{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:W43T6NQBZBVXPTFYVUPEUN6S4G","short_pith_number":"pith:W43T6NQB","schema_version":"1.0","canonical_sha256":"b7373f3601c86b77ccb8ad1e4a37d2e1bb15b3bb988e36eb611feb292e4643a3","source":{"kind":"arxiv","id":"1106.1584","version":1},"attestation_state":"computed","paper":{"title":"The Lennard-Jones Potential Minimization Problem for Prion AGAAAAGA Amyloid Fibril Molecular Modeling","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","math.OC","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Jiapu Zhang","submitted_at":"2011-06-08T15:40:04Z","abstract_excerpt":"The simplified Lennard-Jones (LJ) potential minimization problem is minimize f(x)=4\\sum_{i=1}^N \\sum_{j=1,j<i}^N (\\tau_{ij}^{-6} -\\tau_{ij}^{-3})   subject to   x\\in \\mathbb{R}^n, where $\\tau_{ij}=(x_{3i-2}-x_{3j-2})^2 +(x_{3i-1}-x_{3j-1})^2+(x_{3i} -x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the coordinates of atom $i$ in $\\mathbb{R}^3$, $i,j=1,2,...,N(\\geq 2 \\quad \\text{integer})$, $n=3N$ and $N$ is the whole number of atoms. The nonconvexity of the objective function and the huge number of local minima, which is growing exponentially with $N$, interest many mathematical optimization expert"},"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":"1106.1584","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-08T15:40:04Z","cross_cats_sorted":["math.MP","math.OC","physics.bio-ph"],"title_canon_sha256":"e90b06590c75a2cdfb69ad3739169158c3f090cade6fd9f89c9d3ef710e55cbc","abstract_canon_sha256":"12675daf36f2d7cebf32e6fb7cda403608f2b38260a74d0a76a90fbc7435e9d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:25.585101Z","signature_b64":"Mj3O0n2cJPH8u4yolvSc6mFqMX78hhlOpbmNIv2pCLauAT9CZelyVNRzI+3WjkyXHWS6Ea+ApeXEgzwZnLE/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7373f3601c86b77ccb8ad1e4a37d2e1bb15b3bb988e36eb611feb292e4643a3","last_reissued_at":"2026-05-18T03:01:25.584248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:25.584248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Lennard-Jones Potential Minimization Problem for Prion AGAAAAGA Amyloid Fibril Molecular Modeling","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","math.OC","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Jiapu Zhang","submitted_at":"2011-06-08T15:40:04Z","abstract_excerpt":"The simplified Lennard-Jones (LJ) potential minimization problem is minimize f(x)=4\\sum_{i=1}^N \\sum_{j=1,j<i}^N (\\tau_{ij}^{-6} -\\tau_{ij}^{-3})   subject to   x\\in \\mathbb{R}^n, where $\\tau_{ij}=(x_{3i-2}-x_{3j-2})^2 +(x_{3i-1}-x_{3j-1})^2+(x_{3i} -x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the coordinates of atom $i$ in $\\mathbb{R}^3$, $i,j=1,2,...,N(\\geq 2 \\quad \\text{integer})$, $n=3N$ and $N$ is the whole number of atoms. The nonconvexity of the objective function and the huge number of local minima, which is growing exponentially with $N$, interest many mathematical optimization expert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1584","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":"1106.1584","created_at":"2026-05-18T03:01:25.584406+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1584v1","created_at":"2026-05-18T03:01:25.584406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1584","created_at":"2026-05-18T03:01:25.584406+00:00"},{"alias_kind":"pith_short_12","alias_value":"W43T6NQBZBVX","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"W43T6NQBZBVXPTFY","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"W43T6NQB","created_at":"2026-05-18T12:26:44.992195+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/W43T6NQBZBVXPTFYVUPEUN6S4G","json":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G.json","graph_json":"https://pith.science/api/pith-number/W43T6NQBZBVXPTFYVUPEUN6S4G/graph.json","events_json":"https://pith.science/api/pith-number/W43T6NQBZBVXPTFYVUPEUN6S4G/events.json","paper":"https://pith.science/paper/W43T6NQB"},"agent_actions":{"view_html":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G","download_json":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G.json","view_paper":"https://pith.science/paper/W43T6NQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1584&json=true","fetch_graph":"https://pith.science/api/pith-number/W43T6NQBZBVXPTFYVUPEUN6S4G/graph.json","fetch_events":"https://pith.science/api/pith-number/W43T6NQBZBVXPTFYVUPEUN6S4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G/action/storage_attestation","attest_author":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G/action/author_attestation","sign_citation":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G/action/citation_signature","submit_replication":"https://pith.science/pith/W43T6NQBZBVXPTFYVUPEUN6S4G/action/replication_record"}},"created_at":"2026-05-18T03:01:25.584406+00:00","updated_at":"2026-05-18T03:01:25.584406+00:00"}