{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5IVDDKRADFTHI5JHAT422EFTX2","short_pith_number":"pith:5IVDDKRA","canonical_record":{"source":{"id":"1509.01860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-06T22:03:35Z","cross_cats_sorted":["cs.SI","physics.data-an"],"title_canon_sha256":"8699e90833defeeb1a64405cd356cf2faadffde5518bfd2b4a81345eed960bbf","abstract_canon_sha256":"41e0071d01b94856906ddb0ba1d2268fcdb3f1f24ef50e5b6923876649a96930"},"schema_version":"1.0"},"canonical_sha256":"ea2a31aa20196674752704f9ad10b3be8d6f52e17d740667c3195a1525055e6e","source":{"kind":"arxiv","id":"1509.01860","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01860","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01860v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01860","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"5IVDDKRADFTH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5IVDDKRADFTHI5JH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5IVDDKRA","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5IVDDKRADFTHI5JHAT422EFTX2","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-06T22:03:35Z","cross_cats_sorted":["cs.SI","physics.data-an"],"title_canon_sha256":"8699e90833defeeb1a64405cd356cf2faadffde5518bfd2b4a81345eed960bbf","abstract_canon_sha256":"41e0071d01b94856906ddb0ba1d2268fcdb3f1f24ef50e5b6923876649a96930"},"schema_version":"1.0"},"canonical_sha256":"ea2a31aa20196674752704f9ad10b3be8d6f52e17d740667c3195a1525055e6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.355898Z","signature_b64":"5evsbkaG7FG334LeI2BijXDlzv570Izn9b/FuF/UvBxEjy9zJB7Kwja7JskQYChjw3m2RezDZh+x9K0ibdlUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea2a31aa20196674752704f9ad10b3be8d6f52e17d740667c3195a1525055e6e","last_reissued_at":"2026-05-18T01:33:50.355238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.355238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01860","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veohYTzZwTY9KgxoLymm23ZvIRiohbTuVk9RuOFpQUIADhR0JDK39L5JkW/bvkdXE+4avPcX5LUiNKQ48iLiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:21:18.911329Z"},"content_sha256":"6121b4b0623b8e386737080395665d082874878659ad06d8a84ed22b4fbd6e23","schema_version":"1.0","event_id":"sha256:6121b4b0623b8e386737080395665d082874878659ad06d8a84ed22b4fbd6e23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5IVDDKRADFTHI5JHAT422EFTX2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sensitivity analysis of a branching process evolving on a network with application in epidemiology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"Gautier Krings, Jean-Charles Delvenne, Sophie Hautphenne, Vincent D. Blondel","submitted_at":"2015-09-06T22:03:35Z","abstract_excerpt":"We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the network. We then apply our results to the early stages of an influenza-like epidemic spreading among a set of cities connected by air routes in the United States. We also consider vaccination and analyze the sensitivity of the total size of the epidemic with respect to the fraction of vaccinated people. Our analysis shows that the epidemic growth is more se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01860","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOGLkdcqIOWnhd6IelBmglsEqXkTop16cGek9PgOUjt6NSkAneWVY/TiHQypwLaxT5FN6QzYEucTC1m1HtpaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:21:18.911680Z"},"content_sha256":"0864701ccc90b42113b4105254da524b8d9ada2d5168503e0358e1568c8ca97b","schema_version":"1.0","event_id":"sha256:0864701ccc90b42113b4105254da524b8d9ada2d5168503e0358e1568c8ca97b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5IVDDKRADFTHI5JHAT422EFTX2/bundle.json","state_url":"https://pith.science/pith/5IVDDKRADFTHI5JHAT422EFTX2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5IVDDKRADFTHI5JHAT422EFTX2/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":"2026-06-26T13:21:18Z","links":{"resolver":"https://pith.science/pith/5IVDDKRADFTHI5JHAT422EFTX2","bundle":"https://pith.science/pith/5IVDDKRADFTHI5JHAT422EFTX2/bundle.json","state":"https://pith.science/pith/5IVDDKRADFTHI5JHAT422EFTX2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5IVDDKRADFTHI5JHAT422EFTX2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5IVDDKRADFTHI5JHAT422EFTX2","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":"41e0071d01b94856906ddb0ba1d2268fcdb3f1f24ef50e5b6923876649a96930","cross_cats_sorted":["cs.SI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-06T22:03:35Z","title_canon_sha256":"8699e90833defeeb1a64405cd356cf2faadffde5518bfd2b4a81345eed960bbf"},"schema_version":"1.0","source":{"id":"1509.01860","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01860","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01860v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01860","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"5IVDDKRADFTH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5IVDDKRADFTHI5JH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5IVDDKRA","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:0864701ccc90b42113b4105254da524b8d9ada2d5168503e0358e1568c8ca97b","target":"graph","created_at":"2026-05-18T01:33:50Z","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 perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the network. We then apply our results to the early stages of an influenza-like epidemic spreading among a set of cities connected by air routes in the United States. We also consider vaccination and analyze the sensitivity of the total size of the epidemic with respect to the fraction of vaccinated people. Our analysis shows that the epidemic growth is more se","authors_text":"Gautier Krings, Jean-Charles Delvenne, Sophie Hautphenne, Vincent D. Blondel","cross_cats":["cs.SI","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-06T22:03:35Z","title":"Sensitivity analysis of a branching process evolving on a network with application in epidemiology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01860","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":"sha256:6121b4b0623b8e386737080395665d082874878659ad06d8a84ed22b4fbd6e23","target":"record","created_at":"2026-05-18T01:33:50Z","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":"41e0071d01b94856906ddb0ba1d2268fcdb3f1f24ef50e5b6923876649a96930","cross_cats_sorted":["cs.SI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-06T22:03:35Z","title_canon_sha256":"8699e90833defeeb1a64405cd356cf2faadffde5518bfd2b4a81345eed960bbf"},"schema_version":"1.0","source":{"id":"1509.01860","kind":"arxiv","version":1}},"canonical_sha256":"ea2a31aa20196674752704f9ad10b3be8d6f52e17d740667c3195a1525055e6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea2a31aa20196674752704f9ad10b3be8d6f52e17d740667c3195a1525055e6e","first_computed_at":"2026-05-18T01:33:50.355238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:50.355238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5evsbkaG7FG334LeI2BijXDlzv570Izn9b/FuF/UvBxEjy9zJB7Kwja7JskQYChjw3m2RezDZh+x9K0ibdlUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:50.355898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01860","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6121b4b0623b8e386737080395665d082874878659ad06d8a84ed22b4fbd6e23","sha256:0864701ccc90b42113b4105254da524b8d9ada2d5168503e0358e1568c8ca97b"],"state_sha256":"e4021bf2e4bc1cdf5e356426c6ec464a0b27b794b833b1bc135226dd8758e516"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LK4q8sx2osD1V5cZKvWa3hQ54mpI+dz0VsOKrmteNb2lxd1q9zgCeErdRoWclvJzQfQyTczp8cQLaZvsJTfCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:21:18.913927Z","bundle_sha256":"5abc105de97edd3181401990372fbc6257210c03ab662badd515f021a29b95ac"}}