{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:62KU4LKRKVOJQNJLBY5V7GBIBU","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":"e0374ad7a1cbf9b0620adc2c1b8ce56ab79eff762235eb8e8ff98bab1fe175e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-27T10:53:28Z","title_canon_sha256":"7c9253ba11415d1c588303f52142972eac2d94c11b00c21ab540d4fa39e0774f"},"schema_version":"1.0","source":{"id":"1009.5217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5217","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5217v1","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5217","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"62KU4LKRKVOJ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"62KU4LKRKVOJQNJL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"62KU4LKR","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:85a7c61dbb9414f66fc562f23c015adf5708a3dbc75868bc9e76dead2bebdcb0","target":"graph","created_at":"2026-05-17T23:53:19Z","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":"In a previous paper {GN2} an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the action of G on G/Gamma, and implies uniformity in counting over families of lattice subgroups admitting a uniform spectral gap. In the present paper we extend some methods developed in {NS} and use them to establish several useful consequences of this property, including : Effective upper bounds on lifting for solutions of congruences in affine homogeneous v","authors_text":"Alexander Gorodnik, Amos Nevo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-27T10:53:28Z","title":"Lifting, restricting and sifting integral points on affine homogeneous varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5217","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":"sha256:2a345827a6caf6de743e44e4fd1da8eaf7676f5f058b30192e4e4b06441e908d","target":"record","created_at":"2026-05-17T23:53:19Z","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":"e0374ad7a1cbf9b0620adc2c1b8ce56ab79eff762235eb8e8ff98bab1fe175e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-27T10:53:28Z","title_canon_sha256":"7c9253ba11415d1c588303f52142972eac2d94c11b00c21ab540d4fa39e0774f"},"schema_version":"1.0","source":{"id":"1009.5217","kind":"arxiv","version":1}},"canonical_sha256":"f6954e2d51555c98352b0e3b5f98280d052c050f6f760d4470605bd014e0f5b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6954e2d51555c98352b0e3b5f98280d052c050f6f760d4470605bd014e0f5b2","first_computed_at":"2026-05-17T23:53:19.641303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:19.641303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVyLDoxFkSKe8Eo3WxPV346vhjGmqcb7YiFN8rdCguEv+hMHRCDRpnPfiRonT6wtjdi2b5myW8w8EPKAjx5WAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:19.641950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a345827a6caf6de743e44e4fd1da8eaf7676f5f058b30192e4e4b06441e908d","sha256:85a7c61dbb9414f66fc562f23c015adf5708a3dbc75868bc9e76dead2bebdcb0"],"state_sha256":"e58e468d6e0dca9e8e47853c22151cf6e9118ce87596abb519db08a43af4e6a8"}