{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DTDK67AXTSXMOJB72UPNH6PIJQ","short_pith_number":"pith:DTDK67AX","canonical_record":{"source":{"id":"1812.09542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-22T15:16:48Z","cross_cats_sorted":[],"title_canon_sha256":"780a7cb96fb6439320dd6e7ea0b176589c626da208273a4c0e41f24e9b675554","abstract_canon_sha256":"fc3d56326ff25f0641bc1126e3bb9935a8f8feb6c5c72d5b723544763d67800b"},"schema_version":"1.0"},"canonical_sha256":"1cc6af7c179caec7243fd51ed3f9e84c352dca874d3dab50bee7a32fdf2ffff0","source":{"kind":"arxiv","id":"1812.09542","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09542","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09542v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09542","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"DTDK67AXTSXM","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DTDK67AXTSXMOJB7","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DTDK67AX","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DTDK67AXTSXMOJB72UPNH6PIJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-22T15:16:48Z","cross_cats_sorted":[],"title_canon_sha256":"780a7cb96fb6439320dd6e7ea0b176589c626da208273a4c0e41f24e9b675554","abstract_canon_sha256":"fc3d56326ff25f0641bc1126e3bb9935a8f8feb6c5c72d5b723544763d67800b"},"schema_version":"1.0"},"canonical_sha256":"1cc6af7c179caec7243fd51ed3f9e84c352dca874d3dab50bee7a32fdf2ffff0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:27.601159Z","signature_b64":"p85FyT0XRlnUh6GetKwJDxRcXi/cGHYGK1ORPgKv02kbe6bZk/rJSDB36uWC0mzOWRpyRKz8LtNlhzJeEG96AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cc6af7c179caec7243fd51ed3f9e84c352dca874d3dab50bee7a32fdf2ffff0","last_reissued_at":"2026-05-17T23:57:27.600602Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:27.600602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09542","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eB5eiUwyXR1xWfpq64VAkkl8JjUFT06QR46pfzl+wel+pjceWakF5Fta77LPKEHDldiucKOISuQfOToCvYRWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T23:14:42.092566Z"},"content_sha256":"fa252356c5fed0d69cd32a38a2ad9843ab38bae2ba91d504b441d8ef0143da5f","schema_version":"1.0","event_id":"sha256:fa252356c5fed0d69cd32a38a2ad9843ab38bae2ba91d504b441d8ef0143da5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DTDK67AXTSXMOJB72UPNH6PIJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coincidence and noncoincidence of dimensions in compact subsets of $[0,1]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andrew Mitchell, Lars Olsen","submitted_at":"2018-12-22T15:16:48Z","abstract_excerpt":"We show that given any six numbers $r,s,t,u,v,w \\in (0,1]$ satisfying $r \\leq s \\leq \\min(t,u) \\leq \\max(t,u) \\leq v \\leq w$, it is possible to construct a compact subset of $[0,1]$ with Hausdorff dimension equal to $r$, lower modified box dimension equal to $s$, packing dimension equal to $t$, lower box dimension equal to $u$, upper box dimension equal to $v$ and Assouad dimension equal to $w$. Moreover, the set constructed is an $r$-Hausdorff set and a $t$-packing set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09542","kind":"arxiv","version":1},"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":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GbcSSy7DkDQwnHopaW3ffV5IoJ8k2D5Eb9G+EAHanSRIsqlsyFfy6lbADt1+eNTKaxLEvRXBAsV/QOrc4Dz3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T23:14:42.092915Z"},"content_sha256":"1da78b885b9721d95c416fb08cb55064331db8e572a65540ff939c8abee4c91b","schema_version":"1.0","event_id":"sha256:1da78b885b9721d95c416fb08cb55064331db8e572a65540ff939c8abee4c91b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTDK67AXTSXMOJB72UPNH6PIJQ/bundle.json","state_url":"https://pith.science/pith/DTDK67AXTSXMOJB72UPNH6PIJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTDK67AXTSXMOJB72UPNH6PIJQ/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":"2026-07-10T23:14:42Z","links":{"resolver":"https://pith.science/pith/DTDK67AXTSXMOJB72UPNH6PIJQ","bundle":"https://pith.science/pith/DTDK67AXTSXMOJB72UPNH6PIJQ/bundle.json","state":"https://pith.science/pith/DTDK67AXTSXMOJB72UPNH6PIJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTDK67AXTSXMOJB72UPNH6PIJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DTDK67AXTSXMOJB72UPNH6PIJQ","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":"fc3d56326ff25f0641bc1126e3bb9935a8f8feb6c5c72d5b723544763d67800b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-22T15:16:48Z","title_canon_sha256":"780a7cb96fb6439320dd6e7ea0b176589c626da208273a4c0e41f24e9b675554"},"schema_version":"1.0","source":{"id":"1812.09542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09542","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09542v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09542","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"DTDK67AXTSXM","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DTDK67AXTSXMOJB7","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DTDK67AX","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:1da78b885b9721d95c416fb08cb55064331db8e572a65540ff939c8abee4c91b","target":"graph","created_at":"2026-05-17T23:57:27Z","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 given any six numbers $r,s,t,u,v,w \\in (0,1]$ satisfying $r \\leq s \\leq \\min(t,u) \\leq \\max(t,u) \\leq v \\leq w$, it is possible to construct a compact subset of $[0,1]$ with Hausdorff dimension equal to $r$, lower modified box dimension equal to $s$, packing dimension equal to $t$, lower box dimension equal to $u$, upper box dimension equal to $v$ and Assouad dimension equal to $w$. Moreover, the set constructed is an $r$-Hausdorff set and a $t$-packing set.","authors_text":"Andrew Mitchell, Lars Olsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-22T15:16:48Z","title":"Coincidence and noncoincidence of dimensions in compact subsets of $[0,1]$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09542","kind":"arxiv","version":1},"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:fa252356c5fed0d69cd32a38a2ad9843ab38bae2ba91d504b441d8ef0143da5f","target":"record","created_at":"2026-05-17T23:57:27Z","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":"fc3d56326ff25f0641bc1126e3bb9935a8f8feb6c5c72d5b723544763d67800b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-22T15:16:48Z","title_canon_sha256":"780a7cb96fb6439320dd6e7ea0b176589c626da208273a4c0e41f24e9b675554"},"schema_version":"1.0","source":{"id":"1812.09542","kind":"arxiv","version":1}},"canonical_sha256":"1cc6af7c179caec7243fd51ed3f9e84c352dca874d3dab50bee7a32fdf2ffff0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cc6af7c179caec7243fd51ed3f9e84c352dca874d3dab50bee7a32fdf2ffff0","first_computed_at":"2026-05-17T23:57:27.600602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:27.600602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p85FyT0XRlnUh6GetKwJDxRcXi/cGHYGK1ORPgKv02kbe6bZk/rJSDB36uWC0mzOWRpyRKz8LtNlhzJeEG96AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:27.601159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa252356c5fed0d69cd32a38a2ad9843ab38bae2ba91d504b441d8ef0143da5f","sha256:1da78b885b9721d95c416fb08cb55064331db8e572a65540ff939c8abee4c91b"],"state_sha256":"647a3a65f163f7697072a7e0df24886b8438b0b2b2f0cd40b6fda8c1fb1933ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NQLpG6h07E5oMjtuvSDnuQE4cMVmsdiz1/rNOOQjhc8jwiXd8wAfajFhc6eB0I9rHx4NSCS8Md2DycTe3D1FCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T23:14:42.095091Z","bundle_sha256":"6486a9db9bde556d9775d381146dfcb2e714aec8e56416352bfa05a3af159b91"}}