{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:WPPIEMDT7YNPRFG5AWNPDTCU3T","short_pith_number":"pith:WPPIEMDT","canonical_record":{"source":{"id":"quant-ph/0501040","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-10T20:39:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d69daf74cf3f01c08f994d29b7a2b0adf276616528e177a987ff82d833b6b3a7","abstract_canon_sha256":"2d5aa1d66446d3b7772bee9bcdc5a986899e64cf87b7fc6aba1585edb0281e25"},"schema_version":"1.0"},"canonical_sha256":"b3de823073fe1af894dd059af1cc54dcc79ce425de7ff8bf398d5f7d8a11882c","source":{"kind":"arxiv","id":"quant-ph/0501040","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0501040","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0501040v4","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0501040","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"WPPIEMDT7YNP","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"pith_short_16","alias_value":"WPPIEMDT7YNPRFG5","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"pith_short_8","alias_value":"WPPIEMDT","created_at":"2026-07-04T16:57:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:WPPIEMDT7YNPRFG5AWNPDTCU3T","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0501040","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-10T20:39:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d69daf74cf3f01c08f994d29b7a2b0adf276616528e177a987ff82d833b6b3a7","abstract_canon_sha256":"2d5aa1d66446d3b7772bee9bcdc5a986899e64cf87b7fc6aba1585edb0281e25"},"schema_version":"1.0"},"canonical_sha256":"b3de823073fe1af894dd059af1cc54dcc79ce425de7ff8bf398d5f7d8a11882c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:57:27.957339Z","signature_b64":"WWojWR130mIeWWGSgkVBXoFZPLYEQRUoZ0Hovu/vhfZz2P9BnicP8lujmaPJkba8Twbfvj60iJZocJD9tW5lAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3de823073fe1af894dd059af1cc54dcc79ce425de7ff8bf398d5f7d8a11882c","last_reissued_at":"2026-07-04T16:57:27.956974Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:57:27.956974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0501040","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPhqa7kVE+i/UKMKI6j4PfwxlGO6FXT/ifGTf4BbKvTslUVdLcpkCfzbx5P81HgufjzWcTzZySKTPsjq4qfbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:10:54.378405Z"},"content_sha256":"2c1963fb99584e78575a6301f644f93cb115de098c393188ecf37fc57ffdb819","schema_version":"1.0","event_id":"sha256:2c1963fb99584e78575a6301f644f93cb115de098c393188ecf37fc57ffdb819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:WPPIEMDT7YNPRFG5AWNPDTCU3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric phase around exceptional points","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A.A. Mailybaev, A.P. Seyranian, O.N. Kirillov","submitted_at":"2005-01-10T20:39:03Z","abstract_excerpt":"A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to $\\pi$ for small cycles and cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0501040","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0501040/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UOacDuje0dEfA/5PVtP9ABV5cp9zUfuRrnVYhGYuHqe7R3IL5B4SohuMCQXy449pRCD33IYJHWpcBlhkqPCBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:10:54.378915Z"},"content_sha256":"ca9f5ca02a75e7aeef02d919f4d4c8ecbb8250882c8d54f0dd442db0477eae26","schema_version":"1.0","event_id":"sha256:ca9f5ca02a75e7aeef02d919f4d4c8ecbb8250882c8d54f0dd442db0477eae26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T/bundle.json","state_url":"https://pith.science/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T/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":"2026-08-03T22:10:54Z","links":{"resolver":"https://pith.science/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T","bundle":"https://pith.science/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T/bundle.json","state":"https://pith.science/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPPIEMDT7YNPRFG5AWNPDTCU3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:WPPIEMDT7YNPRFG5AWNPDTCU3T","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":"2d5aa1d66446d3b7772bee9bcdc5a986899e64cf87b7fc6aba1585edb0281e25","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-10T20:39:03Z","title_canon_sha256":"d69daf74cf3f01c08f994d29b7a2b0adf276616528e177a987ff82d833b6b3a7"},"schema_version":"1.0","source":{"id":"quant-ph/0501040","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0501040","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0501040v4","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0501040","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"WPPIEMDT7YNP","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"pith_short_16","alias_value":"WPPIEMDT7YNPRFG5","created_at":"2026-07-04T16:57:27Z"},{"alias_kind":"pith_short_8","alias_value":"WPPIEMDT","created_at":"2026-07-04T16:57:27Z"}],"graph_snapshots":[{"event_id":"sha256:ca9f5ca02a75e7aeef02d919f4d4c8ecbb8250882c8d54f0dd442db0477eae26","target":"graph","created_at":"2026-07-04T16:57:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0501040/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to $\\pi$ for small cycles and cha","authors_text":"A.A. Mailybaev, A.P. Seyranian, O.N. Kirillov","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2005-01-10T20:39:03Z","title":"Geometric phase around exceptional points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0501040","kind":"arxiv","version":4},"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":"sha256:2c1963fb99584e78575a6301f644f93cb115de098c393188ecf37fc57ffdb819","target":"record","created_at":"2026-07-04T16:57:27Z","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":"2d5aa1d66446d3b7772bee9bcdc5a986899e64cf87b7fc6aba1585edb0281e25","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-10T20:39:03Z","title_canon_sha256":"d69daf74cf3f01c08f994d29b7a2b0adf276616528e177a987ff82d833b6b3a7"},"schema_version":"1.0","source":{"id":"quant-ph/0501040","kind":"arxiv","version":4}},"canonical_sha256":"b3de823073fe1af894dd059af1cc54dcc79ce425de7ff8bf398d5f7d8a11882c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3de823073fe1af894dd059af1cc54dcc79ce425de7ff8bf398d5f7d8a11882c","first_computed_at":"2026-07-04T16:57:27.956974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:57:27.956974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WWojWR130mIeWWGSgkVBXoFZPLYEQRUoZ0Hovu/vhfZz2P9BnicP8lujmaPJkba8Twbfvj60iJZocJD9tW5lAg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:57:27.957339Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0501040","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c1963fb99584e78575a6301f644f93cb115de098c393188ecf37fc57ffdb819","sha256:ca9f5ca02a75e7aeef02d919f4d4c8ecbb8250882c8d54f0dd442db0477eae26"],"state_sha256":"6d4bb2f0cc0a61933cf9702b83e46ef6002450ad7ac31895facf14e032d36152"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jfi+1h1YY4C0VvuaFLM7/1ombQaTV5kFbGEadbY40GUEQ7thxwLxeorb9osJc/hn89xY5pq258jtrSiqNKwwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:10:54.383083Z","bundle_sha256":"d9fa9f96b978971dd26d59315103bf93e3c375ca95e15a7766c247803a83ec59"}}