{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4NVS4G2YIFNNNRAIJUGL6DO4YL","short_pith_number":"pith:4NVS4G2Y","schema_version":"1.0","canonical_sha256":"e36b2e1b58415ad6c4084d0cbf0ddcc2c4b48db325d985d935c07a0d89adf10b","source":{"kind":"arxiv","id":"1303.4505","version":4},"attestation_state":"computed","paper":{"title":"Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Victor Ivrii","submitted_at":"2013-03-19T08:06:13Z","abstract_excerpt":"We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\\cdot\\boldsymbol{\\sigma})^2-V $$ with $$V=\\sum_{1\\le m\\le M} \\frac{Z_m}{|x-y_m|}$$ and a corresponding Multiparticle Quantum Hamiltonian $$ \\mathsf{H}=\\sum_{1\\le n\\le N} H_{x_n} +\\sum_{1\\le n < n'\\le N}|x_n-x_{n'}|^{-1} $$ on the Fock space $\\wedge _{1\\le n\\le N} L^2(\\mathbb{R}^3, \\mathbb{C}^2)$. Here $A$ is a self-generated magnetic fiels. Then the ground state energy is given by $$ \\mathsf{E}(A)=\\inf \\operatorname{Spec}(\\mathsf{H})+\\frac{1}{\\al"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.4505","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-19T08:06:13Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"f165881c9375009547963c287d8464ad09c6d202c2e4273ca3c9936266dd96c2","abstract_canon_sha256":"7c70c3a8f61d51125f3189bbfcda789c2c9d480050ee218b53a708810d75f0a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:32.295639Z","signature_b64":"g8G2Hiu40s0wNSv1HQkrPoimhn1E0EIzLJDpuoQdxOBtn7dk3TYE7HuffwdZ7P2lJzYp1pDtfG6uYnV2D/BpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e36b2e1b58415ad6c4084d0cbf0ddcc2c4b48db325d985d935c07a0d89adf10b","last_reissued_at":"2026-05-18T03:03:32.295011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:32.295011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Victor Ivrii","submitted_at":"2013-03-19T08:06:13Z","abstract_excerpt":"We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\\cdot\\boldsymbol{\\sigma})^2-V $$ with $$V=\\sum_{1\\le m\\le M} \\frac{Z_m}{|x-y_m|}$$ and a corresponding Multiparticle Quantum Hamiltonian $$ \\mathsf{H}=\\sum_{1\\le n\\le N} H_{x_n} +\\sum_{1\\le n < n'\\le N}|x_n-x_{n'}|^{-1} $$ on the Fock space $\\wedge _{1\\le n\\le N} L^2(\\mathbb{R}^3, \\mathbb{C}^2)$. Here $A$ is a self-generated magnetic fiels. Then the ground state energy is given by $$ \\mathsf{E}(A)=\\inf \\operatorname{Spec}(\\mathsf{H})+\\frac{1}{\\al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4505","kind":"arxiv","version":4},"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":"1303.4505","created_at":"2026-05-18T03:03:32.295108+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4505v4","created_at":"2026-05-18T03:03:32.295108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4505","created_at":"2026-05-18T03:03:32.295108+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NVS4G2YIFNN","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NVS4G2YIFNNNRAI","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NVS4G2Y","created_at":"2026-05-18T12:27:34.582898+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/4NVS4G2YIFNNNRAIJUGL6DO4YL","json":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL.json","graph_json":"https://pith.science/api/pith-number/4NVS4G2YIFNNNRAIJUGL6DO4YL/graph.json","events_json":"https://pith.science/api/pith-number/4NVS4G2YIFNNNRAIJUGL6DO4YL/events.json","paper":"https://pith.science/paper/4NVS4G2Y"},"agent_actions":{"view_html":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL","download_json":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL.json","view_paper":"https://pith.science/paper/4NVS4G2Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4505&json=true","fetch_graph":"https://pith.science/api/pith-number/4NVS4G2YIFNNNRAIJUGL6DO4YL/graph.json","fetch_events":"https://pith.science/api/pith-number/4NVS4G2YIFNNNRAIJUGL6DO4YL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL/action/storage_attestation","attest_author":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL/action/author_attestation","sign_citation":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL/action/citation_signature","submit_replication":"https://pith.science/pith/4NVS4G2YIFNNNRAIJUGL6DO4YL/action/replication_record"}},"created_at":"2026-05-18T03:03:32.295108+00:00","updated_at":"2026-05-18T03:03:32.295108+00:00"}