{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RWEVNNXEXWX7U5MNM2KYH2NQCH","short_pith_number":"pith:RWEVNNXE","canonical_record":{"source":{"id":"1402.2118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-10T11:45:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f3b48cab2b6cbadbc161142d041fda34860b5594663bd39db69d9444866ad060","abstract_canon_sha256":"82e51b06ccaaa0ca4658f5a6a9120d188abba31f7bc96142dc521d92853357bb"},"schema_version":"1.0"},"canonical_sha256":"8d8956b6e4bdaffa758d669583e9b011d1acc2efe8957331cdaba6506a68c1fd","source":{"kind":"arxiv","id":"1402.2118","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2118","created_at":"2026-05-18T01:32:10Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2118v3","created_at":"2026-05-18T01:32:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2118","created_at":"2026-05-18T01:32:10Z"},{"alias_kind":"pith_short_12","alias_value":"RWEVNNXEXWX7","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RWEVNNXEXWX7U5MN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RWEVNNXE","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RWEVNNXEXWX7U5MNM2KYH2NQCH","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-10T11:45:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f3b48cab2b6cbadbc161142d041fda34860b5594663bd39db69d9444866ad060","abstract_canon_sha256":"82e51b06ccaaa0ca4658f5a6a9120d188abba31f7bc96142dc521d92853357bb"},"schema_version":"1.0"},"canonical_sha256":"8d8956b6e4bdaffa758d669583e9b011d1acc2efe8957331cdaba6506a68c1fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:10.948212Z","signature_b64":"ee35tm83OaTVaEpmqbMrIU7LJz3iax5t0RaQA9gHCpaOObqXaiCj1yfbnhp6zg6E7bHlX01Fdeqt4Gvndl+IDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8956b6e4bdaffa758d669583e9b011d1acc2efe8957331cdaba6506a68c1fd","last_reissued_at":"2026-05-18T01:32:10.947607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:10.947607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2118","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":"2026-05-18T01:32:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBbjmyu5AjC8rMcQcODUKqOavwiCJaJ6s1+VweTwUHYSXqTi+l3XeCMtjBqc/LH6xBgjUMKFC0UhP8g/fR8ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:31:12.788860Z"},"content_sha256":"df53b1ecd475a2c63e56ad6a8bf8c725e744bb52bc7877042010e4e6f416d8bc","schema_version":"1.0","event_id":"sha256:df53b1ecd475a2c63e56ad6a8bf8c725e744bb52bc7877042010e4e6f416d8bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RWEVNNXEXWX7U5MNM2KYH2NQCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterisation of matrix entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank Hansen, Zhihua Zhang","submitted_at":"2014-02-10T11:45:33Z","abstract_excerpt":"The notion of matrix entropy was introduced by Tropp and Chen with the aim of measuring the fluctuations of random matrices. It is a certain entropy functional constructed from a representing function with prescribed properties, and Tropp and Chen gave some examples. We give several abstract characterisations of matrix entropies together with a sufficient condition in terms of the second derivative of their representing function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2118","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":"2026-05-18T01:32:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hqm4Su+qwUsWu+mm10i11pk3IdwmAUpodF95lD0HKuJTNaQ2bbz+NY2W3w8KbLSavjJkZ5TtTUf8toeCm9ltBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:31:12.789199Z"},"content_sha256":"5ddbb8b14b1a7a3b3c75c55ca53f8ab8d2d6faab9c54409775d8c1211fb47785","schema_version":"1.0","event_id":"sha256:5ddbb8b14b1a7a3b3c75c55ca53f8ab8d2d6faab9c54409775d8c1211fb47785"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH/bundle.json","state_url":"https://pith.science/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH/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":"2026-06-12T00:31:12Z","links":{"resolver":"https://pith.science/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH","bundle":"https://pith.science/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH/bundle.json","state":"https://pith.science/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWEVNNXEXWX7U5MNM2KYH2NQCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RWEVNNXEXWX7U5MNM2KYH2NQCH","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":"82e51b06ccaaa0ca4658f5a6a9120d188abba31f7bc96142dc521d92853357bb","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-10T11:45:33Z","title_canon_sha256":"f3b48cab2b6cbadbc161142d041fda34860b5594663bd39db69d9444866ad060"},"schema_version":"1.0","source":{"id":"1402.2118","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2118","created_at":"2026-05-18T01:32:10Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2118v3","created_at":"2026-05-18T01:32:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2118","created_at":"2026-05-18T01:32:10Z"},{"alias_kind":"pith_short_12","alias_value":"RWEVNNXEXWX7","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RWEVNNXEXWX7U5MN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RWEVNNXE","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:5ddbb8b14b1a7a3b3c75c55ca53f8ab8d2d6faab9c54409775d8c1211fb47785","target":"graph","created_at":"2026-05-18T01:32:10Z","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 notion of matrix entropy was introduced by Tropp and Chen with the aim of measuring the fluctuations of random matrices. It is a certain entropy functional constructed from a representing function with prescribed properties, and Tropp and Chen gave some examples. We give several abstract characterisations of matrix entropies together with a sufficient condition in terms of the second derivative of their representing function.","authors_text":"Frank Hansen, Zhihua Zhang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-10T11:45:33Z","title":"Characterisation of matrix entropies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2118","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:df53b1ecd475a2c63e56ad6a8bf8c725e744bb52bc7877042010e4e6f416d8bc","target":"record","created_at":"2026-05-18T01:32:10Z","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":"82e51b06ccaaa0ca4658f5a6a9120d188abba31f7bc96142dc521d92853357bb","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-10T11:45:33Z","title_canon_sha256":"f3b48cab2b6cbadbc161142d041fda34860b5594663bd39db69d9444866ad060"},"schema_version":"1.0","source":{"id":"1402.2118","kind":"arxiv","version":3}},"canonical_sha256":"8d8956b6e4bdaffa758d669583e9b011d1acc2efe8957331cdaba6506a68c1fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d8956b6e4bdaffa758d669583e9b011d1acc2efe8957331cdaba6506a68c1fd","first_computed_at":"2026-05-18T01:32:10.947607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:10.947607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ee35tm83OaTVaEpmqbMrIU7LJz3iax5t0RaQA9gHCpaOObqXaiCj1yfbnhp6zg6E7bHlX01Fdeqt4Gvndl+IDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:10.948212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2118","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df53b1ecd475a2c63e56ad6a8bf8c725e744bb52bc7877042010e4e6f416d8bc","sha256:5ddbb8b14b1a7a3b3c75c55ca53f8ab8d2d6faab9c54409775d8c1211fb47785"],"state_sha256":"ab888af6d71cfd64bde30dff091434ba6f5835c5f5c14208121bba2f36bae1b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpNMt0pnlIJmWwNwvZR0QwTlw30UXfnGsL7jfQxIKABucCqTd9RM86RrctCwsxe2VyMSaWWwBFVpKNQWFhRuCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:31:12.791135Z","bundle_sha256":"cd4f3104708277f3e982cf827361e1324010fd471e3b748317e5cd7741c6ae63"}}