{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:GIHJKSUE44AOKFP6WBTK2H4AGD","short_pith_number":"pith:GIHJKSUE","canonical_record":{"source":{"id":"0902.1235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-02-07T12:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"864c299af17c00f473d61f1070f5a8ce34ee7b06afd2867fef497f8ed17c1e74","abstract_canon_sha256":"ce848c97ba1d3b9b3d05e6ac71925b225be8eb3e5dfbe63fa98695a6f494a1a0"},"schema_version":"1.0"},"canonical_sha256":"320e954a84e700e515feb066ad1f8030fdcd479b5368d0b0220c5b55adec168e","source":{"kind":"arxiv","id":"0902.1235","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1235","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1235v2","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1235","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"GIHJKSUE44AO","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GIHJKSUE44AOKFP6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GIHJKSUE","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:GIHJKSUE44AOKFP6WBTK2H4AGD","target":"record","payload":{"canonical_record":{"source":{"id":"0902.1235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-02-07T12:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"864c299af17c00f473d61f1070f5a8ce34ee7b06afd2867fef497f8ed17c1e74","abstract_canon_sha256":"ce848c97ba1d3b9b3d05e6ac71925b225be8eb3e5dfbe63fa98695a6f494a1a0"},"schema_version":"1.0"},"canonical_sha256":"320e954a84e700e515feb066ad1f8030fdcd479b5368d0b0220c5b55adec168e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:48.881800Z","signature_b64":"KjdIFCTx6CDxgasDsCP4CXroV/ywNFLzXWW2HXDvSDmdpAfpcBFOknSfdbUL/lzX8bqR3AMA5AmpreAQJS+7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"320e954a84e700e515feb066ad1f8030fdcd479b5368d0b0220c5b55adec168e","last_reissued_at":"2026-05-18T02:14:48.881248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:48.881248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.1235","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yj9BR1oXvLrzLTmxuJ+JBoi7ZVgz1jHCfOxYeHYhCYGDOaHJQ05NUNmnnDh7v5e5mWmqaGTkt7XYEi9psvPYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:53:09.471540Z"},"content_sha256":"db80ed3f90f160c513d3467af60c6aaf71a0bc649368dda671f224b94c7b91da","schema_version":"1.0","event_id":"sha256:db80ed3f90f160c513d3467af60c6aaf71a0bc649368dda671f224b94c7b91da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:GIHJKSUE44AOKFP6WBTK2H4AGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized information and entropy measures in physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Christian Beck","submitted_at":"2009-02-07T12:18:25Z","abstract_excerpt":"The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of information measures that are useful for the description of complex systems. Examples treated are the Renyi entropy, Tsallis entropy, Abe entropy, Kaniadakis entropy, Sharma-Mittal entropies, and a few more. Important concepts such as the axiomatic foundations, composability and Lesche stability of information measures are briefly discussed. Potential appli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1235","kind":"arxiv","version":2},"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":"2026-05-18T02:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ccmsTBTzJvc0j7L7I0+2GaoMZ2WZ+OM7gsOrx7xTebmS+1yQW7ns3OCun3T04r6EDKre3MRUeUWZ8lirNnGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:53:09.471902Z"},"content_sha256":"d6fb45cfd302fb15bcc97159ba06a9d4c9e51b6613771fd7c8cc3293bc6ee8a0","schema_version":"1.0","event_id":"sha256:d6fb45cfd302fb15bcc97159ba06a9d4c9e51b6613771fd7c8cc3293bc6ee8a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIHJKSUE44AOKFP6WBTK2H4AGD/bundle.json","state_url":"https://pith.science/pith/GIHJKSUE44AOKFP6WBTK2H4AGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIHJKSUE44AOKFP6WBTK2H4AGD/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":"2026-05-30T08:53:09Z","links":{"resolver":"https://pith.science/pith/GIHJKSUE44AOKFP6WBTK2H4AGD","bundle":"https://pith.science/pith/GIHJKSUE44AOKFP6WBTK2H4AGD/bundle.json","state":"https://pith.science/pith/GIHJKSUE44AOKFP6WBTK2H4AGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIHJKSUE44AOKFP6WBTK2H4AGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GIHJKSUE44AOKFP6WBTK2H4AGD","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":"ce848c97ba1d3b9b3d05e6ac71925b225be8eb3e5dfbe63fa98695a6f494a1a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-02-07T12:18:25Z","title_canon_sha256":"864c299af17c00f473d61f1070f5a8ce34ee7b06afd2867fef497f8ed17c1e74"},"schema_version":"1.0","source":{"id":"0902.1235","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1235","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1235v2","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1235","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"GIHJKSUE44AO","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GIHJKSUE44AOKFP6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GIHJKSUE","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:d6fb45cfd302fb15bcc97159ba06a9d4c9e51b6613771fd7c8cc3293bc6ee8a0","target":"graph","created_at":"2026-05-18T02:14:48Z","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":"The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of information measures that are useful for the description of complex systems. Examples treated are the Renyi entropy, Tsallis entropy, Abe entropy, Kaniadakis entropy, Sharma-Mittal entropies, and a few more. Important concepts such as the axiomatic foundations, composability and Lesche stability of information measures are briefly discussed. Potential appli","authors_text":"Christian Beck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-02-07T12:18:25Z","title":"Generalized information and entropy measures in physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1235","kind":"arxiv","version":2},"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:db80ed3f90f160c513d3467af60c6aaf71a0bc649368dda671f224b94c7b91da","target":"record","created_at":"2026-05-18T02:14:48Z","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":"ce848c97ba1d3b9b3d05e6ac71925b225be8eb3e5dfbe63fa98695a6f494a1a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-02-07T12:18:25Z","title_canon_sha256":"864c299af17c00f473d61f1070f5a8ce34ee7b06afd2867fef497f8ed17c1e74"},"schema_version":"1.0","source":{"id":"0902.1235","kind":"arxiv","version":2}},"canonical_sha256":"320e954a84e700e515feb066ad1f8030fdcd479b5368d0b0220c5b55adec168e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"320e954a84e700e515feb066ad1f8030fdcd479b5368d0b0220c5b55adec168e","first_computed_at":"2026-05-18T02:14:48.881248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:48.881248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KjdIFCTx6CDxgasDsCP4CXroV/ywNFLzXWW2HXDvSDmdpAfpcBFOknSfdbUL/lzX8bqR3AMA5AmpreAQJS+7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:48.881800Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1235","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db80ed3f90f160c513d3467af60c6aaf71a0bc649368dda671f224b94c7b91da","sha256:d6fb45cfd302fb15bcc97159ba06a9d4c9e51b6613771fd7c8cc3293bc6ee8a0"],"state_sha256":"e6b82c706b51cece67168e0cd98c8d7fe84182259d9c11abd1df98c391475ce7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3NlPSQ3umfSm64Lp9Dep9n8DCzUFOk2wCGIKPK1GCPyfUQL/ArgXPUtrMLQsEETXkBCI5FK/TUXGcZcGbQg/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:53:09.474217Z","bundle_sha256":"bc816d265bd3260b4ea0e7e55d15c0414b7761b207c4dcc374b1c7604950df0d"}}