{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DFHPR6ISQWPJVF77PAHH62GDSB","short_pith_number":"pith:DFHPR6IS","canonical_record":{"source":{"id":"1201.5842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-27T17:28:21Z","cross_cats_sorted":[],"title_canon_sha256":"33cf286f082dd9030809b96feb7e1ad5083cdb4284921267becc05ce30cb867b","abstract_canon_sha256":"16d9f1fd4a76e0575ad91d6e424dfa051ce2313d90066163751b80dd75931ef9"},"schema_version":"1.0"},"canonical_sha256":"194ef8f912859e9a97ff780e7f68c3906fe092659f6611f116235bf12eac910b","source":{"kind":"arxiv","id":"1201.5842","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5842","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5842v2","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5842","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"DFHPR6ISQWPJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DFHPR6ISQWPJVF77","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DFHPR6IS","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DFHPR6ISQWPJVF77PAHH62GDSB","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-27T17:28:21Z","cross_cats_sorted":[],"title_canon_sha256":"33cf286f082dd9030809b96feb7e1ad5083cdb4284921267becc05ce30cb867b","abstract_canon_sha256":"16d9f1fd4a76e0575ad91d6e424dfa051ce2313d90066163751b80dd75931ef9"},"schema_version":"1.0"},"canonical_sha256":"194ef8f912859e9a97ff780e7f68c3906fe092659f6611f116235bf12eac910b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:38.573539Z","signature_b64":"QDNDJmtPjOWXzzL2Gys3Uiu2+tDlQcxYTbNXCie1QazVyes/6Gn6DeV6y8AlWs0mg03a+cDWWFxlPKaX8gj1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"194ef8f912859e9a97ff780e7f68c3906fe092659f6611f116235bf12eac910b","last_reissued_at":"2026-05-18T03:57:38.573031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:38.573031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5842","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":"2026-05-18T03:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2M05wvolfzGdzKFRL88Fn7NrrXFPUmTbT5IdpzVJlHjpNuWkV6vWEL2QWZnNAtr/9bObxKxLEqiExg78qYWuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:01:30.592872Z"},"content_sha256":"f71910a58acec1685d134775d0b4ec0e83243721edc1ba705d7cbcdee229575f","schema_version":"1.0","event_id":"sha256:f71910a58acec1685d134775d0b4ec0e83243721edc1ba705d7cbcdee229575f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DFHPR6ISQWPJVF77PAHH62GDSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Multiplicative golden mean shift has infinite Hausdorff measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Boris Solomyak, Yuval Peres","submitted_at":"2012-01-27T17:28:21Z","abstract_excerpt":"In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the \"multiplicative golden mean shift\" defined as the set of all reals in [0,1] whose binary expansion (x_k) satisfies x_k x_{2k}=0 for all k=1,2... Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5842","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":"2026-05-18T03:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vjr/WYU8MY2SYWPcN6t/cy3uAnSnA9Xi7Q7xzFDNoKSdIk5WR6JFrerkw77Zdo7/bAVKzNVWPJGwW6BYdXcjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:01:30.593520Z"},"content_sha256":"b5abfa4ea9449b37663db266f9912d4934161c95a0180bb40fad8eeda7542f98","schema_version":"1.0","event_id":"sha256:b5abfa4ea9449b37663db266f9912d4934161c95a0180bb40fad8eeda7542f98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFHPR6ISQWPJVF77PAHH62GDSB/bundle.json","state_url":"https://pith.science/pith/DFHPR6ISQWPJVF77PAHH62GDSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFHPR6ISQWPJVF77PAHH62GDSB/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":"2026-06-08T21:01:30Z","links":{"resolver":"https://pith.science/pith/DFHPR6ISQWPJVF77PAHH62GDSB","bundle":"https://pith.science/pith/DFHPR6ISQWPJVF77PAHH62GDSB/bundle.json","state":"https://pith.science/pith/DFHPR6ISQWPJVF77PAHH62GDSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFHPR6ISQWPJVF77PAHH62GDSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DFHPR6ISQWPJVF77PAHH62GDSB","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":"16d9f1fd4a76e0575ad91d6e424dfa051ce2313d90066163751b80dd75931ef9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-27T17:28:21Z","title_canon_sha256":"33cf286f082dd9030809b96feb7e1ad5083cdb4284921267becc05ce30cb867b"},"schema_version":"1.0","source":{"id":"1201.5842","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5842","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5842v2","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5842","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"DFHPR6ISQWPJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DFHPR6ISQWPJVF77","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DFHPR6IS","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:b5abfa4ea9449b37663db266f9912d4934161c95a0180bb40fad8eeda7542f98","target":"graph","created_at":"2026-05-18T03:57:38Z","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":"In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the \"multiplicative golden mean shift\" defined as the set of all reals in [0,1] whose binary expansion (x_k) satisfies x_k x_{2k}=0 for all k=1,2... Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obtained.","authors_text":"Boris Solomyak, Yuval Peres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-27T17:28:21Z","title":"The Multiplicative golden mean shift has infinite Hausdorff measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5842","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:f71910a58acec1685d134775d0b4ec0e83243721edc1ba705d7cbcdee229575f","target":"record","created_at":"2026-05-18T03:57:38Z","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":"16d9f1fd4a76e0575ad91d6e424dfa051ce2313d90066163751b80dd75931ef9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-27T17:28:21Z","title_canon_sha256":"33cf286f082dd9030809b96feb7e1ad5083cdb4284921267becc05ce30cb867b"},"schema_version":"1.0","source":{"id":"1201.5842","kind":"arxiv","version":2}},"canonical_sha256":"194ef8f912859e9a97ff780e7f68c3906fe092659f6611f116235bf12eac910b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"194ef8f912859e9a97ff780e7f68c3906fe092659f6611f116235bf12eac910b","first_computed_at":"2026-05-18T03:57:38.573031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:38.573031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QDNDJmtPjOWXzzL2Gys3Uiu2+tDlQcxYTbNXCie1QazVyes/6Gn6DeV6y8AlWs0mg03a+cDWWFxlPKaX8gj1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:38.573539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5842","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f71910a58acec1685d134775d0b4ec0e83243721edc1ba705d7cbcdee229575f","sha256:b5abfa4ea9449b37663db266f9912d4934161c95a0180bb40fad8eeda7542f98"],"state_sha256":"49a800a83b5fc327c1bb46d8e618e96242e436758e8ca177da31b8f6197c85c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qCPBModU7I4PIuZoMjpvSeupOMPKt/7vJLhRx4yBoMQwSL2AcnqG4XjGbauCzTtiF1fTy3SjFUL4MWNC7bARDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:01:30.597297Z","bundle_sha256":"3b5c2e8d13bd19f53058c79c3d55b234387d6d2a254b246b542260e80a4392dc"}}