{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:2AXBBKQ7XKWJCUSHS4YYJVV5IC","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":"2a03354cbb53f71144d5b027e587c4c80cfdb593a96d7a247d7f291596f5c0d6","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.PR","submitted_at":"2007-06-05T09:03:26Z","title_canon_sha256":"d250d95c1cd40c0b45d3169ac5ab196c8f4881eae7c0f1a059fdecb3b670d7f4"},"schema_version":"1.0","source":{"id":"0706.0606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0606","created_at":"2026-05-18T00:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0606v1","created_at":"2026-05-18T00:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0606","created_at":"2026-05-18T00:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"2AXBBKQ7XKWJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"2AXBBKQ7XKWJCUSH","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"2AXBBKQ7","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:a5cac93a04fa8d8bb909cb4d17b9dce9a6a19abc48f4bfac189806ac6b2eb659","target":"graph","created_at":"2026-05-18T00:36:51Z","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 paper we consider the space of those probability distributions which maximize the $q$-R\\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some methods to endow this parameter space with Riemannian metric is presented: the second derivative of the $q$-R\\'enyi entropy, Tsallis-entropy and the relative entropy give rise to a Riemannian metric, the Fisher-information matrix is a natural Riemannian metric, and there are some geometrically motivated metrics which were studied by Siegel, Calvo and Oller, L","authors_text":"Attila Andai","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-06-05T09:03:26Z","title":"On the geometry of generalized Gaussian distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0606","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:f564aa6f9e94e6b585d6c437b22b2d17668cd6b069d80d5c9a03819d80d7ad9c","target":"record","created_at":"2026-05-18T00:36:51Z","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":"2a03354cbb53f71144d5b027e587c4c80cfdb593a96d7a247d7f291596f5c0d6","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.PR","submitted_at":"2007-06-05T09:03:26Z","title_canon_sha256":"d250d95c1cd40c0b45d3169ac5ab196c8f4881eae7c0f1a059fdecb3b670d7f4"},"schema_version":"1.0","source":{"id":"0706.0606","kind":"arxiv","version":1}},"canonical_sha256":"d02e10aa1fbaac915247973184d6bd40866f31404852ea67b741e48a19ea349a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d02e10aa1fbaac915247973184d6bd40866f31404852ea67b741e48a19ea349a","first_computed_at":"2026-05-18T00:36:51.990679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:51.990679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+XaOIcx7pYkJ4Ek7kmvS2dsMBWDhBNSclzlMFqtMLRfnaun2mhNigRPfmrlVvyrxGNEOLb4S7OrngcLCpd+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:51.991338Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.0606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f564aa6f9e94e6b585d6c437b22b2d17668cd6b069d80d5c9a03819d80d7ad9c","sha256:a5cac93a04fa8d8bb909cb4d17b9dce9a6a19abc48f4bfac189806ac6b2eb659"],"state_sha256":"eccd2f876ed502bba42cd7d74553df4b448be0b1ac15d55baa75a457a4c2fc6f"}