{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:G4BOSGSC4LHDMDBRHFOLXCWVQ7","short_pith_number":"pith:G4BOSGSC","canonical_record":{"source":{"id":"1005.2109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T14:16:49Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"c225d2ff4da1818ca9e7d1b13af042b94c44944f2285e2813481dbbbbc72e766","abstract_canon_sha256":"58627c4582e0879610dd1db497b017caf065a84d3a016dc439943b9e7aed1f2a"},"schema_version":"1.0"},"canonical_sha256":"3702e91a42e2ce360c31395cbb8ad587f59c2923ab6306b7040bbccca3cbdeb8","source":{"kind":"arxiv","id":"1005.2109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2109","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2109v2","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2109","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"G4BOSGSC4LHD","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"G4BOSGSC4LHDMDBR","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"G4BOSGSC","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:G4BOSGSC4LHDMDBRHFOLXCWVQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T14:16:49Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"c225d2ff4da1818ca9e7d1b13af042b94c44944f2285e2813481dbbbbc72e766","abstract_canon_sha256":"58627c4582e0879610dd1db497b017caf065a84d3a016dc439943b9e7aed1f2a"},"schema_version":"1.0"},"canonical_sha256":"3702e91a42e2ce360c31395cbb8ad587f59c2923ab6306b7040bbccca3cbdeb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:17.934633Z","signature_b64":"bejVjfuYYQHRR88soF8PqNyrMf3HDPumLVleeNiJki7v9MSknSqnQbMFLhky8guTHVKoc+bdXQWgn55mvrzODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3702e91a42e2ce360c31395cbb8ad587f59c2923ab6306b7040bbccca3cbdeb8","last_reissued_at":"2026-05-18T04:07:17.933903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:17.933903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2109","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":"2026-05-18T04:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWrTCEMqUsRDqBJ4OxGFrICRaB0hqKqqRd84JSfVeRaf4k5ooQWaTKoOhXInlC6sy8Dh5FTjO2Nq20ubCkKtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:07:31.783917Z"},"content_sha256":"e5e1cbf982920380d2ef5e9dc1b242a2a81415f18717ee12667cbd04f4d06aa1","schema_version":"1.0","event_id":"sha256:e5e1cbf982920380d2ef5e9dc1b242a2a81415f18717ee12667cbd04f4d06aa1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:G4BOSGSC4LHDMDBRHFOLXCWVQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of ground states of hydrogen-like atoms in relativistic QED II: The no-pair operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Edgardo Stockmeyer, Martin K\\\"onenberg, Oliver Matte","submitted_at":"2010-05-12T14:16:49Z","abstract_excerpt":"We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of a no-pair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential. We prove that the infimum of the spectrum of the no-pair operator is an evenly degenerate eigenvalue. In particular, we show that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true, for arbitrary values of the fine-structure constant and the ultra-violet cut-off and for all Coulomb coupling constants less than t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2109","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":""},"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":"2026-05-18T04:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1OhkfeLQFcCeM/KESu5l0zElofAEkovWsLAeqcLvl7rwhyzEGFBHowpea0R4xhsPbyHZBkpENm10fn1RLdcxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:07:31.784593Z"},"content_sha256":"d398a0b5a298d4f764d632a6d6afbfc1ae5f3eb0d6075eb2a0592407d407ea71","schema_version":"1.0","event_id":"sha256:d398a0b5a298d4f764d632a6d6afbfc1ae5f3eb0d6075eb2a0592407d407ea71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7/bundle.json","state_url":"https://pith.science/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7/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":"2026-05-30T01:07:31Z","links":{"resolver":"https://pith.science/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7","bundle":"https://pith.science/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7/bundle.json","state":"https://pith.science/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4BOSGSC4LHDMDBRHFOLXCWVQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:G4BOSGSC4LHDMDBRHFOLXCWVQ7","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":"58627c4582e0879610dd1db497b017caf065a84d3a016dc439943b9e7aed1f2a","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T14:16:49Z","title_canon_sha256":"c225d2ff4da1818ca9e7d1b13af042b94c44944f2285e2813481dbbbbc72e766"},"schema_version":"1.0","source":{"id":"1005.2109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2109","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2109v2","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2109","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"G4BOSGSC4LHD","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"G4BOSGSC4LHDMDBR","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"G4BOSGSC","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:d398a0b5a298d4f764d632a6d6afbfc1ae5f3eb0d6075eb2a0592407d407ea71","target":"graph","created_at":"2026-05-18T04:07:17Z","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 a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of a no-pair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential. We prove that the infimum of the spectrum of the no-pair operator is an evenly degenerate eigenvalue. In particular, we show that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true, for arbitrary values of the fine-structure constant and the ultra-violet cut-off and for all Coulomb coupling constants less than t","authors_text":"Edgardo Stockmeyer, Martin K\\\"onenberg, Oliver Matte","cross_cats":["math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T14:16:49Z","title":"Existence of ground states of hydrogen-like atoms in relativistic QED II: The no-pair operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2109","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:e5e1cbf982920380d2ef5e9dc1b242a2a81415f18717ee12667cbd04f4d06aa1","target":"record","created_at":"2026-05-18T04:07:17Z","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":"58627c4582e0879610dd1db497b017caf065a84d3a016dc439943b9e7aed1f2a","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T14:16:49Z","title_canon_sha256":"c225d2ff4da1818ca9e7d1b13af042b94c44944f2285e2813481dbbbbc72e766"},"schema_version":"1.0","source":{"id":"1005.2109","kind":"arxiv","version":2}},"canonical_sha256":"3702e91a42e2ce360c31395cbb8ad587f59c2923ab6306b7040bbccca3cbdeb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3702e91a42e2ce360c31395cbb8ad587f59c2923ab6306b7040bbccca3cbdeb8","first_computed_at":"2026-05-18T04:07:17.933903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:17.933903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bejVjfuYYQHRR88soF8PqNyrMf3HDPumLVleeNiJki7v9MSknSqnQbMFLhky8guTHVKoc+bdXQWgn55mvrzODw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:17.934633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5e1cbf982920380d2ef5e9dc1b242a2a81415f18717ee12667cbd04f4d06aa1","sha256:d398a0b5a298d4f764d632a6d6afbfc1ae5f3eb0d6075eb2a0592407d407ea71"],"state_sha256":"35c0504d32b3dfc9870231277d0059430f46ab8893747f02ab66ab55c4d52325"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVgSz1YTfjKFb6uRImWzS0PycPX+C+R0x9Mvq7VCzVP4DKAxiG83AcGaMvqs2TtDts82Ce4sFD5ubf3gMg9/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:07:31.788266Z","bundle_sha256":"86feb7faeed8cde4199a78f5b65b67f538ec74890c341d4b195456d888980c5b"}}