{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:MFEWHW3XHBKNVCK6V2WUNQEN5Q","short_pith_number":"pith:MFEWHW3X","canonical_record":{"source":{"id":"cond-mat/9603165","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"1996-03-26T22:32:27Z","cross_cats_sorted":[],"title_canon_sha256":"4e3be3d1c1fca6a221e8e6b15bd530ab4b8dd8212faba9c9f0d227a79d6ead36","abstract_canon_sha256":"465972e7848e5363ebcdb9bb63fd6bc9bc6f4647437c9f6e4e27464c473abc27"},"schema_version":"1.0"},"canonical_sha256":"614963db773854da895eaead46c08dec025e076f433a18f18ff3bd7d8ca64b40","source":{"kind":"arxiv","id":"cond-mat/9603165","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9603165","created_at":"2026-05-18T01:07:10Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9603165v1","created_at":"2026-05-18T01:07:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9603165","created_at":"2026-05-18T01:07:10Z"},{"alias_kind":"pith_short_12","alias_value":"MFEWHW3XHBKN","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MFEWHW3XHBKNVCK6","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MFEWHW3X","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:MFEWHW3XHBKNVCK6V2WUNQEN5Q","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9603165","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"1996-03-26T22:32:27Z","cross_cats_sorted":[],"title_canon_sha256":"4e3be3d1c1fca6a221e8e6b15bd530ab4b8dd8212faba9c9f0d227a79d6ead36","abstract_canon_sha256":"465972e7848e5363ebcdb9bb63fd6bc9bc6f4647437c9f6e4e27464c473abc27"},"schema_version":"1.0"},"canonical_sha256":"614963db773854da895eaead46c08dec025e076f433a18f18ff3bd7d8ca64b40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:10.995680Z","signature_b64":"vwP38SaRV+wfy4fcGMFKxRxqw8lNrFkJRDBgGJVnJRIQYy4VH0wUZd1AbczfFKwQCn+kvDTQzbUQ9LWJ9OliCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"614963db773854da895eaead46c08dec025e076f433a18f18ff3bd7d8ca64b40","last_reissued_at":"2026-05-18T01:07:10.995277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:10.995277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9603165","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":"2026-05-18T01:07:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/tOtMZhs2pWTAl9w0iGpprn3355fM9YVQcYaqWOzr6EmynYIPVGZQWeeQwIF2T64nzDHh7CYvwL6I9KlyGEZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T03:26:04.624414Z"},"content_sha256":"8edab7093e2a319d02da01e7538a3d69ee046fbb143581f058835c710842d534","schema_version":"1.0","event_id":"sha256:8edab7093e2a319d02da01e7538a3d69ee046fbb143581f058835c710842d534"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:MFEWHW3XHBKNVCK6V2WUNQEN5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization transitions in non-Hermitian quantum mechanics","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"David R. Nelson (Harvard University), Naomichi Hatano","submitted_at":"1996-03-26T22:32:27Z","abstract_excerpt":"We study the localization transitions which arise in both one and two dimensions when quantum mechanical particles described by a random Schr\\\"odinger equation are subjected to a constant imaginary vector potential. A path-integral formulation relates the transition to flux lines depinned from columnar defects by a transverse magnetic field in superconductors. The theory predicts that the transverse Meissner effect is accompanied by stretched exponential relaxation of the field into the bulk and a diverging penetration depth at the transition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9603165","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":"2026-05-18T01:07:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSBSOAfQ4AKjmPj1LSOXdAB4eBtlYHycb4ydrvhaSp3emveVaD+iWBDT0jbfVVUgVSj7yx5mz5qDb1Skefc0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T03:26:04.625142Z"},"content_sha256":"02208ab8579e9c00cff1a3b1ac296fc8a4c1b849494fc0b91dc88ed5e452c2c3","schema_version":"1.0","event_id":"sha256:02208ab8579e9c00cff1a3b1ac296fc8a4c1b849494fc0b91dc88ed5e452c2c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q/bundle.json","state_url":"https://pith.science/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q/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":"2026-05-24T03:26:04Z","links":{"resolver":"https://pith.science/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q","bundle":"https://pith.science/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q/bundle.json","state":"https://pith.science/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFEWHW3XHBKNVCK6V2WUNQEN5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:MFEWHW3XHBKNVCK6V2WUNQEN5Q","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":"465972e7848e5363ebcdb9bb63fd6bc9bc6f4647437c9f6e4e27464c473abc27","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1996-03-26T22:32:27Z","title_canon_sha256":"4e3be3d1c1fca6a221e8e6b15bd530ab4b8dd8212faba9c9f0d227a79d6ead36"},"schema_version":"1.0","source":{"id":"cond-mat/9603165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9603165","created_at":"2026-05-18T01:07:10Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9603165v1","created_at":"2026-05-18T01:07:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9603165","created_at":"2026-05-18T01:07:10Z"},{"alias_kind":"pith_short_12","alias_value":"MFEWHW3XHBKN","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MFEWHW3XHBKNVCK6","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MFEWHW3X","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:02208ab8579e9c00cff1a3b1ac296fc8a4c1b849494fc0b91dc88ed5e452c2c3","target":"graph","created_at":"2026-05-18T01:07:10Z","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 localization transitions which arise in both one and two dimensions when quantum mechanical particles described by a random Schr\\\"odinger equation are subjected to a constant imaginary vector potential. A path-integral formulation relates the transition to flux lines depinned from columnar defects by a transverse magnetic field in superconductors. The theory predicts that the transverse Meissner effect is accompanied by stretched exponential relaxation of the field into the bulk and a diverging penetration depth at the transition.","authors_text":"David R. Nelson (Harvard University), Naomichi Hatano","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat","submitted_at":"1996-03-26T22:32:27Z","title":"Localization transitions in non-Hermitian quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9603165","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":"sha256:8edab7093e2a319d02da01e7538a3d69ee046fbb143581f058835c710842d534","target":"record","created_at":"2026-05-18T01:07:10Z","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":"465972e7848e5363ebcdb9bb63fd6bc9bc6f4647437c9f6e4e27464c473abc27","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1996-03-26T22:32:27Z","title_canon_sha256":"4e3be3d1c1fca6a221e8e6b15bd530ab4b8dd8212faba9c9f0d227a79d6ead36"},"schema_version":"1.0","source":{"id":"cond-mat/9603165","kind":"arxiv","version":1}},"canonical_sha256":"614963db773854da895eaead46c08dec025e076f433a18f18ff3bd7d8ca64b40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"614963db773854da895eaead46c08dec025e076f433a18f18ff3bd7d8ca64b40","first_computed_at":"2026-05-18T01:07:10.995277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:10.995277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vwP38SaRV+wfy4fcGMFKxRxqw8lNrFkJRDBgGJVnJRIQYy4VH0wUZd1AbczfFKwQCn+kvDTQzbUQ9LWJ9OliCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:10.995680Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9603165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8edab7093e2a319d02da01e7538a3d69ee046fbb143581f058835c710842d534","sha256:02208ab8579e9c00cff1a3b1ac296fc8a4c1b849494fc0b91dc88ed5e452c2c3"],"state_sha256":"21f0b65b129b1a922c897671c87f6cd07569791bf25a819c638af9612a5f5e64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MSAsJ2xy3FtqwFSoC1StK0b5G8rzVNgvt2/wpGZSwVjwg299GkMCA6/GWQsT5LswtgZ5ZYmDX7/egUgEHqLkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T03:26:04.629098Z","bundle_sha256":"31a6a2b13b0181e00b0e89ddfc3f50dd167cc9eea12000cd2e72fe7a674cf0ab"}}