{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:37X7MDEGDD4T5IMTNBJBOJCOIN","short_pith_number":"pith:37X7MDEG","canonical_record":{"source":{"id":"1705.00434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-01T07:36:21Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8ae509b9ff20fbfba5c5e22e71716bbe6b8d53889eaef5015670e325f79f6d8a","abstract_canon_sha256":"b8237b032635296b940cb3893aa2aab29c60c7e65d8374e790870d01f67a19ee"},"schema_version":"1.0"},"canonical_sha256":"dfeff60c8618f93ea193685217244e435abebf2119455dceffb5720d2bbda7d7","source":{"kind":"arxiv","id":"1705.00434","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00434","created_at":"2026-05-18T00:45:17Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00434v1","created_at":"2026-05-18T00:45:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00434","created_at":"2026-05-18T00:45:17Z"},{"alias_kind":"pith_short_12","alias_value":"37X7MDEGDD4T","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"37X7MDEGDD4T5IMT","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"37X7MDEG","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:37X7MDEGDD4T5IMTNBJBOJCOIN","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-01T07:36:21Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8ae509b9ff20fbfba5c5e22e71716bbe6b8d53889eaef5015670e325f79f6d8a","abstract_canon_sha256":"b8237b032635296b940cb3893aa2aab29c60c7e65d8374e790870d01f67a19ee"},"schema_version":"1.0"},"canonical_sha256":"dfeff60c8618f93ea193685217244e435abebf2119455dceffb5720d2bbda7d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:17.255966Z","signature_b64":"3D1+wh5my4wuUYgsNyuEQd4UJLtSSzLkM3aFt0Rqn/ccXfLRdrxaq5F/nLlnCwVnuww09twgERqmQYSi0CG9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfeff60c8618f93ea193685217244e435abebf2119455dceffb5720d2bbda7d7","last_reissued_at":"2026-05-18T00:45:17.255393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:17.255393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00434","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":"2026-05-18T00:45:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jA0OfQzULpp4Tr/jM6XuHnGqZMEjOz5sNITMMU8Zxo7ok6KUut6VsssuPbR5vHNUDN+jm1HrGYmCYKgnT072DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:53:01.079409Z"},"content_sha256":"69b4ac99384f3c1ee3ef7d9007a040386baef6742d65e58243ff7d60c0b22bfa","schema_version":"1.0","event_id":"sha256:69b4ac99384f3c1ee3ef7d9007a040386baef6742d65e58243ff7d60c0b22bfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:37X7MDEGDD4T5IMTNBJBOJCOIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium and ground states from Cayley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Johannes Christensen, Klaus Thomsen","submitted_at":"2017-05-01T07:36:21Z","abstract_excerpt":"We study the KMS states and $KMS_{\\infty}$ states of generalized gauge actions on the $C^*$-algebra of a pointed Cayley graph. Our results provide information for any finitely generated group, but they are only complete for nilpotent groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00434","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":"2026-05-18T00:45:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgqNFKFpu1FVRohvUGABE/lAigh6HI+swzwyKrRje/WGohFpwzLXE2Umcfu4PnAAN6vTZWJdk3dpTqDNZta7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:53:01.080067Z"},"content_sha256":"6628f51206979cf03a243876f5fae4ba65c1df02628b1aaf4e7ae873640b82f8","schema_version":"1.0","event_id":"sha256:6628f51206979cf03a243876f5fae4ba65c1df02628b1aaf4e7ae873640b82f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/37X7MDEGDD4T5IMTNBJBOJCOIN/bundle.json","state_url":"https://pith.science/pith/37X7MDEGDD4T5IMTNBJBOJCOIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/37X7MDEGDD4T5IMTNBJBOJCOIN/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":"2026-06-07T07:53:01Z","links":{"resolver":"https://pith.science/pith/37X7MDEGDD4T5IMTNBJBOJCOIN","bundle":"https://pith.science/pith/37X7MDEGDD4T5IMTNBJBOJCOIN/bundle.json","state":"https://pith.science/pith/37X7MDEGDD4T5IMTNBJBOJCOIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/37X7MDEGDD4T5IMTNBJBOJCOIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:37X7MDEGDD4T5IMTNBJBOJCOIN","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":"b8237b032635296b940cb3893aa2aab29c60c7e65d8374e790870d01f67a19ee","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-01T07:36:21Z","title_canon_sha256":"8ae509b9ff20fbfba5c5e22e71716bbe6b8d53889eaef5015670e325f79f6d8a"},"schema_version":"1.0","source":{"id":"1705.00434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00434","created_at":"2026-05-18T00:45:17Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00434v1","created_at":"2026-05-18T00:45:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00434","created_at":"2026-05-18T00:45:17Z"},{"alias_kind":"pith_short_12","alias_value":"37X7MDEGDD4T","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"37X7MDEGDD4T5IMT","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"37X7MDEG","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:6628f51206979cf03a243876f5fae4ba65c1df02628b1aaf4e7ae873640b82f8","target":"graph","created_at":"2026-05-18T00:45:17Z","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 the KMS states and $KMS_{\\infty}$ states of generalized gauge actions on the $C^*$-algebra of a pointed Cayley graph. Our results provide information for any finitely generated group, but they are only complete for nilpotent groups.","authors_text":"Johannes Christensen, Klaus Thomsen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-01T07:36:21Z","title":"Equilibrium and ground states from Cayley graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00434","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":"sha256:69b4ac99384f3c1ee3ef7d9007a040386baef6742d65e58243ff7d60c0b22bfa","target":"record","created_at":"2026-05-18T00:45:17Z","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":"b8237b032635296b940cb3893aa2aab29c60c7e65d8374e790870d01f67a19ee","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-01T07:36:21Z","title_canon_sha256":"8ae509b9ff20fbfba5c5e22e71716bbe6b8d53889eaef5015670e325f79f6d8a"},"schema_version":"1.0","source":{"id":"1705.00434","kind":"arxiv","version":1}},"canonical_sha256":"dfeff60c8618f93ea193685217244e435abebf2119455dceffb5720d2bbda7d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfeff60c8618f93ea193685217244e435abebf2119455dceffb5720d2bbda7d7","first_computed_at":"2026-05-18T00:45:17.255393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:17.255393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3D1+wh5my4wuUYgsNyuEQd4UJLtSSzLkM3aFt0Rqn/ccXfLRdrxaq5F/nLlnCwVnuww09twgERqmQYSi0CG9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:17.255966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69b4ac99384f3c1ee3ef7d9007a040386baef6742d65e58243ff7d60c0b22bfa","sha256:6628f51206979cf03a243876f5fae4ba65c1df02628b1aaf4e7ae873640b82f8"],"state_sha256":"9580cc04e2676654507adefc48d5642e0a9681f06e98d02626fab2d187de48f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYZWqM1f9WnGySU+0TymbQLbYFEGyi22ejECqgqXlixejGvTgTouN0fP54M3f51i/Tk+3zlqr+VkH3ewBAuCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:53:01.083545Z","bundle_sha256":"19910501cef9d081618428ad9354f93dedbf9e4b8ac556cf06e67841b75da4b4"}}