{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YFCBD52M4NNREZ46W4EBMW6LAP","short_pith_number":"pith:YFCBD52M","canonical_record":{"source":{"id":"0904.2795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-17T23:24:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f86bb79aa5823bdadc23cdb32250ca29118229683b6546fc7f7a2fc87a385ba4","abstract_canon_sha256":"8714d6ca76dc627a572b99662052795d2a629d4b9fb2ea41a30820661d41f872"},"schema_version":"1.0"},"canonical_sha256":"c14411f74ce35b12679eb708165bcb03c1a18feeeb98efcab53c7d9b2a59c3ec","source":{"kind":"arxiv","id":"0904.2795","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2795","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2795v2","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2795","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"YFCBD52M4NNR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YFCBD52M4NNREZ46","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YFCBD52M","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YFCBD52M4NNREZ46W4EBMW6LAP","target":"record","payload":{"canonical_record":{"source":{"id":"0904.2795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-17T23:24:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f86bb79aa5823bdadc23cdb32250ca29118229683b6546fc7f7a2fc87a385ba4","abstract_canon_sha256":"8714d6ca76dc627a572b99662052795d2a629d4b9fb2ea41a30820661d41f872"},"schema_version":"1.0"},"canonical_sha256":"c14411f74ce35b12679eb708165bcb03c1a18feeeb98efcab53c7d9b2a59c3ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:22.421139Z","signature_b64":"UnUI9G1LlUeK6t1rK4e6UBBKCgWRytx8ZdyDsVvuxlXQtB492hKO6ZpgBkaos8DXz1OqmwDLFcFP9cE+G6Z4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c14411f74ce35b12679eb708165bcb03c1a18feeeb98efcab53c7d9b2a59c3ec","last_reissued_at":"2026-05-18T04:20:22.420580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:22.420580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.2795","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgE9wZIzRqxkQH3tq1RAKn6Dn25OyTFBiwLivX/T1AqGo5whRCyHa7BXySPaIHiXl872BLkchslOdaXApK7kCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:22:29.196728Z"},"content_sha256":"206aaec110068ebab787d030db9193364c802b99eed2ce2ae21b5eca35113a31","schema_version":"1.0","event_id":"sha256:206aaec110068ebab787d030db9193364c802b99eed2ce2ae21b5eca35113a31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YFCBD52M4NNREZ46W4EBMW6LAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric Diophantine approximation for systems of linear forms via dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dmitry Kleinbock, Gregory Margulis, Junbo Wang","submitted_at":"2009-04-17T23:24:46Z","abstract_excerpt":"The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong extremality' of arbitrary finite collection of smooth nondegenerate submanifolds of ${\\bold R}^n$. The proofs are based on generalized quantitative nondivergence estimates for translates of measures on the space of lattices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2795","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":""},"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":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n3vdHtT+1SFOMww45B0+D7sXJCUkK/nblUuFdak+dEXMIobS+g8vm+W5wTkvrtfgTQmJ0foIjspC+U7b/ghhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:22:29.197096Z"},"content_sha256":"bc7382ce25558dd19ae39c3cfc4309743ead7fc04ce077f3df61036f58633672","schema_version":"1.0","event_id":"sha256:bc7382ce25558dd19ae39c3cfc4309743ead7fc04ce077f3df61036f58633672"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFCBD52M4NNREZ46W4EBMW6LAP/bundle.json","state_url":"https://pith.science/pith/YFCBD52M4NNREZ46W4EBMW6LAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFCBD52M4NNREZ46W4EBMW6LAP/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":"2026-06-03T00:22:29Z","links":{"resolver":"https://pith.science/pith/YFCBD52M4NNREZ46W4EBMW6LAP","bundle":"https://pith.science/pith/YFCBD52M4NNREZ46W4EBMW6LAP/bundle.json","state":"https://pith.science/pith/YFCBD52M4NNREZ46W4EBMW6LAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFCBD52M4NNREZ46W4EBMW6LAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YFCBD52M4NNREZ46W4EBMW6LAP","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":"8714d6ca76dc627a572b99662052795d2a629d4b9fb2ea41a30820661d41f872","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-17T23:24:46Z","title_canon_sha256":"f86bb79aa5823bdadc23cdb32250ca29118229683b6546fc7f7a2fc87a385ba4"},"schema_version":"1.0","source":{"id":"0904.2795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2795","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2795v2","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2795","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"YFCBD52M4NNR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YFCBD52M4NNREZ46","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YFCBD52M","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:bc7382ce25558dd19ae39c3cfc4309743ead7fc04ce077f3df61036f58633672","target":"graph","created_at":"2026-05-18T04:20:22Z","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":"The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong extremality' of arbitrary finite collection of smooth nondegenerate submanifolds of ${\\bold R}^n$. The proofs are based on generalized quantitative nondivergence estimates for translates of measures on the space of lattices.","authors_text":"Dmitry Kleinbock, Gregory Margulis, Junbo Wang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-17T23:24:46Z","title":"Metric Diophantine approximation for systems of linear forms via dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2795","kind":"arxiv","version":2},"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":"sha256:206aaec110068ebab787d030db9193364c802b99eed2ce2ae21b5eca35113a31","target":"record","created_at":"2026-05-18T04:20:22Z","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":"8714d6ca76dc627a572b99662052795d2a629d4b9fb2ea41a30820661d41f872","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-17T23:24:46Z","title_canon_sha256":"f86bb79aa5823bdadc23cdb32250ca29118229683b6546fc7f7a2fc87a385ba4"},"schema_version":"1.0","source":{"id":"0904.2795","kind":"arxiv","version":2}},"canonical_sha256":"c14411f74ce35b12679eb708165bcb03c1a18feeeb98efcab53c7d9b2a59c3ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c14411f74ce35b12679eb708165bcb03c1a18feeeb98efcab53c7d9b2a59c3ec","first_computed_at":"2026-05-18T04:20:22.420580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:22.420580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UnUI9G1LlUeK6t1rK4e6UBBKCgWRytx8ZdyDsVvuxlXQtB492hKO6ZpgBkaos8DXz1OqmwDLFcFP9cE+G6Z4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:22.421139Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:206aaec110068ebab787d030db9193364c802b99eed2ce2ae21b5eca35113a31","sha256:bc7382ce25558dd19ae39c3cfc4309743ead7fc04ce077f3df61036f58633672"],"state_sha256":"405434b6fc4c51f96fa8f532bff93da6c4825030015e40c958ce80f2f4007c69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WO7RtcBy1M0c7eRqkxLBwcN0EzKKPKKp8lQ24GY8/czXLaKSYtLu49ksMmy9EtZyKrKloJfjSpJX4T/SIZ7YDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:22:29.199069Z","bundle_sha256":"40cdc3e96e21d0298814b0b2bdbcf88ca9b7926f70d6e53536aa308d8e7e1d0a"}}