{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:C54DALD2GFTCWUTSTS3J7CRNC4","short_pith_number":"pith:C54DALD2","canonical_record":{"source":{"id":"1403.2878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-03-12T10:36:29Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"43875cb8628ba4ae473430c5ecd68e2db0c4a2b80cf5401dda5f893743a7afdd","abstract_canon_sha256":"df0b341b46115709bcd0626b8db995b80d351535f5d3f10fcc914ff715bf49eb"},"schema_version":"1.0"},"canonical_sha256":"1778302c7a31662b52729cb69f8a2d170b53a1b0c2be0bdddfa7074c37717c83","source":{"kind":"arxiv","id":"1403.2878","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2878","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2878v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2878","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"C54DALD2GFTC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C54DALD2GFTCWUTS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C54DALD2","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:C54DALD2GFTCWUTSTS3J7CRNC4","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-03-12T10:36:29Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"43875cb8628ba4ae473430c5ecd68e2db0c4a2b80cf5401dda5f893743a7afdd","abstract_canon_sha256":"df0b341b46115709bcd0626b8db995b80d351535f5d3f10fcc914ff715bf49eb"},"schema_version":"1.0"},"canonical_sha256":"1778302c7a31662b52729cb69f8a2d170b53a1b0c2be0bdddfa7074c37717c83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:33.688384Z","signature_b64":"zSniXF65+cqH1WmHKSCnn8V5UY8vSNqbO+Sd5vSw9m2UWS7N8mwLFexEocseatJL7e8fhvV50LUzPKI7YzpbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1778302c7a31662b52729cb69f8a2d170b53a1b0c2be0bdddfa7074c37717c83","last_reissued_at":"2026-05-18T02:56:33.687622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:33.687622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2878","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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oMR7S+ftMb/a6+1r5t8Cy/XGZ/FkSKwHtdi+wm/NPmEGPexWIK5FmWs/CjunQUque13N/yMgjJzZsJCweO9qAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:51:00.441082Z"},"content_sha256":"1cd7791248a4b99d41850c882ec6a6d31a9437b263deaef67985c968b03b1c26","schema_version":"1.0","event_id":"sha256:1cd7791248a4b99d41850c882ec6a6d31a9437b263deaef67985c968b03b1c26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:C54DALD2GFTCWUTSTS3J7CRNC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Markovian stochastic epidemics in extremely heterogeneous populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-bio.PE","authors_text":"Thomas House","submitted_at":"2014-03-12T10:36:29Z","abstract_excerpt":"A feature often observed in epidemiological networks is significant heterogeneity in degree. A popular modelling approach to this has been to consider large populations with highly heterogeneous discrete contact rates. This paper defines an individual-level non-Markovian stochastic process that converges on standard ODE models of such populations in the appropriate asymptotic limit. A generalised Sellke construction is derived for this model, and this is then used to consider final outcomes in the case where heterogeneity follows a truncated Zipf distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2878","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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnxG8IXJcyeUg9572EsHN5630rg0lhTtd825o4w1ZgsAV3X+Ytf4dWPx2igId/93+fya/ggkCxOkJYxcCpJ+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:51:00.441772Z"},"content_sha256":"59b266fe6fb6ead915bb3ca6e1a821da9f7500f2dda7428611b72bf00f0f79e5","schema_version":"1.0","event_id":"sha256:59b266fe6fb6ead915bb3ca6e1a821da9f7500f2dda7428611b72bf00f0f79e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C54DALD2GFTCWUTSTS3J7CRNC4/bundle.json","state_url":"https://pith.science/pith/C54DALD2GFTCWUTSTS3J7CRNC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C54DALD2GFTCWUTSTS3J7CRNC4/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":"2026-06-06T18:51:00Z","links":{"resolver":"https://pith.science/pith/C54DALD2GFTCWUTSTS3J7CRNC4","bundle":"https://pith.science/pith/C54DALD2GFTCWUTSTS3J7CRNC4/bundle.json","state":"https://pith.science/pith/C54DALD2GFTCWUTSTS3J7CRNC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C54DALD2GFTCWUTSTS3J7CRNC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C54DALD2GFTCWUTSTS3J7CRNC4","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":"df0b341b46115709bcd0626b8db995b80d351535f5d3f10fcc914ff715bf49eb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-03-12T10:36:29Z","title_canon_sha256":"43875cb8628ba4ae473430c5ecd68e2db0c4a2b80cf5401dda5f893743a7afdd"},"schema_version":"1.0","source":{"id":"1403.2878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2878","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2878v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2878","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"C54DALD2GFTC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C54DALD2GFTCWUTS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C54DALD2","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:59b266fe6fb6ead915bb3ca6e1a821da9f7500f2dda7428611b72bf00f0f79e5","target":"graph","created_at":"2026-05-18T02:56:33Z","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":"A feature often observed in epidemiological networks is significant heterogeneity in degree. A popular modelling approach to this has been to consider large populations with highly heterogeneous discrete contact rates. This paper defines an individual-level non-Markovian stochastic process that converges on standard ODE models of such populations in the appropriate asymptotic limit. A generalised Sellke construction is derived for this model, and this is then used to consider final outcomes in the case where heterogeneity follows a truncated Zipf distribution.","authors_text":"Thomas House","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-03-12T10:36:29Z","title":"Non-Markovian stochastic epidemics in extremely heterogeneous populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2878","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":"sha256:1cd7791248a4b99d41850c882ec6a6d31a9437b263deaef67985c968b03b1c26","target":"record","created_at":"2026-05-18T02:56:33Z","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":"df0b341b46115709bcd0626b8db995b80d351535f5d3f10fcc914ff715bf49eb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-03-12T10:36:29Z","title_canon_sha256":"43875cb8628ba4ae473430c5ecd68e2db0c4a2b80cf5401dda5f893743a7afdd"},"schema_version":"1.0","source":{"id":"1403.2878","kind":"arxiv","version":1}},"canonical_sha256":"1778302c7a31662b52729cb69f8a2d170b53a1b0c2be0bdddfa7074c37717c83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1778302c7a31662b52729cb69f8a2d170b53a1b0c2be0bdddfa7074c37717c83","first_computed_at":"2026-05-18T02:56:33.687622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:33.687622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zSniXF65+cqH1WmHKSCnn8V5UY8vSNqbO+Sd5vSw9m2UWS7N8mwLFexEocseatJL7e8fhvV50LUzPKI7YzpbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:33.688384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cd7791248a4b99d41850c882ec6a6d31a9437b263deaef67985c968b03b1c26","sha256:59b266fe6fb6ead915bb3ca6e1a821da9f7500f2dda7428611b72bf00f0f79e5"],"state_sha256":"4724de456f9cc2a25b7bf0b661fd0d57dc183e8ea4789496a518156b5da4756c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClueftSqw0jZSCDouFJG0hSSOBsXJsbLtIrXPwY+oQqakTOA2kvv6zhUkHY35cYkJ2gJEamgIUkPgVBej9JfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:51:00.445402Z","bundle_sha256":"fddea1d5149214b8d66117c29e630834d0199261ffeb988fd69da78ad7d4c6a0"}}