{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6PYVPYNP7Z6SCEBHQGWWR2UEVZ","short_pith_number":"pith:6PYVPYNP","canonical_record":{"source":{"id":"1612.04716","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T16:33:34Z","cross_cats_sorted":["math.DS","math.OA"],"title_canon_sha256":"b42db0759df0baac056667b84a35b16adcce518cc15d7ee9261887bf2f3bd016","abstract_canon_sha256":"cfefa1d53755620f762ff78354579e740d4ee0aace6ee22aac75421605ebdd24"},"schema_version":"1.0"},"canonical_sha256":"f3f157e1affe7d21102781ad68ea84ae60ab0ebc8aebd731d9bc33dfa8d3d83b","source":{"kind":"arxiv","id":"1612.04716","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04716","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04716v5","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04716","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"6PYVPYNP7Z6S","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6PYVPYNP7Z6SCEBH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6PYVPYNP","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6PYVPYNP7Z6SCEBHQGWWR2UEVZ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04716","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T16:33:34Z","cross_cats_sorted":["math.DS","math.OA"],"title_canon_sha256":"b42db0759df0baac056667b84a35b16adcce518cc15d7ee9261887bf2f3bd016","abstract_canon_sha256":"cfefa1d53755620f762ff78354579e740d4ee0aace6ee22aac75421605ebdd24"},"schema_version":"1.0"},"canonical_sha256":"f3f157e1affe7d21102781ad68ea84ae60ab0ebc8aebd731d9bc33dfa8d3d83b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:56.632449Z","signature_b64":"cJU00pTRNbsYCgXM+A0GcHoIOjgg5ido7ItdyvwNQgPGSNLOIayXBQpqniQOQBPTAFDWhUoBRcnkx6CFtwfwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3f157e1affe7d21102781ad68ea84ae60ab0ebc8aebd731d9bc33dfa8d3d83b","last_reissued_at":"2026-05-18T00:06:56.631826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:56.631826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04716","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"amlIsJSqEtgL+r/t64L+h+boM2T9ma2JwDEX+PUP7Usiz0sZ2zjDgEk3RY/wAVtxRSCLP++7PTREo60zkufQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:53:39.251306Z"},"content_sha256":"f07661da8582537dbe14b7d5b3205830eea3798c26db89f543b3784dd447cba7","schema_version":"1.0","event_id":"sha256:f07661da8582537dbe14b7d5b3205830eea3798c26db89f543b3784dd447cba7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6PYVPYNP7Z6SCEBHQGWWR2UEVZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"KMS states, conformal measures and ends in digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OA"],"primary_cat":"math.PR","authors_text":"Klaus Thomsen","submitted_at":"2016-12-14T16:33:34Z","abstract_excerpt":"The paper develops a series of tools for the study of KMS-weights on graph C*-algebras and KMS states on their corners. The approach adopts methods and ideas from graph theory, random walks and dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04716","kind":"arxiv","version":5},"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":"2026-05-18T00:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtvLZCDO4muQc/50hEaHJfcBvGNKNk2Lwp85lTj/eVybd1isVYcU1e7svCwTDdhG93aaKx5deeQh8aQDIntrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:53:39.251670Z"},"content_sha256":"7fcdf08a788a791c867fad03b6c55401c9627df91c7a2953c49887e771850ef6","schema_version":"1.0","event_id":"sha256:7fcdf08a788a791c867fad03b6c55401c9627df91c7a2953c49887e771850ef6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ/bundle.json","state_url":"https://pith.science/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ/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":"2026-06-29T00:53:39Z","links":{"resolver":"https://pith.science/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ","bundle":"https://pith.science/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ/bundle.json","state":"https://pith.science/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PYVPYNP7Z6SCEBHQGWWR2UEVZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6PYVPYNP7Z6SCEBHQGWWR2UEVZ","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":"cfefa1d53755620f762ff78354579e740d4ee0aace6ee22aac75421605ebdd24","cross_cats_sorted":["math.DS","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T16:33:34Z","title_canon_sha256":"b42db0759df0baac056667b84a35b16adcce518cc15d7ee9261887bf2f3bd016"},"schema_version":"1.0","source":{"id":"1612.04716","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04716","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04716v5","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04716","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"6PYVPYNP7Z6S","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6PYVPYNP7Z6SCEBH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6PYVPYNP","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:7fcdf08a788a791c867fad03b6c55401c9627df91c7a2953c49887e771850ef6","target":"graph","created_at":"2026-05-18T00:06:56Z","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":"The paper develops a series of tools for the study of KMS-weights on graph C*-algebras and KMS states on their corners. The approach adopts methods and ideas from graph theory, random walks and dynamical systems.","authors_text":"Klaus Thomsen","cross_cats":["math.DS","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T16:33:34Z","title":"KMS states, conformal measures and ends in digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04716","kind":"arxiv","version":5},"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:f07661da8582537dbe14b7d5b3205830eea3798c26db89f543b3784dd447cba7","target":"record","created_at":"2026-05-18T00:06:56Z","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":"cfefa1d53755620f762ff78354579e740d4ee0aace6ee22aac75421605ebdd24","cross_cats_sorted":["math.DS","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T16:33:34Z","title_canon_sha256":"b42db0759df0baac056667b84a35b16adcce518cc15d7ee9261887bf2f3bd016"},"schema_version":"1.0","source":{"id":"1612.04716","kind":"arxiv","version":5}},"canonical_sha256":"f3f157e1affe7d21102781ad68ea84ae60ab0ebc8aebd731d9bc33dfa8d3d83b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3f157e1affe7d21102781ad68ea84ae60ab0ebc8aebd731d9bc33dfa8d3d83b","first_computed_at":"2026-05-18T00:06:56.631826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:56.631826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cJU00pTRNbsYCgXM+A0GcHoIOjgg5ido7ItdyvwNQgPGSNLOIayXBQpqniQOQBPTAFDWhUoBRcnkx6CFtwfwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:56.632449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04716","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f07661da8582537dbe14b7d5b3205830eea3798c26db89f543b3784dd447cba7","sha256:7fcdf08a788a791c867fad03b6c55401c9627df91c7a2953c49887e771850ef6"],"state_sha256":"dcfefb8728019ed37e6c6c5b99c21a91213dfffec5070593058921a47a53c498"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ajDIaTa0G4/9dEwgrkn7rBi5DKlCVVMCJRpgobVAyDJmkhOYiYzUzJPQqE202MZQNuok7L8QYt5jC0hxJaELDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T00:53:39.253549Z","bundle_sha256":"d253eab9111b6054daa6cdf270b9cbc179539e80dfa08b98652cd12c0b874cb7"}}