{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:APWTLUXD3NEX3OYEFSZEV6DJWE","short_pith_number":"pith:APWTLUXD","schema_version":"1.0","canonical_sha256":"03ed35d2e3db497dbb042cb24af869b131e01716cca17a296f961d97a7c99ba6","source":{"kind":"arxiv","id":"2410.05812","version":2},"attestation_state":"computed","paper":{"title":"Conditioned random walks on linear groups I: construction of the target harmonic measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Hui Xiao, Ion Grama, Jean-Fran\\c{c}ois Quint","submitted_at":"2024-10-08T08:42:51Z","abstract_excerpt":"Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper represents the first step toward achieving this goal, specifically entailing the construction of a novel entity -- the target harmonic measure. This measure, together with the harmonic function, serves as a pivotal component in establishing the conditioned local limit theorem. Using a reversal identity, we introduce a reversed sequence characterized as a dual random walk with a perturbation depending on futu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.05812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-08T08:42:51Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b1f3bc158154e1e8e672e058c366104cecdeff27073acbdbba51df63647c7521","abstract_canon_sha256":"1057ee1e5bf43310283bf2aaaa86b736268e8bd8790177720029667e5e2c2481"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:45.113690Z","signature_b64":"YxQhRe0BIT6jjvJGon2r5ZDJpDMttk6N49jYMF6u1iTYw0KR5d798slkuMXTmmtqblKBFMfeh6IpRu38NQ/UBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03ed35d2e3db497dbb042cb24af869b131e01716cca17a296f961d97a7c99ba6","last_reissued_at":"2026-06-02T02:04:45.113212Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:45.113212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditioned random walks on linear groups I: construction of the target harmonic measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Hui Xiao, Ion Grama, Jean-Fran\\c{c}ois Quint","submitted_at":"2024-10-08T08:42:51Z","abstract_excerpt":"Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper represents the first step toward achieving this goal, specifically entailing the construction of a novel entity -- the target harmonic measure. This measure, together with the harmonic function, serves as a pivotal component in establishing the conditioned local limit theorem. Using a reversal identity, we introduce a reversed sequence characterized as a dual random walk with a perturbation depending on futu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.05812","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.05812/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2410.05812","created_at":"2026-06-02T02:04:45.113273+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.05812v2","created_at":"2026-06-02T02:04:45.113273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.05812","created_at":"2026-06-02T02:04:45.113273+00:00"},{"alias_kind":"pith_short_12","alias_value":"APWTLUXD3NEX","created_at":"2026-06-02T02:04:45.113273+00:00"},{"alias_kind":"pith_short_16","alias_value":"APWTLUXD3NEX3OYE","created_at":"2026-06-02T02:04:45.113273+00:00"},{"alias_kind":"pith_short_8","alias_value":"APWTLUXD","created_at":"2026-06-02T02:04:45.113273+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE","json":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE.json","graph_json":"https://pith.science/api/pith-number/APWTLUXD3NEX3OYEFSZEV6DJWE/graph.json","events_json":"https://pith.science/api/pith-number/APWTLUXD3NEX3OYEFSZEV6DJWE/events.json","paper":"https://pith.science/paper/APWTLUXD"},"agent_actions":{"view_html":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE","download_json":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE.json","view_paper":"https://pith.science/paper/APWTLUXD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.05812&json=true","fetch_graph":"https://pith.science/api/pith-number/APWTLUXD3NEX3OYEFSZEV6DJWE/graph.json","fetch_events":"https://pith.science/api/pith-number/APWTLUXD3NEX3OYEFSZEV6DJWE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE/action/storage_attestation","attest_author":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE/action/author_attestation","sign_citation":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE/action/citation_signature","submit_replication":"https://pith.science/pith/APWTLUXD3NEX3OYEFSZEV6DJWE/action/replication_record"}},"created_at":"2026-06-02T02:04:45.113273+00:00","updated_at":"2026-06-02T02:04:45.113273+00:00"}