{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MUPSOWWUVT2U6CAVGBCHRXTLQX","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":"baff2b225a334c2402c4e3cc8fd096b4466bad4f869ef54b8ad5924ad26141c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-10T07:03:43Z","title_canon_sha256":"77057b23873360d492dd41861b3225eba27b0c033bac13323a2d0ed93f5139c9"},"schema_version":"1.0","source":{"id":"1210.2816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2816","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2816v1","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2816","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"MUPSOWWUVT2U","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MUPSOWWUVT2U6CAV","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MUPSOWWU","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:3d5b84f7de4a1438c38f195b7edb2ab61dbfcef72a6da44a2b69f49fe1a88a18","target":"graph","created_at":"2026-05-18T03:43:31Z","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":"We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these chains to singular stable-like processes.","authors_text":"Fangjun Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-10T07:03:43Z","title":"Markov Chain Approximations to Singular Stable-like Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2816","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":"sha256:7ab43e3ea0576b250ca8636c6564a46a5162411d88673af0df3f1cc0a31b1e1f","target":"record","created_at":"2026-05-18T03:43:31Z","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":"baff2b225a334c2402c4e3cc8fd096b4466bad4f869ef54b8ad5924ad26141c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-10T07:03:43Z","title_canon_sha256":"77057b23873360d492dd41861b3225eba27b0c033bac13323a2d0ed93f5139c9"},"schema_version":"1.0","source":{"id":"1210.2816","kind":"arxiv","version":1}},"canonical_sha256":"651f275ad4acf54f0815304478de6b85db71f1f6ee265dcbe8bba17806ec2530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"651f275ad4acf54f0815304478de6b85db71f1f6ee265dcbe8bba17806ec2530","first_computed_at":"2026-05-18T03:43:31.465178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:31.465178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bl+O3DKLs3nezvQyGKKX/hidp1EToSnJpNc2v6BcIGTzhwn2iLAP0d+HhdTScugwUcP8/z+SYEd+41qXT9b8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:31.465898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ab43e3ea0576b250ca8636c6564a46a5162411d88673af0df3f1cc0a31b1e1f","sha256:3d5b84f7de4a1438c38f195b7edb2ab61dbfcef72a6da44a2b69f49fe1a88a18"],"state_sha256":"40695cc4e6e4eb9c6e516a195275359ed599c7eb045f8b68ec53ab1c45013528"}