Sch\\\"olkopf, Manuel Gomez Rodriguez","cross_cats":["cs.DS","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-05-08T12:54:47Z","title":"Influence Maximization in Continuous Time Diffusion Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1682","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:be5279d8e5ae245b7e0f4ea9a43a9ce7a5b4a4c66e2d490d0ce192db6ad7c93b","target":"record","created_at":"2026-05-18T03:56:09Z","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":"70128be8058f4a1613898beffd05d4ad6148609f7a213af3536ce03769031b83","cross_cats_sorted":["cs.DS","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-05-08T12:54:47Z","title_canon_sha256":"925e127dfac87896110f04edcfa1b8872adcd0ac8ee41c53f63e3fe629f3ba71"},"schema_version":"1.0","source":{"id":"1205.1682","kind":"arxiv","version":1}},"canonical_sha256":"3b86f90f8f2ef4c25673d3cba2cb60f58c0c69bfce8ce4642416fcbb306768b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b86f90f8f2ef4c25673d3cba2cb60f58c0c69bfce8ce4642416fcbb306768b1","first_computed_at":"2026-05-18T03:56:09.441775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.441775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qG7OaBAPGmXpwDvZw9z5BRLXGG7pt4W+iYJrCShOdjJjdIwwZL10lWXKKaJgGvnfBTqoI6kl6J2qDs/uTsbUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.442500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5279d8e5ae245b7e0f4ea9a43a9ce7a5b4a4c66e2d490d0ce192db6ad7c93b","sha256:6fbba8a0767ed9935c7a0eb743cf44c89acedefa42df2c70c98124ca41425acf"],"state_sha256":"c93a86e641e18088c89c53c8eaf141cdaecbcb49f4d01eaaab12eef669935407"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZddpOBO1F4UrBBFU7S4YzmNBwRg1DaJqR6vp3hb6ozgZ6IWeMqDYKiaL42Pnv9/uwl0jt+zMCxUqK3qv/MZ5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:15:49.057367Z","bundle_sha256":"3282e761dac8a7a7d0e89112938d0c3fe09eebf6bf7167e3835202c8103694de"}}