{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PIQKMVVPPOYB3X46CXUROXEUGW","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":"a315cf2cac1bb4966c155eb367a5685bc8049661ff4c449d3f79b6cbda47a038","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-27T17:36:34Z","title_canon_sha256":"b9f36ee22188bc28c143014e31f0bf12556df4fc5b07357130d43f4ea1434091"},"schema_version":"1.0","source":{"id":"0901.4293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4293","created_at":"2026-05-18T02:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4293v1","created_at":"2026-05-18T02:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4293","created_at":"2026-05-18T02:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"PIQKMVVPPOYB","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PIQKMVVPPOYB3X46","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PIQKMVVP","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:f855d113c967f266a53902274d04b5c05c742a16f138a4bfa31a5e89a4bedd32","target":"graph","created_at":"2026-05-18T02:35:06Z","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":"Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the group is compact this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is non-compact the group averaging prescription relies upon technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein-Gordon field on Minkowski spacetime by ","authors_text":"C. G. Torre","cross_cats":["gr-qc","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-27T17:36:34Z","title":"Symmetry Reduction of Quasi-Free States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4293","kind":"arxiv","version":1},"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:c9325b12ba26bbb63c2470c1240643be8aee0dcc4e8c00ea520cdbc0e4a8d775","target":"record","created_at":"2026-05-18T02:35:06Z","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":"a315cf2cac1bb4966c155eb367a5685bc8049661ff4c449d3f79b6cbda47a038","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-01-27T17:36:34Z","title_canon_sha256":"b9f36ee22188bc28c143014e31f0bf12556df4fc5b07357130d43f4ea1434091"},"schema_version":"1.0","source":{"id":"0901.4293","kind":"arxiv","version":1}},"canonical_sha256":"7a20a656af7bb01ddf9e15e9175c9435aa2d48d0cb5ec26f3b7f65f7c08390df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a20a656af7bb01ddf9e15e9175c9435aa2d48d0cb5ec26f3b7f65f7c08390df","first_computed_at":"2026-05-18T02:35:06.173846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:06.173846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N5ZhqtxvG7f0uEHqCuKk4VPL67yaosvR/vvBFFS/UuswJTq01kTfKkyNQa9Tk/h+Ip/0BGQWWClxe5YitsD2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:06.174333Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9325b12ba26bbb63c2470c1240643be8aee0dcc4e8c00ea520cdbc0e4a8d775","sha256:f855d113c967f266a53902274d04b5c05c742a16f138a4bfa31a5e89a4bedd32"],"state_sha256":"d1bd5476dc19b79bba3102a175bbde2d109f25eb2a78222398459deb07dc54b4"}