{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FM25SWVA5ACWR4MCDSRSUJYQ4Z","short_pith_number":"pith:FM25SWVA","canonical_record":{"source":{"id":"1312.7533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-29T13:07:20Z","cross_cats_sorted":[],"title_canon_sha256":"f04930c0ba647746c5f53065879027e2c252fe10026dbd4b2470b9c526d4d252","abstract_canon_sha256":"12525e15dcd372bd34404820fa648d392397acb3b33c9f81e2c1a0e6b87d49dc"},"schema_version":"1.0"},"canonical_sha256":"2b35d95aa0e80568f1821ca32a2710e66fc803b99770101a30a09e31d7b0eeca","source":{"kind":"arxiv","id":"1312.7533","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7533","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7533v3","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7533","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"FM25SWVA5ACW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FM25SWVA5ACWR4MC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FM25SWVA","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FM25SWVA5ACWR4MCDSRSUJYQ4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-29T13:07:20Z","cross_cats_sorted":[],"title_canon_sha256":"f04930c0ba647746c5f53065879027e2c252fe10026dbd4b2470b9c526d4d252","abstract_canon_sha256":"12525e15dcd372bd34404820fa648d392397acb3b33c9f81e2c1a0e6b87d49dc"},"schema_version":"1.0"},"canonical_sha256":"2b35d95aa0e80568f1821ca32a2710e66fc803b99770101a30a09e31d7b0eeca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:27.290511Z","signature_b64":"nLtzO4CrsmRoblBlYlFuzMQ5qnYehDYMy2h7jRBgvDw2vFGaAmsMQTCTz/KFYAJWLpip//sm9DFAv32jqfAqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b35d95aa0e80568f1821ca32a2710e66fc803b99770101a30a09e31d7b0eeca","last_reissued_at":"2026-05-18T02:55:27.290102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:27.290102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7533","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UimF/ktFAS/vuK5D5YfvDLgx595K8ipvJ7WDkWl3WxvQ2AlpfjHjSOuoZB8Qc7UCnvtZJ7M8Q634VSYJxVPLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:26:53.590779Z"},"content_sha256":"7b8d0baa9b7ac278d6430c301af7c5e9ba2f8df797cb102682cd7f0c850d64ed","schema_version":"1.0","event_id":"sha256:7b8d0baa9b7ac278d6430c301af7c5e9ba2f8df797cb102682cd7f0c850d64ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FM25SWVA5ACWR4MCDSRSUJYQ4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of the ground state energy of heavy atoms and molecules in combined magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Victor Ivrii","submitted_at":"2013-12-29T13:07:20Z","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 $A=A^0+A'$ where $A^0=\\frac{1}{2}(-B x_2, B x_1,0)$ is an external magnetic field and $A'$ is self-generated magnetic field. Then the ground state ener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7533","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CyQQXm0J/uhKsAyKchneyr51PKbJYwtB8iUrKjA1wxWMBbwYYSc00Jcotv4Cnw0F1vXj+n1u2z9lO6ADPYOjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:26:53.591120Z"},"content_sha256":"6719ada862ad2798ea299af5fd2e36a0a80a975b867ae26df59bcabd5b9a9876","schema_version":"1.0","event_id":"sha256:6719ada862ad2798ea299af5fd2e36a0a80a975b867ae26df59bcabd5b9a9876"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z/bundle.json","state_url":"https://pith.science/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T04:26:53Z","links":{"resolver":"https://pith.science/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z","bundle":"https://pith.science/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z/bundle.json","state":"https://pith.science/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FM25SWVA5ACWR4MCDSRSUJYQ4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FM25SWVA5ACWR4MCDSRSUJYQ4Z","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":"12525e15dcd372bd34404820fa648d392397acb3b33c9f81e2c1a0e6b87d49dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-29T13:07:20Z","title_canon_sha256":"f04930c0ba647746c5f53065879027e2c252fe10026dbd4b2470b9c526d4d252"},"schema_version":"1.0","source":{"id":"1312.7533","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7533","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7533v3","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7533","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"FM25SWVA5ACW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FM25SWVA5ACWR4MC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FM25SWVA","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:6719ada862ad2798ea299af5fd2e36a0a80a975b867ae26df59bcabd5b9a9876","target":"graph","created_at":"2026-05-18T02:55:27Z","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 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 $A=A^0+A'$ where $A^0=\\frac{1}{2}(-B x_2, B x_1,0)$ is an external magnetic field and $A'$ is self-generated magnetic field. Then the ground state ener","authors_text":"Victor Ivrii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-29T13:07:20Z","title":"Asymptotics of the ground state energy of heavy atoms and molecules in combined magnetic field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7533","kind":"arxiv","version":3},"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":"sha256:7b8d0baa9b7ac278d6430c301af7c5e9ba2f8df797cb102682cd7f0c850d64ed","target":"record","created_at":"2026-05-18T02:55:27Z","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":"12525e15dcd372bd34404820fa648d392397acb3b33c9f81e2c1a0e6b87d49dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-29T13:07:20Z","title_canon_sha256":"f04930c0ba647746c5f53065879027e2c252fe10026dbd4b2470b9c526d4d252"},"schema_version":"1.0","source":{"id":"1312.7533","kind":"arxiv","version":3}},"canonical_sha256":"2b35d95aa0e80568f1821ca32a2710e66fc803b99770101a30a09e31d7b0eeca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b35d95aa0e80568f1821ca32a2710e66fc803b99770101a30a09e31d7b0eeca","first_computed_at":"2026-05-18T02:55:27.290102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:27.290102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nLtzO4CrsmRoblBlYlFuzMQ5qnYehDYMy2h7jRBgvDw2vFGaAmsMQTCTz/KFYAJWLpip//sm9DFAv32jqfAqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:27.290511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7533","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b8d0baa9b7ac278d6430c301af7c5e9ba2f8df797cb102682cd7f0c850d64ed","sha256:6719ada862ad2798ea299af5fd2e36a0a80a975b867ae26df59bcabd5b9a9876"],"state_sha256":"4f5b75bb03a3c2b326620c12ee48bd1ff8ae7bdf567614608bebdddfc659fbcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4BHFQoVpk4dEu7TP3X53dia7gw5HjqD6L467ZMncmN4R5FYSucjY7UhG0thnHUcpFNKCV0aIOKSIPdtu88DcDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:26:53.593055Z","bundle_sha256":"eed52b9fe7bf7d716e16312619b24b8aab9a6f3c4225fa0ed23725c70aba1f52"}}