{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:62I3MWWSFSVVAQYST2U6DH32NF","short_pith_number":"pith:62I3MWWS","canonical_record":{"source":{"id":"1401.6581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-25T21:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"61b9e0c6d5c924632aee4bad0ff8a3a0dee2b248712f82a38d0f93aee2c7a448","abstract_canon_sha256":"a8d4e7ec7f9c6c2cade03d85b4db977c4559207415dbca551e92878d12a1d5f5"},"schema_version":"1.0"},"canonical_sha256":"f691b65ad22cab5043129ea9e19f7a6941630f7686182504d68a66ec5572e463","source":{"kind":"arxiv","id":"1401.6581","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6581","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6581v1","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6581","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"62I3MWWSFSVV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"62I3MWWSFSVVAQYS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"62I3MWWS","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:62I3MWWSFSVVAQYST2U6DH32NF","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-25T21:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"61b9e0c6d5c924632aee4bad0ff8a3a0dee2b248712f82a38d0f93aee2c7a448","abstract_canon_sha256":"a8d4e7ec7f9c6c2cade03d85b4db977c4559207415dbca551e92878d12a1d5f5"},"schema_version":"1.0"},"canonical_sha256":"f691b65ad22cab5043129ea9e19f7a6941630f7686182504d68a66ec5572e463","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:01.284387Z","signature_b64":"01gBSMaNwZbKgVVq+jdmpCfir32tQhg6etNcpMQ/uBOc24wSo5jB0zmZLDfgWMNC7MYrBVZeAI3cbERbNpNoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f691b65ad22cab5043129ea9e19f7a6941630f7686182504d68a66ec5572e463","last_reissued_at":"2026-05-18T03:01:01.283776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:01.283776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6581","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lqIcLrns+4fqpcARCfXy2ezfT7ACYjtd5NgBvxURMn83SJoJ5yQZxvI4gN01SleO25WHZMxviCk7nyT4CWwsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:50:32.013061Z"},"content_sha256":"2fcad6505fbaaf1238b0ded920fb035fcbe644d61ecb935cf2feeb88872136ce","schema_version":"1.0","event_id":"sha256:2fcad6505fbaaf1238b0ded920fb035fcbe644d61ecb935cf2feeb88872136ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:62I3MWWSFSVVAQYST2U6DH32NF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diophantine approximation exponents on homogeneous varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Gorodnik, Amos Nevo, Anish Ghosh","submitted_at":"2014-01-25T21:07:12Z","abstract_excerpt":"Recent years have seen very important developments at the interface of Diophantine approximation and homogeneous dynamics. In the first part of the paper we give a brief exposition of a dictionary developed by Dani and Kleinbock-Margulis which relates Diophantine properties of vectors to distribution of orbits of flows on the space of unimodular lattices. In the second part of the paper we briefly describe an extension of this dictionary recently developed by the authors, which establishes an analogous dynamical correspondence for general lattice orbits on homogeneous spaces. We concentrate sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6581","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dC1zE/gJawpb9pGxFHrc453y5+P8OCZrtRZ7pUjNPDePfwtok/JSNRBZw8lQnVF41YuRjAhcMCpWVJuVRxoDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:50:32.013424Z"},"content_sha256":"bdd67a81f06d7d5331059dbacee3cf98eedccd66a76e37eae2e3c467edbcb1b0","schema_version":"1.0","event_id":"sha256:bdd67a81f06d7d5331059dbacee3cf98eedccd66a76e37eae2e3c467edbcb1b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62I3MWWSFSVVAQYST2U6DH32NF/bundle.json","state_url":"https://pith.science/pith/62I3MWWSFSVVAQYST2U6DH32NF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62I3MWWSFSVVAQYST2U6DH32NF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T13:50:32Z","links":{"resolver":"https://pith.science/pith/62I3MWWSFSVVAQYST2U6DH32NF","bundle":"https://pith.science/pith/62I3MWWSFSVVAQYST2U6DH32NF/bundle.json","state":"https://pith.science/pith/62I3MWWSFSVVAQYST2U6DH32NF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62I3MWWSFSVVAQYST2U6DH32NF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:62I3MWWSFSVVAQYST2U6DH32NF","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":"a8d4e7ec7f9c6c2cade03d85b4db977c4559207415dbca551e92878d12a1d5f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-25T21:07:12Z","title_canon_sha256":"61b9e0c6d5c924632aee4bad0ff8a3a0dee2b248712f82a38d0f93aee2c7a448"},"schema_version":"1.0","source":{"id":"1401.6581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6581","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6581v1","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6581","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"62I3MWWSFSVV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"62I3MWWSFSVVAQYS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"62I3MWWS","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:bdd67a81f06d7d5331059dbacee3cf98eedccd66a76e37eae2e3c467edbcb1b0","target":"graph","created_at":"2026-05-18T03:01:01Z","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":"Recent years have seen very important developments at the interface of Diophantine approximation and homogeneous dynamics. In the first part of the paper we give a brief exposition of a dictionary developed by Dani and Kleinbock-Margulis which relates Diophantine properties of vectors to distribution of orbits of flows on the space of unimodular lattices. In the second part of the paper we briefly describe an extension of this dictionary recently developed by the authors, which establishes an analogous dynamical correspondence for general lattice orbits on homogeneous spaces. We concentrate sp","authors_text":"Alexander Gorodnik, Amos Nevo, Anish Ghosh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-25T21:07:12Z","title":"Diophantine approximation exponents on homogeneous varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6581","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":"sha256:2fcad6505fbaaf1238b0ded920fb035fcbe644d61ecb935cf2feeb88872136ce","target":"record","created_at":"2026-05-18T03:01:01Z","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":"a8d4e7ec7f9c6c2cade03d85b4db977c4559207415dbca551e92878d12a1d5f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-25T21:07:12Z","title_canon_sha256":"61b9e0c6d5c924632aee4bad0ff8a3a0dee2b248712f82a38d0f93aee2c7a448"},"schema_version":"1.0","source":{"id":"1401.6581","kind":"arxiv","version":1}},"canonical_sha256":"f691b65ad22cab5043129ea9e19f7a6941630f7686182504d68a66ec5572e463","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f691b65ad22cab5043129ea9e19f7a6941630f7686182504d68a66ec5572e463","first_computed_at":"2026-05-18T03:01:01.283776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:01.283776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"01gBSMaNwZbKgVVq+jdmpCfir32tQhg6etNcpMQ/uBOc24wSo5jB0zmZLDfgWMNC7MYrBVZeAI3cbERbNpNoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:01.284387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fcad6505fbaaf1238b0ded920fb035fcbe644d61ecb935cf2feeb88872136ce","sha256:bdd67a81f06d7d5331059dbacee3cf98eedccd66a76e37eae2e3c467edbcb1b0"],"state_sha256":"a7f72d9ce637bf4ada3e677b63549a588f56ac6b4e518291c8364ff647854a2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7dnZri3v6NdqY/xrFG6KU50wNJUxL9oqdQvcOqSoZsdPSlrLl3qdujFcZW4mZZ+3EErb97dalV1oxbG6irX8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:50:32.015398Z","bundle_sha256":"7a6a2927662d51e6c75c1c73e250c41f901c0cacc5b6462c83b01322b9af3888"}}