{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KNA5WGEVDQPXMYDDWP5FXOMXVI","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":"81144d1172b098a530dd03a11515807b3dba3ee042069f3938f41f15bcfcc36e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T17:50:28Z","title_canon_sha256":"51faabdc1d4a77f2dadbb47aa30706b7ff1771c04748ac87926f6eac30de138e"},"schema_version":"1.0","source":{"id":"2010.05900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.05900","created_at":"2026-05-26T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"2010.05900v2","created_at":"2026-05-26T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.05900","created_at":"2026-05-26T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"KNA5WGEVDQPX","created_at":"2026-05-26T01:03:06Z"},{"alias_kind":"pith_short_16","alias_value":"KNA5WGEVDQPXMYDD","created_at":"2026-05-26T01:03:06Z"},{"alias_kind":"pith_short_8","alias_value":"KNA5WGEV","created_at":"2026-05-26T01:03:06Z"}],"graph_snapshots":[{"event_id":"sha256:aae8be5c86d611bdd252d864c322105011741e4a5a454ae3f52fdf8e6beee105","target":"graph","created_at":"2026-05-26T01:03:06Z","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/2010.05900/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a polynomial upper bound for the localization length of the Lorentz mirror model and the Manhattan model on the even cylinder. The main input is a conditional cylinder-localization theorem in the winding regime: if short-direction crossings of $100n\\times n$ rectangles have probability bounded below, then many closed trajectories wind around the cylinder. These winding trajectories are topological barriers and the localization follows from a two-switch surgery and double-counting argument.","authors_text":"Linjun Li","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T17:50:28Z","title":"Polynomial bound for the localization length of Lorentz mirror model on the 1D cylinder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.05900","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":"sha256:7fa1a9a86e1ed359748585cffe7f37e252c16af998f9aea7dcce0521334458cd","target":"record","created_at":"2026-05-26T01:03:06Z","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":"81144d1172b098a530dd03a11515807b3dba3ee042069f3938f41f15bcfcc36e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T17:50:28Z","title_canon_sha256":"51faabdc1d4a77f2dadbb47aa30706b7ff1771c04748ac87926f6eac30de138e"},"schema_version":"1.0","source":{"id":"2010.05900","kind":"arxiv","version":2}},"canonical_sha256":"5341db18951c1f766063b3fa5bb997aa3cc3bac26adaaaa6737ec5b7c12def30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5341db18951c1f766063b3fa5bb997aa3cc3bac26adaaaa6737ec5b7c12def30","first_computed_at":"2026-05-26T01:03:06.873131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:06.873131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dUsOQmipMe98QAzvOjOC7ie1/0B+BWzBlDJkCJgd3MPAIwzpKaNBeVxaMo6mNIawA43NRiM7liVMuNZ/wmWwBg==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:06.873899Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.05900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fa1a9a86e1ed359748585cffe7f37e252c16af998f9aea7dcce0521334458cd","sha256:aae8be5c86d611bdd252d864c322105011741e4a5a454ae3f52fdf8e6beee105"],"state_sha256":"e406f62fdb68ecf66f77f8fca89a63ff65419523ba8177b0bd39c98a9d491c01"}