{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PG3RVJRSPDIHT6WWRW4WUQUH3F","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":"4b8c1f708594965f564193c876670383606474e9a7465cc0fad3d666ec155b11","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-23T17:59:59Z","title_canon_sha256":"00d729d21fbb67bb58813943e17f24a1447055be3cc11f667f236b89c88c6654"},"schema_version":"1.0","source":{"id":"1711.08791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08791","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08791v1","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08791","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"pith_short_12","alias_value":"PG3RVJRSPDIH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PG3RVJRSPDIHT6WW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PG3RVJRS","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0aad7d96cfcf771673e0c018e1fe56620d0bfa11a3f41b753ce1d3406ede4ead","target":"graph","created_at":"2026-05-18T00:29:44Z","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":"Every element $u$ of $[0,1]$ can be written in the form $u=x^2y$, where $x,y$ are elements of the Cantor set $C$. In particular, every real number between zero and one is the product of three elements of the Cantor set. On the other hand the set of real numbers $v$ that can be written in the form $v=xy$ with $x$ and $y$ in $C$ is a closed subset of $[0,1]$ with Lebesgue measure strictly between $\\tfrac{17}{21}$ and $\\tfrac89$. We also describe the structure of the quotient of $C$ by itself, that is, the image of $C\\times (C \\setminus \\{0\\})$ under the function $f(x,y) = x/y$.","authors_text":"Bruce Reznick, Jayadev S. Athreya, Jeremy T. Tyson","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-23T17:59:59Z","title":"Cantor set arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08791","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:c96080673acad0fc7af6b6721ce7fee44e9e1c0c133e9cd8bd98505986b3f6a7","target":"record","created_at":"2026-05-18T00:29:44Z","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":"4b8c1f708594965f564193c876670383606474e9a7465cc0fad3d666ec155b11","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-23T17:59:59Z","title_canon_sha256":"00d729d21fbb67bb58813943e17f24a1447055be3cc11f667f236b89c88c6654"},"schema_version":"1.0","source":{"id":"1711.08791","kind":"arxiv","version":1}},"canonical_sha256":"79b71aa63278d079fad68db96a4287d97522bdf402178bc9d964f1bd1331fe77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79b71aa63278d079fad68db96a4287d97522bdf402178bc9d964f1bd1331fe77","first_computed_at":"2026-05-18T00:29:44.085158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:44.085158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GqaF7OUyx1W1AsSZ/zF3LWSWL7HeKwu/3tSsNysbd3ynDxNfMwaFVRprSZONgeSzRO7Zztu2OgPPoWj7ebbbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:44.085686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c96080673acad0fc7af6b6721ce7fee44e9e1c0c133e9cd8bd98505986b3f6a7","sha256:0aad7d96cfcf771673e0c018e1fe56620d0bfa11a3f41b753ce1d3406ede4ead"],"state_sha256":"eb2abb0477121e14b7a11021c443dc6356a2c24f3d72d13c75c46b7120a3f65f"}