{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CG2G2RDYUK2HUPGNGV53AEVHZC","short_pith_number":"pith:CG2G2RDY","canonical_record":{"source":{"id":"1204.0110","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-31T15:52:37Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"4baf387ea30afe49fc98989764d2666234b0287dac8e893ebbbcb3818cc701b5","abstract_canon_sha256":"1f861656aa976a527fa14006149bb85df6e019bd51bea524d9ac4e14a2ca8ecd"},"schema_version":"1.0"},"canonical_sha256":"11b46d4478a2b47a3ccd357bb012a7c8913e11d3076aa1fa1af452301115af29","source":{"kind":"arxiv","id":"1204.0110","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0110","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0110v4","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0110","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"CG2G2RDYUK2H","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CG2G2RDYUK2HUPGN","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CG2G2RDY","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CG2G2RDYUK2HUPGNGV53AEVHZC","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0110","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-31T15:52:37Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"4baf387ea30afe49fc98989764d2666234b0287dac8e893ebbbcb3818cc701b5","abstract_canon_sha256":"1f861656aa976a527fa14006149bb85df6e019bd51bea524d9ac4e14a2ca8ecd"},"schema_version":"1.0"},"canonical_sha256":"11b46d4478a2b47a3ccd357bb012a7c8913e11d3076aa1fa1af452301115af29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:01.794539Z","signature_b64":"ZnClPaX7N2WMoj/PcLsC5MSEmgnUT+tTkrjM1jMm/CsDJycar4YTW4zFUdQM8e5DgRn3CQkC9DEZzvWJTU1yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11b46d4478a2b47a3ccd357bb012a7c8913e11d3076aa1fa1af452301115af29","last_reissued_at":"2026-05-18T03:19:01.793673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:01.793673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0110","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kn2caeQsxGRGzcfqyxO/RV32XWLYUvGQluoW+vj26mG/0A4OfhKgVN5K2MwR6AdI083wBiEzTBjsKgKU0FA/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T14:24:59.325764Z"},"content_sha256":"3268d19a7a6565768a58ba0299471ead09829ff7267898a6caa5faf9ef86c9d6","schema_version":"1.0","event_id":"sha256:3268d19a7a6565768a58ba0299471ead09829ff7267898a6caa5faf9ef86c9d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CG2G2RDYUK2HUPGNGV53AEVHZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Badly approximable vectors on a vertical Cantor set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Erez Nesharim","submitted_at":"2012-03-31T15:52:37Z","abstract_excerpt":"For $i, j > 0, i + j = 1$, the set of badly approximable vectors with weight $(i, j)$ is defined by $Bad(i, j) = \\{(x, y) \\in \\R^2 : \\exists c > 0 \\forall q\\in\\N, \\;\\; \\max\\{q||qx||^{1/i}, q||qy||^{1/j} \\} > c\\}$, where $||x||$ is the distance of $x$ to the nearest integer. In 2010 Badziahin-Pollington-Velani solved Schmidt's conjecture which was stated in 1982, proving that $Bad(i, j) \\cap Bad(j, i)$ is nonempty. Using Badziahin-Pollington-Velani's technique with reference to fractal sets, we were able to improve their results: Assume that we are given a sequence $(i_t, j_t)$ with $i_t, j_t >"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0110","kind":"arxiv","version":4},"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":"2026-05-18T03:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAyDoAxMdNm7lgoMzqs0neOccOz0QsXDh+1PzaM4KH3O5UqnVFXkBGqY93O8bhTscdSUprC0ZlioIMzk1pKTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T14:24:59.326113Z"},"content_sha256":"d22ae744cc1f52b58995379449ea8a424846fee07cec51820e7d22fca0824c53","schema_version":"1.0","event_id":"sha256:d22ae744cc1f52b58995379449ea8a424846fee07cec51820e7d22fca0824c53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CG2G2RDYUK2HUPGNGV53AEVHZC/bundle.json","state_url":"https://pith.science/pith/CG2G2RDYUK2HUPGNGV53AEVHZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CG2G2RDYUK2HUPGNGV53AEVHZC/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":"2026-06-25T14:24:59Z","links":{"resolver":"https://pith.science/pith/CG2G2RDYUK2HUPGNGV53AEVHZC","bundle":"https://pith.science/pith/CG2G2RDYUK2HUPGNGV53AEVHZC/bundle.json","state":"https://pith.science/pith/CG2G2RDYUK2HUPGNGV53AEVHZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CG2G2RDYUK2HUPGNGV53AEVHZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CG2G2RDYUK2HUPGNGV53AEVHZC","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":"1f861656aa976a527fa14006149bb85df6e019bd51bea524d9ac4e14a2ca8ecd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-31T15:52:37Z","title_canon_sha256":"4baf387ea30afe49fc98989764d2666234b0287dac8e893ebbbcb3818cc701b5"},"schema_version":"1.0","source":{"id":"1204.0110","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0110","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0110v4","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0110","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"CG2G2RDYUK2H","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CG2G2RDYUK2HUPGN","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CG2G2RDY","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:d22ae744cc1f52b58995379449ea8a424846fee07cec51820e7d22fca0824c53","target":"graph","created_at":"2026-05-18T03:19:01Z","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":"For $i, j > 0, i + j = 1$, the set of badly approximable vectors with weight $(i, j)$ is defined by $Bad(i, j) = \\{(x, y) \\in \\R^2 : \\exists c > 0 \\forall q\\in\\N, \\;\\; \\max\\{q||qx||^{1/i}, q||qy||^{1/j} \\} > c\\}$, where $||x||$ is the distance of $x$ to the nearest integer. In 2010 Badziahin-Pollington-Velani solved Schmidt's conjecture which was stated in 1982, proving that $Bad(i, j) \\cap Bad(j, i)$ is nonempty. Using Badziahin-Pollington-Velani's technique with reference to fractal sets, we were able to improve their results: Assume that we are given a sequence $(i_t, j_t)$ with $i_t, j_t >","authors_text":"Erez Nesharim","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-31T15:52:37Z","title":"Badly approximable vectors on a vertical Cantor set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0110","kind":"arxiv","version":4},"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":"sha256:3268d19a7a6565768a58ba0299471ead09829ff7267898a6caa5faf9ef86c9d6","target":"record","created_at":"2026-05-18T03:19:01Z","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":"1f861656aa976a527fa14006149bb85df6e019bd51bea524d9ac4e14a2ca8ecd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-31T15:52:37Z","title_canon_sha256":"4baf387ea30afe49fc98989764d2666234b0287dac8e893ebbbcb3818cc701b5"},"schema_version":"1.0","source":{"id":"1204.0110","kind":"arxiv","version":4}},"canonical_sha256":"11b46d4478a2b47a3ccd357bb012a7c8913e11d3076aa1fa1af452301115af29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11b46d4478a2b47a3ccd357bb012a7c8913e11d3076aa1fa1af452301115af29","first_computed_at":"2026-05-18T03:19:01.793673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:01.793673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZnClPaX7N2WMoj/PcLsC5MSEmgnUT+tTkrjM1jMm/CsDJycar4YTW4zFUdQM8e5DgRn3CQkC9DEZzvWJTU1yDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:01.794539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0110","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3268d19a7a6565768a58ba0299471ead09829ff7267898a6caa5faf9ef86c9d6","sha256:d22ae744cc1f52b58995379449ea8a424846fee07cec51820e7d22fca0824c53"],"state_sha256":"4ffd16fc18d4078e0b38be91f4594705a12c609153e1898a53e14d617519205a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yazSO4KsjuY+aov0pVa9WOOsDoAnVncPupUR26IZihPs/DSvCrbK5s1ujwuKZlDUASJJ4+UTid6tgrG/JOpQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T14:24:59.328087Z","bundle_sha256":"df46ed7227b90c1eb92f922b114bccffecf1c45187e1580d974b98e33010ae79"}}