{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EJNOCPGZKB6BPMXSOF6IWWYUIE","short_pith_number":"pith:EJNOCPGZ","canonical_record":{"source":{"id":"1506.05759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T17:53:29Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"a10a9f5491815881a4bdca4d3aba6218c165b84d6e72b657628be5b032b93de2","abstract_canon_sha256":"a65e70012489c46bf9076d3888e703c2540c4bd606d1817313a3c0177f0973bf"},"schema_version":"1.0"},"canonical_sha256":"225ae13cd9507c17b2f2717c8b5b144112df205fe0e3abc70878e814a7130bd0","source":{"kind":"arxiv","id":"1506.05759","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05759","created_at":"2026-05-18T01:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05759v1","created_at":"2026-05-18T01:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05759","created_at":"2026-05-18T01:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"EJNOCPGZKB6B","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EJNOCPGZKB6BPMXS","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EJNOCPGZ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EJNOCPGZKB6BPMXSOF6IWWYUIE","target":"record","payload":{"canonical_record":{"source":{"id":"1506.05759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T17:53:29Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"a10a9f5491815881a4bdca4d3aba6218c165b84d6e72b657628be5b032b93de2","abstract_canon_sha256":"a65e70012489c46bf9076d3888e703c2540c4bd606d1817313a3c0177f0973bf"},"schema_version":"1.0"},"canonical_sha256":"225ae13cd9507c17b2f2717c8b5b144112df205fe0e3abc70878e814a7130bd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:09.761160Z","signature_b64":"aXA7SNL/Y7fiJvV2n4s8ybmP2/blPemApetS18VUcNSfFhjPUSP1Q9RRHDRXkH8ffNiVdFcwS5WEzI2gHD8TDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"225ae13cd9507c17b2f2717c8b5b144112df205fe0e3abc70878e814a7130bd0","last_reissued_at":"2026-05-18T01:44:09.760490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:09.760490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.05759","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":"2026-05-18T01:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsFQ0xcKyyH26R4Mtr4tnn3HxNYrguNSbE4HnDdORYX7X1ua3/REPAMEEdnVg8o98fW7J/f0B/+IOd3VzJy+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:40:02.343905Z"},"content_sha256":"99faffdac3b14b632e524f0172590566fa2c07621a2efdf98483eaebeedc15da","schema_version":"1.0","event_id":"sha256:99faffdac3b14b632e524f0172590566fa2c07621a2efdf98483eaebeedc15da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EJNOCPGZKB6BPMXSOF6IWWYUIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral shift function and Resonances near the low ground state for Pauli and Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Diomba Sambou","submitted_at":"2015-06-18T17:53:29Z","abstract_excerpt":"We study the spectral shift function (SSF) $\\xi(\\lambda)$ and the resonances of the operator $H_V := \\big( \\sigma \\cdot (-i\\nabla - \\textbf{A}) \\big)^{2} + V$ in $L^2(\\mathbb{R}^3)$ near the origin. Here $\\sigma := (\\sigma_1,\\sigma_2,\\sigma_3)$ are the $2 \\times 2$ Pauli matrices and $V$ is a hermitian potential decaying exponentially in the direction of the magnetic field $\\textbf{B} := \\text{curl} \\hspace{0.6mm} \\textbf{A}$. We give a representation of the derivative of the SSF as a sum of the imaginary part of a holomorphic function and a harmonic measure related to the resonances of $H_V$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05759","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":"2026-05-18T01:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7PtW3Ck+nXIyUSbYZ0KIcxGhfN1K/MsRNo5MJkzZhz6XiXPPg8r2Cy5CRGEEBvG3su8NFhMJ9/wjYSbsEr2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:40:02.344584Z"},"content_sha256":"a7acff84b16f7428c8da995d9f3d8afcf22a49801d8a834ef6d014459b72b34f","schema_version":"1.0","event_id":"sha256:a7acff84b16f7428c8da995d9f3d8afcf22a49801d8a834ef6d014459b72b34f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE/bundle.json","state_url":"https://pith.science/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE/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":"2026-05-28T22:40:02Z","links":{"resolver":"https://pith.science/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE","bundle":"https://pith.science/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE/bundle.json","state":"https://pith.science/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJNOCPGZKB6BPMXSOF6IWWYUIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EJNOCPGZKB6BPMXSOF6IWWYUIE","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":"a65e70012489c46bf9076d3888e703c2540c4bd606d1817313a3c0177f0973bf","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T17:53:29Z","title_canon_sha256":"a10a9f5491815881a4bdca4d3aba6218c165b84d6e72b657628be5b032b93de2"},"schema_version":"1.0","source":{"id":"1506.05759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05759","created_at":"2026-05-18T01:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05759v1","created_at":"2026-05-18T01:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05759","created_at":"2026-05-18T01:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"EJNOCPGZKB6B","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EJNOCPGZKB6BPMXS","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EJNOCPGZ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:a7acff84b16f7428c8da995d9f3d8afcf22a49801d8a834ef6d014459b72b34f","target":"graph","created_at":"2026-05-18T01:44:09Z","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 study the spectral shift function (SSF) $\\xi(\\lambda)$ and the resonances of the operator $H_V := \\big( \\sigma \\cdot (-i\\nabla - \\textbf{A}) \\big)^{2} + V$ in $L^2(\\mathbb{R}^3)$ near the origin. Here $\\sigma := (\\sigma_1,\\sigma_2,\\sigma_3)$ are the $2 \\times 2$ Pauli matrices and $V$ is a hermitian potential decaying exponentially in the direction of the magnetic field $\\textbf{B} := \\text{curl} \\hspace{0.6mm} \\textbf{A}$. We give a representation of the derivative of the SSF as a sum of the imaginary part of a holomorphic function and a harmonic measure related to the resonances of $H_V$.","authors_text":"Diomba Sambou","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T17:53:29Z","title":"Spectral shift function and Resonances near the low ground state for Pauli and Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05759","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":"sha256:99faffdac3b14b632e524f0172590566fa2c07621a2efdf98483eaebeedc15da","target":"record","created_at":"2026-05-18T01:44:09Z","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":"a65e70012489c46bf9076d3888e703c2540c4bd606d1817313a3c0177f0973bf","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T17:53:29Z","title_canon_sha256":"a10a9f5491815881a4bdca4d3aba6218c165b84d6e72b657628be5b032b93de2"},"schema_version":"1.0","source":{"id":"1506.05759","kind":"arxiv","version":1}},"canonical_sha256":"225ae13cd9507c17b2f2717c8b5b144112df205fe0e3abc70878e814a7130bd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"225ae13cd9507c17b2f2717c8b5b144112df205fe0e3abc70878e814a7130bd0","first_computed_at":"2026-05-18T01:44:09.760490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:09.760490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aXA7SNL/Y7fiJvV2n4s8ybmP2/blPemApetS18VUcNSfFhjPUSP1Q9RRHDRXkH8ffNiVdFcwS5WEzI2gHD8TDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:09.761160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99faffdac3b14b632e524f0172590566fa2c07621a2efdf98483eaebeedc15da","sha256:a7acff84b16f7428c8da995d9f3d8afcf22a49801d8a834ef6d014459b72b34f"],"state_sha256":"ea88a7e8129f9daf99fac23e8719a6518631a74357b49dfec8b3582f6fa2df90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zo7cc7/z89uN24PaQX+6NiNxFazD9JBYHXv36AjgpHF22c6gbpKF9EFhLrq5ucz8JBTFzH9VJPSXWkvopNqXBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:40:02.347937Z","bundle_sha256":"641624521362f24d5b6a9c28c641b41263c98923f63ec6dc307d03e319cd835e"}}