{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3MTRAUNLZRDHRYUIMKFMYFCOHH","short_pith_number":"pith:3MTRAUNL","canonical_record":{"source":{"id":"1412.6762","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-21T11:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"320a7b8d6828c39c84dcac21d00ebd244fbf53aa183d2b06d33de412960e6a1c","abstract_canon_sha256":"fdd4da2d9fa00e466a50978c345adb744d1808fcab69a2a671a74d64abfdcd98"},"schema_version":"1.0"},"canonical_sha256":"db271051abcc4678e288628acc144e39e2c54c8ee4f6683422dfd8fab2a51d39","source":{"kind":"arxiv","id":"1412.6762","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6762","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6762v2","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6762","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"3MTRAUNLZRDH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3MTRAUNLZRDHRYUI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3MTRAUNL","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3MTRAUNLZRDHRYUIMKFMYFCOHH","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6762","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-21T11:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"320a7b8d6828c39c84dcac21d00ebd244fbf53aa183d2b06d33de412960e6a1c","abstract_canon_sha256":"fdd4da2d9fa00e466a50978c345adb744d1808fcab69a2a671a74d64abfdcd98"},"schema_version":"1.0"},"canonical_sha256":"db271051abcc4678e288628acc144e39e2c54c8ee4f6683422dfd8fab2a51d39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:50.954032Z","signature_b64":"CygzSM1EzaVEy0hINOljMEi6L/OljT+slLwhVJpS/XazAfhW/H/zfBDidhrFIU1PFoN5MGR4ms5R20Lw8UVhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db271051abcc4678e288628acc144e39e2c54c8ee4f6683422dfd8fab2a51d39","last_reissued_at":"2026-05-18T02:16:50.953366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:50.953366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6762","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":"2026-05-18T02:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/O8JaH2aCQhBGTWpt0yVJLHbmvUlasTsjBm7U2w0Z5UpdsLGqSrde2r5MfBbdDylgHuaR5gw9BYKlsdicCGJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T22:40:08.114074Z"},"content_sha256":"c5b0e8db5a1b7cb9c6bb3b3ea7aab048712ecf056db26680312b6d79c6a5a73d","schema_version":"1.0","event_id":"sha256:c5b0e8db5a1b7cb9c6bb3b3ea7aab048712ecf056db26680312b6d79c6a5a73d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3MTRAUNLZRDHRYUIMKFMYFCOHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"KMS weights on graph C*-algebras II Factor types and ground states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Klaus Thomsen","submitted_at":"2014-12-21T11:03:34Z","abstract_excerpt":"We determine the factor types of the extremal KMS weights for generalized gauge actions on a graph algebra, and the ground states for the restriction of the action to a corner defined from a vertex. The assumptions on the graph and the action varies a bit, but they all cover, at the very least, the case of the gauge action on a strongly connected graph with at most countably many exits. These are the graphs for which all the KMS weights of the gauge action were determined in the first part of this work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6762","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":"2026-05-18T02:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0iqS9lU5SzyHFcipwKBtSaHnMByYDRzVOpU1dfu6PH4qOjXoEB/7gBNuhahkY9F3RhciUFAPv08tr1uGFh9GBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T22:40:08.114613Z"},"content_sha256":"73520b97d1812943df9756c1eba3422c9a38b8ac0db9a0cc9a596a8d9b8fd1f5","schema_version":"1.0","event_id":"sha256:73520b97d1812943df9756c1eba3422c9a38b8ac0db9a0cc9a596a8d9b8fd1f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH/bundle.json","state_url":"https://pith.science/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH/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":"2026-06-28T22:40:08Z","links":{"resolver":"https://pith.science/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH","bundle":"https://pith.science/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH/bundle.json","state":"https://pith.science/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MTRAUNLZRDHRYUIMKFMYFCOHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3MTRAUNLZRDHRYUIMKFMYFCOHH","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":"fdd4da2d9fa00e466a50978c345adb744d1808fcab69a2a671a74d64abfdcd98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-21T11:03:34Z","title_canon_sha256":"320a7b8d6828c39c84dcac21d00ebd244fbf53aa183d2b06d33de412960e6a1c"},"schema_version":"1.0","source":{"id":"1412.6762","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6762","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6762v2","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6762","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"3MTRAUNLZRDH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3MTRAUNLZRDHRYUI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3MTRAUNL","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:73520b97d1812943df9756c1eba3422c9a38b8ac0db9a0cc9a596a8d9b8fd1f5","target":"graph","created_at":"2026-05-18T02:16:50Z","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 factor types of the extremal KMS weights for generalized gauge actions on a graph algebra, and the ground states for the restriction of the action to a corner defined from a vertex. The assumptions on the graph and the action varies a bit, but they all cover, at the very least, the case of the gauge action on a strongly connected graph with at most countably many exits. These are the graphs for which all the KMS weights of the gauge action were determined in the first part of this work.","authors_text":"Klaus Thomsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-21T11:03:34Z","title":"KMS weights on graph C*-algebras II Factor types and ground states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6762","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:c5b0e8db5a1b7cb9c6bb3b3ea7aab048712ecf056db26680312b6d79c6a5a73d","target":"record","created_at":"2026-05-18T02:16:50Z","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":"fdd4da2d9fa00e466a50978c345adb744d1808fcab69a2a671a74d64abfdcd98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-21T11:03:34Z","title_canon_sha256":"320a7b8d6828c39c84dcac21d00ebd244fbf53aa183d2b06d33de412960e6a1c"},"schema_version":"1.0","source":{"id":"1412.6762","kind":"arxiv","version":2}},"canonical_sha256":"db271051abcc4678e288628acc144e39e2c54c8ee4f6683422dfd8fab2a51d39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db271051abcc4678e288628acc144e39e2c54c8ee4f6683422dfd8fab2a51d39","first_computed_at":"2026-05-18T02:16:50.953366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:50.953366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CygzSM1EzaVEy0hINOljMEi6L/OljT+slLwhVJpS/XazAfhW/H/zfBDidhrFIU1PFoN5MGR4ms5R20Lw8UVhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:50.954032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6762","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5b0e8db5a1b7cb9c6bb3b3ea7aab048712ecf056db26680312b6d79c6a5a73d","sha256:73520b97d1812943df9756c1eba3422c9a38b8ac0db9a0cc9a596a8d9b8fd1f5"],"state_sha256":"85e38a37d4586e5266d86172765c7493859642da33685805f816c43c7c48ed89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9l61KNp4OSAHm0IBb1K0wRixAC2mvcc9ixzokRkOpCm0ZLiB1dCn1NN3UAe0/6bTB7hWKRS8qjNJI8CbqEahAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T22:40:08.117187Z","bundle_sha256":"169818d9d5d34bd16c02d0172a4847c9467b34fc8cb3ce2ca874df8cd384e38e"}}