{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GDESBXNKXK5VNBOFUD4SAMSPZK","short_pith_number":"pith:GDESBXNK","canonical_record":{"source":{"id":"1109.5305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-24T20:47:03Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"3a9531910494799e870294cb610711f956b4d4cc5fb6bb6b4b212ad34ce6507f","abstract_canon_sha256":"a0539b7d4f9dbe91ebd50987fabfbf096b878255c964c316807683a44ed80e7a"},"schema_version":"1.0"},"canonical_sha256":"30c920ddaababb5685c5a0f920324fcaad6b547a82c30f7995cc3ff3eef0177c","source":{"kind":"arxiv","id":"1109.5305","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5305","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5305v1","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5305","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"GDESBXNKXK5V","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GDESBXNKXK5VNBOF","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GDESBXNK","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GDESBXNKXK5VNBOFUD4SAMSPZK","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-24T20:47:03Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"3a9531910494799e870294cb610711f956b4d4cc5fb6bb6b4b212ad34ce6507f","abstract_canon_sha256":"a0539b7d4f9dbe91ebd50987fabfbf096b878255c964c316807683a44ed80e7a"},"schema_version":"1.0"},"canonical_sha256":"30c920ddaababb5685c5a0f920324fcaad6b547a82c30f7995cc3ff3eef0177c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:20.088958Z","signature_b64":"004B8jN1EMf9nwjHKUir4AaBlE48zVT/Oevdr104H3LS4YoLsWfnkk0QtqJ9UVTEl61nXiqjLLbmRZo7FaTlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30c920ddaababb5685c5a0f920324fcaad6b547a82c30f7995cc3ff3eef0177c","last_reissued_at":"2026-05-18T04:12:20.088262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:20.088262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5305","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":"2026-05-18T04:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MyRuKiMdHBWtdCsp4r7sXBf0WHgQSbxrawjYSW/mBy3K9FU8NrvIDJ4qPL17kf9lS4zTxI+CzBtXKs4REav5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:19:58.633753Z"},"content_sha256":"12c7d8d921cf3893ea76123be096ac1c9d92ecb36bf7abf1113671ccdef775cc","schema_version":"1.0","event_id":"sha256:12c7d8d921cf3893ea76123be096ac1c9d92ecb36bf7abf1113671ccdef775cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GDESBXNKXK5VNBOFUD4SAMSPZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measurable Envelopes, Hausdorff Measures and Sierpi\\'nski Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CA","authors_text":"M\\'arton Elekes","submitted_at":"2011-09-24T20:47:03Z","abstract_excerpt":"We show that the existence of measurable envelopes of all subsets of $\\RR^n$ with respect to the $d$-dimensional Hausdorff measure $(0<d<n)$ is independent of $ZFC$. We also investigate the consistency of the existence of Sierpi\\'nski sets measurable with respect to the $d$-dimensional Hausdorff measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5305","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":"2026-05-18T04:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5f7FIpebqk2r8Dd4J1DXyGCukZblsDOAULzvqZ62czJ4aVWlMkVWOx8qjl4JTgxg4tVbZiux+YJQMH+iSCqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:19:58.634095Z"},"content_sha256":"d29e4b59c7689db7bd8629c37ddebcfdc9533b463890543e75c837506d11da8c","schema_version":"1.0","event_id":"sha256:d29e4b59c7689db7bd8629c37ddebcfdc9533b463890543e75c837506d11da8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDESBXNKXK5VNBOFUD4SAMSPZK/bundle.json","state_url":"https://pith.science/pith/GDESBXNKXK5VNBOFUD4SAMSPZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDESBXNKXK5VNBOFUD4SAMSPZK/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":"2026-06-22T12:19:58Z","links":{"resolver":"https://pith.science/pith/GDESBXNKXK5VNBOFUD4SAMSPZK","bundle":"https://pith.science/pith/GDESBXNKXK5VNBOFUD4SAMSPZK/bundle.json","state":"https://pith.science/pith/GDESBXNKXK5VNBOFUD4SAMSPZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDESBXNKXK5VNBOFUD4SAMSPZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GDESBXNKXK5VNBOFUD4SAMSPZK","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":"a0539b7d4f9dbe91ebd50987fabfbf096b878255c964c316807683a44ed80e7a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-24T20:47:03Z","title_canon_sha256":"3a9531910494799e870294cb610711f956b4d4cc5fb6bb6b4b212ad34ce6507f"},"schema_version":"1.0","source":{"id":"1109.5305","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5305","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5305v1","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5305","created_at":"2026-05-18T04:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"GDESBXNKXK5V","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GDESBXNKXK5VNBOF","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GDESBXNK","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:d29e4b59c7689db7bd8629c37ddebcfdc9533b463890543e75c837506d11da8c","target":"graph","created_at":"2026-05-18T04:12:20Z","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 existence of measurable envelopes of all subsets of $\\RR^n$ with respect to the $d$-dimensional Hausdorff measure $(0<d<n)$ is independent of $ZFC$. We also investigate the consistency of the existence of Sierpi\\'nski sets measurable with respect to the $d$-dimensional Hausdorff measure.","authors_text":"M\\'arton Elekes","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-24T20:47:03Z","title":"Measurable Envelopes, Hausdorff Measures and Sierpi\\'nski Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5305","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":"sha256:12c7d8d921cf3893ea76123be096ac1c9d92ecb36bf7abf1113671ccdef775cc","target":"record","created_at":"2026-05-18T04:12:20Z","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":"a0539b7d4f9dbe91ebd50987fabfbf096b878255c964c316807683a44ed80e7a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-24T20:47:03Z","title_canon_sha256":"3a9531910494799e870294cb610711f956b4d4cc5fb6bb6b4b212ad34ce6507f"},"schema_version":"1.0","source":{"id":"1109.5305","kind":"arxiv","version":1}},"canonical_sha256":"30c920ddaababb5685c5a0f920324fcaad6b547a82c30f7995cc3ff3eef0177c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30c920ddaababb5685c5a0f920324fcaad6b547a82c30f7995cc3ff3eef0177c","first_computed_at":"2026-05-18T04:12:20.088262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:20.088262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"004B8jN1EMf9nwjHKUir4AaBlE48zVT/Oevdr104H3LS4YoLsWfnkk0QtqJ9UVTEl61nXiqjLLbmRZo7FaTlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:20.088958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5305","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12c7d8d921cf3893ea76123be096ac1c9d92ecb36bf7abf1113671ccdef775cc","sha256:d29e4b59c7689db7bd8629c37ddebcfdc9533b463890543e75c837506d11da8c"],"state_sha256":"038b8ffe0bebe630f24691f734fe131cbac5347dd42f66c132a67643bbcf41ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z6yffxQ2OlOxNP9IuTQAhycvmm/D0l68rotRgx5MgataunaEc8nJIAbe3tbtRm1WWr3W4KKB9UKjtBnNSCJaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:19:58.636009Z","bundle_sha256":"35710a0d5e9e7d683ebb5803d96d04b2af1d8f07b2dd01177732ed0f5867711e"}}