{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:JZY2HVATEEOWPL4MUH4JYLZPVE","short_pith_number":"pith:JZY2HVAT","canonical_record":{"source":{"id":"0805.2934","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-19T19:31:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b2f882f614a4573c64af6640bf730ee7c9ebd430a25f05480447e523f9da6309","abstract_canon_sha256":"1beb1b34256f0e28da112787579f0e42cb93b92572fab7ca395d05a1c071867e"},"schema_version":"1.0"},"canonical_sha256":"4e71a3d413211d67af8ca1f89c2f2fa9121c8fcb0e57c04c10a519d64f251d55","source":{"kind":"arxiv","id":"0805.2934","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2934","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2934v2","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2934","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"JZY2HVATEEOW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JZY2HVATEEOWPL4M","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JZY2HVAT","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:JZY2HVATEEOWPL4MUH4JYLZPVE","target":"record","payload":{"canonical_record":{"source":{"id":"0805.2934","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-19T19:31:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b2f882f614a4573c64af6640bf730ee7c9ebd430a25f05480447e523f9da6309","abstract_canon_sha256":"1beb1b34256f0e28da112787579f0e42cb93b92572fab7ca395d05a1c071867e"},"schema_version":"1.0"},"canonical_sha256":"4e71a3d413211d67af8ca1f89c2f2fa9121c8fcb0e57c04c10a519d64f251d55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:22.493504Z","signature_b64":"9jSOEIEJ/xFKQO1EmRDIHEcSzs1OJpbR2uGAgJbRscGQGiI5Pkb37ipT0uDPm2RIP2vtSuG1l6SYOyf+JdwqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e71a3d413211d67af8ca1f89c2f2fa9121c8fcb0e57c04c10a519d64f251d55","last_reissued_at":"2026-05-18T04:20:22.493014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:22.493014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.2934","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":"E6ikF+6GxHpm6dHahIkBVSmTHQzY2Q4t2zmnhJufteeWxB8QACsgBPaVEMc8bYdOLwtiKhaX956k1VI7d82EDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:18:23.857817Z"},"content_sha256":"b5c085d94707d87a043cb2e03e087f31c3e601f36c7e830b194142cb123207a9","schema_version":"1.0","event_id":"sha256:b5c085d94707d87a043cb2e03e087f31c3e601f36c7e830b194142cb123207a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:JZY2HVATEEOWPL4MUH4JYLZPVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modified Schmidt games and Diophantine approximation with weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Barak Weiss, Dmitry Kleinbock","submitted_at":"2008-05-19T19:31:44Z","abstract_excerpt":"We show that the sets of weighted badly approximable vectors in $\\Bbb R^n$ are winning sets of certain games, which are modifications of $(\\alpha,\\beta)$-games introduced by W. Schmidt in 1966. The latter winning property is stable with respect to countable intersections, and is shown to imply full Hausdorff dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2934","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":"4VENxVDvwKtMLJG/N6P+ig5ntWeID0BhW+C4Hok2Yzz76o76McNz1kBly6T0grnxD3KwOa6qlj7fvkI7ZGOZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:18:23.858442Z"},"content_sha256":"e8c1d8de021cfd2a79d5704ddf5884f1fedeb2bbc4d2e20812c8bb0f220e1642","schema_version":"1.0","event_id":"sha256:e8c1d8de021cfd2a79d5704ddf5884f1fedeb2bbc4d2e20812c8bb0f220e1642"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZY2HVATEEOWPL4MUH4JYLZPVE/bundle.json","state_url":"https://pith.science/pith/JZY2HVATEEOWPL4MUH4JYLZPVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZY2HVATEEOWPL4MUH4JYLZPVE/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":"2026-06-07T17:18:23Z","links":{"resolver":"https://pith.science/pith/JZY2HVATEEOWPL4MUH4JYLZPVE","bundle":"https://pith.science/pith/JZY2HVATEEOWPL4MUH4JYLZPVE/bundle.json","state":"https://pith.science/pith/JZY2HVATEEOWPL4MUH4JYLZPVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZY2HVATEEOWPL4MUH4JYLZPVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JZY2HVATEEOWPL4MUH4JYLZPVE","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":"1beb1b34256f0e28da112787579f0e42cb93b92572fab7ca395d05a1c071867e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-19T19:31:44Z","title_canon_sha256":"b2f882f614a4573c64af6640bf730ee7c9ebd430a25f05480447e523f9da6309"},"schema_version":"1.0","source":{"id":"0805.2934","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2934","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2934v2","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2934","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"JZY2HVATEEOW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JZY2HVATEEOWPL4M","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JZY2HVAT","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e8c1d8de021cfd2a79d5704ddf5884f1fedeb2bbc4d2e20812c8bb0f220e1642","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":"We show that the sets of weighted badly approximable vectors in $\\Bbb R^n$ are winning sets of certain games, which are modifications of $(\\alpha,\\beta)$-games introduced by W. Schmidt in 1966. The latter winning property is stable with respect to countable intersections, and is shown to imply full Hausdorff dimension.","authors_text":"Barak Weiss, Dmitry Kleinbock","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-19T19:31:44Z","title":"Modified Schmidt games and Diophantine approximation with weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2934","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:b5c085d94707d87a043cb2e03e087f31c3e601f36c7e830b194142cb123207a9","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":"1beb1b34256f0e28da112787579f0e42cb93b92572fab7ca395d05a1c071867e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-19T19:31:44Z","title_canon_sha256":"b2f882f614a4573c64af6640bf730ee7c9ebd430a25f05480447e523f9da6309"},"schema_version":"1.0","source":{"id":"0805.2934","kind":"arxiv","version":2}},"canonical_sha256":"4e71a3d413211d67af8ca1f89c2f2fa9121c8fcb0e57c04c10a519d64f251d55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e71a3d413211d67af8ca1f89c2f2fa9121c8fcb0e57c04c10a519d64f251d55","first_computed_at":"2026-05-18T04:20:22.493014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:22.493014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9jSOEIEJ/xFKQO1EmRDIHEcSzs1OJpbR2uGAgJbRscGQGiI5Pkb37ipT0uDPm2RIP2vtSuG1l6SYOyf+JdwqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:22.493504Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.2934","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5c085d94707d87a043cb2e03e087f31c3e601f36c7e830b194142cb123207a9","sha256:e8c1d8de021cfd2a79d5704ddf5884f1fedeb2bbc4d2e20812c8bb0f220e1642"],"state_sha256":"1adfc7e59563e72b8075ef9545b5aa2035aee9bcede2fa56f078d677224a0963"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PEIa9R7KGXwtWLc2tzCBaZTLUH9D0PUOwYn7Xv7Ba/3yPUm477D2GVhhxQrA4fKDuY2XEtVG3RV16XtPSmIfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:18:23.861885Z","bundle_sha256":"50b706829aa51c7bd59105338135d9dd2bf36cf4da96c381afe273741e139afb"}}