{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KKWPJSLBREKDXCS4P6XGVMZC7J","short_pith_number":"pith:KKWPJSLB","canonical_record":{"source":{"id":"1009.0937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-09-05T17:49:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7b86d254788dfab585c8fdcba7b0393ae873b2a247b70aa84a963b57bcff9a5b","abstract_canon_sha256":"463d1696047c6d43cac6ea3216f911d7dc04513e25475838927f5bb01478cfed"},"schema_version":"1.0"},"canonical_sha256":"52acf4c96189143b8a5c7fae6ab322fa4863b38e588caee05f1706a52bf204d2","source":{"kind":"arxiv","id":"1009.0937","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0937","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0937v1","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0937","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"KKWPJSLBREKD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KKWPJSLBREKDXCS4","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KKWPJSLB","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KKWPJSLBREKDXCS4P6XGVMZC7J","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-09-05T17:49:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7b86d254788dfab585c8fdcba7b0393ae873b2a247b70aa84a963b57bcff9a5b","abstract_canon_sha256":"463d1696047c6d43cac6ea3216f911d7dc04513e25475838927f5bb01478cfed"},"schema_version":"1.0"},"canonical_sha256":"52acf4c96189143b8a5c7fae6ab322fa4863b38e588caee05f1706a52bf204d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:24.288935Z","signature_b64":"tCtSkMJVN0leQZrSZwJ8NCswk7pDfFFnCLYhC7+Ia2iXEWTo7g3dfNPISXOiwaoxd+yBPfCJeVsXGct88j7fCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52acf4c96189143b8a5c7fae6ab322fa4863b38e588caee05f1706a52bf204d2","last_reissued_at":"2026-05-18T04:41:24.288273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:24.288273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0937","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":"2026-05-18T04:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHBXp8UFh53O0b2hbChuWTVNTBQ5Kdud0HrneWx3nzJLvhh9o6yjhbeh/Ekv32ZG/Wd3g4ZgqhRfH4E0dKYOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:47:48.020237Z"},"content_sha256":"492d4967016b8fbafc65919e3b9a1d20844b02f587b87f07cec5a5a4d99ebb34","schema_version":"1.0","event_id":"sha256:492d4967016b8fbafc65919e3b9a1d20844b02f587b87f07cec5a5a4d99ebb34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KKWPJSLBREKDXCS4P6XGVMZC7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The uncertainty measure for q-exponential distribution function","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Aziz El Kaabouchi, Congjie Ou, Jincan Chen, Qiuping A. Wang","submitted_at":"2010-09-05T17:49:25Z","abstract_excerpt":"Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained here can be considered as a new entropic form for the abnormal physical systems with complex interaction. The entropy obtained here also presents non-additive property for two independent subsystems and it will tend to the Boltzmann-Gibbs entropy when the nonextensive parameter q->1. It is very important to find that for different systems with any q, this ent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0937","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":"2026-05-18T04:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJTrklrJ36v0+qEdhpzI4MSQkwfAF0QDgqbgghquYppLNjsVoXtZqUgsTLhHd1Jq7eL7VNDddGTVkw5VPsFfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:47:48.020604Z"},"content_sha256":"f9871b6c08640f4655eff514b775e43c69d2fdcd1abf8418790d807556d63a64","schema_version":"1.0","event_id":"sha256:f9871b6c08640f4655eff514b775e43c69d2fdcd1abf8418790d807556d63a64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKWPJSLBREKDXCS4P6XGVMZC7J/bundle.json","state_url":"https://pith.science/pith/KKWPJSLBREKDXCS4P6XGVMZC7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKWPJSLBREKDXCS4P6XGVMZC7J/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":"2026-06-05T18:47:48Z","links":{"resolver":"https://pith.science/pith/KKWPJSLBREKDXCS4P6XGVMZC7J","bundle":"https://pith.science/pith/KKWPJSLBREKDXCS4P6XGVMZC7J/bundle.json","state":"https://pith.science/pith/KKWPJSLBREKDXCS4P6XGVMZC7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKWPJSLBREKDXCS4P6XGVMZC7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KKWPJSLBREKDXCS4P6XGVMZC7J","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":"463d1696047c6d43cac6ea3216f911d7dc04513e25475838927f5bb01478cfed","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-09-05T17:49:25Z","title_canon_sha256":"7b86d254788dfab585c8fdcba7b0393ae873b2a247b70aa84a963b57bcff9a5b"},"schema_version":"1.0","source":{"id":"1009.0937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0937","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0937v1","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0937","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"KKWPJSLBREKD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KKWPJSLBREKDXCS4","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KKWPJSLB","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:f9871b6c08640f4655eff514b775e43c69d2fdcd1abf8418790d807556d63a64","target":"graph","created_at":"2026-05-18T04:41:24Z","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":"Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained here can be considered as a new entropic form for the abnormal physical systems with complex interaction. The entropy obtained here also presents non-additive property for two independent subsystems and it will tend to the Boltzmann-Gibbs entropy when the nonextensive parameter q->1. It is very important to find that for different systems with any q, this ent","authors_text":"Aziz El Kaabouchi, Congjie Ou, Jincan Chen, Qiuping A. Wang","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-09-05T17:49:25Z","title":"The uncertainty measure for q-exponential distribution function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0937","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":"sha256:492d4967016b8fbafc65919e3b9a1d20844b02f587b87f07cec5a5a4d99ebb34","target":"record","created_at":"2026-05-18T04:41:24Z","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":"463d1696047c6d43cac6ea3216f911d7dc04513e25475838927f5bb01478cfed","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-09-05T17:49:25Z","title_canon_sha256":"7b86d254788dfab585c8fdcba7b0393ae873b2a247b70aa84a963b57bcff9a5b"},"schema_version":"1.0","source":{"id":"1009.0937","kind":"arxiv","version":1}},"canonical_sha256":"52acf4c96189143b8a5c7fae6ab322fa4863b38e588caee05f1706a52bf204d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52acf4c96189143b8a5c7fae6ab322fa4863b38e588caee05f1706a52bf204d2","first_computed_at":"2026-05-18T04:41:24.288273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:24.288273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tCtSkMJVN0leQZrSZwJ8NCswk7pDfFFnCLYhC7+Ia2iXEWTo7g3dfNPISXOiwaoxd+yBPfCJeVsXGct88j7fCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:24.288935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:492d4967016b8fbafc65919e3b9a1d20844b02f587b87f07cec5a5a4d99ebb34","sha256:f9871b6c08640f4655eff514b775e43c69d2fdcd1abf8418790d807556d63a64"],"state_sha256":"f31bd5a955f7a295b4c544c1de017de87153cf9b6bf6f138a3db69d537ac13db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3C/nz19A37ZEB1G6tltOhlI403kSPIqQjkp746VicooDb6ioB5Y+lT9bG6nwYqLjYcuBPQl7yrIKHlTZttk1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:47:48.022661Z","bundle_sha256":"40a26b69f65544a9b6beb394a8325c91256147a8eed7015372be41ffc555eca8"}}