{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XEQDD4VPAECSPMULD6RFD4WOXH","short_pith_number":"pith:XEQDD4VP","canonical_record":{"source":{"id":"1412.5364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-17T12:41:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4fa29bf3dba75e16052725ffa4e3e2016207b02fc7117b10e2ab587da3eeb0a3","abstract_canon_sha256":"97c5569c923594469de586374f1ad853509018a1ef8f5e09f4262a9405294c91"},"schema_version":"1.0"},"canonical_sha256":"b92031f2af010527b28b1fa251f2ceb9f3355661621bdc6f7a52903995b509c1","source":{"kind":"arxiv","id":"1412.5364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5364","created_at":"2026-05-18T02:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5364v1","created_at":"2026-05-18T02:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5364","created_at":"2026-05-18T02:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"XEQDD4VPAECS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XEQDD4VPAECSPMUL","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XEQDD4VP","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XEQDD4VPAECSPMULD6RFD4WOXH","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-17T12:41:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4fa29bf3dba75e16052725ffa4e3e2016207b02fc7117b10e2ab587da3eeb0a3","abstract_canon_sha256":"97c5569c923594469de586374f1ad853509018a1ef8f5e09f4262a9405294c91"},"schema_version":"1.0"},"canonical_sha256":"b92031f2af010527b28b1fa251f2ceb9f3355661621bdc6f7a52903995b509c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:07.869639Z","signature_b64":"oxtSIdctoN8NgoYt960nyl1nAV+R9pQzWG1/9bxTJrgCiOdZYzLGM0a3QvLL6pzDtn1JRdpbN6K4aXMO6quBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b92031f2af010527b28b1fa251f2ceb9f3355661621bdc6f7a52903995b509c1","last_reissued_at":"2026-05-18T02:04:07.868992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:07.868992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5364","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":"2026-05-18T02:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBS3zimnm1Mf5RlM4wjqHMWpA846OklAs7vFt8aDlWgJ0cdTCc262h2HuJGimaw+5dZBiNO2083ePyviSrd+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:06:06.879631Z"},"content_sha256":"4c2038d9538eb0d4e3ed78b1095f450354cb6f2742fa4a04e15f0c651d7b0849","schema_version":"1.0","event_id":"sha256:4c2038d9538eb0d4e3ed78b1095f450354cb6f2742fa4a04e15f0c651d7b0849"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XEQDD4VPAECSPMULD6RFD4WOXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Edgeworth Expansion: Corrections to the Gaussian-L\\'evy Central Limit Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"David A. Kessler, Eli Barkai, Netanel Hazut, Shlomi Medalion","submitted_at":"2014-12-17T12:41:54Z","abstract_excerpt":"In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of variables with an infinite variance which converge by the generalized central limit theorem to a L\\'evy $\\alpha$-stable density function. Our correction may be written by means of a series of fractional derivatives of the L\\'evy and the conjugate L\\'evy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the ser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5364","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":"2026-05-18T02:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8teqb09WQul4sVZ/yEU5mZ1BOuGFM3nTwxmSLuD0Y+C22XhSmKvzJFeM7YyJMcOKCm+p7f1Kc32QD4bEVxtBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:06:06.879980Z"},"content_sha256":"717dd0b050a5dac08147b01924e8591a9b7039d7f08d4b1232cfb0f97f5b6571","schema_version":"1.0","event_id":"sha256:717dd0b050a5dac08147b01924e8591a9b7039d7f08d4b1232cfb0f97f5b6571"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XEQDD4VPAECSPMULD6RFD4WOXH/bundle.json","state_url":"https://pith.science/pith/XEQDD4VPAECSPMULD6RFD4WOXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XEQDD4VPAECSPMULD6RFD4WOXH/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":"2026-05-22T19:06:06Z","links":{"resolver":"https://pith.science/pith/XEQDD4VPAECSPMULD6RFD4WOXH","bundle":"https://pith.science/pith/XEQDD4VPAECSPMULD6RFD4WOXH/bundle.json","state":"https://pith.science/pith/XEQDD4VPAECSPMULD6RFD4WOXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XEQDD4VPAECSPMULD6RFD4WOXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XEQDD4VPAECSPMULD6RFD4WOXH","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":"97c5569c923594469de586374f1ad853509018a1ef8f5e09f4262a9405294c91","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-17T12:41:54Z","title_canon_sha256":"4fa29bf3dba75e16052725ffa4e3e2016207b02fc7117b10e2ab587da3eeb0a3"},"schema_version":"1.0","source":{"id":"1412.5364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5364","created_at":"2026-05-18T02:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5364v1","created_at":"2026-05-18T02:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5364","created_at":"2026-05-18T02:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"XEQDD4VPAECS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XEQDD4VPAECSPMUL","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XEQDD4VP","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:717dd0b050a5dac08147b01924e8591a9b7039d7f08d4b1232cfb0f97f5b6571","target":"graph","created_at":"2026-05-18T02:04:07Z","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 article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of variables with an infinite variance which converge by the generalized central limit theorem to a L\\'evy $\\alpha$-stable density function. Our correction may be written by means of a series of fractional derivatives of the L\\'evy and the conjugate L\\'evy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the ser","authors_text":"David A. Kessler, Eli Barkai, Netanel Hazut, Shlomi Medalion","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-17T12:41:54Z","title":"Fractional Edgeworth Expansion: Corrections to the Gaussian-L\\'evy Central Limit Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5364","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":"sha256:4c2038d9538eb0d4e3ed78b1095f450354cb6f2742fa4a04e15f0c651d7b0849","target":"record","created_at":"2026-05-18T02:04:07Z","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":"97c5569c923594469de586374f1ad853509018a1ef8f5e09f4262a9405294c91","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-17T12:41:54Z","title_canon_sha256":"4fa29bf3dba75e16052725ffa4e3e2016207b02fc7117b10e2ab587da3eeb0a3"},"schema_version":"1.0","source":{"id":"1412.5364","kind":"arxiv","version":1}},"canonical_sha256":"b92031f2af010527b28b1fa251f2ceb9f3355661621bdc6f7a52903995b509c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b92031f2af010527b28b1fa251f2ceb9f3355661621bdc6f7a52903995b509c1","first_computed_at":"2026-05-18T02:04:07.868992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:07.868992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oxtSIdctoN8NgoYt960nyl1nAV+R9pQzWG1/9bxTJrgCiOdZYzLGM0a3QvLL6pzDtn1JRdpbN6K4aXMO6quBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:07.869639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c2038d9538eb0d4e3ed78b1095f450354cb6f2742fa4a04e15f0c651d7b0849","sha256:717dd0b050a5dac08147b01924e8591a9b7039d7f08d4b1232cfb0f97f5b6571"],"state_sha256":"303b403fd629ef721a5df8f7fedd48cc83a446365193a77a4fd17f3c1c1a45fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NgUSJ/b+qMnoPUJwMWUqfhuU1amw9iF3WCUaE3SfRgLEq5Zjx8OUNu1LJrdKwME9EdaLCtDjYB/3kfJGCssQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:06:06.882213Z","bundle_sha256":"173aaa014e9b5ebecbb4052984c7af6a7043410d768ef966f50658142eada711"}}