{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SQ3DNNFYJZNXRQ3ZWTFFMM3XO7","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":"aef92d5bfe5fee9f43b9760cf9a12ba05bddbd325ab98dc525b069e4c2b843ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-06T08:43:44Z","title_canon_sha256":"843bad464d175114373675696fe569e2fcdd9e27b0bc930054ddc0d0c28e998e"},"schema_version":"1.0","source":{"id":"1109.1113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1113","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1113v1","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1113","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"SQ3DNNFYJZNX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SQ3DNNFYJZNXRQ3Z","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SQ3DNNFY","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:d6e4de930995ff16990552bf3d144c499127ec2fdcd632d8ad850f582c81c84d","target":"graph","created_at":"2026-05-18T03:16:59Z","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":"In this article, we analyze a system modeling bacteriophage treatments for infections in a noisy context. In the small noise regime, we show that after a reasonable amount of time the system is close to a sane equilibrium (which is a relevant biologic information) with high probability. Mathematically speaking, our study hinges on concentration techniques for delayed stochastic differential equations.","authors_text":"Carles Rovira, David Bascompte, Samy Tindel (IECN), Xavier Bardina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-06T08:43:44Z","title":"A stochastic model for bacteriophage therapies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1113","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":"sha256:246e4cddee3908aec2bde28f7669da0680095ceceac8f24ca6c1aad11dfb9fa5","target":"record","created_at":"2026-05-18T03:16:59Z","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":"aef92d5bfe5fee9f43b9760cf9a12ba05bddbd325ab98dc525b069e4c2b843ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-06T08:43:44Z","title_canon_sha256":"843bad464d175114373675696fe569e2fcdd9e27b0bc930054ddc0d0c28e998e"},"schema_version":"1.0","source":{"id":"1109.1113","kind":"arxiv","version":1}},"canonical_sha256":"943636b4b84e5b78c379b4ca56337777e20abca835e0639014f5e6542abd8390","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"943636b4b84e5b78c379b4ca56337777e20abca835e0639014f5e6542abd8390","first_computed_at":"2026-05-18T03:16:59.169370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:59.169370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SfPmgrkyxGXxiAuehmoM+ZG/NUN/B+tcWn+mi9r+xm/ZW29SHwrXOjzLt8cpJjajXBvyhfTljuwfhRl7MVjeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:59.170168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:246e4cddee3908aec2bde28f7669da0680095ceceac8f24ca6c1aad11dfb9fa5","sha256:d6e4de930995ff16990552bf3d144c499127ec2fdcd632d8ad850f582c81c84d"],"state_sha256":"2d951af3c0a79229072ba51c366a311ee5289f9bd996b2e24cbca1d5d65f3f63"}