{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L67SPDTLZ6DSKR56M7Z4OAIYBA","short_pith_number":"pith:L67SPDTL","canonical_record":{"source":{"id":"1811.02032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-11-05T20:58:19Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","physics.chem-ph"],"title_canon_sha256":"46324a24fe20fa10295b086d2d318164332b839ff57cd979472e99fa69b3a411","abstract_canon_sha256":"b255478d7aa7dc7229e2d622a1af0dc7263702855c8b7a795f72ce8460d39693"},"schema_version":"1.0"},"canonical_sha256":"5fbf278e6bcf872547be67f3c701180807d757b325d5abc8ecaa899a9b8079f3","source":{"kind":"arxiv","id":"1811.02032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02032","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02032v1","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02032","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"pith_short_12","alias_value":"L67SPDTLZ6DS","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L67SPDTLZ6DSKR56","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L67SPDTL","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L67SPDTLZ6DSKR56M7Z4OAIYBA","target":"record","payload":{"canonical_record":{"source":{"id":"1811.02032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-11-05T20:58:19Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","physics.chem-ph"],"title_canon_sha256":"46324a24fe20fa10295b086d2d318164332b839ff57cd979472e99fa69b3a411","abstract_canon_sha256":"b255478d7aa7dc7229e2d622a1af0dc7263702855c8b7a795f72ce8460d39693"},"schema_version":"1.0"},"canonical_sha256":"5fbf278e6bcf872547be67f3c701180807d757b325d5abc8ecaa899a9b8079f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:32.509639Z","signature_b64":"sRSADeIiDUJ21hD2V18V5BSDEEjMbgbfU+q0Z5vzUccZTYDc6cbyGvctZu8C1/GKCV1twv6kcU0lUnp4X73lDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fbf278e6bcf872547be67f3c701180807d757b325d5abc8ecaa899a9b8079f3","last_reissued_at":"2026-05-18T00:01:32.508992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:32.508992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.02032","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZVf3mC4ZUzXRGfpOKJWZfVTxZcuBicwPONh4Ij0mvGYMlmasaIrGl43PbtpD+4wa2D1WfV4Z6oM7jrHALGA3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:31:31.334545Z"},"content_sha256":"ac128684c899f4162d7b1fdf1766881f28f0527355e85d9d4bbd189bde4f2b49","schema_version":"1.0","event_id":"sha256:ac128684c899f4162d7b1fdf1766881f28f0527355e85d9d4bbd189bde4f2b49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L67SPDTLZ6DSKR56M7Z4OAIYBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Statistical Mechanics in Classical Phase Space. Test Results for Quantum Harmonic Oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Phil Attard","submitted_at":"2018-11-05T20:58:19Z","abstract_excerpt":"The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave function symmetrization is also given. The method is tested for quantum harmonic oscillators. For both the boson and fermion cases, the grand potential and the average energy obtained by numerical quadrature over classical phase space are shown to agree with the known analytic results. A mean field approximation is given which is suitable for condensed matter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02032","kind":"arxiv","version":1},"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":"2026-05-18T00:01:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqYrBfUIQ2Sq7Ozv2fQpqtVK8ZubhjXQz/SmG+JMxrpKnVTMpE/9/9PCPHEJ8bLMrkk8WdavB62dG/Bex40NCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:31:31.334907Z"},"content_sha256":"ade8db1a6f56abed0b845ab679fee17e25406abfc6895cf4459eacc05d4df21f","schema_version":"1.0","event_id":"sha256:ade8db1a6f56abed0b845ab679fee17e25406abfc6895cf4459eacc05d4df21f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA/bundle.json","state_url":"https://pith.science/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA/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":"2026-06-01T11:31:31Z","links":{"resolver":"https://pith.science/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA","bundle":"https://pith.science/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA/bundle.json","state":"https://pith.science/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L67SPDTLZ6DSKR56M7Z4OAIYBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L67SPDTLZ6DSKR56M7Z4OAIYBA","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":"b255478d7aa7dc7229e2d622a1af0dc7263702855c8b7a795f72ce8460d39693","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-11-05T20:58:19Z","title_canon_sha256":"46324a24fe20fa10295b086d2d318164332b839ff57cd979472e99fa69b3a411"},"schema_version":"1.0","source":{"id":"1811.02032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02032","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02032v1","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02032","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"pith_short_12","alias_value":"L67SPDTLZ6DS","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L67SPDTLZ6DSKR56","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L67SPDTL","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:ade8db1a6f56abed0b845ab679fee17e25406abfc6895cf4459eacc05d4df21f","target":"graph","created_at":"2026-05-18T00:01:32Z","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":"The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave function symmetrization is also given. The method is tested for quantum harmonic oscillators. For both the boson and fermion cases, the grand potential and the average energy obtained by numerical quadrature over classical phase space are shown to agree with the known analytic results. A mean field approximation is given which is suitable for condensed matter","authors_text":"Phil Attard","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-11-05T20:58:19Z","title":"Quantum Statistical Mechanics in Classical Phase Space. Test Results for Quantum Harmonic Oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02032","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:ac128684c899f4162d7b1fdf1766881f28f0527355e85d9d4bbd189bde4f2b49","target":"record","created_at":"2026-05-18T00:01:32Z","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":"b255478d7aa7dc7229e2d622a1af0dc7263702855c8b7a795f72ce8460d39693","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-11-05T20:58:19Z","title_canon_sha256":"46324a24fe20fa10295b086d2d318164332b839ff57cd979472e99fa69b3a411"},"schema_version":"1.0","source":{"id":"1811.02032","kind":"arxiv","version":1}},"canonical_sha256":"5fbf278e6bcf872547be67f3c701180807d757b325d5abc8ecaa899a9b8079f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fbf278e6bcf872547be67f3c701180807d757b325d5abc8ecaa899a9b8079f3","first_computed_at":"2026-05-18T00:01:32.508992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:32.508992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sRSADeIiDUJ21hD2V18V5BSDEEjMbgbfU+q0Z5vzUccZTYDc6cbyGvctZu8C1/GKCV1twv6kcU0lUnp4X73lDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:32.509639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac128684c899f4162d7b1fdf1766881f28f0527355e85d9d4bbd189bde4f2b49","sha256:ade8db1a6f56abed0b845ab679fee17e25406abfc6895cf4459eacc05d4df21f"],"state_sha256":"d9c5c4c0fdef99577b608398d1f6162a65b3a96ce05b419defc494fa54578bfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPkNjPYhhYauyjqfm1KuoVshIYmC/CzzTZBfgP7sVdFh49ps/C5EKsnsTYf/ASa+Bz0JQgPf0g9WvsTgPSCgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:31:31.337122Z","bundle_sha256":"ccfc2b58f35b75fc1a252292135595ca1b6cf74ccae5d045f2b966e7c4de7fe2"}}