{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NNKJVMJRDX5FFLJX5PBY2ULQDZ","short_pith_number":"pith:NNKJVMJR","canonical_record":{"source":{"id":"2501.12768","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-01-22T10:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"ad8fed0e20ac5a62b997da84f3821ce1f7ca8e5452a3cdfc15d0d28512c3ef1f","abstract_canon_sha256":"0f087a287e9d9434654adb58aaba003a32f1e145997d7d21fc7de8bd64eff975"},"schema_version":"1.0"},"canonical_sha256":"6b549ab1311dfa52ad37ebc38d51701e71638e5376480f906b47a5a6febd659e","source":{"kind":"arxiv","id":"2501.12768","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.12768","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"arxiv_version","alias_value":"2501.12768v1","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.12768","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"pith_short_12","alias_value":"NNKJVMJRDX5F","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"pith_short_16","alias_value":"NNKJVMJRDX5FFLJX","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"pith_short_8","alias_value":"NNKJVMJR","created_at":"2026-07-05T10:03:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NNKJVMJRDX5FFLJX5PBY2ULQDZ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.12768","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-01-22T10:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"ad8fed0e20ac5a62b997da84f3821ce1f7ca8e5452a3cdfc15d0d28512c3ef1f","abstract_canon_sha256":"0f087a287e9d9434654adb58aaba003a32f1e145997d7d21fc7de8bd64eff975"},"schema_version":"1.0"},"canonical_sha256":"6b549ab1311dfa52ad37ebc38d51701e71638e5376480f906b47a5a6febd659e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:03:58.371068Z","signature_b64":"yKr65d9SApz+0TZPLbb888v/eWq24XqP02BaJWxFViddmgM7fb7m0vrbS02NSRh2hlSjBPbcRIZymOhRdszSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b549ab1311dfa52ad37ebc38d51701e71638e5376480f906b47a5a6febd659e","last_reissued_at":"2026-07-05T10:03:58.370631Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:03:58.370631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.12768","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":"2026-07-05T10:03:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xw9FesyVqeLucb0Xw68J6xtexBtbqUJPIiJjXqD1cGjPFdsaclgUdIHLR9Jt5R2mxcm4PcS5w3YeD3qciO2KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:39:12.010014Z"},"content_sha256":"3e5538e6e903ad3924c9901ee070c29d81df1ae81f35159b3df6b70d04f7a71c","schema_version":"1.0","event_id":"sha256:3e5538e6e903ad3924c9901ee070c29d81df1ae81f35159b3df6b70d04f7a71c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NNKJVMJRDX5FFLJX5PBY2ULQDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Bayesian Modelling Framework with Model Comparison for Epidemics with Super-Spreading","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.QM","authors_text":"Hannah Craddock, Simon EF Spencer, Xavier Didelot","submitted_at":"2025-01-22T10:05:28Z","abstract_excerpt":"The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case data, the expected distribution of which is known as the offspring distribution. However, this data is seldom available. Here we introduce a multi-model framework fit to incidence time-series, data that is much more readily available. The framework consists of five discrete-time, stochastic, branching-process models of epidemics spread through a susceptible "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12768","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.12768/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":"2026-07-05T10:03:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"duKPotbiwHMagayI98Z40PlNBXoGgNsosCbGLk7wIdoj0ctTsuOWJgRLl/FpOc8kFPhTj+bouLLTSyVVybzOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:39:12.010550Z"},"content_sha256":"1089be41256aa0f00589399f2cbd84816334ce4ec4b917f0443b75095e5fcf9e","schema_version":"1.0","event_id":"sha256:1089be41256aa0f00589399f2cbd84816334ce4ec4b917f0443b75095e5fcf9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ/bundle.json","state_url":"https://pith.science/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ/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":"2026-08-04T04:39:12Z","links":{"resolver":"https://pith.science/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ","bundle":"https://pith.science/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ/bundle.json","state":"https://pith.science/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNKJVMJRDX5FFLJX5PBY2ULQDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NNKJVMJRDX5FFLJX5PBY2ULQDZ","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":"0f087a287e9d9434654adb58aaba003a32f1e145997d7d21fc7de8bd64eff975","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-01-22T10:05:28Z","title_canon_sha256":"ad8fed0e20ac5a62b997da84f3821ce1f7ca8e5452a3cdfc15d0d28512c3ef1f"},"schema_version":"1.0","source":{"id":"2501.12768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.12768","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"arxiv_version","alias_value":"2501.12768v1","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.12768","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"pith_short_12","alias_value":"NNKJVMJRDX5F","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"pith_short_16","alias_value":"NNKJVMJRDX5FFLJX","created_at":"2026-07-05T10:03:58Z"},{"alias_kind":"pith_short_8","alias_value":"NNKJVMJR","created_at":"2026-07-05T10:03:58Z"}],"graph_snapshots":[{"event_id":"sha256:1089be41256aa0f00589399f2cbd84816334ce4ec4b917f0443b75095e5fcf9e","target":"graph","created_at":"2026-07-05T10:03:58Z","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/2501.12768/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case data, the expected distribution of which is known as the offspring distribution. However, this data is seldom available. Here we introduce a multi-model framework fit to incidence time-series, data that is much more readily available. The framework consists of five discrete-time, stochastic, branching-process models of epidemics spread through a susceptible ","authors_text":"Hannah Craddock, Simon EF Spencer, Xavier Didelot","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-01-22T10:05:28Z","title":"A Bayesian Modelling Framework with Model Comparison for Epidemics with Super-Spreading"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12768","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":"sha256:3e5538e6e903ad3924c9901ee070c29d81df1ae81f35159b3df6b70d04f7a71c","target":"record","created_at":"2026-07-05T10:03:58Z","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":"0f087a287e9d9434654adb58aaba003a32f1e145997d7d21fc7de8bd64eff975","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-01-22T10:05:28Z","title_canon_sha256":"ad8fed0e20ac5a62b997da84f3821ce1f7ca8e5452a3cdfc15d0d28512c3ef1f"},"schema_version":"1.0","source":{"id":"2501.12768","kind":"arxiv","version":1}},"canonical_sha256":"6b549ab1311dfa52ad37ebc38d51701e71638e5376480f906b47a5a6febd659e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b549ab1311dfa52ad37ebc38d51701e71638e5376480f906b47a5a6febd659e","first_computed_at":"2026-07-05T10:03:58.370631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:03:58.370631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yKr65d9SApz+0TZPLbb888v/eWq24XqP02BaJWxFViddmgM7fb7m0vrbS02NSRh2hlSjBPbcRIZymOhRdszSBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:03:58.371068Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.12768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e5538e6e903ad3924c9901ee070c29d81df1ae81f35159b3df6b70d04f7a71c","sha256:1089be41256aa0f00589399f2cbd84816334ce4ec4b917f0443b75095e5fcf9e"],"state_sha256":"779f133b9cd9a796d3274cd07eb70d7d3a4f881262d606961b2da4ec466fde08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4yThTjPGe55l2IL25GtyfMSffcInYORbL7Cs8X2r5ydvHOgyGQ7w6CHuUMu6HoRzv4lOJv5uLIcEgefQ7edBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:39:12.016002Z","bundle_sha256":"0ccc63017597140efe0e70ade4e3cf064549f24c50f9293bb98d898b1296ab90"}}