{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WYSHBXA6PFF5L4WZI3LUQKN2AW","short_pith_number":"pith:WYSHBXA6","canonical_record":{"source":{"id":"1312.2208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-08T13:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"b974b8887900e928794a6c000000f59a69b246887879f886b21d5f43b1c4ea52","abstract_canon_sha256":"0112969bc9f5d5df19448670be0108d518c472994844aee8b187fb77e58429d8"},"schema_version":"1.0"},"canonical_sha256":"b62470dc1e794bd5f2d946d74829ba05964034e553f55d1b77e0192ef92a70b0","source":{"kind":"arxiv","id":"1312.2208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2208","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2208v1","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2208","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"pith_short_12","alias_value":"WYSHBXA6PFF5","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYSHBXA6PFF5L4WZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYSHBXA6","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WYSHBXA6PFF5L4WZI3LUQKN2AW","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-08T13:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"b974b8887900e928794a6c000000f59a69b246887879f886b21d5f43b1c4ea52","abstract_canon_sha256":"0112969bc9f5d5df19448670be0108d518c472994844aee8b187fb77e58429d8"},"schema_version":"1.0"},"canonical_sha256":"b62470dc1e794bd5f2d946d74829ba05964034e553f55d1b77e0192ef92a70b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:33.949372Z","signature_b64":"UmQKBLBB4gqpx62v90SX1qsOmZJWy5Vxsd0M6ZjGqJoYNSM3Sh2XrYoAv+6eclku4Wc+sfLtCPFWPo8tx41BCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b62470dc1e794bd5f2d946d74829ba05964034e553f55d1b77e0192ef92a70b0","last_reissued_at":"2026-05-18T03:02:33.948430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:33.948430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2208","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":"2026-05-18T03:02:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TykKiPm9yc7N84/j0egF3og1l/qhbXjvUxoiEUDBzbAAOKhxINKeu5/4H4mF6tH5BxTFkOy4K21HdOvT2HYmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:52:15.583057Z"},"content_sha256":"cc9f672d287728f21360899f9e0992cf0d72e504157b2bb6257479eb27fe9b6c","schema_version":"1.0","event_id":"sha256:cc9f672d287728f21360899f9e0992cf0d72e504157b2bb6257479eb27fe9b6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WYSHBXA6PFF5L4WZI3LUQKN2AW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rita Giuliano, Zbigniew S. Szewczak","submitted_at":"2013-12-08T13:09:52Z","abstract_excerpt":"In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $\\alpha$--stable law, $\\alpha\\in(1,2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2208","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":"2026-05-18T03:02:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6gjiidz51Rjya7McIR9zPlh1vrKLVdY5CNqlRF4q2SifReAASvYaM7g/vE6OqYjeyPbVJN2DWbwd0SRXB+xTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:52:15.583412Z"},"content_sha256":"9924d6a86e30fe7e989d160e077d992d449c6111c808e8372d50c9a01dd030df","schema_version":"1.0","event_id":"sha256:9924d6a86e30fe7e989d160e077d992d449c6111c808e8372d50c9a01dd030df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW/bundle.json","state_url":"https://pith.science/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW/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":"2026-06-23T00:52:15Z","links":{"resolver":"https://pith.science/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW","bundle":"https://pith.science/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW/bundle.json","state":"https://pith.science/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYSHBXA6PFF5L4WZI3LUQKN2AW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WYSHBXA6PFF5L4WZI3LUQKN2AW","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":"0112969bc9f5d5df19448670be0108d518c472994844aee8b187fb77e58429d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-08T13:09:52Z","title_canon_sha256":"b974b8887900e928794a6c000000f59a69b246887879f886b21d5f43b1c4ea52"},"schema_version":"1.0","source":{"id":"1312.2208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2208","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2208v1","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2208","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"pith_short_12","alias_value":"WYSHBXA6PFF5","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYSHBXA6PFF5L4WZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYSHBXA6","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:9924d6a86e30fe7e989d160e077d992d449c6111c808e8372d50c9a01dd030df","target":"graph","created_at":"2026-05-18T03:02:33Z","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 the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $\\alpha$--stable law, $\\alpha\\in(1,2)$.","authors_text":"Rita Giuliano, Zbigniew S. Szewczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-08T13:09:52Z","title":"A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2208","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:cc9f672d287728f21360899f9e0992cf0d72e504157b2bb6257479eb27fe9b6c","target":"record","created_at":"2026-05-18T03:02:33Z","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":"0112969bc9f5d5df19448670be0108d518c472994844aee8b187fb77e58429d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-08T13:09:52Z","title_canon_sha256":"b974b8887900e928794a6c000000f59a69b246887879f886b21d5f43b1c4ea52"},"schema_version":"1.0","source":{"id":"1312.2208","kind":"arxiv","version":1}},"canonical_sha256":"b62470dc1e794bd5f2d946d74829ba05964034e553f55d1b77e0192ef92a70b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b62470dc1e794bd5f2d946d74829ba05964034e553f55d1b77e0192ef92a70b0","first_computed_at":"2026-05-18T03:02:33.948430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:33.948430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UmQKBLBB4gqpx62v90SX1qsOmZJWy5Vxsd0M6ZjGqJoYNSM3Sh2XrYoAv+6eclku4Wc+sfLtCPFWPo8tx41BCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:33.949372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc9f672d287728f21360899f9e0992cf0d72e504157b2bb6257479eb27fe9b6c","sha256:9924d6a86e30fe7e989d160e077d992d449c6111c808e8372d50c9a01dd030df"],"state_sha256":"2d8d4aa5f274cfe1803c57c6812648263d0f8054acde3fb73bb46a6a14b67e76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cLCPgaq/PfKtQ66OWTH60hJOb674SiUOGVmtxBKBn/Bmb6REbxGbCup96h7luGXSctjpnzvSM9gIG5RNIqY8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:52:15.585335Z","bundle_sha256":"7bceba394e4b472f5abd6a968f1430491f28778cbf7692f2077cbee635f57435"}}