{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T3KVYGNWOUFFGUC6546HINNY2N","short_pith_number":"pith:T3KVYGNW","canonical_record":{"source":{"id":"1509.02190","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-07T21:05:01Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"c9e91cb2b54ab4a696662368cf025aeda41f66a6f4fa5f8eb9c6c684613b71ba","abstract_canon_sha256":"c4f01160977e7f1b4c365b5f08521b73515f2b11c040e7a4583959f2b2f1bea1"},"schema_version":"1.0"},"canonical_sha256":"9ed55c19b6750a53505eef3c7435b8d362bee2b28cfb9929ba8568ec609cb55e","source":{"kind":"arxiv","id":"1509.02190","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02190","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02190v4","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02190","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"T3KVYGNWOUFF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T3KVYGNWOUFFGUC6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T3KVYGNW","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T3KVYGNWOUFFGUC6546HINNY2N","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02190","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-07T21:05:01Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"c9e91cb2b54ab4a696662368cf025aeda41f66a6f4fa5f8eb9c6c684613b71ba","abstract_canon_sha256":"c4f01160977e7f1b4c365b5f08521b73515f2b11c040e7a4583959f2b2f1bea1"},"schema_version":"1.0"},"canonical_sha256":"9ed55c19b6750a53505eef3c7435b8d362bee2b28cfb9929ba8568ec609cb55e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:07.729972Z","signature_b64":"IR1J/X2oBXexSfHA/G8dGyE9kKOLVyjzDZXQtFC3dlhRRyw9So4MtsdSpCYuk7YLraWyfTKTVQct3f/DDFc/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ed55c19b6750a53505eef3c7435b8d362bee2b28cfb9929ba8568ec609cb55e","last_reissued_at":"2026-05-18T01:30:07.729464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:07.729464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02190","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aBf5yYUOlDbTwodjioiEsKT33kwawzb1AxHT1YJBvOaklYutZ63h5Z0pndLRyABN0hyWKoSdNbwqUuBEWlOAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:58:20.741060Z"},"content_sha256":"99a88e1f4a94cafceb803de2175bec125de25299dd18b0ad572a8ade3f69309e","schema_version":"1.0","event_id":"sha256:99a88e1f4a94cafceb803de2175bec125de25299dd18b0ad572a8ade3f69309e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T3KVYGNWOUFFGUC6546HINNY2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended inequalities for weighted Renyi entropy involving generalized Gaussian densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Salimeh Yasaei Sekeh","submitted_at":"2015-09-07T21:05:01Z","abstract_excerpt":"In this paper the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\\alpha$-th generalized derivation and ($\\alpha$; p)-th weighted Fisher information, extended versions of the moment-entropy, Fisher information and Cramer-Rao inequalities in terms of generalized Gaussian densities are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02190","kind":"arxiv","version":4},"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":"2026-05-18T01:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bo0LFMGssFQLIArV9rPCFc6DrNs5mXu/ydpx1GJChOsq0FUum3TDUzsIS7UkpjpZpb5nO8r4KQtHB/7XBwMRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:58:20.741711Z"},"content_sha256":"70888dd3efafab4d3c8613f0e783b6da1e4dedc1c6e1df48c6bbee02d02f16a4","schema_version":"1.0","event_id":"sha256:70888dd3efafab4d3c8613f0e783b6da1e4dedc1c6e1df48c6bbee02d02f16a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3KVYGNWOUFFGUC6546HINNY2N/bundle.json","state_url":"https://pith.science/pith/T3KVYGNWOUFFGUC6546HINNY2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3KVYGNWOUFFGUC6546HINNY2N/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":"2026-06-09T13:58:20Z","links":{"resolver":"https://pith.science/pith/T3KVYGNWOUFFGUC6546HINNY2N","bundle":"https://pith.science/pith/T3KVYGNWOUFFGUC6546HINNY2N/bundle.json","state":"https://pith.science/pith/T3KVYGNWOUFFGUC6546HINNY2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3KVYGNWOUFFGUC6546HINNY2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T3KVYGNWOUFFGUC6546HINNY2N","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":"c4f01160977e7f1b4c365b5f08521b73515f2b11c040e7a4583959f2b2f1bea1","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-07T21:05:01Z","title_canon_sha256":"c9e91cb2b54ab4a696662368cf025aeda41f66a6f4fa5f8eb9c6c684613b71ba"},"schema_version":"1.0","source":{"id":"1509.02190","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02190","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02190v4","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02190","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"T3KVYGNWOUFF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T3KVYGNWOUFFGUC6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T3KVYGNW","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:70888dd3efafab4d3c8613f0e783b6da1e4dedc1c6e1df48c6bbee02d02f16a4","target":"graph","created_at":"2026-05-18T01:30:07Z","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 paper the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\\alpha$-th generalized derivation and ($\\alpha$; p)-th weighted Fisher information, extended versions of the moment-entropy, Fisher information and Cramer-Rao inequalities in terms of generalized Gaussian densities are given.","authors_text":"Salimeh Yasaei Sekeh","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-07T21:05:01Z","title":"Extended inequalities for weighted Renyi entropy involving generalized Gaussian densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02190","kind":"arxiv","version":4},"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":"sha256:99a88e1f4a94cafceb803de2175bec125de25299dd18b0ad572a8ade3f69309e","target":"record","created_at":"2026-05-18T01:30:07Z","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":"c4f01160977e7f1b4c365b5f08521b73515f2b11c040e7a4583959f2b2f1bea1","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-07T21:05:01Z","title_canon_sha256":"c9e91cb2b54ab4a696662368cf025aeda41f66a6f4fa5f8eb9c6c684613b71ba"},"schema_version":"1.0","source":{"id":"1509.02190","kind":"arxiv","version":4}},"canonical_sha256":"9ed55c19b6750a53505eef3c7435b8d362bee2b28cfb9929ba8568ec609cb55e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ed55c19b6750a53505eef3c7435b8d362bee2b28cfb9929ba8568ec609cb55e","first_computed_at":"2026-05-18T01:30:07.729464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:07.729464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IR1J/X2oBXexSfHA/G8dGyE9kKOLVyjzDZXQtFC3dlhRRyw9So4MtsdSpCYuk7YLraWyfTKTVQct3f/DDFc/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:07.729972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02190","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99a88e1f4a94cafceb803de2175bec125de25299dd18b0ad572a8ade3f69309e","sha256:70888dd3efafab4d3c8613f0e783b6da1e4dedc1c6e1df48c6bbee02d02f16a4"],"state_sha256":"74a3b5c56bc821bc61552ea1b309eace4bbf86b54c9e55b565118e205ed3fb9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RivAJgONEd39uiYzyo2eFDLasw21j0uiqRP4YlE0B+6g+E0F0R1zdLw4oaMBLQ5wOMIuEQ0+VWY5TU9iieXPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:58:20.745581Z","bundle_sha256":"59f4b10d5166b321eab28cc648470557c6d9e7923aa1d32e6d2ca49d8bce6e21"}}