{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:SNYNOIT4BOGMA5XNIFDY4C4HSW","short_pith_number":"pith:SNYNOIT4","canonical_record":{"source":{"id":"2302.03936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-02-08T08:28:11Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"49b1815633aaae855539dca1b43125b91c702ef97440b70b42fed444f695ba8e","abstract_canon_sha256":"aab599f330f9fe4f0d336d9f00d84648da8c74548a000e4f903931e8cb51c816"},"schema_version":"1.0"},"canonical_sha256":"9370d7227c0b8cc076ed41478e0b8795850f84faf75eecf89706a97c87407e20","source":{"kind":"arxiv","id":"2302.03936","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.03936","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"2302.03936v3","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.03936","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"SNYNOIT4BOGM","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"pith_short_16","alias_value":"SNYNOIT4BOGMA5XN","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"pith_short_8","alias_value":"SNYNOIT4","created_at":"2026-07-05T10:33:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:SNYNOIT4BOGMA5XNIFDY4C4HSW","target":"record","payload":{"canonical_record":{"source":{"id":"2302.03936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-02-08T08:28:11Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"49b1815633aaae855539dca1b43125b91c702ef97440b70b42fed444f695ba8e","abstract_canon_sha256":"aab599f330f9fe4f0d336d9f00d84648da8c74548a000e4f903931e8cb51c816"},"schema_version":"1.0"},"canonical_sha256":"9370d7227c0b8cc076ed41478e0b8795850f84faf75eecf89706a97c87407e20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:33:29.764675Z","signature_b64":"2LgnoiQHN6cOaNTKjUoKFWXREPVeos757QssZn4bypwIzHIk99WyEekQoT8M85ZZ/JZ+vGhrK/Cs7DgqeSLuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9370d7227c0b8cc076ed41478e0b8795850f84faf75eecf89706a97c87407e20","last_reissued_at":"2026-07-05T10:33:29.764226Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:33:29.764226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.03936","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:33:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mBlxgfPhwTe8hc2hDkqzJ9cezDUqDXa744wEAA/Sru1j8fpeyS/INOk5L9UZO3MwbU/a7Augc9W5VnoE13ngBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:31:13.323538Z"},"content_sha256":"021ee40a9459800e972b39782433dde2920ef7e15d56799b28424c39a05c475b","schema_version":"1.0","event_id":"sha256:021ee40a9459800e972b39782433dde2920ef7e15d56799b28424c39a05c475b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:SNYNOIT4BOGMA5XNIFDY4C4HSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-full law for well approximable sets in missing digit sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Bing Li, Ruofan Li, Yufeng Wu","submitted_at":"2023-02-08T08:28:11Z","abstract_excerpt":"Let $b \\geq 3$ be an integer and $C(b,D)$ be the set of real numbers in $[0,1]$ whose base $b$ expansion only consists of digits in a set $D \\subseteq \\{0,...,b-1\\}$. We study how close can numbers in $C(b,D)$ be approximated by rational numbers with denominators being powers of some integer $t$ and obtain a zero-full law for its Hausdorff measure in several circumstances. When $b$ and $t$ are multiplicatively dependent, our results correct an error of Levesley, Salp and Velani (Math. Ann., 338:97-118, 2007) and generalize their theorem. When $b$ and $t$ are multiplicatively independent but ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03936","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.03936/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:33:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCyhLlqVmAnmI1aNSwIIT6BNcG6r+17jx7aWsPSVKZuZg/1Tlc5Ql86QSmmrJ0nkIqMMdEh0apE8+Z9PGb2eCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:31:13.323920Z"},"content_sha256":"443528e7ad85c28c9e6b7660a2c0324fc8618fe07cb4771ef62679da15ddfa96","schema_version":"1.0","event_id":"sha256:443528e7ad85c28c9e6b7660a2c0324fc8618fe07cb4771ef62679da15ddfa96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW/bundle.json","state_url":"https://pith.science/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW/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":"2026-07-06T08:31:13Z","links":{"resolver":"https://pith.science/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW","bundle":"https://pith.science/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW/bundle.json","state":"https://pith.science/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SNYNOIT4BOGMA5XNIFDY4C4HSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SNYNOIT4BOGMA5XNIFDY4C4HSW","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":"aab599f330f9fe4f0d336d9f00d84648da8c74548a000e4f903931e8cb51c816","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-02-08T08:28:11Z","title_canon_sha256":"49b1815633aaae855539dca1b43125b91c702ef97440b70b42fed444f695ba8e"},"schema_version":"1.0","source":{"id":"2302.03936","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.03936","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"2302.03936v3","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.03936","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"SNYNOIT4BOGM","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"pith_short_16","alias_value":"SNYNOIT4BOGMA5XN","created_at":"2026-07-05T10:33:29Z"},{"alias_kind":"pith_short_8","alias_value":"SNYNOIT4","created_at":"2026-07-05T10:33:29Z"}],"graph_snapshots":[{"event_id":"sha256:443528e7ad85c28c9e6b7660a2c0324fc8618fe07cb4771ef62679da15ddfa96","target":"graph","created_at":"2026-07-05T10:33:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.03936/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $b \\geq 3$ be an integer and $C(b,D)$ be the set of real numbers in $[0,1]$ whose base $b$ expansion only consists of digits in a set $D \\subseteq \\{0,...,b-1\\}$. We study how close can numbers in $C(b,D)$ be approximated by rational numbers with denominators being powers of some integer $t$ and obtain a zero-full law for its Hausdorff measure in several circumstances. When $b$ and $t$ are multiplicatively dependent, our results correct an error of Levesley, Salp and Velani (Math. Ann., 338:97-118, 2007) and generalize their theorem. When $b$ and $t$ are multiplicatively independent but ha","authors_text":"Bing Li, Ruofan Li, Yufeng Wu","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-02-08T08:28:11Z","title":"Zero-full law for well approximable sets in missing digit sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03936","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":"sha256:021ee40a9459800e972b39782433dde2920ef7e15d56799b28424c39a05c475b","target":"record","created_at":"2026-07-05T10:33:29Z","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":"aab599f330f9fe4f0d336d9f00d84648da8c74548a000e4f903931e8cb51c816","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-02-08T08:28:11Z","title_canon_sha256":"49b1815633aaae855539dca1b43125b91c702ef97440b70b42fed444f695ba8e"},"schema_version":"1.0","source":{"id":"2302.03936","kind":"arxiv","version":3}},"canonical_sha256":"9370d7227c0b8cc076ed41478e0b8795850f84faf75eecf89706a97c87407e20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9370d7227c0b8cc076ed41478e0b8795850f84faf75eecf89706a97c87407e20","first_computed_at":"2026-07-05T10:33:29.764226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:33:29.764226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2LgnoiQHN6cOaNTKjUoKFWXREPVeos757QssZn4bypwIzHIk99WyEekQoT8M85ZZ/JZ+vGhrK/Cs7DgqeSLuAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:33:29.764675Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.03936","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:021ee40a9459800e972b39782433dde2920ef7e15d56799b28424c39a05c475b","sha256:443528e7ad85c28c9e6b7660a2c0324fc8618fe07cb4771ef62679da15ddfa96"],"state_sha256":"1e34ab12f2c03837c201118616ce3964b864b15618b85d725dbccbb02ff39532"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFgom/z57MD87fkebH89y/BJ7IO65esZrvsxY5emX04/Yy1muxHPHcLdx+CUC6aBNGC5fwybNaqorw9Ei88iBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T08:31:13.325898Z","bundle_sha256":"a865c3081f3b9328653b07c154cfe8a46a6ad47fc76c0725d9cab12f93d8a2f2"}}