{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2BT74WXSWK2X5TNGPWRFNVRPJL","short_pith_number":"pith:2BT74WXS","canonical_record":{"source":{"id":"1611.01052","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-03T14:58:24Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3490d08aaa9858c8151a6c6176c460baef04a7e437d18f658acd47df948cd1e6","abstract_canon_sha256":"b0cff40e483f43c8f5d968210e76740feb88969c1a7c81571188e4da1198e68d"},"schema_version":"1.0"},"canonical_sha256":"d067fe5af2b2b57ecda67da256d62f4ad3016acdef00d244f4fd606c121522eb","source":{"kind":"arxiv","id":"1611.01052","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01052","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01052v2","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01052","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"2BT74WXSWK2X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2BT74WXSWK2X5TNG","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2BT74WXS","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2BT74WXSWK2X5TNGPWRFNVRPJL","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01052","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-03T14:58:24Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3490d08aaa9858c8151a6c6176c460baef04a7e437d18f658acd47df948cd1e6","abstract_canon_sha256":"b0cff40e483f43c8f5d968210e76740feb88969c1a7c81571188e4da1198e68d"},"schema_version":"1.0"},"canonical_sha256":"d067fe5af2b2b57ecda67da256d62f4ad3016acdef00d244f4fd606c121522eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:36.979797Z","signature_b64":"oA9b0aT/w/lbLdxoKEfWGmIOv+2F7C7UTSz8six2yoFtX9EHUmQPOv60S8LCuBdvrkluLOJMhyFdOkfuUBCDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d067fe5af2b2b57ecda67da256d62f4ad3016acdef00d244f4fd606c121522eb","last_reissued_at":"2026-05-17T23:54:36.979211Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:36.979211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01052","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INLZsKgZqX2JinMpnSThkNFXbDV4Ut6C1HXZivUKMSj9wnM8uKZTgbw3gXScEt1JbgBxvfdy8/GwaYojyHIhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:29:18.908277Z"},"content_sha256":"627582b7959fec31fa9536a2a05c3d50587df01ef3bbeb33698103ac5431686e","schema_version":"1.0","event_id":"sha256:627582b7959fec31fa9536a2a05c3d50587df01ef3bbeb33698103ac5431686e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2BT74WXSWK2X5TNGPWRFNVRPJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium states on right LCM semigroup C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Nadia S. Larsen, Nathan Brownlowe, Nicolai Stammeier, Zahra Afsar","submitted_at":"2016-11-03T14:58:24Z","abstract_excerpt":"We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^*$-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on $\\mathbb{N} \\rtimes \\mathbb{N}^\\times$, dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the same time, it provides new results for large classes of right LCM semigroups, including those associated to algebraic dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01052","kind":"arxiv","version":2},"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":"2026-05-17T23:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2gbTNcB5IDEIv64jE/PmEN4LGaKEZohO2RpB40QAt2iVsw8FsBUNJ9P4WB/MyEYTDQc2+a8r4AWBZFGO4IwJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:29:18.908993Z"},"content_sha256":"521bafffbfa26a402b08643366da46747b8c4862118c4deb8f1cc5ca340b5355","schema_version":"1.0","event_id":"sha256:521bafffbfa26a402b08643366da46747b8c4862118c4deb8f1cc5ca340b5355"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2BT74WXSWK2X5TNGPWRFNVRPJL/bundle.json","state_url":"https://pith.science/pith/2BT74WXSWK2X5TNGPWRFNVRPJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2BT74WXSWK2X5TNGPWRFNVRPJL/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":"2026-06-06T22:29:18Z","links":{"resolver":"https://pith.science/pith/2BT74WXSWK2X5TNGPWRFNVRPJL","bundle":"https://pith.science/pith/2BT74WXSWK2X5TNGPWRFNVRPJL/bundle.json","state":"https://pith.science/pith/2BT74WXSWK2X5TNGPWRFNVRPJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2BT74WXSWK2X5TNGPWRFNVRPJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2BT74WXSWK2X5TNGPWRFNVRPJL","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":"b0cff40e483f43c8f5d968210e76740feb88969c1a7c81571188e4da1198e68d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-03T14:58:24Z","title_canon_sha256":"3490d08aaa9858c8151a6c6176c460baef04a7e437d18f658acd47df948cd1e6"},"schema_version":"1.0","source":{"id":"1611.01052","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01052","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01052v2","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01052","created_at":"2026-05-17T23:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"2BT74WXSWK2X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2BT74WXSWK2X5TNG","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2BT74WXS","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:521bafffbfa26a402b08643366da46747b8c4862118c4deb8f1cc5ca340b5355","target":"graph","created_at":"2026-05-17T23:54:36Z","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 determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^*$-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on $\\mathbb{N} \\rtimes \\mathbb{N}^\\times$, dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the same time, it provides new results for large classes of right LCM semigroups, including those associated to algebraic dynamical systems.","authors_text":"Nadia S. Larsen, Nathan Brownlowe, Nicolai Stammeier, Zahra Afsar","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-03T14:58:24Z","title":"Equilibrium states on right LCM semigroup C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01052","kind":"arxiv","version":2},"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":"sha256:627582b7959fec31fa9536a2a05c3d50587df01ef3bbeb33698103ac5431686e","target":"record","created_at":"2026-05-17T23:54:36Z","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":"b0cff40e483f43c8f5d968210e76740feb88969c1a7c81571188e4da1198e68d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-03T14:58:24Z","title_canon_sha256":"3490d08aaa9858c8151a6c6176c460baef04a7e437d18f658acd47df948cd1e6"},"schema_version":"1.0","source":{"id":"1611.01052","kind":"arxiv","version":2}},"canonical_sha256":"d067fe5af2b2b57ecda67da256d62f4ad3016acdef00d244f4fd606c121522eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d067fe5af2b2b57ecda67da256d62f4ad3016acdef00d244f4fd606c121522eb","first_computed_at":"2026-05-17T23:54:36.979211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:36.979211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oA9b0aT/w/lbLdxoKEfWGmIOv+2F7C7UTSz8six2yoFtX9EHUmQPOv60S8LCuBdvrkluLOJMhyFdOkfuUBCDCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:36.979797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01052","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:627582b7959fec31fa9536a2a05c3d50587df01ef3bbeb33698103ac5431686e","sha256:521bafffbfa26a402b08643366da46747b8c4862118c4deb8f1cc5ca340b5355"],"state_sha256":"30fa8de12c2447e81f79c6e8b771758c29649d7f70ef9afa0fef23b9ea6da57a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0Ver9IFYQOfLxwMRttN3bh+iYLfWYWpgC5obtvXZDrDuBEDF+WZpVDoqPaKx6egxp7RYLgfzWtAl4Fn2ywFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:29:18.913103Z","bundle_sha256":"79f562ad1d61cd2f922555b29b4ba1bbb86e906edacdaab20f7d062876c9dbfb"}}