{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OWVCZDQCSRJC7APRJM6IML5WOT","short_pith_number":"pith:OWVCZDQC","canonical_record":{"source":{"id":"1803.05166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-14T08:44:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"066aa2179faee8c23172d1989fbd403082c5b4a33d96cc8241ee8537076dea0e","abstract_canon_sha256":"8ec14913af7de6962c0ea0cb95202ec3e1966715726779cbd643d25777f29d16"},"schema_version":"1.0"},"canonical_sha256":"75aa2c8e0294522f81f14b3c862fb674ce61626a5115656d6cbb7c0e2a84e546","source":{"kind":"arxiv","id":"1803.05166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05166","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05166v2","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05166","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"OWVCZDQCSRJC","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OWVCZDQCSRJC7APR","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OWVCZDQC","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OWVCZDQCSRJC7APRJM6IML5WOT","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-14T08:44:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"066aa2179faee8c23172d1989fbd403082c5b4a33d96cc8241ee8537076dea0e","abstract_canon_sha256":"8ec14913af7de6962c0ea0cb95202ec3e1966715726779cbd643d25777f29d16"},"schema_version":"1.0"},"canonical_sha256":"75aa2c8e0294522f81f14b3c862fb674ce61626a5115656d6cbb7c0e2a84e546","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:04.433497Z","signature_b64":"4GujYoxRu30JFm91jas83YgvlI+LlkWwovaTmibDcMpvX35IZwhfJYSMDiDIsYJYpR0sxqA0p/E+Lr2PVT53Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75aa2c8e0294522f81f14b3c862fb674ce61626a5115656d6cbb7c0e2a84e546","last_reissued_at":"2026-05-18T00:13:04.432887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:04.432887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05166","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":"2026-05-18T00:13:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKkYcB+Pn1jwmoTZ/YY7V3vrBRh6a076L8gbYVYDodtq2W8MgMUkOyetPAZeQAlcYTBrHl/YBrIFH1V0Ux1FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:21:02.972866Z"},"content_sha256":"833c3f8bfe419b0e8045b1d299081fb880409475391d3f8ab2924d8cb0f0058a","schema_version":"1.0","event_id":"sha256:833c3f8bfe419b0e8045b1d299081fb880409475391d3f8ab2924d8cb0f0058a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OWVCZDQCSRJC7APRJM6IML5WOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1D Mott variable-range hopping with external field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alessandra Faggionato","submitted_at":"2018-03-14T08:44:27Z","abstract_excerpt":"Mott variable-range hopping is a fundamental mechanism for electron transport in disordered solids in the regime of strong Anderson localization. We give a brief description of this mechanism, recall some results concerning the behavior of the conductivity at low temperature and describe in more detail recent results (obtained in collaboration with N. Gantert and M. Salvi) concerning the one-dimensional Mott variable-range hopping under an external field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05166","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":"2026-05-18T00:13:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VYapqiQU70AKOw1LADdXylN60Ljec205TtHZkcww33/u1hQeGFucLkmpRQxtX4Ia5fs5GtEQ1X5Yd5JzJZiSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:21:02.973220Z"},"content_sha256":"407de8b3146a22f650c2162c881ddc7e43a58819d23294c6d7893754be37c68a","schema_version":"1.0","event_id":"sha256:407de8b3146a22f650c2162c881ddc7e43a58819d23294c6d7893754be37c68a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWVCZDQCSRJC7APRJM6IML5WOT/bundle.json","state_url":"https://pith.science/pith/OWVCZDQCSRJC7APRJM6IML5WOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWVCZDQCSRJC7APRJM6IML5WOT/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":"2026-06-04T15:21:02Z","links":{"resolver":"https://pith.science/pith/OWVCZDQCSRJC7APRJM6IML5WOT","bundle":"https://pith.science/pith/OWVCZDQCSRJC7APRJM6IML5WOT/bundle.json","state":"https://pith.science/pith/OWVCZDQCSRJC7APRJM6IML5WOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWVCZDQCSRJC7APRJM6IML5WOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OWVCZDQCSRJC7APRJM6IML5WOT","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":"8ec14913af7de6962c0ea0cb95202ec3e1966715726779cbd643d25777f29d16","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-14T08:44:27Z","title_canon_sha256":"066aa2179faee8c23172d1989fbd403082c5b4a33d96cc8241ee8537076dea0e"},"schema_version":"1.0","source":{"id":"1803.05166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05166","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05166v2","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05166","created_at":"2026-05-18T00:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"OWVCZDQCSRJC","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OWVCZDQCSRJC7APR","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OWVCZDQC","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:407de8b3146a22f650c2162c881ddc7e43a58819d23294c6d7893754be37c68a","target":"graph","created_at":"2026-05-18T00:13:04Z","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":"Mott variable-range hopping is a fundamental mechanism for electron transport in disordered solids in the regime of strong Anderson localization. We give a brief description of this mechanism, recall some results concerning the behavior of the conductivity at low temperature and describe in more detail recent results (obtained in collaboration with N. Gantert and M. Salvi) concerning the one-dimensional Mott variable-range hopping under an external field.","authors_text":"Alessandra Faggionato","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-14T08:44:27Z","title":"1D Mott variable-range hopping with external field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05166","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":"sha256:833c3f8bfe419b0e8045b1d299081fb880409475391d3f8ab2924d8cb0f0058a","target":"record","created_at":"2026-05-18T00:13:04Z","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":"8ec14913af7de6962c0ea0cb95202ec3e1966715726779cbd643d25777f29d16","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-14T08:44:27Z","title_canon_sha256":"066aa2179faee8c23172d1989fbd403082c5b4a33d96cc8241ee8537076dea0e"},"schema_version":"1.0","source":{"id":"1803.05166","kind":"arxiv","version":2}},"canonical_sha256":"75aa2c8e0294522f81f14b3c862fb674ce61626a5115656d6cbb7c0e2a84e546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75aa2c8e0294522f81f14b3c862fb674ce61626a5115656d6cbb7c0e2a84e546","first_computed_at":"2026-05-18T00:13:04.432887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:04.432887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4GujYoxRu30JFm91jas83YgvlI+LlkWwovaTmibDcMpvX35IZwhfJYSMDiDIsYJYpR0sxqA0p/E+Lr2PVT53Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:04.433497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:833c3f8bfe419b0e8045b1d299081fb880409475391d3f8ab2924d8cb0f0058a","sha256:407de8b3146a22f650c2162c881ddc7e43a58819d23294c6d7893754be37c68a"],"state_sha256":"3062b016871df395e484d7ec613979af29781786c6fae85f0d934e7c0980e976"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMTZdLPy0StKFhp5lMB8/x7wWretPmXQACd4snKWRVhEfRgsuqstX+/QmLOAblDeynQ7Zdk2WxWDWx2GfnCZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:21:02.975690Z","bundle_sha256":"c5a04ba8b9f731d6489024838615a47ebcf1401c00841d2eb992c52ddbd3dbc2"}}