{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TQKMRVD7GXXPMJTDN5LS7BLWPM","short_pith_number":"pith:TQKMRVD7","canonical_record":{"source":{"id":"1710.04412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-12T08:49:04Z","cross_cats_sorted":[],"title_canon_sha256":"af231b17d4ec2748578f6dc1c1f0682393e73bbf05c48c34b782ea9de01f31fb","abstract_canon_sha256":"07607366cd72cf98365e1dca89c9cc3f9d563ddbaaf02161cb850f538da69d24"},"schema_version":"1.0"},"canonical_sha256":"9c14c8d47f35eef626636f572f85767b1cce26321960fb4feb4d960f8983d658","source":{"kind":"arxiv","id":"1710.04412","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TQKMRVD7GXXPMJTDN5LS7BLWPM","target":"record","payload":{"canonical_record":{"source":{"id":"1710.04412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-12T08:49:04Z","cross_cats_sorted":[],"title_canon_sha256":"af231b17d4ec2748578f6dc1c1f0682393e73bbf05c48c34b782ea9de01f31fb","abstract_canon_sha256":"07607366cd72cf98365e1dca89c9cc3f9d563ddbaaf02161cb850f538da69d24"},"schema_version":"1.0"},"canonical_sha256":"9c14c8d47f35eef626636f572f85767b1cce26321960fb4feb4d960f8983d658","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:09.407374Z","signature_b64":"DSz6ESqXi9lb234+baImLT8KBV7Cih6oeGBK6ZmNysYpmtpJL/PpQYGSlaUu1nrKulq6br4UVzCr6U5Q/kGDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c14c8d47f35eef626636f572f85767b1cce26321960fb4feb4d960f8983d658","last_reissued_at":"2026-05-18T00:03:09.406799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:09.406799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.04412","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":"2026-05-18T00:03:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LJhZOUGE4QTKXp8XUn7uLlNlzyU+7X06L68gAodHWieyUVVXuhZF5pMeDZ6BdJqxZTZvRcRQnHdZJMYGtdHZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:31:09.819187Z"},"content_sha256":"dd8f5652453e00ccf4e63559e01580d563422d2e5d4859a441d7bf9ab8a767d4","schema_version":"1.0","event_id":"sha256:dd8f5652453e00ccf4e63559e01580d563422d2e5d4859a441d7bf9ab8a767d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TQKMRVD7GXXPMJTDN5LS7BLWPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetries of the KMS simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Johannes Christensen","submitted_at":"2017-10-12T08:49:04Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04412","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":"2026-05-18T00:03:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NAy2IYvgaB3JVrHvfuy6KI5qFq9LX1UQGEFXkfGW/qbNJvd+rVqYq8J/q2cTPCkUWNQsgvEsi9JTLrNFN9CGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:31:09.819537Z"},"content_sha256":"8496f5913f73f963489726786d258fc2af00db7e29aec466d69068bbd02048ae","schema_version":"1.0","event_id":"sha256:8496f5913f73f963489726786d258fc2af00db7e29aec466d69068bbd02048ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM/bundle.json","state_url":"https://pith.science/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM/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":"2026-06-29T10:31:09Z","links":{"resolver":"https://pith.science/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM","bundle":"https://pith.science/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM/bundle.json","state":"https://pith.science/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQKMRVD7GXXPMJTDN5LS7BLWPM/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCdmde+zv3Ud4XqTUVxSB0D63/9wcGH9ylJwRxKhyYp6L2stP34MXTkBnXS7+ZsK129aY+euF/V9WhVNn29GDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T10:31:09.821347Z","bundle_sha256":"adeb6e85877899c55de8ed36725126ccb4426ec18986430513f9c91f5c0ecee1"}}