{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JEIFSV3IIHTOFZ7VQDKTTPVPGP","short_pith_number":"pith:JEIFSV3I","canonical_record":{"source":{"id":"1310.0192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T09:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"90618c3901381bfa3ddc231b7c1fcba699bf3ac967e5b15bd8053adbadd9b9b1","abstract_canon_sha256":"afae0b0f2bea978e8d576d5b91a6afc4adb9d31ddaf271ad5f247fde7e571a5f"},"schema_version":"1.0"},"canonical_sha256":"491059576841e6e2e7f580d539beaf33c422dfea16856cd514359b609ae42cae","source":{"kind":"arxiv","id":"1310.0192","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0192","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0192v2","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0192","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"JEIFSV3IIHTO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JEIFSV3IIHTOFZ7V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JEIFSV3I","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JEIFSV3IIHTOFZ7VQDKTTPVPGP","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T09:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"90618c3901381bfa3ddc231b7c1fcba699bf3ac967e5b15bd8053adbadd9b9b1","abstract_canon_sha256":"afae0b0f2bea978e8d576d5b91a6afc4adb9d31ddaf271ad5f247fde7e571a5f"},"schema_version":"1.0"},"canonical_sha256":"491059576841e6e2e7f580d539beaf33c422dfea16856cd514359b609ae42cae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:01.032757Z","signature_b64":"Oc0tSHRQaIGFnmixIHttU0En8GFyFO2w6f1QgaM9SbPDLIVlOBGwI3rsNAKws/acrrcj0tMkz3o1nMF7V3VODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"491059576841e6e2e7f580d539beaf33c422dfea16856cd514359b609ae42cae","last_reissued_at":"2026-05-18T02:48:01.032240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:01.032240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0192","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x69gVZMh+MW70mLf6xw0WLWcIjkSB2pCSwSh2XrhnhAUgRB7HIAbzl7RK8/ODrzPCL31xG8f4w4nknDWXY4nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:05:39.316978Z"},"content_sha256":"dff2f37cfdd996226187f19461cb977fbf57559331fbe99aaeb9e5c351b60910","schema_version":"1.0","event_id":"sha256:dff2f37cfdd996226187f19461cb977fbf57559331fbe99aaeb9e5c351b60910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JEIFSV3IIHTOFZ7VQDKTTPVPGP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"State space collapse for critical multistage epidemics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florian Simatos","submitted_at":"2013-10-01T09:01:02Z","abstract_excerpt":"We study a multistage epidemic model which generalizes the SIR model and where infected individuals go through K>0 stages of the epidemic before being removed. An infected individual in stage k=1,...,K may infect a susceptible individual, who directly goes to stage k of the epidemic; or it may go to the next stage k+1 of the epidemic. For this model, we identify the critical regime in which we establish diffusion approximations. Surprisingly, the limiting diffusion exhibits an unusual form of state space collapse which we analyze in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0192","kind":"arxiv","version":2},"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":"2026-05-18T02:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAYtouSmX5cH++tN3rxX6j9R+ImN1wiwMJt8hsVP0XKSjZZ8AFTBhZ0u0y5/j+aam9yHvgD6kpOmJGiA2jAqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:05:39.317339Z"},"content_sha256":"ac5062ebecd27052d99c9a37061aa905b8f57936ff8fcb4e833109fd6501294f","schema_version":"1.0","event_id":"sha256:ac5062ebecd27052d99c9a37061aa905b8f57936ff8fcb4e833109fd6501294f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP/bundle.json","state_url":"https://pith.science/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP/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":"2026-05-30T06:05:39Z","links":{"resolver":"https://pith.science/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP","bundle":"https://pith.science/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP/bundle.json","state":"https://pith.science/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEIFSV3IIHTOFZ7VQDKTTPVPGP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JEIFSV3IIHTOFZ7VQDKTTPVPGP","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":"afae0b0f2bea978e8d576d5b91a6afc4adb9d31ddaf271ad5f247fde7e571a5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T09:01:02Z","title_canon_sha256":"90618c3901381bfa3ddc231b7c1fcba699bf3ac967e5b15bd8053adbadd9b9b1"},"schema_version":"1.0","source":{"id":"1310.0192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0192","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0192v2","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0192","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"JEIFSV3IIHTO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JEIFSV3IIHTOFZ7V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JEIFSV3I","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ac5062ebecd27052d99c9a37061aa905b8f57936ff8fcb4e833109fd6501294f","target":"graph","created_at":"2026-05-18T02:48:01Z","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 a multistage epidemic model which generalizes the SIR model and where infected individuals go through K>0 stages of the epidemic before being removed. An infected individual in stage k=1,...,K may infect a susceptible individual, who directly goes to stage k of the epidemic; or it may go to the next stage k+1 of the epidemic. For this model, we identify the critical regime in which we establish diffusion approximations. Surprisingly, the limiting diffusion exhibits an unusual form of state space collapse which we analyze in detail.","authors_text":"Florian Simatos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T09:01:02Z","title":"State space collapse for critical multistage epidemics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0192","kind":"arxiv","version":2},"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:dff2f37cfdd996226187f19461cb977fbf57559331fbe99aaeb9e5c351b60910","target":"record","created_at":"2026-05-18T02:48:01Z","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":"afae0b0f2bea978e8d576d5b91a6afc4adb9d31ddaf271ad5f247fde7e571a5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T09:01:02Z","title_canon_sha256":"90618c3901381bfa3ddc231b7c1fcba699bf3ac967e5b15bd8053adbadd9b9b1"},"schema_version":"1.0","source":{"id":"1310.0192","kind":"arxiv","version":2}},"canonical_sha256":"491059576841e6e2e7f580d539beaf33c422dfea16856cd514359b609ae42cae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"491059576841e6e2e7f580d539beaf33c422dfea16856cd514359b609ae42cae","first_computed_at":"2026-05-18T02:48:01.032240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:01.032240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oc0tSHRQaIGFnmixIHttU0En8GFyFO2w6f1QgaM9SbPDLIVlOBGwI3rsNAKws/acrrcj0tMkz3o1nMF7V3VODA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:01.032757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dff2f37cfdd996226187f19461cb977fbf57559331fbe99aaeb9e5c351b60910","sha256:ac5062ebecd27052d99c9a37061aa905b8f57936ff8fcb4e833109fd6501294f"],"state_sha256":"fa3fdcc9d41cfe8a838ce251499752de27fb291f6db899d4c79e0c525b5fa1a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rGABTer0eiU4gGY7eMiblO6DF1WqxRfH9vam9B7Gc39KXCc0blvko5JWq+CEyaEz0XJ9J584lhtGK5gqB3gJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:05:39.319343Z","bundle_sha256":"3441cf51f75668b0d39e4c2fd43c158e0bd7d3769707e27be33c8b3cce67938f"}}