{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GFCX7NBFCBWUL7VU5MQILPVMQJ","short_pith_number":"pith:GFCX7NBF","canonical_record":{"source":{"id":"1202.3041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T14:02:23Z","cross_cats_sorted":[],"title_canon_sha256":"f694aa191f042b6011a166008b5a164be764f4863a8decb44d3f9276c4687ba2","abstract_canon_sha256":"2815f339e39086ef37cd5b080c9f865fbe96e6811d833ea0baa9182a4360def0"},"schema_version":"1.0"},"canonical_sha256":"31457fb425106d45feb4eb2085beac826a32e6a5564ff89bf10c3b11b33f1d21","source":{"kind":"arxiv","id":"1202.3041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3041","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3041v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3041","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"GFCX7NBFCBWU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GFCX7NBFCBWUL7VU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GFCX7NBF","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GFCX7NBFCBWUL7VU5MQILPVMQJ","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T14:02:23Z","cross_cats_sorted":[],"title_canon_sha256":"f694aa191f042b6011a166008b5a164be764f4863a8decb44d3f9276c4687ba2","abstract_canon_sha256":"2815f339e39086ef37cd5b080c9f865fbe96e6811d833ea0baa9182a4360def0"},"schema_version":"1.0"},"canonical_sha256":"31457fb425106d45feb4eb2085beac826a32e6a5564ff89bf10c3b11b33f1d21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:24.282528Z","signature_b64":"g1lnyp0Qh4qU1tdd5vyI3SIuD9r5S8LXcKi/pVE4OVSgOPaSbbgWtorcus14wVdfG4taHbnTIpFRIMzoVd2uAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31457fb425106d45feb4eb2085beac826a32e6a5564ff89bf10c3b11b33f1d21","last_reissued_at":"2026-05-18T04:02:24.281835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:24.281835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3041","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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWY7RobxyvtOBtNA/dtoLS+SJ3B5ihcFaV4HuK/Chon61lb038smoRSIDvuBPsMx3pEnY1IvnnDbJS4dw1NxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:43:16.923750Z"},"content_sha256":"9707fefa8f9e1748e38857492ff5ad66b90689a3f05358cdfa9860ecda8df44e","schema_version":"1.0","event_id":"sha256:9707fefa8f9e1748e38857492ff5ad66b90689a3f05358cdfa9860ecda8df44e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GFCX7NBFCBWUL7VU5MQILPVMQJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florin Avram, Ludmila Sakhno, Nikolai Leonenko","submitted_at":"2012-02-14T14:02:23Z","abstract_excerpt":"We prove central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities, which are derived using the Holder-Young-Brascamp-Lieb inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3041","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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RMaEbpxTaOKz5VP8RlyAkg6ZKMTEH/HF5VbKgFJ+X8rOMvb+0x2tOiiwUZaQNh/yFB6Hu2XlkEAOH2YWgQsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:43:16.924360Z"},"content_sha256":"7aa29b96e0329e508158c8572744b17f5d57e783f1a12ff5173c87edee1a08b6","schema_version":"1.0","event_id":"sha256:7aa29b96e0329e508158c8572744b17f5d57e783f1a12ff5173c87edee1a08b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ/bundle.json","state_url":"https://pith.science/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ/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":"2026-06-04T04:43:16Z","links":{"resolver":"https://pith.science/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ","bundle":"https://pith.science/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ/bundle.json","state":"https://pith.science/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFCX7NBFCBWUL7VU5MQILPVMQJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GFCX7NBFCBWUL7VU5MQILPVMQJ","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":"2815f339e39086ef37cd5b080c9f865fbe96e6811d833ea0baa9182a4360def0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T14:02:23Z","title_canon_sha256":"f694aa191f042b6011a166008b5a164be764f4863a8decb44d3f9276c4687ba2"},"schema_version":"1.0","source":{"id":"1202.3041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3041","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3041v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3041","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"GFCX7NBFCBWU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GFCX7NBFCBWUL7VU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GFCX7NBF","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:7aa29b96e0329e508158c8572744b17f5d57e783f1a12ff5173c87edee1a08b6","target":"graph","created_at":"2026-05-18T04:02:24Z","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 prove central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities, which are derived using the Holder-Young-Brascamp-Lieb inequality.","authors_text":"Florin Avram, Ludmila Sakhno, Nikolai Leonenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T14:02:23Z","title":"Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3041","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":"sha256:9707fefa8f9e1748e38857492ff5ad66b90689a3f05358cdfa9860ecda8df44e","target":"record","created_at":"2026-05-18T04:02:24Z","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":"2815f339e39086ef37cd5b080c9f865fbe96e6811d833ea0baa9182a4360def0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T14:02:23Z","title_canon_sha256":"f694aa191f042b6011a166008b5a164be764f4863a8decb44d3f9276c4687ba2"},"schema_version":"1.0","source":{"id":"1202.3041","kind":"arxiv","version":1}},"canonical_sha256":"31457fb425106d45feb4eb2085beac826a32e6a5564ff89bf10c3b11b33f1d21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31457fb425106d45feb4eb2085beac826a32e6a5564ff89bf10c3b11b33f1d21","first_computed_at":"2026-05-18T04:02:24.281835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:24.281835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1lnyp0Qh4qU1tdd5vyI3SIuD9r5S8LXcKi/pVE4OVSgOPaSbbgWtorcus14wVdfG4taHbnTIpFRIMzoVd2uAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:24.282528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9707fefa8f9e1748e38857492ff5ad66b90689a3f05358cdfa9860ecda8df44e","sha256:7aa29b96e0329e508158c8572744b17f5d57e783f1a12ff5173c87edee1a08b6"],"state_sha256":"17dc245ec1e27ba5a130c98b7768f956ab90d70eb3e5e14d5db2d2105397fe90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2nJeacpgeceu9yqI1cxmx4OHnOncN5HE/PUwRExuMRLLvOaJwkTqMNJYNlflypDpPxBEyG3s1Y1zl1VGM+wAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:43:16.928168Z","bundle_sha256":"2b1435c591af5f7292ad58407b9c287b83fe62eb43b1e6176865fe6b50c45d11"}}