{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V6WAYVZYXJC6P7IAVDZ5MVQLYS","short_pith_number":"pith:V6WAYVZY","canonical_record":{"source":{"id":"1106.1791","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-09T12:47:00Z","cross_cats_sorted":["math-ph","math.IT","math.MP","quant-ph"],"title_canon_sha256":"6e6f71d9568a7a23cda1ca884b432fa17806bdbafa21fd0368740e4dabf671af","abstract_canon_sha256":"1e26db7cce20f320bf21e383bdb88e897f55a6c1e3a7232b446fa19ddfb1bf45"},"schema_version":"1.0"},"canonical_sha256":"afac0c5738ba45e7fd00a8f3d6560bc4bd10cfcba65325d4077f6099df4ba29a","source":{"kind":"arxiv","id":"1106.1791","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1791","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1791v3","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1791","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"V6WAYVZYXJC6","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V6WAYVZYXJC6P7IA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V6WAYVZY","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V6WAYVZYXJC6P7IAVDZ5MVQLYS","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1791","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-09T12:47:00Z","cross_cats_sorted":["math-ph","math.IT","math.MP","quant-ph"],"title_canon_sha256":"6e6f71d9568a7a23cda1ca884b432fa17806bdbafa21fd0368740e4dabf671af","abstract_canon_sha256":"1e26db7cce20f320bf21e383bdb88e897f55a6c1e3a7232b446fa19ddfb1bf45"},"schema_version":"1.0"},"canonical_sha256":"afac0c5738ba45e7fd00a8f3d6560bc4bd10cfcba65325d4077f6099df4ba29a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:49.204222Z","signature_b64":"jIEc90ok7i8nLM9T8HM2Ea4gVkoSV+xc0nLskSmUrQAeIs25OE98pjphHH53UcRZ5dmwoKY6RTRNZI+Q/FPzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afac0c5738ba45e7fd00a8f3d6560bc4bd10cfcba65325d4077f6099df4ba29a","last_reissued_at":"2026-05-18T00:37:49.203556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:49.203556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1791","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:37:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9KcOshHXCsmWtSORSOXHIkGc3pCxWCPxyKYygdyl4FyTZ7VpudZdJ3bvA5/gID0a8yP/auK4eo/QIAlbk3e6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:44:29.879200Z"},"content_sha256":"610d0747a72987ea1d65031fff3cdd781208502f1e476ecbcc3fc543d74618ea","schema_version":"1.0","event_id":"sha256:610d0747a72987ea1d65031fff3cdd781208502f1e476ecbcc3fc543d74618ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V6WAYVZYXJC6P7IAVDZ5MVQLYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Characterization of Entropy in Terms of Information Loss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.IT","math.MP","quant-ph"],"primary_cat":"cs.IT","authors_text":"John C. Baez, Tobias Fritz, Tom Leinster","submitted_at":"2011-06-09T12:47:00Z","abstract_excerpt":"There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set, this characterization focuses on the `information loss', or change in entropy, associated with a measure-preserving function. Information loss is a special case of conditional entropy: namely, it is the entropy of a random variable conditioned on some function of that variable. We show that Shannon entropy gives "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1791","kind":"arxiv","version":3},"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":"2026-05-18T00:37:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Cq+kR3t9ubuCzR79FNYp0kxvyEObFpUxVIiM8rY+T5vokzb6xbw4fLFj7VRqWFNODM20hSZAokm6SEEXUVYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:44:29.879904Z"},"content_sha256":"696f09f41e945ba1030d0294c0bb83932e5f34c0fa654132bde2b3d21e5382e9","schema_version":"1.0","event_id":"sha256:696f09f41e945ba1030d0294c0bb83932e5f34c0fa654132bde2b3d21e5382e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS/bundle.json","state_url":"https://pith.science/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS/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":"2026-05-25T13:44:29Z","links":{"resolver":"https://pith.science/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS","bundle":"https://pith.science/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS/bundle.json","state":"https://pith.science/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6WAYVZYXJC6P7IAVDZ5MVQLYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V6WAYVZYXJC6P7IAVDZ5MVQLYS","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":"1e26db7cce20f320bf21e383bdb88e897f55a6c1e3a7232b446fa19ddfb1bf45","cross_cats_sorted":["math-ph","math.IT","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-09T12:47:00Z","title_canon_sha256":"6e6f71d9568a7a23cda1ca884b432fa17806bdbafa21fd0368740e4dabf671af"},"schema_version":"1.0","source":{"id":"1106.1791","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1791","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1791v3","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1791","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"V6WAYVZYXJC6","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V6WAYVZYXJC6P7IA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V6WAYVZY","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:696f09f41e945ba1030d0294c0bb83932e5f34c0fa654132bde2b3d21e5382e9","target":"graph","created_at":"2026-05-18T00:37:49Z","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":"There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set, this characterization focuses on the `information loss', or change in entropy, associated with a measure-preserving function. Information loss is a special case of conditional entropy: namely, it is the entropy of a random variable conditioned on some function of that variable. We show that Shannon entropy gives ","authors_text":"John C. Baez, Tobias Fritz, Tom Leinster","cross_cats":["math-ph","math.IT","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-09T12:47:00Z","title":"A Characterization of Entropy in Terms of Information Loss"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1791","kind":"arxiv","version":3},"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":"sha256:610d0747a72987ea1d65031fff3cdd781208502f1e476ecbcc3fc543d74618ea","target":"record","created_at":"2026-05-18T00:37:49Z","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":"1e26db7cce20f320bf21e383bdb88e897f55a6c1e3a7232b446fa19ddfb1bf45","cross_cats_sorted":["math-ph","math.IT","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-09T12:47:00Z","title_canon_sha256":"6e6f71d9568a7a23cda1ca884b432fa17806bdbafa21fd0368740e4dabf671af"},"schema_version":"1.0","source":{"id":"1106.1791","kind":"arxiv","version":3}},"canonical_sha256":"afac0c5738ba45e7fd00a8f3d6560bc4bd10cfcba65325d4077f6099df4ba29a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afac0c5738ba45e7fd00a8f3d6560bc4bd10cfcba65325d4077f6099df4ba29a","first_computed_at":"2026-05-18T00:37:49.203556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:49.203556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jIEc90ok7i8nLM9T8HM2Ea4gVkoSV+xc0nLskSmUrQAeIs25OE98pjphHH53UcRZ5dmwoKY6RTRNZI+Q/FPzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:49.204222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1791","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:610d0747a72987ea1d65031fff3cdd781208502f1e476ecbcc3fc543d74618ea","sha256:696f09f41e945ba1030d0294c0bb83932e5f34c0fa654132bde2b3d21e5382e9"],"state_sha256":"1f8e7db11915a9f547557042c8169d3c74348ebd8f34edb8e7c60b1bcd43fcc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mbqB28o487TieICfE0MpgWCuqy4xotDsMor3R0tJxjVooHWi/23e/vqmv/W1LMY+b+349V2hbHk0owesl2gVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T13:44:29.883751Z","bundle_sha256":"d1be99e2b67e3b042676d96357cc96bc3ee7b8fff2d97a015821576658b22367"}}