{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QSOC7IZHOJJQNIEKAYUU27EPWI","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":"cf6132e54d4227aa020c5bfceb2697bd92f5a29fcbf84a3a9576fcdf7afbbea8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2013-04-30T14:56:26Z","title_canon_sha256":"debc3d70f357bac82c29a80b53226b668b44b1fb1d1703c04f5d8a83b030791e"},"schema_version":"1.0","source":{"id":"1304.8015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8015","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8015v2","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8015","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"pith_short_12","alias_value":"QSOC7IZHOJJQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QSOC7IZHOJJQNIEK","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QSOC7IZH","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:81885a00e59a109a0b2fb94fce1268765f13aac65d5f7913d3c3ca0687d14f14","target":"graph","created_at":"2026-05-18T00:44:52Z","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":"An imaginary-time nonuniform mesh method is presented and used to find the first 50 eigenstates and energies of up to five strongly interacting spinless quantum Lennard-Jones particles trapped in a one-dimensional harmonic potential. We show that the use of tailored grids reduces drastically the computational effort needed to diagonalize the Hamiltonian and results in a favorable scaling with dimensionality. Solutions to both bosonic and fermionic counterparts of this strongly interacting system are obtained, the bosonic case clustering as a Tonks-Girardeau crystal exhibiting the phenomenon of","authors_text":"Alberto Hernando, Jiri Vanicek","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2013-04-30T14:56:26Z","title":"Imaginary-time nonuniform mesh method for solving the multidimensional Schrodinger equation: Fermionization and melting of quantum Lennard-Jones crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8015","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":"sha256:90eab9692de3279bf10ab0e46adf029f583024c02e76a7a215b9505791ec59db","target":"record","created_at":"2026-05-18T00:44:52Z","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":"cf6132e54d4227aa020c5bfceb2697bd92f5a29fcbf84a3a9576fcdf7afbbea8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2013-04-30T14:56:26Z","title_canon_sha256":"debc3d70f357bac82c29a80b53226b668b44b1fb1d1703c04f5d8a83b030791e"},"schema_version":"1.0","source":{"id":"1304.8015","kind":"arxiv","version":2}},"canonical_sha256":"849c2fa327725306a08a06294d7c8fb22155562edfca8887e6ef8777ae14ecc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"849c2fa327725306a08a06294d7c8fb22155562edfca8887e6ef8777ae14ecc9","first_computed_at":"2026-05-18T00:44:52.973219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:52.973219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0cBnFdLps6MA+rKauNqoWvzvS1ecM5X3sJnbdRdbFTMCXnRVCIJQBsAM8VryYX+adHda4wwzRczZ64jTe6LzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:52.973875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.8015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90eab9692de3279bf10ab0e46adf029f583024c02e76a7a215b9505791ec59db","sha256:81885a00e59a109a0b2fb94fce1268765f13aac65d5f7913d3c3ca0687d14f14"],"state_sha256":"d2a66e86e91e5b43ad1bc17f662df0b606e4ed2013ec4ed23ed4b45e67af23d1"}