{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:4BKWFYVTYOP6JNER7W2N6WXBX4","short_pith_number":"pith:4BKWFYVT","canonical_record":{"source":{"id":"nucl-th/0012040","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2000-12-12T08:22:13Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","physics.flu-dyn","physics.plasm-ph"],"title_canon_sha256":"1808802a8b986760940b3e8273bbb302f24fd0d81fc375e0b8915321ad318dd9","abstract_canon_sha256":"87b9b10245fbde714dcfc517a5789fbc3c7f9d8cf73fc2e134b94afe4d7cddd5"},"schema_version":"1.0"},"canonical_sha256":"e05562e2b3c39fe4b491fdb4df5ae1bf26cb55a7a6c24e427cf60561796d7650","source":{"kind":"arxiv","id":"nucl-th/0012040","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0012040","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0012040v2","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0012040","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"4BKWFYVTYOP6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"4BKWFYVTYOP6JNER","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"4BKWFYVT","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:4BKWFYVTYOP6JNER7W2N6WXBX4","target":"record","payload":{"canonical_record":{"source":{"id":"nucl-th/0012040","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2000-12-12T08:22:13Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","physics.flu-dyn","physics.plasm-ph"],"title_canon_sha256":"1808802a8b986760940b3e8273bbb302f24fd0d81fc375e0b8915321ad318dd9","abstract_canon_sha256":"87b9b10245fbde714dcfc517a5789fbc3c7f9d8cf73fc2e134b94afe4d7cddd5"},"schema_version":"1.0"},"canonical_sha256":"e05562e2b3c39fe4b491fdb4df5ae1bf26cb55a7a6c24e427cf60561796d7650","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:21.222856Z","signature_b64":"ZXfI6w7uVFGjhHhPL2rQRZ8exu5CyEfcBLCKlV0NXW2uBLiZvVAPsdX/XHdw2ES7jhlWJusOaEAlbjtdi0nwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e05562e2b3c39fe4b491fdb4df5ae1bf26cb55a7a6c24e427cf60561796d7650","last_reissued_at":"2026-05-18T01:05:21.222287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:21.222287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nucl-th/0012040","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":"2026-05-18T01:05:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmn/ytkrzB3ZvtkCNsiCZEov/g5irzdac+hMKZAl8zvsakVybi35JawvfoSwlJg06C4s5Ozk6xWHt/Tzy6m8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:48:43.513450Z"},"content_sha256":"dcbf59dde91358ffdfa35def6dbe2034f85d7ccd88421f7998ef2a15ef2a654c","schema_version":"1.0","event_id":"sha256:dcbf59dde91358ffdfa35def6dbe2034f85d7ccd88421f7998ef2a15ef2a654c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:4BKWFYVTYOP6JNER7W2N6WXBX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Space-time versus particle-hole symmetry in quantum Enskog equations","license":"","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.str-el","physics.flu-dyn","physics.plasm-ph"],"primary_cat":"nucl-th","authors_text":"Klaus Morawetz, Pavel Lipavsk\\'y, V\\'aclav \\v{S}pi\\v{c}ka","submitted_at":"2000-12-12T08:22:13Z","abstract_excerpt":"The non-local scattering-in and -out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the -in and -out processes are conjugated by the space and time inversions. Generalisations of the Enskog equation to Fermi liquid systems are hindered by a request of the particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can only be fulfilled simultaneously for the Bruckner-type of internal Pauli-blocking while the Feynman-G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0012040","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":"2026-05-18T01:05:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vYoDYlFX2WVaf+8v1w5TKa4bpxakbt3V9PTDEBhWYEI3StleiBLJQqbqaq1yhIwfVBSjXu0Pltrw+HUbhrj3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:48:43.513815Z"},"content_sha256":"ab7273da72c19e2bd7ae0e384278925c93d4fa88ebcb0890e81274bf59be87f9","schema_version":"1.0","event_id":"sha256:ab7273da72c19e2bd7ae0e384278925c93d4fa88ebcb0890e81274bf59be87f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BKWFYVTYOP6JNER7W2N6WXBX4/bundle.json","state_url":"https://pith.science/pith/4BKWFYVTYOP6JNER7W2N6WXBX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BKWFYVTYOP6JNER7W2N6WXBX4/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":"2026-06-02T19:48:43Z","links":{"resolver":"https://pith.science/pith/4BKWFYVTYOP6JNER7W2N6WXBX4","bundle":"https://pith.science/pith/4BKWFYVTYOP6JNER7W2N6WXBX4/bundle.json","state":"https://pith.science/pith/4BKWFYVTYOP6JNER7W2N6WXBX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BKWFYVTYOP6JNER7W2N6WXBX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:4BKWFYVTYOP6JNER7W2N6WXBX4","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":"87b9b10245fbde714dcfc517a5789fbc3c7f9d8cf73fc2e134b94afe4d7cddd5","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","physics.flu-dyn","physics.plasm-ph"],"license":"","primary_cat":"nucl-th","submitted_at":"2000-12-12T08:22:13Z","title_canon_sha256":"1808802a8b986760940b3e8273bbb302f24fd0d81fc375e0b8915321ad318dd9"},"schema_version":"1.0","source":{"id":"nucl-th/0012040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0012040","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0012040v2","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0012040","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"4BKWFYVTYOP6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"4BKWFYVTYOP6JNER","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"4BKWFYVT","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:ab7273da72c19e2bd7ae0e384278925c93d4fa88ebcb0890e81274bf59be87f9","target":"graph","created_at":"2026-05-18T01:05:21Z","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 non-local scattering-in and -out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the -in and -out processes are conjugated by the space and time inversions. Generalisations of the Enskog equation to Fermi liquid systems are hindered by a request of the particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can only be fulfilled simultaneously for the Bruckner-type of internal Pauli-blocking while the Feynman-G","authors_text":"Klaus Morawetz, Pavel Lipavsk\\'y, V\\'aclav \\v{S}pi\\v{c}ka","cross_cats":["cond-mat.mes-hall","cond-mat.str-el","physics.flu-dyn","physics.plasm-ph"],"headline":"","license":"","primary_cat":"nucl-th","submitted_at":"2000-12-12T08:22:13Z","title":"Space-time versus particle-hole symmetry in quantum Enskog equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0012040","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:dcbf59dde91358ffdfa35def6dbe2034f85d7ccd88421f7998ef2a15ef2a654c","target":"record","created_at":"2026-05-18T01:05:21Z","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":"87b9b10245fbde714dcfc517a5789fbc3c7f9d8cf73fc2e134b94afe4d7cddd5","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","physics.flu-dyn","physics.plasm-ph"],"license":"","primary_cat":"nucl-th","submitted_at":"2000-12-12T08:22:13Z","title_canon_sha256":"1808802a8b986760940b3e8273bbb302f24fd0d81fc375e0b8915321ad318dd9"},"schema_version":"1.0","source":{"id":"nucl-th/0012040","kind":"arxiv","version":2}},"canonical_sha256":"e05562e2b3c39fe4b491fdb4df5ae1bf26cb55a7a6c24e427cf60561796d7650","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e05562e2b3c39fe4b491fdb4df5ae1bf26cb55a7a6c24e427cf60561796d7650","first_computed_at":"2026-05-18T01:05:21.222287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:21.222287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZXfI6w7uVFGjhHhPL2rQRZ8exu5CyEfcBLCKlV0NXW2uBLiZvVAPsdX/XHdw2ES7jhlWJusOaEAlbjtdi0nwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:21.222856Z","signed_message":"canonical_sha256_bytes"},"source_id":"nucl-th/0012040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcbf59dde91358ffdfa35def6dbe2034f85d7ccd88421f7998ef2a15ef2a654c","sha256:ab7273da72c19e2bd7ae0e384278925c93d4fa88ebcb0890e81274bf59be87f9"],"state_sha256":"34b2b1c5ce4d7cae3302bca4e407b06a7aeed845496e203212d90900ae22aee7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLhaL7WtCRmkuxBb0z7cUAIalgjH5724vaGYJW2zRakiawZmISr4Z7gmXooLuKAMW/SL2tSUljj7BiaEMwWaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:48:43.516040Z","bundle_sha256":"167a13b177f3c7b40556ad30907cc47667ed344a2fdbec01842a1ed3debfed48"}}