{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:Y2TJ57CWGSNBGF4AOWRBCVND2A","short_pith_number":"pith:Y2TJ57CW","canonical_record":{"source":{"id":"cond-mat/0102189","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.supr-con","submitted_at":"2001-02-10T16:50:09Z","cross_cats_sorted":[],"title_canon_sha256":"70fc9e69cc72757b87b9bf2e77fe7604ad637a7e994b75156f1b880157963661","abstract_canon_sha256":"6252c01afdc705a9665dc756746acc5b6d835858b10fcdb65f5daf3c1a21f111"},"schema_version":"1.0"},"canonical_sha256":"c6a69efc56349a13178075a21155a3d0025b6440de2faaf8b0d4467fae828499","source":{"kind":"arxiv","id":"cond-mat/0102189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0102189","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0102189v1","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0102189","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y2TJ57CWGSNB","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"pith_short_16","alias_value":"Y2TJ57CWGSNBGF4A","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"pith_short_8","alias_value":"Y2TJ57CW","created_at":"2026-07-04T16:24:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:Y2TJ57CWGSNBGF4AOWRBCVND2A","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0102189","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.supr-con","submitted_at":"2001-02-10T16:50:09Z","cross_cats_sorted":[],"title_canon_sha256":"70fc9e69cc72757b87b9bf2e77fe7604ad637a7e994b75156f1b880157963661","abstract_canon_sha256":"6252c01afdc705a9665dc756746acc5b6d835858b10fcdb65f5daf3c1a21f111"},"schema_version":"1.0"},"canonical_sha256":"c6a69efc56349a13178075a21155a3d0025b6440de2faaf8b0d4467fae828499","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:24:59.097742Z","signature_b64":"4DP4i4bCWbF6aDby/UE2zKOsql/H6T4hKEwgzItnSrwOVeoU0XwEPOUjCUbNkdnzEPC32DVhor6+H7LAw8yTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6a69efc56349a13178075a21155a3d0025b6440de2faaf8b0d4467fae828499","last_reissued_at":"2026-07-04T16:24:59.097389Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:24:59.097389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0102189","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":"2026-07-04T16:24:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/llOTjv1YJJx4308QR4E3ZGUy8QHRWs7m8aDw0upiiG3LqWevUMpn3K8eQFv2x8XcXp2ywdWRd8JqOwpiJlAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T11:06:19.229893Z"},"content_sha256":"325aa061ec7ef594b110900245e8fe306007edb3fa2c013b7ece55f16378eea6","schema_version":"1.0","event_id":"sha256:325aa061ec7ef594b110900245e8fe306007edb3fa2c013b7ece55f16378eea6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:Y2TJ57CWGSNBGF4AOWRBCVND2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.supr-con","authors_text":"A. S. Alexandrov (Department of Physics, Loughborough University, United Kingdom)","submitted_at":"2001-02-10T16:50:09Z","abstract_excerpt":"In view of some recent works on the role of vertex corrections in the electron-phonon system we readress an important question of the validity of the Migdal-Eliashberg theory.\n  Based on the solution of the Holstein model and inverse coupling constant expansion, we argue that the standard Feynman-Dyson perturbation theory by Migdal and Eliashberg with or without vertex corrections cannot be applied if the electron-phonon coupling constant $\\lambda$ is larger than 1 for any ratio of the phonon and Fermi energies.\n  In the extreme adiabatic limit of the Holstein model electrons collapse into sel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0102189","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0102189/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":"2026-07-04T16:24:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDBb5ersXvv3RfGbRBrPrYKi/JEftBM43qe6GgUUM/X7MqkAacZvuFhMEz03o5fPPjqbfiCk1jc4qf9bEvulDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T11:06:19.230253Z"},"content_sha256":"63df8740b03c920c66166e4121ec6e6f7a87783b62480093ac218476998b5772","schema_version":"1.0","event_id":"sha256:63df8740b03c920c66166e4121ec6e6f7a87783b62480093ac218476998b5772"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A/bundle.json","state_url":"https://pith.science/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A/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":"2026-07-18T11:06:19Z","links":{"resolver":"https://pith.science/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A","bundle":"https://pith.science/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A/bundle.json","state":"https://pith.science/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2TJ57CWGSNBGF4AOWRBCVND2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:Y2TJ57CWGSNBGF4AOWRBCVND2A","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":"6252c01afdc705a9665dc756746acc5b6d835858b10fcdb65f5daf3c1a21f111","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.supr-con","submitted_at":"2001-02-10T16:50:09Z","title_canon_sha256":"70fc9e69cc72757b87b9bf2e77fe7604ad637a7e994b75156f1b880157963661"},"schema_version":"1.0","source":{"id":"cond-mat/0102189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0102189","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0102189v1","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0102189","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y2TJ57CWGSNB","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"pith_short_16","alias_value":"Y2TJ57CWGSNBGF4A","created_at":"2026-07-04T16:24:59Z"},{"alias_kind":"pith_short_8","alias_value":"Y2TJ57CW","created_at":"2026-07-04T16:24:59Z"}],"graph_snapshots":[{"event_id":"sha256:63df8740b03c920c66166e4121ec6e6f7a87783b62480093ac218476998b5772","target":"graph","created_at":"2026-07-04T16:24:59Z","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/cond-mat/0102189/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In view of some recent works on the role of vertex corrections in the electron-phonon system we readress an important question of the validity of the Migdal-Eliashberg theory.\n  Based on the solution of the Holstein model and inverse coupling constant expansion, we argue that the standard Feynman-Dyson perturbation theory by Migdal and Eliashberg with or without vertex corrections cannot be applied if the electron-phonon coupling constant $\\lambda$ is larger than 1 for any ratio of the phonon and Fermi energies.\n  In the extreme adiabatic limit of the Holstein model electrons collapse into sel","authors_text":"A. S. Alexandrov (Department of Physics, Loughborough University, United Kingdom)","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.supr-con","submitted_at":"2001-02-10T16:50:09Z","title":"Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0102189","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":"sha256:325aa061ec7ef594b110900245e8fe306007edb3fa2c013b7ece55f16378eea6","target":"record","created_at":"2026-07-04T16:24:59Z","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":"6252c01afdc705a9665dc756746acc5b6d835858b10fcdb65f5daf3c1a21f111","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.supr-con","submitted_at":"2001-02-10T16:50:09Z","title_canon_sha256":"70fc9e69cc72757b87b9bf2e77fe7604ad637a7e994b75156f1b880157963661"},"schema_version":"1.0","source":{"id":"cond-mat/0102189","kind":"arxiv","version":1}},"canonical_sha256":"c6a69efc56349a13178075a21155a3d0025b6440de2faaf8b0d4467fae828499","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6a69efc56349a13178075a21155a3d0025b6440de2faaf8b0d4467fae828499","first_computed_at":"2026-07-04T16:24:59.097389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:24:59.097389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4DP4i4bCWbF6aDby/UE2zKOsql/H6T4hKEwgzItnSrwOVeoU0XwEPOUjCUbNkdnzEPC32DVhor6+H7LAw8yTCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:24:59.097742Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0102189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:325aa061ec7ef594b110900245e8fe306007edb3fa2c013b7ece55f16378eea6","sha256:63df8740b03c920c66166e4121ec6e6f7a87783b62480093ac218476998b5772"],"state_sha256":"5cd1e8dc927f93b8fc71559125b342d93f70a10a414b2016ea3f5f6168aecdd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxRxNBW69eiSbBEdCDkP5IDQXZKxXDp+ftzaIL2YutFoeEd4zpUjbHPSr+Utzb7S0KZvQS8qkxHHdZlsCDItAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-18T11:06:19.232370Z","bundle_sha256":"fe276a23e34ba967d3ce25957f1873f88a1ee4ff971eb8af47ca838f9b06df5b"}}