{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NQPNS2NZK3MUJWGZ4FKUY4IF3H","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":"e39871ce3b93d7d4cb9dd8f49c36ebf5c1439aab08430cf94e861b14980c35d9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-30T14:43:04Z","title_canon_sha256":"f6200456bb43cd60e2d780ae1d5a7f8940b96e79bbfa9c4c026e57a95da11d14"},"schema_version":"1.0","source":{"id":"1007.5464","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5464","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5464v3","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5464","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"NQPNS2NZK3MU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NQPNS2NZK3MUJWGZ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NQPNS2NZ","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:7fb632fd9745049f4faea9e74918d5cafac7f7e20ca5842edbd4abb57be48bb9","target":"graph","created_at":"2026-05-18T01:14:53Z","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":"We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.","authors_text":"Andreas Knauf, Stephan Weis","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-30T14:43:04Z","title":"Entropy Distance: New Quantum Phenomena"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5464","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":"sha256:56328705e7048ba1ab6c631276c3156fdcea4c80b2ffe9c0c12dcf1a49d843c7","target":"record","created_at":"2026-05-18T01:14:53Z","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":"e39871ce3b93d7d4cb9dd8f49c36ebf5c1439aab08430cf94e861b14980c35d9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-30T14:43:04Z","title_canon_sha256":"f6200456bb43cd60e2d780ae1d5a7f8940b96e79bbfa9c4c026e57a95da11d14"},"schema_version":"1.0","source":{"id":"1007.5464","kind":"arxiv","version":3}},"canonical_sha256":"6c1ed969b956d944d8d9e1554c7105d9fc587f438bf9b506b03f06462adc0569","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c1ed969b956d944d8d9e1554c7105d9fc587f438bf9b506b03f06462adc0569","first_computed_at":"2026-05-18T01:14:53.726209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:53.726209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DarbkZcESdHfp8fD3gH8reTozhnN9EJbqnxLOgPtIlnf1m3Ha6o1qk+/xHkZ1IGuE3+qltTh9CYrdBFQJeV4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:53.726738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5464","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56328705e7048ba1ab6c631276c3156fdcea4c80b2ffe9c0c12dcf1a49d843c7","sha256:7fb632fd9745049f4faea9e74918d5cafac7f7e20ca5842edbd4abb57be48bb9"],"state_sha256":"c7ce06367cce5a0b203224f00a09a64d25466c4a43935c8d99d41d02b699f648"}