{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XLEXBEY5UHFSQYFZE64IHSDRSJ","short_pith_number":"pith:XLEXBEY5","canonical_record":{"source":{"id":"1609.02425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-08T13:40:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ebdf405abf12f381c3f4edea25514f5ed14d4bc83dd38dd5b24e739c198a3c43","abstract_canon_sha256":"24d88e37f6ab4f4606b52cf74d0e2924cb50c7ccb1b0c4a3382226a29f0d9b5d"},"schema_version":"1.0"},"canonical_sha256":"bac970931da1cb2860b927b883c8719277a6d8940261eaaad7229a63977c1741","source":{"kind":"arxiv","id":"1609.02425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02425","created_at":"2026-05-18T01:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02425v1","created_at":"2026-05-18T01:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02425","created_at":"2026-05-18T01:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"XLEXBEY5UHFS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XLEXBEY5UHFSQYFZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XLEXBEY5","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XLEXBEY5UHFSQYFZE64IHSDRSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-08T13:40:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ebdf405abf12f381c3f4edea25514f5ed14d4bc83dd38dd5b24e739c198a3c43","abstract_canon_sha256":"24d88e37f6ab4f4606b52cf74d0e2924cb50c7ccb1b0c4a3382226a29f0d9b5d"},"schema_version":"1.0"},"canonical_sha256":"bac970931da1cb2860b927b883c8719277a6d8940261eaaad7229a63977c1741","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:36.764203Z","signature_b64":"bxoxpRKmKnGSIkbjOFI/YEcZXJVLBF8BFHCPrtvcy2CrpUgg1gJ4UPhlH8Ada1cS5h3JPYvWiH9FVWEesd5nCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bac970931da1cb2860b927b883c8719277a6d8940261eaaad7229a63977c1741","last_reissued_at":"2026-05-18T01:02:36.763543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:36.763543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02425","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":"2026-05-18T01:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NngbSbixkXPR8VbCMyNkWxif+2taAfxy8L+puIpq4C75hsMgiEJFkEuOE/+br+Z7PzJEQft8y6edvJmFrGifAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:44:30.129885Z"},"content_sha256":"4723dea8286070a934fd595822582ac6a38692f06d55e4aeff6d50bbc5e9a15f","schema_version":"1.0","event_id":"sha256:4723dea8286070a934fd595822582ac6a38692f06d55e4aeff6d50bbc5e9a15f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XLEXBEY5UHFSQYFZE64IHSDRSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The limit distribution in the $q$-CLT for $q \\ge 1$ is unique and can not have a compact support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Constantino Tsallis, Sabir Umarov","submitted_at":"2016-09-08T13:40:05Z","abstract_excerpt":"In a paper by Umarov, Tsallis and Steinberg (2008), a generalization of the Fourier transform, called the $q$-Fourier transform, was introduced and applied for the proof of a $q$-generalized central limit theorem ($q$-CLT). Subsequently, Hilhorst illustrated (2009 and 2010) that the $q$-Fourier transform for $q>1$ is not invertible in the space of density functions. Indeed, using an invariance principle, he constructed a family of densities with the same $q$-Fourier transform and noted that \"as a consequence, the $q$-central limit theorem falls short of achieving its stated goal\". The distribu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02425","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":"2026-05-18T01:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLtbVE3k6fCK97B0GQuIqIP4r9a3tr/ppbWL/p4/Xjp8tnhBe+t3Kw8h2XelsU1HO8AbSp7mCOrWqfC0J3u/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:44:30.130247Z"},"content_sha256":"b4d090b8dfd2bccbd3670b80e8fe6e36dff99bc4cba2a499bf03cbda865a9cd3","schema_version":"1.0","event_id":"sha256:b4d090b8dfd2bccbd3670b80e8fe6e36dff99bc4cba2a499bf03cbda865a9cd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ/bundle.json","state_url":"https://pith.science/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ/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":"2026-06-05T08:44:30Z","links":{"resolver":"https://pith.science/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ","bundle":"https://pith.science/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ/bundle.json","state":"https://pith.science/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLEXBEY5UHFSQYFZE64IHSDRSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XLEXBEY5UHFSQYFZE64IHSDRSJ","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":"24d88e37f6ab4f4606b52cf74d0e2924cb50c7ccb1b0c4a3382226a29f0d9b5d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-08T13:40:05Z","title_canon_sha256":"ebdf405abf12f381c3f4edea25514f5ed14d4bc83dd38dd5b24e739c198a3c43"},"schema_version":"1.0","source":{"id":"1609.02425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02425","created_at":"2026-05-18T01:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02425v1","created_at":"2026-05-18T01:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02425","created_at":"2026-05-18T01:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"XLEXBEY5UHFS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XLEXBEY5UHFSQYFZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XLEXBEY5","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:b4d090b8dfd2bccbd3670b80e8fe6e36dff99bc4cba2a499bf03cbda865a9cd3","target":"graph","created_at":"2026-05-18T01:02:36Z","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":"In a paper by Umarov, Tsallis and Steinberg (2008), a generalization of the Fourier transform, called the $q$-Fourier transform, was introduced and applied for the proof of a $q$-generalized central limit theorem ($q$-CLT). Subsequently, Hilhorst illustrated (2009 and 2010) that the $q$-Fourier transform for $q>1$ is not invertible in the space of density functions. Indeed, using an invariance principle, he constructed a family of densities with the same $q$-Fourier transform and noted that \"as a consequence, the $q$-central limit theorem falls short of achieving its stated goal\". The distribu","authors_text":"Constantino Tsallis, Sabir Umarov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-08T13:40:05Z","title":"The limit distribution in the $q$-CLT for $q \\ge 1$ is unique and can not have a compact support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02425","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":"sha256:4723dea8286070a934fd595822582ac6a38692f06d55e4aeff6d50bbc5e9a15f","target":"record","created_at":"2026-05-18T01:02:36Z","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":"24d88e37f6ab4f4606b52cf74d0e2924cb50c7ccb1b0c4a3382226a29f0d9b5d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-08T13:40:05Z","title_canon_sha256":"ebdf405abf12f381c3f4edea25514f5ed14d4bc83dd38dd5b24e739c198a3c43"},"schema_version":"1.0","source":{"id":"1609.02425","kind":"arxiv","version":1}},"canonical_sha256":"bac970931da1cb2860b927b883c8719277a6d8940261eaaad7229a63977c1741","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bac970931da1cb2860b927b883c8719277a6d8940261eaaad7229a63977c1741","first_computed_at":"2026-05-18T01:02:36.763543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:36.763543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bxoxpRKmKnGSIkbjOFI/YEcZXJVLBF8BFHCPrtvcy2CrpUgg1gJ4UPhlH8Ada1cS5h3JPYvWiH9FVWEesd5nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:36.764203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4723dea8286070a934fd595822582ac6a38692f06d55e4aeff6d50bbc5e9a15f","sha256:b4d090b8dfd2bccbd3670b80e8fe6e36dff99bc4cba2a499bf03cbda865a9cd3"],"state_sha256":"a4334e36b28331a20fc49f1e6b540289f3225d433e6a6e4a24089aba8d090192"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7z/BQuOUqh83yqxa9RsVDHqQLfRC+Tc2k40mCGsBsmVgdQnKJD0sWNNgOgoq5E8lMoi8B1GsraNzKlW4lvO1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:44:30.132660Z","bundle_sha256":"3fcea4658a459833f6eb2f823876767e1f14f973b2cdd7e133b43d73ab1e205e"}}