{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MG7FM6WG2T23DT3EOSS2UGGGIR","short_pith_number":"pith:MG7FM6WG","canonical_record":{"source":{"id":"1702.06177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-20T21:18:13Z","cross_cats_sorted":[],"title_canon_sha256":"553c4a7ecb347eaf2845cc50b95df2a045264ee3252e7d17ae9cf6921f969e80","abstract_canon_sha256":"4f4035831c5fabb728ba7ec6b45160c8bf0a2c7761882d254097fa0532b13427"},"schema_version":"1.0"},"canonical_sha256":"61be567ac6d4f5b1cf6474a5aa18c6445190fdd4b2bfcba1f647e7efb6247b25","source":{"kind":"arxiv","id":"1702.06177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06177","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06177v1","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06177","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"MG7FM6WG2T23","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MG7FM6WG2T23DT3E","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MG7FM6WG","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MG7FM6WG2T23DT3EOSS2UGGGIR","target":"record","payload":{"canonical_record":{"source":{"id":"1702.06177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-20T21:18:13Z","cross_cats_sorted":[],"title_canon_sha256":"553c4a7ecb347eaf2845cc50b95df2a045264ee3252e7d17ae9cf6921f969e80","abstract_canon_sha256":"4f4035831c5fabb728ba7ec6b45160c8bf0a2c7761882d254097fa0532b13427"},"schema_version":"1.0"},"canonical_sha256":"61be567ac6d4f5b1cf6474a5aa18c6445190fdd4b2bfcba1f647e7efb6247b25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:14.786068Z","signature_b64":"baExzfwWx4cdHSgvzLUZeH8Qp9BeX9IIWcbjNLbV2MK2/o8qA4t+bPqyPn1M2zJgdVVJbbGGwv4lLGfa9ZZoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61be567ac6d4f5b1cf6474a5aa18c6445190fdd4b2bfcba1f647e7efb6247b25","last_reissued_at":"2026-05-18T00:50:14.785587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:14.785587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.06177","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":"2026-05-18T00:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aSEqfGba4aB1NfQRbYivI1gZIpWsRy4KWC3vZp2B5zFiskUABo3JDMF5cyWTcNexaADvQPPJfP8eehLnVARvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:22:47.295441Z"},"content_sha256":"f40a5ee2a3444ad45c486d71dd882aef431a3ec2afd7c16581f2acb6cd17addf","schema_version":"1.0","event_id":"sha256:f40a5ee2a3444ad45c486d71dd882aef431a3ec2afd7c16581f2acb6cd17addf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MG7FM6WG2T23DT3EOSS2UGGGIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coinfection in a stochastic model for bacteriophage systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carles Rovira, Xavier Bardina","submitted_at":"2017-02-20T21:18:13Z","abstract_excerpt":"A system modeling bacteriophage treatments with coinfections in a noisy context is analyzed. We prove that in a small noise regime, the system converges in the long term to a bacteria free equilibrium. Moreover, we compare the treatment with coinfection with the treatment without coinfection, showing how the coinfection affects the dose of bacteriophages that is needed to eliminate the bacteria and the velocity of convergence to the free bacteria equilibrium."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06177","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":"2026-05-18T00:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8ca1M94hJJkwuTr4AxJfzXrR09mnOnN+bvQogyytR3bnn1dlSKpvOfuoPkcffeaKa/sX2wtHYV4GAFv75XmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:22:47.296197Z"},"content_sha256":"75a76c5feee13170efb54c7ce6027c59c378c35de3e4ce8ff4db3516a0468507","schema_version":"1.0","event_id":"sha256:75a76c5feee13170efb54c7ce6027c59c378c35de3e4ce8ff4db3516a0468507"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MG7FM6WG2T23DT3EOSS2UGGGIR/bundle.json","state_url":"https://pith.science/pith/MG7FM6WG2T23DT3EOSS2UGGGIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MG7FM6WG2T23DT3EOSS2UGGGIR/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":"2026-05-30T02:22:47Z","links":{"resolver":"https://pith.science/pith/MG7FM6WG2T23DT3EOSS2UGGGIR","bundle":"https://pith.science/pith/MG7FM6WG2T23DT3EOSS2UGGGIR/bundle.json","state":"https://pith.science/pith/MG7FM6WG2T23DT3EOSS2UGGGIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MG7FM6WG2T23DT3EOSS2UGGGIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MG7FM6WG2T23DT3EOSS2UGGGIR","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":"4f4035831c5fabb728ba7ec6b45160c8bf0a2c7761882d254097fa0532b13427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-20T21:18:13Z","title_canon_sha256":"553c4a7ecb347eaf2845cc50b95df2a045264ee3252e7d17ae9cf6921f969e80"},"schema_version":"1.0","source":{"id":"1702.06177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06177","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06177v1","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06177","created_at":"2026-05-18T00:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"MG7FM6WG2T23","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MG7FM6WG2T23DT3E","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MG7FM6WG","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:75a76c5feee13170efb54c7ce6027c59c378c35de3e4ce8ff4db3516a0468507","target":"graph","created_at":"2026-05-18T00:50:14Z","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 system modeling bacteriophage treatments with coinfections in a noisy context is analyzed. We prove that in a small noise regime, the system converges in the long term to a bacteria free equilibrium. Moreover, we compare the treatment with coinfection with the treatment without coinfection, showing how the coinfection affects the dose of bacteriophages that is needed to eliminate the bacteria and the velocity of convergence to the free bacteria equilibrium.","authors_text":"Carles Rovira, Xavier Bardina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-20T21:18:13Z","title":"Coinfection in a stochastic model for bacteriophage systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06177","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:f40a5ee2a3444ad45c486d71dd882aef431a3ec2afd7c16581f2acb6cd17addf","target":"record","created_at":"2026-05-18T00:50:14Z","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":"4f4035831c5fabb728ba7ec6b45160c8bf0a2c7761882d254097fa0532b13427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-20T21:18:13Z","title_canon_sha256":"553c4a7ecb347eaf2845cc50b95df2a045264ee3252e7d17ae9cf6921f969e80"},"schema_version":"1.0","source":{"id":"1702.06177","kind":"arxiv","version":1}},"canonical_sha256":"61be567ac6d4f5b1cf6474a5aa18c6445190fdd4b2bfcba1f647e7efb6247b25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61be567ac6d4f5b1cf6474a5aa18c6445190fdd4b2bfcba1f647e7efb6247b25","first_computed_at":"2026-05-18T00:50:14.785587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:14.785587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"baExzfwWx4cdHSgvzLUZeH8Qp9BeX9IIWcbjNLbV2MK2/o8qA4t+bPqyPn1M2zJgdVVJbbGGwv4lLGfa9ZZoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:14.786068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f40a5ee2a3444ad45c486d71dd882aef431a3ec2afd7c16581f2acb6cd17addf","sha256:75a76c5feee13170efb54c7ce6027c59c378c35de3e4ce8ff4db3516a0468507"],"state_sha256":"00f424b32ed08d20d8a21af792195c3d4b8b84a86e1b3a0c5f67b885e7e07dfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iM0txirErKWDmpEdE36MBTEYshGUEVK32lou01Ze8SJyZRCetj4DPHGfeQ6z3gAQBWJ5goCxMG+OR1J9ZzCqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:22:47.299955Z","bundle_sha256":"4337c8d0574ed15d6ceb58c08127a9fec3f4fb73ed3e87d6e6b6f083f0c373ab"}}