{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:YZODMUZUKGHQ7M4TYVIPJB7PPP","short_pith_number":"pith:YZODMUZU","canonical_record":{"source":{"id":"2003.04051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-03-09T11:52:16Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"17d355664f882393f14a6326fad7dd83b1dfbebdae9a57878a50296ba837a228","abstract_canon_sha256":"c5e3fc129eb0e96125964a0bbb091e51fdde9eb91e2df65e5b1277a241631e18"},"schema_version":"1.0"},"canonical_sha256":"c65c365334518f0fb393c550f487ef7bc4c21e67d1cace7024e265c68c8a5173","source":{"kind":"arxiv","id":"2003.04051","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:YZODMUZUKGHQ7M4TYVIPJB7PPP","target":"record","payload":{"canonical_record":{"source":{"id":"2003.04051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2020-03-09T11:52:16Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"17d355664f882393f14a6326fad7dd83b1dfbebdae9a57878a50296ba837a228","abstract_canon_sha256":"c5e3fc129eb0e96125964a0bbb091e51fdde9eb91e2df65e5b1277a241631e18"},"schema_version":"1.0"},"canonical_sha256":"c65c365334518f0fb393c550f487ef7bc4c21e67d1cace7024e265c68c8a5173","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:06:16.369683Z","signature_b64":"FDviEw5gr72FY6QSshjn2s+AYV/o4Mj99uAg7c5fOAL0brUznQdQbAVCB+uIRVBYSJgKb1alUdrl5quCDEv1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65c365334518f0fb393c550f487ef7bc4c21e67d1cace7024e265c68c8a5173","last_reissued_at":"2026-07-05T07:06:16.369222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:06:16.369222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.04051","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKb68OgIrUJMPGX5W9NMb6f7AhoyuMNj0UxSLbkyuaw08mIF0hUxXlyPiczzWc8qdBLHkNffjdIsbiCkvHO8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:37:56.895468Z"},"content_sha256":"0998be4e3e000e43d3114e23c8a29661f3c0ec9c5c3bc13ad5f6bce06cf58fd6","schema_version":"1.0","event_id":"sha256:0998be4e3e000e43d3114e23c8a29661f3c0ec9c5c3bc13ad5f6bce06cf58fd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:YZODMUZUKGHQ7M4TYVIPJB7PPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac-Coulomb operators with general charge distribution. II. The lowest eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"\\'Eric S\\'er\\'e, Maria J. Esteban, Mathieu Lewin","submitted_at":"2020-03-09T11:52:16Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.04051","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.04051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OzWXvMrph7MSXCNK6OlXJsGJ6yS7bJn7O0FZ0VrWXri7o+8f2xT7kc504oANA4eTOQTk3m82ZvWr4iPZTPM2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:37:56.895963Z"},"content_sha256":"a117f6b1cee1127f45074c931e9cf71974fe2f83b92bccc76c20130a2d76ee2e","schema_version":"1.0","event_id":"sha256:a117f6b1cee1127f45074c931e9cf71974fe2f83b92bccc76c20130a2d76ee2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP/bundle.json","state_url":"https://pith.science/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP/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":"2026-08-04T10:37:56Z","links":{"resolver":"https://pith.science/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP","bundle":"https://pith.science/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP/bundle.json","state":"https://pith.science/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZODMUZUKGHQ7M4TYVIPJB7PPP/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4sMhoJ34mwrBJZvE/gFHn/rpLOEjHyuTDJUp/VgAHK3s6o9NS1S1EioE0NLHodFXScrlsxAHsZHZ65Dc8rpNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T10:37:56.899563Z","bundle_sha256":"65de7354ea8246c3db288c61a1746ff8e8d84604002443608265c2df32a10f0d"}}