{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:BK6DU3BXPWR73TIZB3TNIBZ4AE","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":"ac792f6db39af8133ba64fdb2812dbafe4e115cedcbaeb1565585b24a7e5f742","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.str-el","submitted_at":"1998-12-11T12:28:08Z","title_canon_sha256":"d23a30c9ab4d51aeae226f695998254d9c74db95ffc94066a7e0d5cae5478914"},"schema_version":"1.0","source":{"id":"cond-mat/9812195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9812195","created_at":"2026-07-04T14:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9812195v1","created_at":"2026-07-04T14:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9812195","created_at":"2026-07-04T14:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"BK6DU3BXPWR7","created_at":"2026-07-04T14:23:26Z"},{"alias_kind":"pith_short_16","alias_value":"BK6DU3BXPWR73TIZ","created_at":"2026-07-04T14:23:26Z"},{"alias_kind":"pith_short_8","alias_value":"BK6DU3BX","created_at":"2026-07-04T14:23:26Z"}],"graph_snapshots":[{"event_id":"sha256:3b64d5c4d39bc32c68d029ab18604fa5fa373f600ccaedeed14f4a9f7e921d5c","target":"graph","created_at":"2026-07-04T14:23:26Z","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/9812195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The crossover from quasi free electron to small polaron in the Holstein model for a single electron is studied by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice, in order to understand the role of dimensionality in such a crossover. We show that a small polaron ground-state occurs when both strong coupling ($\\lambda>1$) and multiphonon ($\\alpha^2 >1$) conditions are fulfilled leading to different relevant coupling constants ($\\lambda$) in adiabatic and ($\\alpha^2$) anti adiabatic region of the parameters space. We also show that th","authors_text":"C. Grimaldi, M. Capone, S. Ciuchi","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.str-el","submitted_at":"1998-12-11T12:28:08Z","title":"The Small Polaron Crossover: Role of Dimensionality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9812195","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":"sha256:08bd61ed322446171734976f7d35dc269ab60d7fcfeba534f35c1dd82abbfa34","target":"record","created_at":"2026-07-04T14:23:26Z","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":"ac792f6db39af8133ba64fdb2812dbafe4e115cedcbaeb1565585b24a7e5f742","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.str-el","submitted_at":"1998-12-11T12:28:08Z","title_canon_sha256":"d23a30c9ab4d51aeae226f695998254d9c74db95ffc94066a7e0d5cae5478914"},"schema_version":"1.0","source":{"id":"cond-mat/9812195","kind":"arxiv","version":1}},"canonical_sha256":"0abc3a6c377da3fdcd190ee6d4073c0136e19aaea2a92c565ce6634b45988554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0abc3a6c377da3fdcd190ee6d4073c0136e19aaea2a92c565ce6634b45988554","first_computed_at":"2026-07-04T14:23:26.656721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:23:26.656721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r7x/ubFxxBZag7c7ss1uryl1m+0BMhEbSLyj4at1geriaMdVlQm3OgVKmS2K8qX6NGJ17H+atINNTSMS9KyNBA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:23:26.657126Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9812195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08bd61ed322446171734976f7d35dc269ab60d7fcfeba534f35c1dd82abbfa34","sha256:3b64d5c4d39bc32c68d029ab18604fa5fa373f600ccaedeed14f4a9f7e921d5c"],"state_sha256":"3375d639e94f96abd4b46042a9d4700d46eba72685d1b652a4b382a146d9513a"}