{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WZSYUL77KGPQQXFTNPCJMLGRCC","short_pith_number":"pith:WZSYUL77","schema_version":"1.0","canonical_sha256":"b6658a2fff519f085cb36bc4962cd110a757373ae4fae63a7b240369c3cad392","source":{"kind":"arxiv","id":"1602.05246","version":1},"attestation_state":"computed","paper":{"title":"Maximizing the hyperpolarizability of 1D potentials with multiple electrons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Christopher J. Burke, Joseph Lesnefsky, Rolfe G. Petschek, Timothy J. Atherton","submitted_at":"2016-02-17T00:07:41Z","abstract_excerpt":"We optimize the first and second intrinsic hyperpolarizabilities for a 1D piecewise linear potential dressed with Dirac delta functions for $N$ non-interacting electrons. The optimized values fall rapidly for $N>1$, but approach constant values of $\\beta_{int}=0.40$, $\\gamma_{int}^{+}=0.16$ and $\\gamma_{int}^{-}=-0.061$ above $N\\gtrsim8$. These apparent bounds are achieved with only 2 parameters with more general potentials achieving no better value. In contrast to previous studies, analysis of the hessian matrices of $\\beta_{int}$ and $\\gamma_{int}$ taken with respect to these parameters show"},"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":"1602.05246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2016-02-17T00:07:41Z","cross_cats_sorted":[],"title_canon_sha256":"48c49c65c1dcddd7a6a326104d3d251943a3285532790a43d855166f8891e734","abstract_canon_sha256":"3eaeefdeb49c6b04ec4d1c6c900646a341e4b7a93bbd07648173690520acca2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:18.448435Z","signature_b64":"5aA6TLyacUKa+HmX+G79FUsvfZuHsl0UJRpUOvRrXLUO053biC2ZFNGBi05l+IQuDq3PCF7qJl6szQ+dzzBvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6658a2fff519f085cb36bc4962cd110a757373ae4fae63a7b240369c3cad392","last_reissued_at":"2026-05-18T01:08:18.447842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:18.447842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximizing the hyperpolarizability of 1D potentials with multiple electrons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Christopher J. Burke, Joseph Lesnefsky, Rolfe G. Petschek, Timothy J. Atherton","submitted_at":"2016-02-17T00:07:41Z","abstract_excerpt":"We optimize the first and second intrinsic hyperpolarizabilities for a 1D piecewise linear potential dressed with Dirac delta functions for $N$ non-interacting electrons. The optimized values fall rapidly for $N>1$, but approach constant values of $\\beta_{int}=0.40$, $\\gamma_{int}^{+}=0.16$ and $\\gamma_{int}^{-}=-0.061$ above $N\\gtrsim8$. These apparent bounds are achieved with only 2 parameters with more general potentials achieving no better value. In contrast to previous studies, analysis of the hessian matrices of $\\beta_{int}$ and $\\gamma_{int}$ taken with respect to these parameters show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05246","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":"1602.05246","created_at":"2026-05-18T01:08:18.447923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05246v1","created_at":"2026-05-18T01:08:18.447923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05246","created_at":"2026-05-18T01:08:18.447923+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZSYUL77KGPQ","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZSYUL77KGPQQXFT","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZSYUL77","created_at":"2026-05-18T12:30:51.357362+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/WZSYUL77KGPQQXFTNPCJMLGRCC","json":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC.json","graph_json":"https://pith.science/api/pith-number/WZSYUL77KGPQQXFTNPCJMLGRCC/graph.json","events_json":"https://pith.science/api/pith-number/WZSYUL77KGPQQXFTNPCJMLGRCC/events.json","paper":"https://pith.science/paper/WZSYUL77"},"agent_actions":{"view_html":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC","download_json":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC.json","view_paper":"https://pith.science/paper/WZSYUL77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05246&json=true","fetch_graph":"https://pith.science/api/pith-number/WZSYUL77KGPQQXFTNPCJMLGRCC/graph.json","fetch_events":"https://pith.science/api/pith-number/WZSYUL77KGPQQXFTNPCJMLGRCC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC/action/storage_attestation","attest_author":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC/action/author_attestation","sign_citation":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC/action/citation_signature","submit_replication":"https://pith.science/pith/WZSYUL77KGPQQXFTNPCJMLGRCC/action/replication_record"}},"created_at":"2026-05-18T01:08:18.447923+00:00","updated_at":"2026-05-18T01:08:18.447923+00:00"}