{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:M56HVYPJ5JHKTZ777AMERGGKGA","short_pith_number":"pith:M56HVYPJ","canonical_record":{"source":{"id":"1607.08902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-29T19:29:00Z","cross_cats_sorted":["math.CA","math.MP","math.SP","quant-ph"],"title_canon_sha256":"4da7195bf8697a3ea379960c8765574b2e74f699800228d0ba7ceaa4f6e4806e","abstract_canon_sha256":"22b5aaad089c06f3fd8711fd6c455c65142e81196f9c55c42ddfc30989485195"},"schema_version":"1.0"},"canonical_sha256":"677c7ae1e9ea4ea9e7fff8184898ca3000b4d904bffe97cc2c77b91c4716ed67","source":{"kind":"arxiv","id":"1607.08902","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08902","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08902v1","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08902","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"M56HVYPJ5JHK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M56HVYPJ5JHKTZ77","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M56HVYPJ","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:M56HVYPJ5JHKTZ777AMERGGKGA","target":"record","payload":{"canonical_record":{"source":{"id":"1607.08902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-29T19:29:00Z","cross_cats_sorted":["math.CA","math.MP","math.SP","quant-ph"],"title_canon_sha256":"4da7195bf8697a3ea379960c8765574b2e74f699800228d0ba7ceaa4f6e4806e","abstract_canon_sha256":"22b5aaad089c06f3fd8711fd6c455c65142e81196f9c55c42ddfc30989485195"},"schema_version":"1.0"},"canonical_sha256":"677c7ae1e9ea4ea9e7fff8184898ca3000b4d904bffe97cc2c77b91c4716ed67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:07.500954Z","signature_b64":"wNVprA9b8z73x5Uq3ge2AdLFTTa0H3IxEFtcExU0Bho9SfGQN/PiU9N6pXr90ah7h7gjEycQI3LPMGvLqjQZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"677c7ae1e9ea4ea9e7fff8184898ca3000b4d904bffe97cc2c77b91c4716ed67","last_reissued_at":"2026-05-18T00:20:07.500367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:07.500367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.08902","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":"2026-05-18T00:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+oyV6XLXmEyayiJ1T7LHK+coHFkSBrZvK72ugo/T6hm65C1sYB6EPY6hvX+PlaANxAxv+9De/eSOwLaDUIDSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:30:55.926130Z"},"content_sha256":"b5f59549e3971f4cb790672177e1ea612112819057b4dde0ce22840dd5bbd058","schema_version":"1.0","event_id":"sha256:b5f59549e3971f4cb790672177e1ea612112819057b4dde0ce22840dd5bbd058"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:M56HVYPJ5JHKTZ777AMERGGKGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the virtual levels of positively projected massless Coulomb-Dirac operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"David M\\\"uller, Sergey Morozov","submitted_at":"2016-07-29T19:29:00Z","abstract_excerpt":"Considering different self-adjoint realisations of positively projected massless Coulomb-Dirac operators we find out, under which conditions any negative perturbation, however small, leads to emergence of negative spectrum. We also prove some weighted Lieb-Thirring estimates for negative eigenvalues of such operators. In the process we find explicit spectral representations for all self-adjoint realisations of massless Coulomb-Dirac operators on the half-line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08902","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":"2026-05-18T00:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ev7DN38RTCaUjmAcgL2dhrXsci/ABH9SRBSfj+U6b3esflkvGhRA3EiRVyosk/Cp8SP5PFrbFZAQ1zaHPAGtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:30:55.926680Z"},"content_sha256":"8e71ae1f47e713979a285fed8486bc067a6ab9954ba33a2ffd22bd15f82e0b07","schema_version":"1.0","event_id":"sha256:8e71ae1f47e713979a285fed8486bc067a6ab9954ba33a2ffd22bd15f82e0b07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M56HVYPJ5JHKTZ777AMERGGKGA/bundle.json","state_url":"https://pith.science/pith/M56HVYPJ5JHKTZ777AMERGGKGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M56HVYPJ5JHKTZ777AMERGGKGA/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":"2026-06-05T06:30:55Z","links":{"resolver":"https://pith.science/pith/M56HVYPJ5JHKTZ777AMERGGKGA","bundle":"https://pith.science/pith/M56HVYPJ5JHKTZ777AMERGGKGA/bundle.json","state":"https://pith.science/pith/M56HVYPJ5JHKTZ777AMERGGKGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M56HVYPJ5JHKTZ777AMERGGKGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M56HVYPJ5JHKTZ777AMERGGKGA","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":"22b5aaad089c06f3fd8711fd6c455c65142e81196f9c55c42ddfc30989485195","cross_cats_sorted":["math.CA","math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-29T19:29:00Z","title_canon_sha256":"4da7195bf8697a3ea379960c8765574b2e74f699800228d0ba7ceaa4f6e4806e"},"schema_version":"1.0","source":{"id":"1607.08902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08902","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08902v1","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08902","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"M56HVYPJ5JHK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M56HVYPJ5JHKTZ77","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M56HVYPJ","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:8e71ae1f47e713979a285fed8486bc067a6ab9954ba33a2ffd22bd15f82e0b07","target":"graph","created_at":"2026-05-18T00:20:07Z","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":"Considering different self-adjoint realisations of positively projected massless Coulomb-Dirac operators we find out, under which conditions any negative perturbation, however small, leads to emergence of negative spectrum. We also prove some weighted Lieb-Thirring estimates for negative eigenvalues of such operators. In the process we find explicit spectral representations for all self-adjoint realisations of massless Coulomb-Dirac operators on the half-line.","authors_text":"David M\\\"uller, Sergey Morozov","cross_cats":["math.CA","math.MP","math.SP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-29T19:29:00Z","title":"On the virtual levels of positively projected massless Coulomb-Dirac operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08902","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:b5f59549e3971f4cb790672177e1ea612112819057b4dde0ce22840dd5bbd058","target":"record","created_at":"2026-05-18T00:20:07Z","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":"22b5aaad089c06f3fd8711fd6c455c65142e81196f9c55c42ddfc30989485195","cross_cats_sorted":["math.CA","math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-29T19:29:00Z","title_canon_sha256":"4da7195bf8697a3ea379960c8765574b2e74f699800228d0ba7ceaa4f6e4806e"},"schema_version":"1.0","source":{"id":"1607.08902","kind":"arxiv","version":1}},"canonical_sha256":"677c7ae1e9ea4ea9e7fff8184898ca3000b4d904bffe97cc2c77b91c4716ed67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"677c7ae1e9ea4ea9e7fff8184898ca3000b4d904bffe97cc2c77b91c4716ed67","first_computed_at":"2026-05-18T00:20:07.500367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.500367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wNVprA9b8z73x5Uq3ge2AdLFTTa0H3IxEFtcExU0Bho9SfGQN/PiU9N6pXr90ah7h7gjEycQI3LPMGvLqjQZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.500954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5f59549e3971f4cb790672177e1ea612112819057b4dde0ce22840dd5bbd058","sha256:8e71ae1f47e713979a285fed8486bc067a6ab9954ba33a2ffd22bd15f82e0b07"],"state_sha256":"8cbcc0417365252d0d70a2c01cbd239ffacc7a5e3625079668a068020d6175fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHyK0eVjXKxw6I/zZMW8mdHjXmtRY+OMuyLU9+KGYWbnKpxux7CSuYRcgHzRGm21TnJ3N+v8MbHWhNfdioGnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:30:55.930979Z","bundle_sha256":"fb63c568001915a15e172836e0ae6471cb57ac796253d491977a5840272a0377"}}