{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FXX5KR5IY7JMMHSIDXZIDRZLNO","short_pith_number":"pith:FXX5KR5I","canonical_record":{"source":{"id":"1604.01573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-06T10:54:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0863c3e7ec2808836a09f9fb0b892de59413be2b517fb153a8d113cbf8ac9ac7","abstract_canon_sha256":"822d3689aba877ea5c68833b6a324294661b8a69478eeb49f945c1ad4bfef113"},"schema_version":"1.0"},"canonical_sha256":"2defd547a8c7d2c61e481df281c72b6bb015c10ef83d8b1dd4240a5dd07ff8fa","source":{"kind":"arxiv","id":"1604.01573","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01573","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01573v2","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01573","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"FXX5KR5IY7JM","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FXX5KR5IY7JMMHSI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FXX5KR5I","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FXX5KR5IY7JMMHSIDXZIDRZLNO","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-06T10:54:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0863c3e7ec2808836a09f9fb0b892de59413be2b517fb153a8d113cbf8ac9ac7","abstract_canon_sha256":"822d3689aba877ea5c68833b6a324294661b8a69478eeb49f945c1ad4bfef113"},"schema_version":"1.0"},"canonical_sha256":"2defd547a8c7d2c61e481df281c72b6bb015c10ef83d8b1dd4240a5dd07ff8fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:07.596804Z","signature_b64":"Nh3FvWM3axxdZs2owkJT21Vi0dkwScZDx6WKEOsY4+32LLP4R43r3b0OIyCVOIVxdIY4bzi2E1ZCYOPb5Bc/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2defd547a8c7d2c61e481df281c72b6bb015c10ef83d8b1dd4240a5dd07ff8fa","last_reissued_at":"2026-05-18T00:20:07.596286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:07.596286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01573","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":"2026-05-18T00:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNVKlK5D+dGIMu9i3rL0QKgARbMFpBMhSDlhIIrxstZaxRM1RfKOEvYap+UgQV5Y414fvkFGy/+ldyTsH/0LCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:24:05.464234Z"},"content_sha256":"b56057a030680ad73cc61e5119c761f5aab25c614f164f1a4b619885f61d491b","schema_version":"1.0","event_id":"sha256:b56057a030680ad73cc61e5119c761f5aab25c614f164f1a4b619885f61d491b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FXX5KR5IY7JMMHSIDXZIDRZLNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schr\\\"odinger operators with random $\\delta$ magnetic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Takuya Mine, Yuji Nomura","submitted_at":"2016-04-06T10:54:46Z","abstract_excerpt":"We shall consider the Schr\\\"odinger operators on $\\mathbf{R}^2$ with random $\\delta$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $\\delta$-fields, we prove the spectrum coincides with $[0,\\infty)$ and the integrated density of states (IDS) decays exponentially at the bottom of the spectrum (Lifshitz tail), by using the Hardy type inequality by Laptev-Weidl. We also give a lower bound for IDS at the bottom of the spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01573","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":"2026-05-18T00:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBUQ5fmivutQy+mmJHiDb+BfVygT652K+2HDqfvMytQLSACn3iRZm3UzXXzmCRdFxi8FSJKevkgQnJfE3gG9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:24:05.464942Z"},"content_sha256":"79e98c6dd9552a39a84360aae0dc359037808c8f3852ec89aa1cbf4136baa909","schema_version":"1.0","event_id":"sha256:79e98c6dd9552a39a84360aae0dc359037808c8f3852ec89aa1cbf4136baa909"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO/bundle.json","state_url":"https://pith.science/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO/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":"2026-05-29T18:24:05Z","links":{"resolver":"https://pith.science/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO","bundle":"https://pith.science/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO/bundle.json","state":"https://pith.science/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXX5KR5IY7JMMHSIDXZIDRZLNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FXX5KR5IY7JMMHSIDXZIDRZLNO","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":"822d3689aba877ea5c68833b6a324294661b8a69478eeb49f945c1ad4bfef113","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-06T10:54:46Z","title_canon_sha256":"0863c3e7ec2808836a09f9fb0b892de59413be2b517fb153a8d113cbf8ac9ac7"},"schema_version":"1.0","source":{"id":"1604.01573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01573","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01573v2","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01573","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"FXX5KR5IY7JM","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FXX5KR5IY7JMMHSI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FXX5KR5I","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:79e98c6dd9552a39a84360aae0dc359037808c8f3852ec89aa1cbf4136baa909","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":"We shall consider the Schr\\\"odinger operators on $\\mathbf{R}^2$ with random $\\delta$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $\\delta$-fields, we prove the spectrum coincides with $[0,\\infty)$ and the integrated density of states (IDS) decays exponentially at the bottom of the spectrum (Lifshitz tail), by using the Hardy type inequality by Laptev-Weidl. We also give a lower bound for IDS at the bottom of the spectrum.","authors_text":"Takuya Mine, Yuji Nomura","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-06T10:54:46Z","title":"Schr\\\"odinger operators with random $\\delta$ magnetic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01573","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:b56057a030680ad73cc61e5119c761f5aab25c614f164f1a4b619885f61d491b","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":"822d3689aba877ea5c68833b6a324294661b8a69478eeb49f945c1ad4bfef113","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-06T10:54:46Z","title_canon_sha256":"0863c3e7ec2808836a09f9fb0b892de59413be2b517fb153a8d113cbf8ac9ac7"},"schema_version":"1.0","source":{"id":"1604.01573","kind":"arxiv","version":2}},"canonical_sha256":"2defd547a8c7d2c61e481df281c72b6bb015c10ef83d8b1dd4240a5dd07ff8fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2defd547a8c7d2c61e481df281c72b6bb015c10ef83d8b1dd4240a5dd07ff8fa","first_computed_at":"2026-05-18T00:20:07.596286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.596286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nh3FvWM3axxdZs2owkJT21Vi0dkwScZDx6WKEOsY4+32LLP4R43r3b0OIyCVOIVxdIY4bzi2E1ZCYOPb5Bc/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.596804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b56057a030680ad73cc61e5119c761f5aab25c614f164f1a4b619885f61d491b","sha256:79e98c6dd9552a39a84360aae0dc359037808c8f3852ec89aa1cbf4136baa909"],"state_sha256":"0739d986c7142c2d2939e83871c5809f0ed53db0650aee0a95a1b4c6631be3c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0h/q5kRHknpXBnO5rzkocBMA11SJr/lfThpEPEg7tVkblVr+EYWG20BBKciKppZgM3Q38UQfUENvVtDIu+axDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:24:05.468732Z","bundle_sha256":"f91cd2cdef17254a96c614c56893cfa003a940064d03ebd0e98f8e8cf117da09"}}