{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:M6VT4QV32Z5CJCF6LXNTEZXD6P","short_pith_number":"pith:M6VT4QV3","canonical_record":{"source":{"id":"1108.2431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-11T15:35:42Z","cross_cats_sorted":[],"title_canon_sha256":"f4981d90630892958ecb58553560000472f489a53afff2042265ba9f1ca1dd61","abstract_canon_sha256":"69f87785f9446d11d77812af88e5e47ed00049b64d8f3bc4a48ef5962d2ba12c"},"schema_version":"1.0"},"canonical_sha256":"67ab3e42bbd67a2488be5ddb3266e3f3d95e9da81d08f6873ae0919f7b7c64f9","source":{"kind":"arxiv","id":"1108.2431","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2431","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2431v3","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2431","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"M6VT4QV32Z5C","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M6VT4QV32Z5CJCF6","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M6VT4QV3","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:M6VT4QV32Z5CJCF6LXNTEZXD6P","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-11T15:35:42Z","cross_cats_sorted":[],"title_canon_sha256":"f4981d90630892958ecb58553560000472f489a53afff2042265ba9f1ca1dd61","abstract_canon_sha256":"69f87785f9446d11d77812af88e5e47ed00049b64d8f3bc4a48ef5962d2ba12c"},"schema_version":"1.0"},"canonical_sha256":"67ab3e42bbd67a2488be5ddb3266e3f3d95e9da81d08f6873ae0919f7b7c64f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:04.141301Z","signature_b64":"pd46Ku0TFkL2/PcdjS88OZuVcF4E7vITpZ9UXQNuzOwXWUnau9U3tE0LAYj5bJQ5Omq1KurIaKPyRO+DyqiPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ab3e42bbd67a2488be5ddb3266e3f3d95e9da81d08f6873ae0919f7b7c64f9","last_reissued_at":"2026-05-18T02:40:04.140857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:04.140857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2431","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SKWXtnredLgz25qFP//VtTy5Xi19cfUlg+LWRQNSk2ExnRYk0YRiWxbhJLHnq7dZyzQhnYgvhG7i5Zzj+26DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:01:23.394935Z"},"content_sha256":"0f05940726bcf68930c3d2b7ca2062283b1e2a6536a7cc4591f36bfb90275f8f","schema_version":"1.0","event_id":"sha256:0f05940726bcf68930c3d2b7ca2062283b1e2a6536a7cc4591f36bfb90275f8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:M6VT4QV32Z5CJCF6LXNTEZXD6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Process-Level Large Deviations for Nonlinear Hawkes Point Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lingjiong Zhu","submitted_at":"2011-08-11T15:35:42Z","abstract_excerpt":"In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2431","kind":"arxiv","version":3},"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":"2026-05-18T02:40:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+3Mv5AAyhfaOLgGFreexiDRKxZ3/ZrLeERzfKFQthZtiO3EuJkBpRAIYYQeaeVUDPTqbl2uIgbBaGSpDqORCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:01:23.395564Z"},"content_sha256":"b70a360c40ec8fb6749b6a577f68aabc95c035789be8685b9b2b32979f09b80c","schema_version":"1.0","event_id":"sha256:b70a360c40ec8fb6749b6a577f68aabc95c035789be8685b9b2b32979f09b80c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P/bundle.json","state_url":"https://pith.science/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P/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":"2026-05-25T18:01:23Z","links":{"resolver":"https://pith.science/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P","bundle":"https://pith.science/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P/bundle.json","state":"https://pith.science/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6VT4QV32Z5CJCF6LXNTEZXD6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:M6VT4QV32Z5CJCF6LXNTEZXD6P","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":"69f87785f9446d11d77812af88e5e47ed00049b64d8f3bc4a48ef5962d2ba12c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-11T15:35:42Z","title_canon_sha256":"f4981d90630892958ecb58553560000472f489a53afff2042265ba9f1ca1dd61"},"schema_version":"1.0","source":{"id":"1108.2431","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2431","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2431v3","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2431","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"M6VT4QV32Z5C","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M6VT4QV32Z5CJCF6","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M6VT4QV3","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:b70a360c40ec8fb6749b6a577f68aabc95c035789be8685b9b2b32979f09b80c","target":"graph","created_at":"2026-05-18T02:40:04Z","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 paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.","authors_text":"Lingjiong Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-11T15:35:42Z","title":"Process-Level Large Deviations for Nonlinear Hawkes Point Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2431","kind":"arxiv","version":3},"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":"sha256:0f05940726bcf68930c3d2b7ca2062283b1e2a6536a7cc4591f36bfb90275f8f","target":"record","created_at":"2026-05-18T02:40:04Z","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":"69f87785f9446d11d77812af88e5e47ed00049b64d8f3bc4a48ef5962d2ba12c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-11T15:35:42Z","title_canon_sha256":"f4981d90630892958ecb58553560000472f489a53afff2042265ba9f1ca1dd61"},"schema_version":"1.0","source":{"id":"1108.2431","kind":"arxiv","version":3}},"canonical_sha256":"67ab3e42bbd67a2488be5ddb3266e3f3d95e9da81d08f6873ae0919f7b7c64f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ab3e42bbd67a2488be5ddb3266e3f3d95e9da81d08f6873ae0919f7b7c64f9","first_computed_at":"2026-05-18T02:40:04.140857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:04.140857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pd46Ku0TFkL2/PcdjS88OZuVcF4E7vITpZ9UXQNuzOwXWUnau9U3tE0LAYj5bJQ5Omq1KurIaKPyRO+DyqiPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:04.141301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2431","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f05940726bcf68930c3d2b7ca2062283b1e2a6536a7cc4591f36bfb90275f8f","sha256:b70a360c40ec8fb6749b6a577f68aabc95c035789be8685b9b2b32979f09b80c"],"state_sha256":"4d0b74294617bcd57a379912a09dcf02ee86f063ca45929f8efa0c51e7591833"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"619Sow2YY/40bYciMC+FDoeQgg466SN0D/Q7MPqPgNHUyL7T8K8mmD/x4cOJdXz0WcIkCFEqgACK/KXZfE13Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:01:23.399367Z","bundle_sha256":"c06e13ce999dc3c13b0ece124dae285feb933af53c0e70499f5f52f3600dd943"}}