{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LA2RILCLO6OPLRUYWVYOBMU4I4","short_pith_number":"pith:LA2RILCL","canonical_record":{"source":{"id":"1507.02940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-07-10T15:35:42Z","cross_cats_sorted":[],"title_canon_sha256":"dfdaf3ec6e7f0083e4b4a7fea1a748aa2c802bea0e329b0f730b59533dc32b59","abstract_canon_sha256":"eaa35de8af715cc637038881d85c903e0fae3e5e1129eb816d13cba0b501ee3f"},"schema_version":"1.0"},"canonical_sha256":"5835142c4b779cf5c698b570e0b29c471286594f84b948543e101804d5c69290","source":{"kind":"arxiv","id":"1507.02940","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02940","created_at":"2026-05-18T01:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02940v2","created_at":"2026-05-18T01:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02940","created_at":"2026-05-18T01:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"LA2RILCLO6OP","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LA2RILCLO6OPLRUY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LA2RILCL","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LA2RILCLO6OPLRUYWVYOBMU4I4","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-07-10T15:35:42Z","cross_cats_sorted":[],"title_canon_sha256":"dfdaf3ec6e7f0083e4b4a7fea1a748aa2c802bea0e329b0f730b59533dc32b59","abstract_canon_sha256":"eaa35de8af715cc637038881d85c903e0fae3e5e1129eb816d13cba0b501ee3f"},"schema_version":"1.0"},"canonical_sha256":"5835142c4b779cf5c698b570e0b29c471286594f84b948543e101804d5c69290","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:43.836219Z","signature_b64":"3lNHTXFu+P8Gi6XmpEqCAppp6mDKy00GPRg22XX9AXR1xqQyrLjL/QUJQRTcj+3nDKZv0h7SDgDELXDxA279Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5835142c4b779cf5c698b570e0b29c471286594f84b948543e101804d5c69290","last_reissued_at":"2026-05-18T01:17:43.835505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:43.835505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02940","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":"2026-05-18T01:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3grRvLo1E/ra13ajXrcIRaWhyEGF6VX8nTTuffBRbpj1wwa7REI2EzIDbgVxFYq5oCoNoOTdJ3+h10FTJBX9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:02:46.622933Z"},"content_sha256":"645197135805747d5f007dbf37d2218103f68d625632eacc3c2d505b7f8900bd","schema_version":"1.0","event_id":"sha256:645197135805747d5f007dbf37d2218103f68d625632eacc3c2d505b7f8900bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LA2RILCLO6OPLRUYWVYOBMU4I4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Vaccination Strategies and Rational Behaviour in Seasonal Epidemics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Fabio A. C. C. Chalub, Maria do C\\'eu Soares, Paula Rodrigues, Paulo Doutor","submitted_at":"2015-07-10T15:35:42Z","abstract_excerpt":"We consider a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We study two types of vaccination strategies: i) optimal vaccination, in the sense that it minimizes the effort of vaccination in the set of vaccination strategies for which, for any sufficiently small perturbation of the disease free state, the number of infectious individuals is monotonically decreasing; ii) Nash-equilibria strategies where all individuals simultaneously minimize the joint risk of vaccination versus t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02940","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":"2026-05-18T01:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jaPcCDpm0EVBqCcY++6C0vNW5BCFnQgLNdNCCaqeQdm+RHKw3P/dYFAycIwNDypP39qeVaSeMUKD33IrTeGlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:02:46.623287Z"},"content_sha256":"77a0d73830959c061c617a4f9991058a7b219acc9f8b7d651de8e93e42ff3246","schema_version":"1.0","event_id":"sha256:77a0d73830959c061c617a4f9991058a7b219acc9f8b7d651de8e93e42ff3246"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LA2RILCLO6OPLRUYWVYOBMU4I4/bundle.json","state_url":"https://pith.science/pith/LA2RILCLO6OPLRUYWVYOBMU4I4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LA2RILCLO6OPLRUYWVYOBMU4I4/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":"2026-05-30T05:02:46Z","links":{"resolver":"https://pith.science/pith/LA2RILCLO6OPLRUYWVYOBMU4I4","bundle":"https://pith.science/pith/LA2RILCLO6OPLRUYWVYOBMU4I4/bundle.json","state":"https://pith.science/pith/LA2RILCLO6OPLRUYWVYOBMU4I4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LA2RILCLO6OPLRUYWVYOBMU4I4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LA2RILCLO6OPLRUYWVYOBMU4I4","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":"eaa35de8af715cc637038881d85c903e0fae3e5e1129eb816d13cba0b501ee3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-07-10T15:35:42Z","title_canon_sha256":"dfdaf3ec6e7f0083e4b4a7fea1a748aa2c802bea0e329b0f730b59533dc32b59"},"schema_version":"1.0","source":{"id":"1507.02940","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02940","created_at":"2026-05-18T01:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02940v2","created_at":"2026-05-18T01:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02940","created_at":"2026-05-18T01:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"LA2RILCLO6OP","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LA2RILCLO6OPLRUY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LA2RILCL","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:77a0d73830959c061c617a4f9991058a7b219acc9f8b7d651de8e93e42ff3246","target":"graph","created_at":"2026-05-18T01:17:43Z","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 a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We study two types of vaccination strategies: i) optimal vaccination, in the sense that it minimizes the effort of vaccination in the set of vaccination strategies for which, for any sufficiently small perturbation of the disease free state, the number of infectious individuals is monotonically decreasing; ii) Nash-equilibria strategies where all individuals simultaneously minimize the joint risk of vaccination versus t","authors_text":"Fabio A. C. C. Chalub, Maria do C\\'eu Soares, Paula Rodrigues, Paulo Doutor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-07-10T15:35:42Z","title":"Optimal Vaccination Strategies and Rational Behaviour in Seasonal Epidemics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02940","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":"sha256:645197135805747d5f007dbf37d2218103f68d625632eacc3c2d505b7f8900bd","target":"record","created_at":"2026-05-18T01:17:43Z","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":"eaa35de8af715cc637038881d85c903e0fae3e5e1129eb816d13cba0b501ee3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-07-10T15:35:42Z","title_canon_sha256":"dfdaf3ec6e7f0083e4b4a7fea1a748aa2c802bea0e329b0f730b59533dc32b59"},"schema_version":"1.0","source":{"id":"1507.02940","kind":"arxiv","version":2}},"canonical_sha256":"5835142c4b779cf5c698b570e0b29c471286594f84b948543e101804d5c69290","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5835142c4b779cf5c698b570e0b29c471286594f84b948543e101804d5c69290","first_computed_at":"2026-05-18T01:17:43.835505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:43.835505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3lNHTXFu+P8Gi6XmpEqCAppp6mDKy00GPRg22XX9AXR1xqQyrLjL/QUJQRTcj+3nDKZv0h7SDgDELXDxA279Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:43.836219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02940","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:645197135805747d5f007dbf37d2218103f68d625632eacc3c2d505b7f8900bd","sha256:77a0d73830959c061c617a4f9991058a7b219acc9f8b7d651de8e93e42ff3246"],"state_sha256":"6c346d8a20037450950c187bd5d04a58714a0f0ee51b4546f6f1881aedf3dacd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wgaK2BcY0NFZEr1Rr4L906TmK4OvP5kxtej4u+zO/Jv8KgTeR1Lb1mtD7bid2fRr9gfjf3FiBeePvIMJK5moDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:02:46.625619Z","bundle_sha256":"c5ecf8a05f770b8c1f0f3bb4495ac6cbcadb90e92275b94fa01163d40dac6d68"}}