{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IJ5QJ5MUV7AM4QBOO6QA3NXIGZ","short_pith_number":"pith:IJ5QJ5MU","canonical_record":{"source":{"id":"1603.05757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-18T03:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"c4a207edbcf039cb14f7f7d544409f37c3addfe04ddf16697e7ab5b87f255b92","abstract_canon_sha256":"ef1d7e8955b6c3802343bdbbc3e78c2fb7f4cfdb4c2c732ef29c7135121b6245"},"schema_version":"1.0"},"canonical_sha256":"427b04f594afc0ce402e77a00db6e8365db7647fef6741001b7a982653bf56ae","source":{"kind":"arxiv","id":"1603.05757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05757","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05757v1","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05757","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"IJ5QJ5MUV7AM","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IJ5QJ5MUV7AM4QBO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IJ5QJ5MU","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IJ5QJ5MUV7AM4QBOO6QA3NXIGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-18T03:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"c4a207edbcf039cb14f7f7d544409f37c3addfe04ddf16697e7ab5b87f255b92","abstract_canon_sha256":"ef1d7e8955b6c3802343bdbbc3e78c2fb7f4cfdb4c2c732ef29c7135121b6245"},"schema_version":"1.0"},"canonical_sha256":"427b04f594afc0ce402e77a00db6e8365db7647fef6741001b7a982653bf56ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:53.618293Z","signature_b64":"5/DeZJlOXxK7y/UE1LS+FVRpYQ/5h6ZpoOklbhwhG08xKnpOZ16WLZ9d69qyIqmX500yLXpQyE16AQXI4nyoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"427b04f594afc0ce402e77a00db6e8365db7647fef6741001b7a982653bf56ae","last_reissued_at":"2026-05-18T01:18:53.617729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:53.617729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05757","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuDVyO3rQe5hypsjIgxLgDuiuHUyzDIKSsAJ9+l14vqN4QPRNBnlXvphDXycBEZzF3xqepOMAGHuu23YJg85Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:32:27.993148Z"},"content_sha256":"24fb70d7b4162d1054a68ab6937e5f974eb9bfff1de9f8249f7d57c92607a4b6","schema_version":"1.0","event_id":"sha256:24fb70d7b4162d1054a68ab6937e5f974eb9bfff1de9f8249f7d57c92607a4b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IJ5QJ5MUV7AM4QBOO6QA3NXIGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium states on graph algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Astrid an Huef, Iain Raeburn","submitted_at":"2016-03-18T03:32:39Z","abstract_excerpt":"We consider operator-algebraic dynamical systems given by actions of the real line on unital $C^*$-algebras, and especially the equilibrium states (or KMS states) of such systems. We are particularly interested in systems built from the gauge action on the Toeplitz algebra and graph algebra of a finite directed graph, and we describe a complete classification of the KMS states obtained in joint work with Laca and Sims. We then discuss applications of these results to Cuntz-Pimsner algebras associated to local homeomorphisms, obtained in collaboration with Afsar. Thomsen has given bounds on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05757","kind":"arxiv","version":1},"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":"2026-05-18T01:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwF6Cx8n/5ALPabzsr/yYeUS/cF//gjjOh5SvCxakcnklXXA+/4kJAg49bn3K6rVc2zmuKrvL8r8mYBOHWPXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:32:27.993820Z"},"content_sha256":"2eaef46450d8e7d138e4fcc2e50d44db8113da492e3a8bfc89441517816fbd3b","schema_version":"1.0","event_id":"sha256:2eaef46450d8e7d138e4fcc2e50d44db8113da492e3a8bfc89441517816fbd3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ/bundle.json","state_url":"https://pith.science/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ/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":"2026-05-29T20:32:27Z","links":{"resolver":"https://pith.science/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ","bundle":"https://pith.science/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ/bundle.json","state":"https://pith.science/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJ5QJ5MUV7AM4QBOO6QA3NXIGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IJ5QJ5MUV7AM4QBOO6QA3NXIGZ","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":"ef1d7e8955b6c3802343bdbbc3e78c2fb7f4cfdb4c2c732ef29c7135121b6245","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-18T03:32:39Z","title_canon_sha256":"c4a207edbcf039cb14f7f7d544409f37c3addfe04ddf16697e7ab5b87f255b92"},"schema_version":"1.0","source":{"id":"1603.05757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05757","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05757v1","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05757","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"IJ5QJ5MUV7AM","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IJ5QJ5MUV7AM4QBO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IJ5QJ5MU","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:2eaef46450d8e7d138e4fcc2e50d44db8113da492e3a8bfc89441517816fbd3b","target":"graph","created_at":"2026-05-18T01:18:53Z","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 consider operator-algebraic dynamical systems given by actions of the real line on unital $C^*$-algebras, and especially the equilibrium states (or KMS states) of such systems. We are particularly interested in systems built from the gauge action on the Toeplitz algebra and graph algebra of a finite directed graph, and we describe a complete classification of the KMS states obtained in joint work with Laca and Sims. We then discuss applications of these results to Cuntz-Pimsner algebras associated to local homeomorphisms, obtained in collaboration with Afsar. Thomsen has given bounds on the","authors_text":"Astrid an Huef, Iain Raeburn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-18T03:32:39Z","title":"Equilibrium states on graph algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05757","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":"sha256:24fb70d7b4162d1054a68ab6937e5f974eb9bfff1de9f8249f7d57c92607a4b6","target":"record","created_at":"2026-05-18T01:18:53Z","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":"ef1d7e8955b6c3802343bdbbc3e78c2fb7f4cfdb4c2c732ef29c7135121b6245","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-18T03:32:39Z","title_canon_sha256":"c4a207edbcf039cb14f7f7d544409f37c3addfe04ddf16697e7ab5b87f255b92"},"schema_version":"1.0","source":{"id":"1603.05757","kind":"arxiv","version":1}},"canonical_sha256":"427b04f594afc0ce402e77a00db6e8365db7647fef6741001b7a982653bf56ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"427b04f594afc0ce402e77a00db6e8365db7647fef6741001b7a982653bf56ae","first_computed_at":"2026-05-18T01:18:53.617729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:53.617729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5/DeZJlOXxK7y/UE1LS+FVRpYQ/5h6ZpoOklbhwhG08xKnpOZ16WLZ9d69qyIqmX500yLXpQyE16AQXI4nyoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:53.618293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24fb70d7b4162d1054a68ab6937e5f974eb9bfff1de9f8249f7d57c92607a4b6","sha256:2eaef46450d8e7d138e4fcc2e50d44db8113da492e3a8bfc89441517816fbd3b"],"state_sha256":"0de3c7c86147406f80eb8c251bdc7f518bc2a4bc9b23f2c173a8db77426fa98e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rY7EboxRLwyXbObyCFPdJCj5xaPD3zniQgGfO4YZKhSI9ovBfZ6leIkiCWIl61xmMpcH7qJ43zckLyP5aUI9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:32:27.997152Z","bundle_sha256":"c4adb5844bb43fcd9b84f856f1fd0479fb2afd64108dc55b3dcd3157baa67408"}}