{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YZODMUZUKGHQ7M4TYVIPJB7PPP","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":"c5e3fc129eb0e96125964a0bbb091e51fdde9eb91e2df65e5b1277a241631e18","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-03-09T11:52:16Z","title_canon_sha256":"17d355664f882393f14a6326fad7dd83b1dfbebdae9a57878a50296ba837a228"},"schema_version":"1.0","source":{"id":"2003.04051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.04051","created_at":"2026-07-05T07:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"2003.04051v2","created_at":"2026-07-05T07:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.04051","created_at":"2026-07-05T07:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"YZODMUZUKGHQ","created_at":"2026-07-05T07:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"YZODMUZUKGHQ7M4T","created_at":"2026-07-05T07:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"YZODMUZU","created_at":"2026-07-05T07:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:a117f6b1cee1127f45074c931e9cf71974fe2f83b92bccc76c20130a2d76ee2e","target":"graph","created_at":"2026-07-05T07:06:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.04051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider the Coulomb potential $-\\mu\\ast|x|^{-1}$ generated by a non-negative finite measure $\\mu$. It is well known that the lowest eigenvalue of the corresponding Schr\\\"odinger operator $-\\Delta/2-\\mu\\ast|x|^{-1}$ is minimized, at fixed mass $\\mu(\\mathbb{R}^3)=\\nu$, when $\\mu$ is proportional to a delta. In this paper we investigate the conjecture that the same holds for the Dirac operator $-i\\alpha\\cdot\\nabla+\\beta-\\mu\\ast|x|^{-1}$. In a previous work on the subject we proved that this operator is self-adjoint when $\\mu$ has no atom of mass larger than or equal to 1, and that its eigenvalue","authors_text":"\\'Eric S\\'er\\'e, Maria J. Esteban, Mathieu Lewin","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-03-09T11:52:16Z","title":"Dirac-Coulomb operators with general charge distribution. II. The lowest eigenvalue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.04051","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":"sha256:0998be4e3e000e43d3114e23c8a29661f3c0ec9c5c3bc13ad5f6bce06cf58fd6","target":"record","created_at":"2026-07-05T07:06:16Z","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":"c5e3fc129eb0e96125964a0bbb091e51fdde9eb91e2df65e5b1277a241631e18","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-03-09T11:52:16Z","title_canon_sha256":"17d355664f882393f14a6326fad7dd83b1dfbebdae9a57878a50296ba837a228"},"schema_version":"1.0","source":{"id":"2003.04051","kind":"arxiv","version":2}},"canonical_sha256":"c65c365334518f0fb393c550f487ef7bc4c21e67d1cace7024e265c68c8a5173","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65c365334518f0fb393c550f487ef7bc4c21e67d1cace7024e265c68c8a5173","first_computed_at":"2026-07-05T07:06:16.369222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:06:16.369222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FDviEw5gr72FY6QSshjn2s+AYV/o4Mj99uAg7c5fOAL0brUznQdQbAVCB+uIRVBYSJgKb1alUdrl5quCDEv1CA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:06:16.369683Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.04051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0998be4e3e000e43d3114e23c8a29661f3c0ec9c5c3bc13ad5f6bce06cf58fd6","sha256:a117f6b1cee1127f45074c931e9cf71974fe2f83b92bccc76c20130a2d76ee2e"],"state_sha256":"d7858e92fc67a9a492beb2cb1ea9c09cc33e17ad88ea5c8fa0fc17bc25d7dc79"}