{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VA6EGOUBRKS7RTMVTWBDQZVEIP","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":"553dcd34300a1ef422dda853830a4e7b00b6c17af8ab31c9b035475bd5d41c25","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-15T17:22:24Z","title_canon_sha256":"5f59142d0ecf8ca90eab284efe9957d499a02a801bcddd105b472ccf13fe8696"},"schema_version":"1.0","source":{"id":"1811.06484","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06484","created_at":"2026-07-05T00:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06484v2","created_at":"2026-07-05T00:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06484","created_at":"2026-07-05T00:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"VA6EGOUBRKS7","created_at":"2026-07-05T00:58:01Z"},{"alias_kind":"pith_short_16","alias_value":"VA6EGOUBRKS7RTMV","created_at":"2026-07-05T00:58:01Z"},{"alias_kind":"pith_short_8","alias_value":"VA6EGOUB","created_at":"2026-07-05T00:58:01Z"}],"graph_snapshots":[{"event_id":"sha256:36b94ffbd63d6d4d81655aa4a6e6cf4115cc8907c3d06aea2e9bccfe970b4ac0","target":"graph","created_at":"2026-07-05T00:58:01Z","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/1811.06484/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool is the Fourier decay of the Furstenberg measures on the projective spaces, which is a higher dimensional generalization of a recent work of Bourgain-Dyatlov.","authors_text":"Jialun Li","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-15T17:22:24Z","title":"Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06484","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":"sha256:4bdbcf5d8b394675493978dc88a8e74484b3aa166b324bfdcfd1c3d3087e55dd","target":"record","created_at":"2026-07-05T00:58:01Z","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":"553dcd34300a1ef422dda853830a4e7b00b6c17af8ab31c9b035475bd5d41c25","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-15T17:22:24Z","title_canon_sha256":"5f59142d0ecf8ca90eab284efe9957d499a02a801bcddd105b472ccf13fe8696"},"schema_version":"1.0","source":{"id":"1811.06484","kind":"arxiv","version":2}},"canonical_sha256":"a83c433a818aa5f8cd959d823866a443d34905149cc506a834599185ce24809a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a83c433a818aa5f8cd959d823866a443d34905149cc506a834599185ce24809a","first_computed_at":"2026-07-05T00:58:01.481755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:58:01.481755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FUB1nNWaQN16EXzg9NE37M/mtXjnn+tN2H17fwt3clHW569s5WiI0xh15Bh9aMg4gDy5+UNq9R75LrrtdfYuBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:58:01.482223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06484","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bdbcf5d8b394675493978dc88a8e74484b3aa166b324bfdcfd1c3d3087e55dd","sha256:36b94ffbd63d6d4d81655aa4a6e6cf4115cc8907c3d06aea2e9bccfe970b4ac0"],"state_sha256":"2589b64f9b3c2b05abe64325655146e674db98ec4c4f160b2d022b57408636eb"}