{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KENSGYNSSW7GR4TKE53RXYHW52","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":"ce88eb16bf0219cbf8ff933b33ef2d783202ca53c4f35f0af3cb6fe520eb6fcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-30T12:06:06Z","title_canon_sha256":"25541166e663543191a9a087dc8f8c27fc7fd5f5a34b481f53fc734a55c519c4"},"schema_version":"1.0","source":{"id":"1506.09049","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.09049","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"1506.09049v3","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.09049","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"KENSGYNSSW7G","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KENSGYNSSW7GR4TK","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KENSGYNS","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:a53c24e5c05b137831e63c17098c85c36dfc73bf506cc02a8a994c1e7baf7d0c","target":"graph","created_at":"2026-05-18T01:24:14Z","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 this paper we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold $M \\subset \\mathbb{R}^n$ is of dimension strictly greater than $(n+1)/2$ and satisfies a natural non-degeneracy condition, then $M$ is of Khintchine type for convergence. The key lies in obtaining essentially the best possible upper bound regarding the distribution of rational points near manifolds.","authors_text":"Evgeniy Zorin, Robert C. Vaughan, Sanju Velani, Victor Beresnevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-30T12:06:06Z","title":"Diophantine approximation on manifolds and the distribution of rational points: contributions to the convergence theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09049","kind":"arxiv","version":3},"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":"sha256:235f0ad5ba8aabf93657b017c2853584638d16f1d7bd0b5c8d27c52210c5762f","target":"record","created_at":"2026-05-18T01:24:14Z","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":"ce88eb16bf0219cbf8ff933b33ef2d783202ca53c4f35f0af3cb6fe520eb6fcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-30T12:06:06Z","title_canon_sha256":"25541166e663543191a9a087dc8f8c27fc7fd5f5a34b481f53fc734a55c519c4"},"schema_version":"1.0","source":{"id":"1506.09049","kind":"arxiv","version":3}},"canonical_sha256":"511b2361b295be68f26a27771be0f6eeb7ea5187b7641dfbfc960d4a99083b3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"511b2361b295be68f26a27771be0f6eeb7ea5187b7641dfbfc960d4a99083b3e","first_computed_at":"2026-05-18T01:24:14.352551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:14.352551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MOYjOQk1eUiuyoIinhhiqbV5mbIZu0ZtxjUwByzC0EpMWjEVRa6aKJvP8wXKHOmWFXMHPpk/+yEUGRdvf7qTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:14.353033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.09049","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:235f0ad5ba8aabf93657b017c2853584638d16f1d7bd0b5c8d27c52210c5762f","sha256:a53c24e5c05b137831e63c17098c85c36dfc73bf506cc02a8a994c1e7baf7d0c"],"state_sha256":"ae773e5eea01bc109424214c04a8a209f3027656d65d67385c0d8fb263543943"}