{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BDD4EXT32OGKHLCMIUNRR3CSLC","short_pith_number":"pith:BDD4EXT3","canonical_record":{"source":{"id":"1601.00153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-02T09:28:59Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"cfe731818d8c7d9f3317c883d3fb78655f355a5e6041de69f0f6f9eff1b7bdbb","abstract_canon_sha256":"0b7caf020c540f5e9f2ec7e01b3a57b346b57872aa7f2bd721ffd84ae7f72bc7"},"schema_version":"1.0"},"canonical_sha256":"08c7c25e7bd38ca3ac4c451b18ec5258a1b7b66a78dd181b53cecf9cab574adf","source":{"kind":"arxiv","id":"1601.00153","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00153","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00153v2","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00153","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"BDD4EXT32OGK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDD4EXT32OGKHLCM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDD4EXT3","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BDD4EXT32OGKHLCMIUNRR3CSLC","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-02T09:28:59Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"cfe731818d8c7d9f3317c883d3fb78655f355a5e6041de69f0f6f9eff1b7bdbb","abstract_canon_sha256":"0b7caf020c540f5e9f2ec7e01b3a57b346b57872aa7f2bd721ffd84ae7f72bc7"},"schema_version":"1.0"},"canonical_sha256":"08c7c25e7bd38ca3ac4c451b18ec5258a1b7b66a78dd181b53cecf9cab574adf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.778899Z","signature_b64":"Jwwhoi5EtGx5pEikzBf8T0Wt6zMXdX/dOHTiE8Lzx9Gk0Ds2ZapirsbKqUtuNx/8AgLGCyj/y6L342Yht4m4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08c7c25e7bd38ca3ac4c451b18ec5258a1b7b66a78dd181b53cecf9cab574adf","last_reissued_at":"2026-05-18T00:35:55.778281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.778281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00153","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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cd1Rm98/HXc1ORm/snYlBAGQx46BeBL0OcZok30CyJgNwGnUqxHIn/cMJUXOW5OKoqsbW8AXmj58VpuulxbtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:47:44.409098Z"},"content_sha256":"36b5f316db8a1dc2fb5385af80ddfbe3d2dc1e6abd5463ef69242f3e3c8ee313","schema_version":"1.0","event_id":"sha256:36b5f316db8a1dc2fb5385af80ddfbe3d2dc1e6abd5463ef69242f3e3c8ee313"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BDD4EXT32OGKHLCMIUNRR3CSLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irrationality Exponent, Hausdorff Dimension and Effectivization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.NT","authors_text":"Jan Reimann, Theodore A. Slaman, Ver\\'onica Becher","submitted_at":"2016-01-02T09:28:59Z","abstract_excerpt":"We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension. Let a be any real number greater than or equal to 2 and let b be any non-negative real less than or equal to 2/a. We show that there is a Cantor-like set with Hausdorff dimension equal to b such that, with respect to its uniform measure, almost all real numbers have irrationality exponent equal to a. We give an analogous result relating the irrationality exponent and the effective Hausdorff dimension of individual real numbers. We prove that there is a Cantor-li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00153","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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAvwvHo0kg2TtTP8GtBk0ltROqonWV4HclK8oaqc9Wfm32j/ZAOUnFVUH7wRgxjG8mAnFt0BP4h8BYFMyziwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:47:44.409588Z"},"content_sha256":"51dedf1f1ee0db1ece50a75f923129c58913723d0c5aef7071c5797da0ddb79e","schema_version":"1.0","event_id":"sha256:51dedf1f1ee0db1ece50a75f923129c58913723d0c5aef7071c5797da0ddb79e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDD4EXT32OGKHLCMIUNRR3CSLC/bundle.json","state_url":"https://pith.science/pith/BDD4EXT32OGKHLCMIUNRR3CSLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDD4EXT32OGKHLCMIUNRR3CSLC/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":"2026-05-25T08:47:44Z","links":{"resolver":"https://pith.science/pith/BDD4EXT32OGKHLCMIUNRR3CSLC","bundle":"https://pith.science/pith/BDD4EXT32OGKHLCMIUNRR3CSLC/bundle.json","state":"https://pith.science/pith/BDD4EXT32OGKHLCMIUNRR3CSLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDD4EXT32OGKHLCMIUNRR3CSLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BDD4EXT32OGKHLCMIUNRR3CSLC","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":"0b7caf020c540f5e9f2ec7e01b3a57b346b57872aa7f2bd721ffd84ae7f72bc7","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-02T09:28:59Z","title_canon_sha256":"cfe731818d8c7d9f3317c883d3fb78655f355a5e6041de69f0f6f9eff1b7bdbb"},"schema_version":"1.0","source":{"id":"1601.00153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00153","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00153v2","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00153","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"BDD4EXT32OGK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDD4EXT32OGKHLCM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDD4EXT3","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:51dedf1f1ee0db1ece50a75f923129c58913723d0c5aef7071c5797da0ddb79e","target":"graph","created_at":"2026-05-18T00:35:55Z","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 generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension. Let a be any real number greater than or equal to 2 and let b be any non-negative real less than or equal to 2/a. We show that there is a Cantor-like set with Hausdorff dimension equal to b such that, with respect to its uniform measure, almost all real numbers have irrationality exponent equal to a. We give an analogous result relating the irrationality exponent and the effective Hausdorff dimension of individual real numbers. We prove that there is a Cantor-li","authors_text":"Jan Reimann, Theodore A. Slaman, Ver\\'onica Becher","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-02T09:28:59Z","title":"Irrationality Exponent, Hausdorff Dimension and Effectivization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00153","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":"sha256:36b5f316db8a1dc2fb5385af80ddfbe3d2dc1e6abd5463ef69242f3e3c8ee313","target":"record","created_at":"2026-05-18T00:35:55Z","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":"0b7caf020c540f5e9f2ec7e01b3a57b346b57872aa7f2bd721ffd84ae7f72bc7","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-02T09:28:59Z","title_canon_sha256":"cfe731818d8c7d9f3317c883d3fb78655f355a5e6041de69f0f6f9eff1b7bdbb"},"schema_version":"1.0","source":{"id":"1601.00153","kind":"arxiv","version":2}},"canonical_sha256":"08c7c25e7bd38ca3ac4c451b18ec5258a1b7b66a78dd181b53cecf9cab574adf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08c7c25e7bd38ca3ac4c451b18ec5258a1b7b66a78dd181b53cecf9cab574adf","first_computed_at":"2026-05-18T00:35:55.778281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.778281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jwwhoi5EtGx5pEikzBf8T0Wt6zMXdX/dOHTiE8Lzx9Gk0Ds2ZapirsbKqUtuNx/8AgLGCyj/y6L342Yht4m4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.778899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36b5f316db8a1dc2fb5385af80ddfbe3d2dc1e6abd5463ef69242f3e3c8ee313","sha256:51dedf1f1ee0db1ece50a75f923129c58913723d0c5aef7071c5797da0ddb79e"],"state_sha256":"3dd27471a3564d9e67209f60f1bc2af84789ec8b1cff92c8a3059266b8bd4d97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Eejbwsm9lyqP6dKnmOdRVVSDnbjSYpknhcG8v73XbFRs8cJFEtPrY+0ic2eTysCROU+kx1GU7V/e2PLqSajBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:47:44.412502Z","bundle_sha256":"ee71f7ef50a2855d7070f273689cc7f7f19971de70558970bb6c5ff48b96ad78"}}