{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:I53UHXFNNC2KY4NIFM3SNUCBNA","short_pith_number":"pith:I53UHXFN","canonical_record":{"source":{"id":"1012.5027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-22T16:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"8f74f10878bcacfa94ad05e8d8415cea605cde248f65337f3f0702047ed1311e","abstract_canon_sha256":"dccf306211f296a147dba296c76ca52e96475bbd9a84403d41e49d12f3716e87"},"schema_version":"1.0"},"canonical_sha256":"477743dcad68b4ac71a82b3726d0416821d63b296e3665c08c979ade63ec7cf6","source":{"kind":"arxiv","id":"1012.5027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5027","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5027v1","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5027","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"I53UHXFNNC2K","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I53UHXFNNC2KY4NI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I53UHXFN","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:I53UHXFNNC2KY4NIFM3SNUCBNA","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-22T16:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"8f74f10878bcacfa94ad05e8d8415cea605cde248f65337f3f0702047ed1311e","abstract_canon_sha256":"dccf306211f296a147dba296c76ca52e96475bbd9a84403d41e49d12f3716e87"},"schema_version":"1.0"},"canonical_sha256":"477743dcad68b4ac71a82b3726d0416821d63b296e3665c08c979ade63ec7cf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:36.407563Z","signature_b64":"+1AjIiqL2w5lnPOkDYv4/7HnJGnUPvsXfs6TF5AAirVEYv/Y9eUfYidgMdHRX4YLhlkiVHSqnKCXcUcdr4/ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"477743dcad68b4ac71a82b3726d0416821d63b296e3665c08c979ade63ec7cf6","last_reissued_at":"2026-05-18T03:44:36.406785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:36.406785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5027","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":"2026-05-18T03:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtLKTAFgc8VuMGgFlRCoy0cJO0D1U26BB+qooKlUCXuBY1L3M/Fnn98eMrZSwPFIiEFJHjnbF6JjNXbNen4aDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:37:12.431252Z"},"content_sha256":"58611f478d8a810454641f5bfd905a3763d0aca2bf0f8984e21b4fd8353951d3","schema_version":"1.0","event_id":"sha256:58611f478d8a810454641f5bfd905a3763d0aca2bf0f8984e21b4fd8353951d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:I53UHXFNNC2KY4NIFM3SNUCBNA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moderate deviations via cumulants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hanna Doering, Peter Eichelsbacher","submitted_at":"2010-12-22T16:42:04Z","abstract_excerpt":"The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis and Statulevicius. The examples of random objects we treat include dependency graphs, subgraph-counting statistics in Erd\\H{o}s-R\\'enyi random graphs and $U$-statistics. Moreover, we prove moderate deviation principles for certain statistics appearing in random matrix theory, namely characteristic polynomials of random unitary ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5027","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":"2026-05-18T03:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"asaLSyJSNHEqoHbxkKRZmcEwMa/H8GofLp08CpRZkcrEOcws1GTeEpI9uBHKW3YqHfhFl62aIy6x5cfv7bYoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:37:12.431615Z"},"content_sha256":"eb8478e2322bca7218b706f45af9f2a4ea7ce8ba3d98e7fe40ad87403c6e2874","schema_version":"1.0","event_id":"sha256:eb8478e2322bca7218b706f45af9f2a4ea7ce8ba3d98e7fe40ad87403c6e2874"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I53UHXFNNC2KY4NIFM3SNUCBNA/bundle.json","state_url":"https://pith.science/pith/I53UHXFNNC2KY4NIFM3SNUCBNA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I53UHXFNNC2KY4NIFM3SNUCBNA/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":"2026-06-26T15:37:12Z","links":{"resolver":"https://pith.science/pith/I53UHXFNNC2KY4NIFM3SNUCBNA","bundle":"https://pith.science/pith/I53UHXFNNC2KY4NIFM3SNUCBNA/bundle.json","state":"https://pith.science/pith/I53UHXFNNC2KY4NIFM3SNUCBNA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I53UHXFNNC2KY4NIFM3SNUCBNA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:I53UHXFNNC2KY4NIFM3SNUCBNA","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":"dccf306211f296a147dba296c76ca52e96475bbd9a84403d41e49d12f3716e87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-22T16:42:04Z","title_canon_sha256":"8f74f10878bcacfa94ad05e8d8415cea605cde248f65337f3f0702047ed1311e"},"schema_version":"1.0","source":{"id":"1012.5027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5027","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5027v1","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5027","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"I53UHXFNNC2K","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I53UHXFNNC2KY4NI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I53UHXFN","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:eb8478e2322bca7218b706f45af9f2a4ea7ce8ba3d98e7fe40ad87403c6e2874","target":"graph","created_at":"2026-05-18T03:44:36Z","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":"The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis and Statulevicius. The examples of random objects we treat include dependency graphs, subgraph-counting statistics in Erd\\H{o}s-R\\'enyi random graphs and $U$-statistics. Moreover, we prove moderate deviation principles for certain statistics appearing in random matrix theory, namely characteristic polynomials of random unitary ma","authors_text":"Hanna Doering, Peter Eichelsbacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-22T16:42:04Z","title":"Moderate deviations via cumulants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5027","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":"sha256:58611f478d8a810454641f5bfd905a3763d0aca2bf0f8984e21b4fd8353951d3","target":"record","created_at":"2026-05-18T03:44:36Z","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":"dccf306211f296a147dba296c76ca52e96475bbd9a84403d41e49d12f3716e87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-22T16:42:04Z","title_canon_sha256":"8f74f10878bcacfa94ad05e8d8415cea605cde248f65337f3f0702047ed1311e"},"schema_version":"1.0","source":{"id":"1012.5027","kind":"arxiv","version":1}},"canonical_sha256":"477743dcad68b4ac71a82b3726d0416821d63b296e3665c08c979ade63ec7cf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"477743dcad68b4ac71a82b3726d0416821d63b296e3665c08c979ade63ec7cf6","first_computed_at":"2026-05-18T03:44:36.406785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:36.406785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+1AjIiqL2w5lnPOkDYv4/7HnJGnUPvsXfs6TF5AAirVEYv/Y9eUfYidgMdHRX4YLhlkiVHSqnKCXcUcdr4/ECw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:36.407563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58611f478d8a810454641f5bfd905a3763d0aca2bf0f8984e21b4fd8353951d3","sha256:eb8478e2322bca7218b706f45af9f2a4ea7ce8ba3d98e7fe40ad87403c6e2874"],"state_sha256":"3508ac8abdd54d05915160a4fcd85dde310ea227365dcf3f9d8ec900992850bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dv5WqqaDR403VNAlhtmdG92iGIqpiyjCTO9wtaFRk0I5RweVqEIkskXMqWmJU+fhEAaAAXanCZ7nL0XBVHikBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:37:12.433556Z","bundle_sha256":"92bc299cf54644c871a0678a8b68216c35a3400312b60588c7114f861400e660"}}