{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TQY2CVAQKQZTEOWZ52IX5HD3B7","short_pith_number":"pith:TQY2CVAQ","canonical_record":{"source":{"id":"2505.15617","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-21T15:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"96500edf8e93c65c86a0600adb67414bd63e71bed8a9329eb478a89135425792","abstract_canon_sha256":"8a7e4761d58899d59c0fffa56158762eb7346be9629caba22e2a80c832c06fa5"},"schema_version":"1.0"},"canonical_sha256":"9c31a154105433323ad9ee917e9c7b0fc24da152a0107687d7e5a4502d61f346","source":{"kind":"arxiv","id":"2505.15617","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.15617","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"2505.15617v2","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.15617","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"TQY2CVAQKQZT","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"pith_short_16","alias_value":"TQY2CVAQKQZTEOWZ","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"pith_short_8","alias_value":"TQY2CVAQ","created_at":"2026-07-05T11:10:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TQY2CVAQKQZTEOWZ52IX5HD3B7","target":"record","payload":{"canonical_record":{"source":{"id":"2505.15617","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-21T15:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"96500edf8e93c65c86a0600adb67414bd63e71bed8a9329eb478a89135425792","abstract_canon_sha256":"8a7e4761d58899d59c0fffa56158762eb7346be9629caba22e2a80c832c06fa5"},"schema_version":"1.0"},"canonical_sha256":"9c31a154105433323ad9ee917e9c7b0fc24da152a0107687d7e5a4502d61f346","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:09.018702Z","signature_b64":"Hssj5GePe1whm4EVv+qZDevv+X16a/lrQzpx0t8KrkHMEvxqbQGPCmQRUgrrDkWlO7J4T4Pe028PkMSf4sINAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c31a154105433323ad9ee917e9c7b0fc24da152a0107687d7e5a4502d61f346","last_reissued_at":"2026-07-05T11:10:09.018189Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:09.018189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.15617","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":"2026-07-05T11:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eWt32nLSHhmwfN5xkSELV97ENqiE1W3BNVik4+opSISBquneMS2UnVZVOjWtYNgBtciG6GJD00/vzoUGaN6oBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:46:48.513979Z"},"content_sha256":"13899bddf6ac5ebed0732828e188bfbe24943a0845f409bfc6217267044f9080","schema_version":"1.0","event_id":"sha256:13899bddf6ac5ebed0732828e188bfbe24943a0845f409bfc6217267044f9080"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TQY2CVAQKQZTEOWZ52IX5HD3B7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional Central Limit Theorem and SPDE for epidemic model with memory of the last infection and waning immunity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arsene Brice Zotsa-Ngoufack","submitted_at":"2025-05-21T15:07:07Z","abstract_excerpt":"We study the fluctuations of a stochastic epidemic model with memory of the last infections, varying infectivity, and waning immunity, as introduced in Guerin and Zotsa-Ngoufack:arXiv preprint arXiv:2505.00601. The dynamics of the epidemic model are described by a measure-valued process with respect to infection age and individual traits. The Functional Law of Large Numbers (FLLN) is formulated as an integral equation, which is solved by a deterministic measure. In this article, we establish the Functional Central Limit Theorem (FCLT), capturing the fluctuations of the stochastic model around "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15617","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.15617/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QRWkIk2UqyN8W87G+cTVQsh4vUrXSsA98d0r7k0LNwLKvuT8v+LFzETWqzpISj3ygUGzSuO46Lxjnz2W6YDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:46:48.514597Z"},"content_sha256":"f3a1ad2b1370265ab2d830a51ca579e460e26f557f1dca16872e4b96411837ac","schema_version":"1.0","event_id":"sha256:f3a1ad2b1370265ab2d830a51ca579e460e26f557f1dca16872e4b96411837ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7/bundle.json","state_url":"https://pith.science/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7/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":"2026-08-17T18:46:48Z","links":{"resolver":"https://pith.science/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7","bundle":"https://pith.science/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7/bundle.json","state":"https://pith.science/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQY2CVAQKQZTEOWZ52IX5HD3B7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TQY2CVAQKQZTEOWZ52IX5HD3B7","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":"8a7e4761d58899d59c0fffa56158762eb7346be9629caba22e2a80c832c06fa5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-21T15:07:07Z","title_canon_sha256":"96500edf8e93c65c86a0600adb67414bd63e71bed8a9329eb478a89135425792"},"schema_version":"1.0","source":{"id":"2505.15617","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.15617","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"2505.15617v2","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.15617","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"TQY2CVAQKQZT","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"pith_short_16","alias_value":"TQY2CVAQKQZTEOWZ","created_at":"2026-07-05T11:10:09Z"},{"alias_kind":"pith_short_8","alias_value":"TQY2CVAQ","created_at":"2026-07-05T11:10:09Z"}],"graph_snapshots":[{"event_id":"sha256:f3a1ad2b1370265ab2d830a51ca579e460e26f557f1dca16872e4b96411837ac","target":"graph","created_at":"2026-07-05T11:10:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.15617/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the fluctuations of a stochastic epidemic model with memory of the last infections, varying infectivity, and waning immunity, as introduced in Guerin and Zotsa-Ngoufack:arXiv preprint arXiv:2505.00601. The dynamics of the epidemic model are described by a measure-valued process with respect to infection age and individual traits. The Functional Law of Large Numbers (FLLN) is formulated as an integral equation, which is solved by a deterministic measure. In this article, we establish the Functional Central Limit Theorem (FCLT), capturing the fluctuations of the stochastic model around ","authors_text":"Arsene Brice Zotsa-Ngoufack","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-21T15:07:07Z","title":"Functional Central Limit Theorem and SPDE for epidemic model with memory of the last infection and waning immunity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15617","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":"sha256:13899bddf6ac5ebed0732828e188bfbe24943a0845f409bfc6217267044f9080","target":"record","created_at":"2026-07-05T11:10:09Z","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":"8a7e4761d58899d59c0fffa56158762eb7346be9629caba22e2a80c832c06fa5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-21T15:07:07Z","title_canon_sha256":"96500edf8e93c65c86a0600adb67414bd63e71bed8a9329eb478a89135425792"},"schema_version":"1.0","source":{"id":"2505.15617","kind":"arxiv","version":2}},"canonical_sha256":"9c31a154105433323ad9ee917e9c7b0fc24da152a0107687d7e5a4502d61f346","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c31a154105433323ad9ee917e9c7b0fc24da152a0107687d7e5a4502d61f346","first_computed_at":"2026-07-05T11:10:09.018189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:09.018189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hssj5GePe1whm4EVv+qZDevv+X16a/lrQzpx0t8KrkHMEvxqbQGPCmQRUgrrDkWlO7J4T4Pe028PkMSf4sINAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:09.018702Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.15617","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13899bddf6ac5ebed0732828e188bfbe24943a0845f409bfc6217267044f9080","sha256:f3a1ad2b1370265ab2d830a51ca579e460e26f557f1dca16872e4b96411837ac"],"state_sha256":"303e6efb2f819f7727d208c2d8aa6efe6686ef64376d3cec584bef0fb5e60f51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"inPVsHBkTHISsOjocwJcT0T1viGmNGi+G8dHjYJ4g8KxmIDcDPThkGeWjEC/PaG05JkV153j0M96i4IY3N2eCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:46:48.520400Z","bundle_sha256":"8ec2ab7979401e945c4022180c37814969106ce0ac3774713fd4ac02477f33f2"}}