{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GQGM47W7AYCM3VVX74TJ5YUWR3","short_pith_number":"pith:GQGM47W7","canonical_record":{"source":{"id":"1708.07375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-08-24T12:32:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5096507efcb1a8487273c35e0938f596e1da7578d3efee71f3425cbda94e2c71","abstract_canon_sha256":"168a77b6f7c3f1471b6becb1921bdc07ba7342bde47e6e23a488fd132cf3b73c"},"schema_version":"1.0"},"canonical_sha256":"340cce7edf0604cdd6b7ff269ee2968ee20a233dd9a45a3469e4ee94b3e9e416","source":{"kind":"arxiv","id":"1708.07375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07375","created_at":"2026-05-18T00:30:00Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07375v1","created_at":"2026-05-18T00:30:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07375","created_at":"2026-05-18T00:30:00Z"},{"alias_kind":"pith_short_12","alias_value":"GQGM47W7AYCM","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GQGM47W7AYCM3VVX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GQGM47W7","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GQGM47W7AYCM3VVX74TJ5YUWR3","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-08-24T12:32:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5096507efcb1a8487273c35e0938f596e1da7578d3efee71f3425cbda94e2c71","abstract_canon_sha256":"168a77b6f7c3f1471b6becb1921bdc07ba7342bde47e6e23a488fd132cf3b73c"},"schema_version":"1.0"},"canonical_sha256":"340cce7edf0604cdd6b7ff269ee2968ee20a233dd9a45a3469e4ee94b3e9e416","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:00.417437Z","signature_b64":"REVVp9ld7YWdU2J7D9KkYPMpW1G+/WKsah07hYZdENBebZ/tiOBNzLTXDmsKENHZ2bbjeEkADeXQmNa1fZjvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"340cce7edf0604cdd6b7ff269ee2968ee20a233dd9a45a3469e4ee94b3e9e416","last_reissued_at":"2026-05-18T00:30:00.416724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:00.416724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07375","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":"2026-05-18T00:30:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GsyxVjvXC/q0o+JH1jhK6yoTowpdeNZ6xvF8UMdhYL1rAY135pB9Bb3PRwmQnqiIYgUfU8SiAVz8xVGquDXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:39:15.514031Z"},"content_sha256":"f6047b9d3b5d92347f1daba0167ce7adb7324e9526a34b0f62dcb0dbc3f5477d","schema_version":"1.0","event_id":"sha256:f6047b9d3b5d92347f1daba0167ce7adb7324e9526a34b0f62dcb0dbc3f5477d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GQGM47W7AYCM3VVX74TJ5YUWR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A magnetic version of the Smilansky-Solomyak model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Diana Barseghyan, Pavel Exner","submitted_at":"2017-08-24T12:32:22Z","abstract_excerpt":"We analyze spectral properties of two mutually related families of magnetic Schr\\\"{o}dinger operators, $H_{\\mathrm{Sm}}(A)=(i \\nabla +A)^2+\\omega^2 y^2+\\lambda y \\delta(x)$ and $H(A)=(i \\nabla +A)^2+\\omega^2 y^2+ \\lambda y^2 V(x y)$ in $L^2(R^2)$, with the parameters $\\omega>0$ and $\\lambda<0$, where $A$ is a vector potential corresponding to a homogeneous magnetic field perpendicular to the plane and $V$ is a regular nonnegative and compactly supported potential. We show that the spectral properties of the operators depend crucially on the one-dimensional Schr\\\"{o}dinger operators $L= -\\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07375","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":"2026-05-18T00:30:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aRlB4NHAl3j+eHogu68lzPEag5nt4SkK2504aZAipmgxRxxn1CNItnAQlBF7ERvY0GJFIjJ1zEb/MAaQKmXRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:39:15.514927Z"},"content_sha256":"9843eefb275072fcef538655c89c0103ce0f1fc5f9c694c9cb7bdc375259ce87","schema_version":"1.0","event_id":"sha256:9843eefb275072fcef538655c89c0103ce0f1fc5f9c694c9cb7bdc375259ce87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQGM47W7AYCM3VVX74TJ5YUWR3/bundle.json","state_url":"https://pith.science/pith/GQGM47W7AYCM3VVX74TJ5YUWR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQGM47W7AYCM3VVX74TJ5YUWR3/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":"2026-05-31T11:39:15Z","links":{"resolver":"https://pith.science/pith/GQGM47W7AYCM3VVX74TJ5YUWR3","bundle":"https://pith.science/pith/GQGM47W7AYCM3VVX74TJ5YUWR3/bundle.json","state":"https://pith.science/pith/GQGM47W7AYCM3VVX74TJ5YUWR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQGM47W7AYCM3VVX74TJ5YUWR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GQGM47W7AYCM3VVX74TJ5YUWR3","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":"168a77b6f7c3f1471b6becb1921bdc07ba7342bde47e6e23a488fd132cf3b73c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-08-24T12:32:22Z","title_canon_sha256":"5096507efcb1a8487273c35e0938f596e1da7578d3efee71f3425cbda94e2c71"},"schema_version":"1.0","source":{"id":"1708.07375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07375","created_at":"2026-05-18T00:30:00Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07375v1","created_at":"2026-05-18T00:30:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07375","created_at":"2026-05-18T00:30:00Z"},{"alias_kind":"pith_short_12","alias_value":"GQGM47W7AYCM","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GQGM47W7AYCM3VVX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GQGM47W7","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:9843eefb275072fcef538655c89c0103ce0f1fc5f9c694c9cb7bdc375259ce87","target":"graph","created_at":"2026-05-18T00:30:00Z","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 analyze spectral properties of two mutually related families of magnetic Schr\\\"{o}dinger operators, $H_{\\mathrm{Sm}}(A)=(i \\nabla +A)^2+\\omega^2 y^2+\\lambda y \\delta(x)$ and $H(A)=(i \\nabla +A)^2+\\omega^2 y^2+ \\lambda y^2 V(x y)$ in $L^2(R^2)$, with the parameters $\\omega>0$ and $\\lambda<0$, where $A$ is a vector potential corresponding to a homogeneous magnetic field perpendicular to the plane and $V$ is a regular nonnegative and compactly supported potential. We show that the spectral properties of the operators depend crucially on the one-dimensional Schr\\\"{o}dinger operators $L= -\\frac{","authors_text":"Diana Barseghyan, Pavel Exner","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-08-24T12:32:22Z","title":"A magnetic version of the Smilansky-Solomyak model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07375","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:f6047b9d3b5d92347f1daba0167ce7adb7324e9526a34b0f62dcb0dbc3f5477d","target":"record","created_at":"2026-05-18T00:30:00Z","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":"168a77b6f7c3f1471b6becb1921bdc07ba7342bde47e6e23a488fd132cf3b73c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-08-24T12:32:22Z","title_canon_sha256":"5096507efcb1a8487273c35e0938f596e1da7578d3efee71f3425cbda94e2c71"},"schema_version":"1.0","source":{"id":"1708.07375","kind":"arxiv","version":1}},"canonical_sha256":"340cce7edf0604cdd6b7ff269ee2968ee20a233dd9a45a3469e4ee94b3e9e416","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"340cce7edf0604cdd6b7ff269ee2968ee20a233dd9a45a3469e4ee94b3e9e416","first_computed_at":"2026-05-18T00:30:00.416724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:00.416724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"REVVp9ld7YWdU2J7D9KkYPMpW1G+/WKsah07hYZdENBebZ/tiOBNzLTXDmsKENHZ2bbjeEkADeXQmNa1fZjvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:00.417437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6047b9d3b5d92347f1daba0167ce7adb7324e9526a34b0f62dcb0dbc3f5477d","sha256:9843eefb275072fcef538655c89c0103ce0f1fc5f9c694c9cb7bdc375259ce87"],"state_sha256":"d7c4c2c4e94620d62409ae40a967a41069a07a864900f477c36ebebe4f067643"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/IEv/VNa2Sa2QoHuaj+bI5klATe+eTjvc/XNyYte/vfvh33cqwGUwDT//Xo4pWwwMDjMOmQM1qtcKjNNth/pAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:39:15.519662Z","bundle_sha256":"1cf1811c41df0287063bf28864cc94c26b015889a702ab7011d4897d54f65224"}}