{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IQWYNBHY57TJLRDM67JZFKM457","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":"e6bed43da38146b9d32ed7ccce05a9904f28e691bb93c5ec4a5d184bc5f33ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-21T13:17:19Z","title_canon_sha256":"f1df6054e9ba2b4f5ecdbb4511910ecb32d6c1c44a2889af70420a38c659c5ce"},"schema_version":"1.0","source":{"id":"2605.22450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22450","created_at":"2026-05-22T01:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22450v1","created_at":"2026-05-22T01:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22450","created_at":"2026-05-22T01:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"IQWYNBHY57TJ","created_at":"2026-05-22T01:04:43Z"},{"alias_kind":"pith_short_16","alias_value":"IQWYNBHY57TJLRDM","created_at":"2026-05-22T01:04:43Z"},{"alias_kind":"pith_short_8","alias_value":"IQWYNBHY","created_at":"2026-05-22T01:04:43Z"}],"graph_snapshots":[{"event_id":"sha256:8de306f84ddac3c478b486b71f7152f5fda216caf3fa55680c80f65b87e4135a","target":"graph","created_at":"2026-05-22T01:04:43Z","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/2605.22450/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A variant of the Falconer distance problem asks for fixed $k\\geq 1$ and $d\\geq k+1$, how large does the Hausdorff dimension of a Borel set $E\\subset\\mathbb{R}^d$ need to be to guarantee that there exist $x_0,\\ldots,x_{k}\\in E$ such that $\\text{Vol}_{k+1}^{(x_0,\\ldots,x_{k})}(E) = \\lbrace \\text{Vol}_{k+1}(x_0,\\ldots,x_{k},x_{k+1}) : x_{k+1}\\in E \\rbrace$ has positive Lebesgue measure. Here $\\text{Vol}_{k+1}(x_0,\\ldots,x_{k},x_{k+1})$ denotes the $k+1$-volume of the $k+1$ simplex formed by $x_0,\\ldots,x_{k},x_{k+1}$. Recently, Shmerkin and Yavicoli established a sharp dimensional threshold $k$ i","authors_text":"Eyvindur Ari Palsson, Jos\\'e Gaitan Montejo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-21T13:17:19Z","title":"On volumes of simplices in intermediate dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22450","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:b51a7405bad7f3fb9b75b5e82b30ac823a2c9d9213057078ef7e052f9d7cd51d","target":"record","created_at":"2026-05-22T01:04:43Z","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":"e6bed43da38146b9d32ed7ccce05a9904f28e691bb93c5ec4a5d184bc5f33ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-21T13:17:19Z","title_canon_sha256":"f1df6054e9ba2b4f5ecdbb4511910ecb32d6c1c44a2889af70420a38c659c5ce"},"schema_version":"1.0","source":{"id":"2605.22450","kind":"arxiv","version":1}},"canonical_sha256":"442d8684f8efe695c46cf7d392a99ceff2741db8493fc0d23dcdf58ca67c1f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"442d8684f8efe695c46cf7d392a99ceff2741db8493fc0d23dcdf58ca67c1f4d","first_computed_at":"2026-05-22T01:04:43.528422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:43.528422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OvhN342I5CShFyRC8Waj7t9EjexC93iK8hdUGQK6qE6llBshjqcyfpwInemqOpLXMSzmGk0818j7R900KhBKBQ==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:43.529038Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b51a7405bad7f3fb9b75b5e82b30ac823a2c9d9213057078ef7e052f9d7cd51d","sha256:8de306f84ddac3c478b486b71f7152f5fda216caf3fa55680c80f65b87e4135a"],"state_sha256":"9e6566889313230901ca13b2c0423a41afea263fa72d9113a79ddd67b487c783"}