{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PH7E4GIR52JSS72HPV6UGCGVCX","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":"854ad770de194a25e887228233c2c52b2fd57b5f94785e43a60fdf0c60712558","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-05-05T19:23:39Z","title_canon_sha256":"81c9b9276dc8f5c71a4f7c5e1376d497fe38083c4b3a7bd48c192d21f35483c0"},"schema_version":"1.0","source":{"id":"1405.1003","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1003","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1003v4","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1003","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"PH7E4GIR52JS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PH7E4GIR52JSS72H","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PH7E4GIR","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:7118d58db8c0ac34f9ad330603af0be1db2db2d5eeb2cb7f1b5d571ecd97451c","target":"graph","created_at":"2026-05-18T01:18:23Z","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":"These expository notes propose to follow, across fields, some aspects of the concept of entropy. Starting from the work of Boltzmann in the kinetic theory of gases, various universes are visited, including Markov processes and their Helmholtz free energy, the Shannon monotonicity problem in the central limit theorem, the Voiculescu free probability theory and the free central limit theorem, random walks on regular trees, the circular law for the complex Ginibre ensemble of random matrices, and finally the asymptotic analysis of mean-field particle systems in arbitrary dimension, confined by an","authors_text":"Djalil Chafa\\\"i","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-05-05T19:23:39Z","title":"From Boltzmann to random matrices and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1003","kind":"arxiv","version":4},"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:ce18a58ec5bcccfffe4859a5565523cb72993bfc5183cab3db19d351c7e99910","target":"record","created_at":"2026-05-18T01:18:23Z","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":"854ad770de194a25e887228233c2c52b2fd57b5f94785e43a60fdf0c60712558","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-05-05T19:23:39Z","title_canon_sha256":"81c9b9276dc8f5c71a4f7c5e1376d497fe38083c4b3a7bd48c192d21f35483c0"},"schema_version":"1.0","source":{"id":"1405.1003","kind":"arxiv","version":4}},"canonical_sha256":"79fe4e1911ee93297f477d7d4308d515d5a384e3f13aadbddf076761b2d7c206","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79fe4e1911ee93297f477d7d4308d515d5a384e3f13aadbddf076761b2d7c206","first_computed_at":"2026-05-18T01:18:23.605854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:23.605854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MooOJTxgY9rF1/iyUcWiBaZGNXCG7P0mfk2m5OI8eMIQGIVKQvj2r6WgG4j+NLHY/79AmhVV+UbfDXvIF0JFAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:23.606371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1003","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce18a58ec5bcccfffe4859a5565523cb72993bfc5183cab3db19d351c7e99910","sha256:7118d58db8c0ac34f9ad330603af0be1db2db2d5eeb2cb7f1b5d571ecd97451c"],"state_sha256":"19c50a18e6f2f7042a2b675aec4bd629615b0c644e4ca327411ddd2f16cdd17b"}