{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:GSE33CQS7CZQTZMQIAKAN5AJ2W","short_pith_number":"pith:GSE33CQS","schema_version":"1.0","canonical_sha256":"3489bd8a12f8b309e590401406f409d58ede0def17b0c37d8320d5ba0249209d","source":{"kind":"arxiv","id":"1010.5558","version":1},"attestation_state":"computed","paper":{"title":"Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Shoichi Ichinose","submitted_at":"2010-10-27T02:56:47Z","abstract_excerpt":"A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {\\it coordinate} system (X$^i$,$\\tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\\it Euclidean time} variable ($\\tau$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$\\tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\\it mecha"},"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":"1010.5558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-10-27T02:56:47Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"57797234d014da885319311d95c7f8ea936db35335b85dfb60fcd5e780b385bb","abstract_canon_sha256":"d37138c587301ad9e8e5f3585b3ccb0f185e228c6aa3af10cc96094af18f4621"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:36.188566Z","signature_b64":"JbJN4dRmp96lCI6hKcYQIkJJoQf5Gs6ctskyXOmmlvGs4SqI0211B3gO4Th3qhH6Y2/qBD/ewbSLg3DmEgVtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3489bd8a12f8b309e590401406f409d58ede0def17b0c37d8320d5ba0249209d","last_reissued_at":"2026-05-18T04:30:36.188121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:36.188121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Shoichi Ichinose","submitted_at":"2010-10-27T02:56:47Z","abstract_excerpt":"A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {\\it coordinate} system (X$^i$,$\\tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\\it Euclidean time} variable ($\\tau$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$\\tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\\it mecha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5558","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1010.5558","created_at":"2026-05-18T04:30:36.188178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5558v1","created_at":"2026-05-18T04:30:36.188178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5558","created_at":"2026-05-18T04:30:36.188178+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSE33CQS7CZQ","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSE33CQS7CZQTZMQ","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSE33CQS","created_at":"2026-05-18T12:26:07.630475+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/GSE33CQS7CZQTZMQIAKAN5AJ2W","json":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W.json","graph_json":"https://pith.science/api/pith-number/GSE33CQS7CZQTZMQIAKAN5AJ2W/graph.json","events_json":"https://pith.science/api/pith-number/GSE33CQS7CZQTZMQIAKAN5AJ2W/events.json","paper":"https://pith.science/paper/GSE33CQS"},"agent_actions":{"view_html":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W","download_json":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W.json","view_paper":"https://pith.science/paper/GSE33CQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5558&json=true","fetch_graph":"https://pith.science/api/pith-number/GSE33CQS7CZQTZMQIAKAN5AJ2W/graph.json","fetch_events":"https://pith.science/api/pith-number/GSE33CQS7CZQTZMQIAKAN5AJ2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W/action/storage_attestation","attest_author":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W/action/author_attestation","sign_citation":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W/action/citation_signature","submit_replication":"https://pith.science/pith/GSE33CQS7CZQTZMQIAKAN5AJ2W/action/replication_record"}},"created_at":"2026-05-18T04:30:36.188178+00:00","updated_at":"2026-05-18T04:30:36.188178+00:00"}