{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TQKMRVD7GXXPMJTDN5LS7BLWPM","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":"07607366cd72cf98365e1dca89c9cc3f9d563ddbaaf02161cb850f538da69d24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-12T08:49:04Z","title_canon_sha256":"af231b17d4ec2748578f6dc1c1f0682393e73bbf05c48c34b782ea9de01f31fb"},"schema_version":"1.0","source":{"id":"1710.04412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04412","created_at":"2026-05-18T00:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04412v2","created_at":"2026-05-18T00:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04412","created_at":"2026-05-18T00:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"TQKMRVD7GXXP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TQKMRVD7GXXPMJTD","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TQKMRVD7","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:8496f5913f73f963489726786d258fc2af00db7e29aec466d69068bbd02048ae","target":"graph","created_at":"2026-05-18T00:03:09Z","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":"A continuous groupoid homomorphism $c$ on a locally compact second countable Hausdorff \\'etale groupoid $\\mathcal{G}$ gives rise to a $C^{*}$-dynamical system in which every $\\beta$-KMS state can be associated to a $e^{-\\beta c}$-quasi-invariant measure $\\mu$ on $\\mathcal{G}^{(0)}$. Letting $\\Delta_{\\mu}$ denote the set of KMS states associated to such a $\\mu$, we will prove that $\\Delta_{\\mu}$ is a simplex for a large class of groupoids, and we will show that there is an abelian group that acts transitively and freely on the extremal points of $\\Delta_{\\mu}$. This group can be described using","authors_text":"Johannes Christensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-12T08:49:04Z","title":"Symmetries of the KMS simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04412","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:dd8f5652453e00ccf4e63559e01580d563422d2e5d4859a441d7bf9ab8a767d4","target":"record","created_at":"2026-05-18T00:03:09Z","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":"07607366cd72cf98365e1dca89c9cc3f9d563ddbaaf02161cb850f538da69d24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-12T08:49:04Z","title_canon_sha256":"af231b17d4ec2748578f6dc1c1f0682393e73bbf05c48c34b782ea9de01f31fb"},"schema_version":"1.0","source":{"id":"1710.04412","kind":"arxiv","version":2}},"canonical_sha256":"9c14c8d47f35eef626636f572f85767b1cce26321960fb4feb4d960f8983d658","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c14c8d47f35eef626636f572f85767b1cce26321960fb4feb4d960f8983d658","first_computed_at":"2026-05-18T00:03:09.406799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:09.406799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DSz6ESqXi9lb234+baImLT8KBV7Cih6oeGBK6ZmNysYpmtpJL/PpQYGSlaUu1nrKulq6br4UVzCr6U5Q/kGDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:09.407374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd8f5652453e00ccf4e63559e01580d563422d2e5d4859a441d7bf9ab8a767d4","sha256:8496f5913f73f963489726786d258fc2af00db7e29aec466d69068bbd02048ae"],"state_sha256":"21811785750946a2abc27e5a1da50e0f07a52c43921ff35a20f8b224c15cf24c"}