{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KSWL76WT4VIMRAEURBFWNQVWB2","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":"c28c1845c932b26d5c2456bceae14ade028a2c0c1fa759740775cbc22e23c2ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-28T14:39:08Z","title_canon_sha256":"f72561c47c098557f9609a50bb6262db0f8c8cc3ec34f579bb5a8d416d9ec76f"},"schema_version":"1.0","source":{"id":"1111.6451","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6451","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6451v3","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6451","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"KSWL76WT4VIM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KSWL76WT4VIMRAEU","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KSWL76WT","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:286012e6c5257bc50cd8a661db422cca0c267b48c91de76fadf4baa9d37ec8e3","target":"graph","created_at":"2026-05-18T03:02:21Z","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 consider measure-valued processes $X=(X_t)$ that solve the following martingale problem: for a given initial measure $X_0$, and for all smooth, compactly supported test functions $\\varphi$, \\begin{eqnarray*}X_t(\\varphi )=X_0(\\varphi)+\\frac{1}{2}\\int _0^tX_s(\\Delta \\varphi )\\,ds+\\theta \\int_0^tX_s(\\varphi )\\,ds\\\\{}-\\int_0^tX_s(L_s\\varphi )\\,ds+M_t(\\varphi ).\\end{eqnarray*} Here $L_s(x)$ is the local time density process associated with $X$, and $M_t(\\varphi )$ is a martingale with quadratic variation $[M(\\varphi )]_t=\\int_0^tX_s(\\varphi ^2)\\,ds$. Such processes arise as scaling limits of SIR","authors_text":"Edwin A. Perkins, Steven P. Lalley, Xinghua Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-28T14:39:08Z","title":"A phase transition for measure-valued SIR epidemic processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6451","kind":"arxiv","version":3},"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":"sha256:9d120ad8f273b1fbaeb9dac8887a1e75029f8d2213d78d3c36d8e0064f9c855c","target":"record","created_at":"2026-05-18T03:02:21Z","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":"c28c1845c932b26d5c2456bceae14ade028a2c0c1fa759740775cbc22e23c2ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-28T14:39:08Z","title_canon_sha256":"f72561c47c098557f9609a50bb6262db0f8c8cc3ec34f579bb5a8d416d9ec76f"},"schema_version":"1.0","source":{"id":"1111.6451","kind":"arxiv","version":3}},"canonical_sha256":"54acbffad3e550c88094884b66c2b60eb79fc291d5e7427eaed2371f95188349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54acbffad3e550c88094884b66c2b60eb79fc291d5e7427eaed2371f95188349","first_computed_at":"2026-05-18T03:02:21.484276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:21.484276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A2JItcbU3a7ISUF0omw55jQkztHEO3ZBfPfVJJvUYf+HeuBYD/nGKZMze6Z7dGGoyfvKSv4n0JnCdB11+0azBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:21.485073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6451","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d120ad8f273b1fbaeb9dac8887a1e75029f8d2213d78d3c36d8e0064f9c855c","sha256:286012e6c5257bc50cd8a661db422cca0c267b48c91de76fadf4baa9d37ec8e3"],"state_sha256":"663a1f38c9a2ddb1b17f9661a454c1d8c9e9af59b0069e5d6f5ff2b00938bd06"}