{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FKFNV5M3TWOOZVKPGEBIKCRFNJ","short_pith_number":"pith:FKFNV5M3","canonical_record":{"source":{"id":"1512.00832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-02T20:27:00Z","cross_cats_sorted":[],"title_canon_sha256":"fbccb475454e9b2c81a2b089687fdb4d9f61955a15eb93afb6471f0f0c916448","abstract_canon_sha256":"a46afc1a215c78eca0ced6b74dac01267974cc1d8b30d1a7566c99ccec2ca1b3"},"schema_version":"1.0"},"canonical_sha256":"2a8adaf59b9d9cecd54f3102850a256a4054b2d4383a9328600fd080b0ff5366","source":{"kind":"arxiv","id":"1512.00832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00832","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00832v1","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00832","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"FKFNV5M3TWOO","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FKFNV5M3TWOOZVKP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FKFNV5M3","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FKFNV5M3TWOOZVKPGEBIKCRFNJ","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-02T20:27:00Z","cross_cats_sorted":[],"title_canon_sha256":"fbccb475454e9b2c81a2b089687fdb4d9f61955a15eb93afb6471f0f0c916448","abstract_canon_sha256":"a46afc1a215c78eca0ced6b74dac01267974cc1d8b30d1a7566c99ccec2ca1b3"},"schema_version":"1.0"},"canonical_sha256":"2a8adaf59b9d9cecd54f3102850a256a4054b2d4383a9328600fd080b0ff5366","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:25.007113Z","signature_b64":"B3IBVtsYp3kNXHjsrX15AX6dRjWoX4Ma6bNn1W988uI74rgx83dqda+chBEENsZUtEKtHtVcUlZ7fKqIvmRYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a8adaf59b9d9cecd54f3102850a256a4054b2d4383a9328600fd080b0ff5366","last_reissued_at":"2026-05-18T01:25:25.006670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:25.006670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00832","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":"2026-05-18T01:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GiP5I5TCZAASVLlbOi4a09u+H3ANdT0taapNbBJQKcV53jeyHyoidO04C2gJusOUAVMar2iblVvXGQkMPrJuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:06:08.178016Z"},"content_sha256":"b16a62a39db459c6c4059fd9ef302459586a022a62026ce9af8e80e93f1b5581","schema_version":"1.0","event_id":"sha256:b16a62a39db459c6c4059fd9ef302459586a022a62026ce9af8e80e93f1b5581"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FKFNV5M3TWOOZVKPGEBIKCRFNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spread of infections on evolving scale-free networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Jacob, Peter M\\\"orters","submitted_at":"2015-12-02T20:27:00Z","abstract_excerpt":"We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most like the square root of the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast to that of the contac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00832","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":"2026-05-18T01:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Un7nDdJf2tZacNr+1xK0OR6c/ToPptyswPabCerRBZTfPgaWR3YHTCnXS0+CwpPhuzsK3QPwlmNFIbfesTOYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:06:08.178367Z"},"content_sha256":"e0fa45f512fb300983317a2ab1e3f50040071c0cfe89254ae91094d097e2df90","schema_version":"1.0","event_id":"sha256:e0fa45f512fb300983317a2ab1e3f50040071c0cfe89254ae91094d097e2df90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ/bundle.json","state_url":"https://pith.science/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ/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":"2026-06-28T09:06:08Z","links":{"resolver":"https://pith.science/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ","bundle":"https://pith.science/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ/bundle.json","state":"https://pith.science/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FKFNV5M3TWOOZVKPGEBIKCRFNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FKFNV5M3TWOOZVKPGEBIKCRFNJ","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":"a46afc1a215c78eca0ced6b74dac01267974cc1d8b30d1a7566c99ccec2ca1b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-02T20:27:00Z","title_canon_sha256":"fbccb475454e9b2c81a2b089687fdb4d9f61955a15eb93afb6471f0f0c916448"},"schema_version":"1.0","source":{"id":"1512.00832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00832","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00832v1","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00832","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"FKFNV5M3TWOO","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FKFNV5M3TWOOZVKP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FKFNV5M3","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:e0fa45f512fb300983317a2ab1e3f50040071c0cfe89254ae91094d097e2df90","target":"graph","created_at":"2026-05-18T01:25:25Z","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 study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most like the square root of the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast to that of the contac","authors_text":"Emmanuel Jacob, Peter M\\\"orters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-02T20:27:00Z","title":"The spread of infections on evolving scale-free networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00832","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:b16a62a39db459c6c4059fd9ef302459586a022a62026ce9af8e80e93f1b5581","target":"record","created_at":"2026-05-18T01:25:25Z","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":"a46afc1a215c78eca0ced6b74dac01267974cc1d8b30d1a7566c99ccec2ca1b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-02T20:27:00Z","title_canon_sha256":"fbccb475454e9b2c81a2b089687fdb4d9f61955a15eb93afb6471f0f0c916448"},"schema_version":"1.0","source":{"id":"1512.00832","kind":"arxiv","version":1}},"canonical_sha256":"2a8adaf59b9d9cecd54f3102850a256a4054b2d4383a9328600fd080b0ff5366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a8adaf59b9d9cecd54f3102850a256a4054b2d4383a9328600fd080b0ff5366","first_computed_at":"2026-05-18T01:25:25.006670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:25.006670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3IBVtsYp3kNXHjsrX15AX6dRjWoX4Ma6bNn1W988uI74rgx83dqda+chBEENsZUtEKtHtVcUlZ7fKqIvmRYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:25.007113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b16a62a39db459c6c4059fd9ef302459586a022a62026ce9af8e80e93f1b5581","sha256:e0fa45f512fb300983317a2ab1e3f50040071c0cfe89254ae91094d097e2df90"],"state_sha256":"6829066596177d58364abc225b336835a2f72441043851173bb003837f358607"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2INfuWTabrNuNvBQ3g0hLzMNzZ80DnBt9douEMPcghET/ZKYyNitJWEKQjwdUbmNsNdg6KdrV+zJ/Pslmd0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:06:08.180382Z","bundle_sha256":"fcfea7a0613a62d42c306576eaf20afb021b82268aa0ea41f195ca803513a14a"}}