{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DALG7RV5VOTJMSEOSZRE2FWNWE","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":"fbef774138c0c5ccb80d9a6bbe430e00f09712a71d6f4e2b046c7f836aa9abb9","cross_cats_sorted":["physics.comp-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-17T16:08:02Z","title_canon_sha256":"b2d7022043c39b20d9964ec7a031e8f579c3f05adfcb0d59edd56541e9200ba2"},"schema_version":"1.0","source":{"id":"1410.5356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5356","created_at":"2026-05-18T01:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5356v1","created_at":"2026-05-18T01:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5356","created_at":"2026-05-18T01:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"DALG7RV5VOTJ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DALG7RV5VOTJMSEO","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DALG7RV5","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:2a5e91a9e68355e721f939a47cf6930563ade1d900a1beadb09ecd6b175255e7","target":"graph","created_at":"2026-05-18T01:41:43Z","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 work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel e","authors_text":"Min Li, Ning Sui, Ping He","cross_cats":["physics.comp-ph","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-17T16:08:02Z","title":"Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5356","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":"sha256:003dc7cf25f7f0157360ca1d4eecebc2951c09b7e42a7fa07a7ccd7f47752d3c","target":"record","created_at":"2026-05-18T01:41:43Z","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":"fbef774138c0c5ccb80d9a6bbe430e00f09712a71d6f4e2b046c7f836aa9abb9","cross_cats_sorted":["physics.comp-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-17T16:08:02Z","title_canon_sha256":"b2d7022043c39b20d9964ec7a031e8f579c3f05adfcb0d59edd56541e9200ba2"},"schema_version":"1.0","source":{"id":"1410.5356","kind":"arxiv","version":1}},"canonical_sha256":"18166fc6bdaba696488e96624d16cdb12ae0e2822b41b4cd23481007d83d5b86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18166fc6bdaba696488e96624d16cdb12ae0e2822b41b4cd23481007d83d5b86","first_computed_at":"2026-05-18T01:41:43.461842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:43.461842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HcyJnNKJbk+1FTk4YkJppwxlHb06ods4jcBKD+w3xZZ22Jpf2+aeFtlZURR3Ycnlc1VH9jjAfrYGrFk8lC37BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:43.462464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:003dc7cf25f7f0157360ca1d4eecebc2951c09b7e42a7fa07a7ccd7f47752d3c","sha256:2a5e91a9e68355e721f939a47cf6930563ade1d900a1beadb09ecd6b175255e7"],"state_sha256":"8bb7af95840d6acf255525e560f01cc598fa81a15c1f3d3514769d90beeb49cc"}