{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:OFAW6OI3G5P5L767C67MFFRX54","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":"2496e8b7872908d394c7953d7a0ceeef4fc5f9ca8bb4de23deedee0af6d95acb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-09-03T15:44:18Z","title_canon_sha256":"bb071b8e92323ee45e5f762e2997000d0dd40886c74c0b9fb257a2f629b29fd5"},"schema_version":"1.0","source":{"id":"2309.01204","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.01204","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"2309.01204v3","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.01204","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"OFAW6OI3G5P5","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_16","alias_value":"OFAW6OI3G5P5L767","created_at":"2026-07-05T09:24:31Z"},{"alias_kind":"pith_short_8","alias_value":"OFAW6OI3","created_at":"2026-07-05T09:24:31Z"}],"graph_snapshots":[{"event_id":"sha256:f0edc140fc7c398ffe2d6702e7b48650e2bad8b82e9c7c7db104343e640b66dd","target":"graph","created_at":"2026-07-05T09:24:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.01204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\\dim_{\\mathcal{H}}(E)>\\frac d2+\\frac14+\\frac{1-(-1)^d}{8d}.$$","authors_text":"Bochen Liu, Changbiao Jian, Yakun Xi","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-09-03T15:44:18Z","title":"Falconer distance problem on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.01204","kind":"arxiv","version":3},"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:b2c8b0b29913a3d0da2b75a5328a5426e7e713a1b148e975832366ae8aa9839d","target":"record","created_at":"2026-07-05T09:24:31Z","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":"2496e8b7872908d394c7953d7a0ceeef4fc5f9ca8bb4de23deedee0af6d95acb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-09-03T15:44:18Z","title_canon_sha256":"bb071b8e92323ee45e5f762e2997000d0dd40886c74c0b9fb257a2f629b29fd5"},"schema_version":"1.0","source":{"id":"2309.01204","kind":"arxiv","version":3}},"canonical_sha256":"71416f391b375fd5ffdf17bec29637ef1e68079f8fe9f57f9d1ebdfe776ba3c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71416f391b375fd5ffdf17bec29637ef1e68079f8fe9f57f9d1ebdfe776ba3c0","first_computed_at":"2026-07-05T09:24:31.183788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:24:31.183788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nhz05FW2FCd31sz7MGE+7Be/tn8MGjKProEgag9Z1ZXP+XtREoYX5hluCrDvWSkyp2REqxcz1MaC8VEbP+xcCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:24:31.184286Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.01204","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2c8b0b29913a3d0da2b75a5328a5426e7e713a1b148e975832366ae8aa9839d","sha256:f0edc140fc7c398ffe2d6702e7b48650e2bad8b82e9c7c7db104343e640b66dd"],"state_sha256":"ec316a2087e483c0844391f75bcc6a06a1d9c10dece81b1bf1b467a27e7f034a"}