{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TPBLKSG2IKRRXWJ3J6SOD6SZ6K","short_pith_number":"pith:TPBLKSG2","canonical_record":{"source":{"id":"1403.5532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T18:15:44Z","cross_cats_sorted":["math.CA","math.MP","physics.bio-ph"],"title_canon_sha256":"f9be5ea1c0207751f8ebb100688816b6ce2aabff2aceede0ca01955075114172","abstract_canon_sha256":"75959b6be0f01793c8043c9bda423c211eb051f6ad11cb9cc421e4e35515dfc1"},"schema_version":"1.0"},"canonical_sha256":"9bc2b548da42a31bd93b4fa4e1fa59f2939db8f21af22377e5b32c09b5fe7e0b","source":{"kind":"arxiv","id":"1403.5532","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5532","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5532v2","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5532","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"TPBLKSG2IKRR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TPBLKSG2IKRRXWJ3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TPBLKSG2","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TPBLKSG2IKRRXWJ3J6SOD6SZ6K","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T18:15:44Z","cross_cats_sorted":["math.CA","math.MP","physics.bio-ph"],"title_canon_sha256":"f9be5ea1c0207751f8ebb100688816b6ce2aabff2aceede0ca01955075114172","abstract_canon_sha256":"75959b6be0f01793c8043c9bda423c211eb051f6ad11cb9cc421e4e35515dfc1"},"schema_version":"1.0"},"canonical_sha256":"9bc2b548da42a31bd93b4fa4e1fa59f2939db8f21af22377e5b32c09b5fe7e0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:39.190205Z","signature_b64":"ZxHrROEO9KdhyQe0u3tglPt9ZL0a5tvjNVqcXbaBFuCmYwxGRpkGJHxiE4URSuRPGHhAOKvZKe5qP5mx4YyTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bc2b548da42a31bd93b4fa4e1fa59f2939db8f21af22377e5b32c09b5fe7e0b","last_reissued_at":"2026-05-18T02:26:39.189762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:39.189762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5532","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":"2026-05-18T02:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ebZm5fKgXwUF1W4BV80jz5up21OdoF1GrSi3kxIodYB/VwB5K0kltwuv5LMeTl3DKx6sgM3x35GvAiiwJzIxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:15:12.041426Z"},"content_sha256":"e20abab7b88f6d85db49e45e18476360c96476801bf65f2732db76c4f53960be","schema_version":"1.0","event_id":"sha256:e20abab7b88f6d85db49e45e18476360c96476801bf65f2732db76c4f53960be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TPBLKSG2IKRRXWJ3J6SOD6SZ6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Laplace's method for series and the semiclassical analysis of epidemiological models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Davide Masoero","submitted_at":"2014-03-21T18:15:44Z","abstract_excerpt":"We develop a Laplace's method to compute the asymptotic expansions of sums of sharply peaked sequences. These series arise as discretizations (Riemann sums) of sharply-peaked integrals, whose asymptotic behavior can be computed by the standard Laplace's method. We apply the Laplace's method for series to the WKB (i.e. semiclassical) analysis of stochastic models of population biology, with special focus on the SIS model. In particular we show that two different and widely-used approaches to the semiclassical limit, i.e. either considering a semiclassical probability distribution or a semiclass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5532","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":"2026-05-18T02:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ogt+QJCxpK11Pghqfc4StpMnZW73Mvb1e1LeYljzVvlm0gbWLdHYYe7r9+UODdjfoB61qcjutn7rWJb/jbF1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:15:12.042096Z"},"content_sha256":"6312c0cdd9b2a45170e26abf4eba77186983af642c3a4c9ffd497a0642db8d78","schema_version":"1.0","event_id":"sha256:6312c0cdd9b2a45170e26abf4eba77186983af642c3a4c9ffd497a0642db8d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K/bundle.json","state_url":"https://pith.science/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K/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":"2026-06-07T06:15:12Z","links":{"resolver":"https://pith.science/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K","bundle":"https://pith.science/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K/bundle.json","state":"https://pith.science/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPBLKSG2IKRRXWJ3J6SOD6SZ6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TPBLKSG2IKRRXWJ3J6SOD6SZ6K","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":"75959b6be0f01793c8043c9bda423c211eb051f6ad11cb9cc421e4e35515dfc1","cross_cats_sorted":["math.CA","math.MP","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T18:15:44Z","title_canon_sha256":"f9be5ea1c0207751f8ebb100688816b6ce2aabff2aceede0ca01955075114172"},"schema_version":"1.0","source":{"id":"1403.5532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5532","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5532v2","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5532","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"TPBLKSG2IKRR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TPBLKSG2IKRRXWJ3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TPBLKSG2","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:6312c0cdd9b2a45170e26abf4eba77186983af642c3a4c9ffd497a0642db8d78","target":"graph","created_at":"2026-05-18T02:26:39Z","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 develop a Laplace's method to compute the asymptotic expansions of sums of sharply peaked sequences. These series arise as discretizations (Riemann sums) of sharply-peaked integrals, whose asymptotic behavior can be computed by the standard Laplace's method. We apply the Laplace's method for series to the WKB (i.e. semiclassical) analysis of stochastic models of population biology, with special focus on the SIS model. In particular we show that two different and widely-used approaches to the semiclassical limit, i.e. either considering a semiclassical probability distribution or a semiclass","authors_text":"Davide Masoero","cross_cats":["math.CA","math.MP","physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T18:15:44Z","title":"A Laplace's method for series and the semiclassical analysis of epidemiological models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5532","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:e20abab7b88f6d85db49e45e18476360c96476801bf65f2732db76c4f53960be","target":"record","created_at":"2026-05-18T02:26:39Z","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":"75959b6be0f01793c8043c9bda423c211eb051f6ad11cb9cc421e4e35515dfc1","cross_cats_sorted":["math.CA","math.MP","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T18:15:44Z","title_canon_sha256":"f9be5ea1c0207751f8ebb100688816b6ce2aabff2aceede0ca01955075114172"},"schema_version":"1.0","source":{"id":"1403.5532","kind":"arxiv","version":2}},"canonical_sha256":"9bc2b548da42a31bd93b4fa4e1fa59f2939db8f21af22377e5b32c09b5fe7e0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bc2b548da42a31bd93b4fa4e1fa59f2939db8f21af22377e5b32c09b5fe7e0b","first_computed_at":"2026-05-18T02:26:39.189762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:39.189762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZxHrROEO9KdhyQe0u3tglPt9ZL0a5tvjNVqcXbaBFuCmYwxGRpkGJHxiE4URSuRPGHhAOKvZKe5qP5mx4YyTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:39.190205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e20abab7b88f6d85db49e45e18476360c96476801bf65f2732db76c4f53960be","sha256:6312c0cdd9b2a45170e26abf4eba77186983af642c3a4c9ffd497a0642db8d78"],"state_sha256":"fc68e6cc90eecc64234223e28041a5bd17dd532cfc8cbb26cb3da2394b0c6c3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrMv/S9Ae/xTikPOw3lGGkawFKxKPM5Ht7JWu6xusO+yqrzEhj3WpzJjjs3UhAItfVNlW8BdTEDxLCbPO2pcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:15:12.045343Z","bundle_sha256":"333ca08d13f93182aaf9097b5153a9c3859ffd58773fb7614bb1481fe7ad30ec"}}