{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UJQRT3KU5FHWFH7EKIPKUIPQRW","short_pith_number":"pith:UJQRT3KU","schema_version":"1.0","canonical_sha256":"a26119ed54e94f629fe4521eaa21f08d9cc1227e372b4b48533165cc4c8cf917","source":{"kind":"arxiv","id":"1703.03086","version":3},"attestation_state":"computed","paper":{"title":"Invariant measures for the actions of the modular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Shilei Fan, Yanqi Qiu","submitted_at":"2017-03-09T00:38:59Z","abstract_excerpt":"In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability measure for each p."},"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":"1703.03086","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-09T00:38:59Z","cross_cats_sorted":[],"title_canon_sha256":"d6f40cf837915baec0554526622d5724cb4b7c080c0dfa51a12fca28fc48a3b5","abstract_canon_sha256":"b3f6763395c792ec40f8b5530557cb6716a57ee27cbcbc89e2b0bc7c63f49e46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:51.223628Z","signature_b64":"SDk1IIvfJBovs7d30Ksj0m5F69z019r5FvansR3fUPQCeaQmHXUkTRZzdFr25IKpLv94wwmPaiJHf5ZwGP43Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a26119ed54e94f629fe4521eaa21f08d9cc1227e372b4b48533165cc4c8cf917","last_reissued_at":"2026-05-18T00:42:51.222922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:51.222922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant measures for the actions of the modular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Shilei Fan, Yanqi Qiu","submitted_at":"2017-03-09T00:38:59Z","abstract_excerpt":"In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability measure for each p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03086","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.03086","created_at":"2026-05-18T00:42:51.223026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03086v3","created_at":"2026-05-18T00:42:51.223026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03086","created_at":"2026-05-18T00:42:51.223026+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJQRT3KU5FHW","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJQRT3KU5FHWFH7E","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJQRT3KU","created_at":"2026-05-18T12:31:46.661854+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/UJQRT3KU5FHWFH7EKIPKUIPQRW","json":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW.json","graph_json":"https://pith.science/api/pith-number/UJQRT3KU5FHWFH7EKIPKUIPQRW/graph.json","events_json":"https://pith.science/api/pith-number/UJQRT3KU5FHWFH7EKIPKUIPQRW/events.json","paper":"https://pith.science/paper/UJQRT3KU"},"agent_actions":{"view_html":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW","download_json":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW.json","view_paper":"https://pith.science/paper/UJQRT3KU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03086&json=true","fetch_graph":"https://pith.science/api/pith-number/UJQRT3KU5FHWFH7EKIPKUIPQRW/graph.json","fetch_events":"https://pith.science/api/pith-number/UJQRT3KU5FHWFH7EKIPKUIPQRW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW/action/storage_attestation","attest_author":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW/action/author_attestation","sign_citation":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW/action/citation_signature","submit_replication":"https://pith.science/pith/UJQRT3KU5FHWFH7EKIPKUIPQRW/action/replication_record"}},"created_at":"2026-05-18T00:42:51.223026+00:00","updated_at":"2026-05-18T00:42:51.223026+00:00"}