{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:4D4G6YQ5HINYDHFT7VZ5OBSSKV","short_pith_number":"pith:4D4G6YQ5","schema_version":"1.0","canonical_sha256":"e0f86f621d3a1b819cb3fd73d706525553e45f6b28371fa20a653b7a83049880","source":{"kind":"arxiv","id":"1012.1814","version":1},"attestation_state":"computed","paper":{"title":"Limit distribution in the $q$-CLT for $q \\ge 1$ 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":"2010-12-08T17:35:33Z","abstract_excerpt":"In a recent paper Hilhorst \\cite{Hilhorst2010} illustrated that the $q$-Fourier transform for $q>1$ is not invertible in the space of density functions. Using an invariance principle he constructed a family of densities with the same $q$-Fourier transform and claimed that $q$-Gaussians are not mathematically proved to be attractors. We show here that none of the distributions constructed in Hilhorst's counterexamples can be a limit distribution in the $q$-CLT, except the one whose support covers the whole real axis, which is precisely the $q$-Gaussian distribution."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.1814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-12-08T17:35:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f32aa3dc4997d0422737e11a97f314259d1d14c7d1a2bb4b18cc027d3eec5c47","abstract_canon_sha256":"3647bafd5c41a718f5d9c3f556ed969dce3ed5ba7dc2b919b6cfb237413ad82b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:51.215080Z","signature_b64":"IY504+uJZiKDWVHMwFWPeABhTKu87r1apHmhRwSAsv7FHvCAGHXvkGSf6wdso2hwIV4Y24lRI+782BnhmbkCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f86f621d3a1b819cb3fd73d706525553e45f6b28371fa20a653b7a83049880","last_reissued_at":"2026-05-18T04:33:51.214547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:51.214547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit distribution in the $q$-CLT for $q \\ge 1$ 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":"2010-12-08T17:35:33Z","abstract_excerpt":"In a recent paper Hilhorst \\cite{Hilhorst2010} illustrated that the $q$-Fourier transform for $q>1$ is not invertible in the space of density functions. Using an invariance principle he constructed a family of densities with the same $q$-Fourier transform and claimed that $q$-Gaussians are not mathematically proved to be attractors. We show here that none of the distributions constructed in Hilhorst's counterexamples can be a limit distribution in the $q$-CLT, except the one whose support covers the whole real axis, which is precisely the $q$-Gaussian distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1814","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.1814","created_at":"2026-05-18T04:33:51.214642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.1814v1","created_at":"2026-05-18T04:33:51.214642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1814","created_at":"2026-05-18T04:33:51.214642+00:00"},{"alias_kind":"pith_short_12","alias_value":"4D4G6YQ5HINY","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"4D4G6YQ5HINYDHFT","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"4D4G6YQ5","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV","json":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV.json","graph_json":"https://pith.science/api/pith-number/4D4G6YQ5HINYDHFT7VZ5OBSSKV/graph.json","events_json":"https://pith.science/api/pith-number/4D4G6YQ5HINYDHFT7VZ5OBSSKV/events.json","paper":"https://pith.science/paper/4D4G6YQ5"},"agent_actions":{"view_html":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV","download_json":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV.json","view_paper":"https://pith.science/paper/4D4G6YQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.1814&json=true","fetch_graph":"https://pith.science/api/pith-number/4D4G6YQ5HINYDHFT7VZ5OBSSKV/graph.json","fetch_events":"https://pith.science/api/pith-number/4D4G6YQ5HINYDHFT7VZ5OBSSKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV/action/storage_attestation","attest_author":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV/action/author_attestation","sign_citation":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV/action/citation_signature","submit_replication":"https://pith.science/pith/4D4G6YQ5HINYDHFT7VZ5OBSSKV/action/replication_record"}},"created_at":"2026-05-18T04:33:51.214642+00:00","updated_at":"2026-05-18T04:33:51.214642+00:00"}