{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:THLPWQH7OEA7WS64OVN4QMR7QL","short_pith_number":"pith:THLPWQH7","schema_version":"1.0","canonical_sha256":"99d6fb40ff7101fb4bdc755bc8323f82c1f43080b8b5658a75cafd06a43189a2","source":{"kind":"arxiv","id":"1209.6068","version":2},"attestation_state":"computed","paper":{"title":"Thermal equilibrium states of a linear scalar quantum field in stationary spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ko Sanders","submitted_at":"2012-09-26T20:25:45Z","abstract_excerpt":"The linear scalar quantum field, propagating in a globally hyperbolic spacetime, is a relatively simple physical model that allows us to study many aspects in explicit detail. In this review we focus on the theory of thermal equilibrium (KMS) states of such a field in a stationary spacetime. Our presentation draws on several existing sources and aims to give a unified exposition. We also take the opportunity to weaken some of the technical assumptions of the earlier literature. In particular, we completely drop any assumptions on the behaviour of the norm and lapse of the Killing field. This i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.6068","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-26T20:25:45Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"63f02f1e90df254c66075f9b20dee923583b894c29ca6ec53e8a660defd8fed5","abstract_canon_sha256":"271a692e8219d3b59c07f7732962b9ff38b7d7645f2b7071eb3cf0e62b5f9803"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:17.396470Z","signature_b64":"HkVjWlJsR7HyfOPynXnyaHImCzMFuucG9Ly7C9K8qHdiIv9Bp+UXWdqLRa92QgcOGrs2f+lzO/FUgZrfOi3QDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99d6fb40ff7101fb4bdc755bc8323f82c1f43080b8b5658a75cafd06a43189a2","last_reissued_at":"2026-05-18T03:28:17.395869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:17.395869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thermal equilibrium states of a linear scalar quantum field in stationary spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ko Sanders","submitted_at":"2012-09-26T20:25:45Z","abstract_excerpt":"The linear scalar quantum field, propagating in a globally hyperbolic spacetime, is a relatively simple physical model that allows us to study many aspects in explicit detail. In this review we focus on the theory of thermal equilibrium (KMS) states of such a field in a stationary spacetime. Our presentation draws on several existing sources and aims to give a unified exposition. We also take the opportunity to weaken some of the technical assumptions of the earlier literature. In particular, we completely drop any assumptions on the behaviour of the norm and lapse of the Killing field. This i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6068","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.6068","created_at":"2026-05-18T03:28:17.395972+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.6068v2","created_at":"2026-05-18T03:28:17.395972+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6068","created_at":"2026-05-18T03:28:17.395972+00:00"},{"alias_kind":"pith_short_12","alias_value":"THLPWQH7OEA7","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"THLPWQH7OEA7WS64","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"THLPWQH7","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL","json":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL.json","graph_json":"https://pith.science/api/pith-number/THLPWQH7OEA7WS64OVN4QMR7QL/graph.json","events_json":"https://pith.science/api/pith-number/THLPWQH7OEA7WS64OVN4QMR7QL/events.json","paper":"https://pith.science/paper/THLPWQH7"},"agent_actions":{"view_html":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL","download_json":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL.json","view_paper":"https://pith.science/paper/THLPWQH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.6068&json=true","fetch_graph":"https://pith.science/api/pith-number/THLPWQH7OEA7WS64OVN4QMR7QL/graph.json","fetch_events":"https://pith.science/api/pith-number/THLPWQH7OEA7WS64OVN4QMR7QL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL/action/storage_attestation","attest_author":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL/action/author_attestation","sign_citation":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL/action/citation_signature","submit_replication":"https://pith.science/pith/THLPWQH7OEA7WS64OVN4QMR7QL/action/replication_record"}},"created_at":"2026-05-18T03:28:17.395972+00:00","updated_at":"2026-05-18T03:28:17.395972+00:00"}