{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M7QS3IHZW4VRG5JZNEMFEZWWKW","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":"9db30a4d721f975f878ed4367a57023808151046b74daf132385a65b042750cd","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-04T12:54:05Z","title_canon_sha256":"3a94a3cbcb9019c023ed48f0cebd9a2338a543f4b8e61e4ccd1ff910b36bc162"},"schema_version":"1.0","source":{"id":"1508.00759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00759","created_at":"2026-05-18T00:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00759v1","created_at":"2026-05-18T00:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00759","created_at":"2026-05-18T00:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"M7QS3IHZW4VR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M7QS3IHZW4VRG5JZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M7QS3IHZ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:11593c35c3cc1a7d8462022682ea2a1e42e644e49858a5341b283472d2c77119","target":"graph","created_at":"2026-05-18T00:40:14Z","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":"We study one-dimensional systems of $N$ particles in a one-dimensional harmonic trap with an inverse power law interaction $\\sim|x|^{-d}$. Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of $N$. A closed form asymptotic expressio","authors_text":"Przemyslaw Koscik","cross_cats":["cond-mat.quant-gas","cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-04T12:54:05Z","title":"The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00759","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:ef7dd6ff62c9f45194ff447dead629a66ff9e6b04f49ed4ded4248b7fc2a3e4c","target":"record","created_at":"2026-05-18T00:40:14Z","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":"9db30a4d721f975f878ed4367a57023808151046b74daf132385a65b042750cd","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-04T12:54:05Z","title_canon_sha256":"3a94a3cbcb9019c023ed48f0cebd9a2338a543f4b8e61e4ccd1ff910b36bc162"},"schema_version":"1.0","source":{"id":"1508.00759","kind":"arxiv","version":1}},"canonical_sha256":"67e12da0f9b72b13753969185266d655a51700453ccfff03f4c9df462bb89b48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67e12da0f9b72b13753969185266d655a51700453ccfff03f4c9df462bb89b48","first_computed_at":"2026-05-18T00:40:14.203739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:14.203739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OM9zZiSLG8yoHw9QeoRWT7CFIHXPukHvP9BbAHNwZ5fb7kkCDU4/5D2B/I4H6DHfqSeG3RJ7kyhqV2YBiYgpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:14.204291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef7dd6ff62c9f45194ff447dead629a66ff9e6b04f49ed4ded4248b7fc2a3e4c","sha256:11593c35c3cc1a7d8462022682ea2a1e42e644e49858a5341b283472d2c77119"],"state_sha256":"cb338dfd69045d861295ea9fd4564c05b3d4b6ccd3b3d28729c6c862f78f430a"}