{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PHERBM75PRRWNNA4RG6HCSPYEA","short_pith_number":"pith:PHERBM75","canonical_record":{"source":{"id":"1301.5370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-23T01:04:32Z","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.atom-ph"],"title_canon_sha256":"bf95fa7774e1344e57d1a4361cba2024e0017d6bed79f9e73b4e731fb954508e","abstract_canon_sha256":"dc0b56379386441b39a59d1aa9d92a0ca5b5bf8bf2ec8cb5cb70d65aaebcd84e"},"schema_version":"1.0"},"canonical_sha256":"79c910b3fd7c6366b41c89bc7149f8201615259f4860fb563ee9f4b549d14861","source":{"kind":"arxiv","id":"1301.5370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5370","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5370v1","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5370","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"PHERBM75PRRW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PHERBM75PRRWNNA4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PHERBM75","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PHERBM75PRRWNNA4RG6HCSPYEA","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-23T01:04:32Z","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.atom-ph"],"title_canon_sha256":"bf95fa7774e1344e57d1a4361cba2024e0017d6bed79f9e73b4e731fb954508e","abstract_canon_sha256":"dc0b56379386441b39a59d1aa9d92a0ca5b5bf8bf2ec8cb5cb70d65aaebcd84e"},"schema_version":"1.0"},"canonical_sha256":"79c910b3fd7c6366b41c89bc7149f8201615259f4860fb563ee9f4b549d14861","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:32.710446Z","signature_b64":"qaA4Fvp9fAef9vb0Etw+RiEWAxr1tlWRVnXZKBhOUavnWs2TVITRc6EutesyF2twbGqZxJpq9y0GVi+7vO0GDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79c910b3fd7c6366b41c89bc7149f8201615259f4860fb563ee9f4b549d14861","last_reissued_at":"2026-05-18T02:58:32.709882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:32.709882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5370","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VXXUbPvf9mE7e+kjajOBHxwVz7VywXJrVN7TSAyPcxIY4LEFMz2MYlzW5Gs7N2fL50jng/AHzTr9TmEjMrRiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:54:56.434810Z"},"content_sha256":"919c165eb4066b3f81e8875e9333b8fe4c60cc485beacf23413af8f50e5d5565","schema_version":"1.0","event_id":"sha256:919c165eb4066b3f81e8875e9333b8fe4c60cc485beacf23413af8f50e5d5565"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PHERBM75PRRWNNA4RG6HCSPYEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of ground states for negative ions at the binding threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP","physics.atom-ph"],"primary_cat":"math-ph","authors_text":"Elliott H. Lieb, Jacopo Bellazzini, Robert Seiringer, Rupert L. Frank","submitted_at":"2013-01-23T01:04:32Z","abstract_excerpt":"As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition at some critical Z_c. We investigate whether the electrons remain bound when Z=Z_c and whether the radius of the system stays finite as Z_c is approached. Existence of a ground state at Z_c is shown under the condition Z_c<N-K, where K is the maximal number of electrons that can be removed at Z_c without changing the ground state energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5370","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezQuMDg7+eS+zEcMCjLHuASKYho+QAuuCUFuig2yKJrphYOgcG8+WuCB5cDBYo80i49KidW2QixXV9kjeIXcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:54:56.435249Z"},"content_sha256":"f7476e4096b2f8929a7e8887ab3a074c9d4f3d50249598d5cc410ea79ef53a10","schema_version":"1.0","event_id":"sha256:f7476e4096b2f8929a7e8887ab3a074c9d4f3d50249598d5cc410ea79ef53a10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PHERBM75PRRWNNA4RG6HCSPYEA/bundle.json","state_url":"https://pith.science/pith/PHERBM75PRRWNNA4RG6HCSPYEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PHERBM75PRRWNNA4RG6HCSPYEA/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":"2026-05-30T20:54:56Z","links":{"resolver":"https://pith.science/pith/PHERBM75PRRWNNA4RG6HCSPYEA","bundle":"https://pith.science/pith/PHERBM75PRRWNNA4RG6HCSPYEA/bundle.json","state":"https://pith.science/pith/PHERBM75PRRWNNA4RG6HCSPYEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PHERBM75PRRWNNA4RG6HCSPYEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PHERBM75PRRWNNA4RG6HCSPYEA","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":"dc0b56379386441b39a59d1aa9d92a0ca5b5bf8bf2ec8cb5cb70d65aaebcd84e","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-23T01:04:32Z","title_canon_sha256":"bf95fa7774e1344e57d1a4361cba2024e0017d6bed79f9e73b4e731fb954508e"},"schema_version":"1.0","source":{"id":"1301.5370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5370","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5370v1","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5370","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"PHERBM75PRRW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PHERBM75PRRWNNA4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PHERBM75","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:f7476e4096b2f8929a7e8887ab3a074c9d4f3d50249598d5cc410ea79ef53a10","target":"graph","created_at":"2026-05-18T02:58:32Z","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":"As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition at some critical Z_c. We investigate whether the electrons remain bound when Z=Z_c and whether the radius of the system stays finite as Z_c is approached. Existence of a ground state at Z_c is shown under the condition Z_c<N-K, where K is the maximal number of electrons that can be removed at Z_c without changing the ground state energy.","authors_text":"Elliott H. Lieb, Jacopo Bellazzini, Robert Seiringer, Rupert L. Frank","cross_cats":["math.AP","math.MP","math.SP","physics.atom-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-23T01:04:32Z","title":"Existence of ground states for negative ions at the binding threshold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5370","kind":"arxiv","version":1},"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":"sha256:919c165eb4066b3f81e8875e9333b8fe4c60cc485beacf23413af8f50e5d5565","target":"record","created_at":"2026-05-18T02:58:32Z","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":"dc0b56379386441b39a59d1aa9d92a0ca5b5bf8bf2ec8cb5cb70d65aaebcd84e","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-23T01:04:32Z","title_canon_sha256":"bf95fa7774e1344e57d1a4361cba2024e0017d6bed79f9e73b4e731fb954508e"},"schema_version":"1.0","source":{"id":"1301.5370","kind":"arxiv","version":1}},"canonical_sha256":"79c910b3fd7c6366b41c89bc7149f8201615259f4860fb563ee9f4b549d14861","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79c910b3fd7c6366b41c89bc7149f8201615259f4860fb563ee9f4b549d14861","first_computed_at":"2026-05-18T02:58:32.709882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:32.709882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qaA4Fvp9fAef9vb0Etw+RiEWAxr1tlWRVnXZKBhOUavnWs2TVITRc6EutesyF2twbGqZxJpq9y0GVi+7vO0GDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:32.710446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:919c165eb4066b3f81e8875e9333b8fe4c60cc485beacf23413af8f50e5d5565","sha256:f7476e4096b2f8929a7e8887ab3a074c9d4f3d50249598d5cc410ea79ef53a10"],"state_sha256":"c02b1c38e4947eff56be674a2ab94cc602bccda8d73e29001d0d3abc6264b310"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tm1OjQmPLPATU2hr+sCxcq1JqwU3YKSkUQ5HcxzeEP01pXxKBI1HrJEKmbFCXjoWgT6sxCuilKRAyZ2Av4o4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:54:56.437913Z","bundle_sha256":"2ee4045a5c70249a1f3c2030437cbab4649b13e1b10f994511c91aeab9b790dd"}}