{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4BPKXR54MAYQTPJ4MWIGDTX5XM","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":"48c42e3664ce2e1218804fce6f3010d36bed5a609920cba4de3c4c9b2a2b90cb","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T19:38:52Z","title_canon_sha256":"e3075fa0477d70c297c150f369c816a4473eeba1734037e1541bf70882f3a7cb"},"schema_version":"1.0","source":{"id":"0902.0964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0964","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0964v1","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0964","created_at":"2026-05-18T04:37:34Z"},{"alias_kind":"pith_short_12","alias_value":"4BPKXR54MAYQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BPKXR54MAYQTPJ4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BPKXR54","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:826b9b9aa483c066b490c18070a6479d8992db9b768a13b57ac7e59a72c79876","target":"graph","created_at":"2026-05-18T04:37:34Z","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":"Nazarov, Peres and Volberg proved recently that the Favard length of the $n$-th iteration of the four-corner Cantor set is bounded from above by $n^{-c}$ for an appropriate $c$. We generalize this result to all product Cantor sets whose projection in some direction has positive 1-dimensional measure.","authors_text":"Izabella Laba, Kelan Zhai","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T19:38:52Z","title":"The Favard length of product Cantor sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0964","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":"sha256:7f0bbc0d41e09090ee7d88d973ce7240128ae68e95f5c2de63840e83a6e28e96","target":"record","created_at":"2026-05-18T04:37:34Z","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":"48c42e3664ce2e1218804fce6f3010d36bed5a609920cba4de3c4c9b2a2b90cb","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T19:38:52Z","title_canon_sha256":"e3075fa0477d70c297c150f369c816a4473eeba1734037e1541bf70882f3a7cb"},"schema_version":"1.0","source":{"id":"0902.0964","kind":"arxiv","version":1}},"canonical_sha256":"e05eabc7bc603109bd3c659061cefdbb25bd9d06abf698fbdb593e3305c4bbf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e05eabc7bc603109bd3c659061cefdbb25bd9d06abf698fbdb593e3305c4bbf4","first_computed_at":"2026-05-18T04:37:34.394953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:34.394953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ChWq+CkO76O9ZPH9bTOa+2Zj9Q8vkkRKvcahAHlc4VdqZgFhFcfjcSfWfxVia0EAX0qr4p7RDONro0VLztmfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:34.395695Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f0bbc0d41e09090ee7d88d973ce7240128ae68e95f5c2de63840e83a6e28e96","sha256:826b9b9aa483c066b490c18070a6479d8992db9b768a13b57ac7e59a72c79876"],"state_sha256":"4d1e986ebc54ed5dc68fa2d9a2ba591e98bd4a45ab2340f8a338f35ec96f7038"}