{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SRHEOLEWRWQG3B2HT7FEOXKHRI","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":"9efda9d6359c6ca8783297e03307124bdcbeda3235bfd2cafe9db7cb02c1939a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-22T17:54:42Z","title_canon_sha256":"9a64d233043a5b7e5a1cdced2eb807736d20107abc6d277425fbc3cb6839e232"},"schema_version":"1.0","source":{"id":"2607.20416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20416","created_at":"2026-07-23T01:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20416v1","created_at":"2026-07-23T01:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20416","created_at":"2026-07-23T01:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"SRHEOLEWRWQG","created_at":"2026-07-23T01:25:19Z"},{"alias_kind":"pith_short_16","alias_value":"SRHEOLEWRWQG3B2H","created_at":"2026-07-23T01:25:19Z"},{"alias_kind":"pith_short_8","alias_value":"SRHEOLEW","created_at":"2026-07-23T01:25:19Z"}],"graph_snapshots":[{"event_id":"sha256:c4fec8d40558f1d36eb437fcb4cee9a3d65575bc4ff96180a7ef67b299e9b44b","target":"graph","created_at":"2026-07-23T01:25:19Z","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/2607.20416/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study pinned nonempty-interior problems for scalar two-point configurations and for volumes of simplices. For $E\\subset\\mathbb{R}^d$, $d\\geq 2$, compact and a smooth scalar configuration map $\\Phi(x,y)$, whose corresponding localized generalized Radon transforms are nondegenerate Fourier integral operators of smoothing order $(d-1)/2$, we first note how a calculation due to Greenleaf, Iosevich and Taylor can be used to obtain positive Lebesgue measure of $\\Delta_\\Phi^y(E)=\\{\\Phi(x,y):x\\in E\\}$ for almost every pin $y$ when $\\dim_{\\mathcal H}(E)>(d+1)/2$. Our first main result is to prove th","authors_text":"Eyvindur Ari Palsson, Georgios Psaromiligkos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-22T17:54:42Z","title":"Pinned nonempty interior and volumes of simplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20416","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":"sha256:08e3efecc3843b8445574e6ba26dd09bb358472113b871c60f0e15f3281d37f1","target":"record","created_at":"2026-07-23T01:25:19Z","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":"9efda9d6359c6ca8783297e03307124bdcbeda3235bfd2cafe9db7cb02c1939a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-22T17:54:42Z","title_canon_sha256":"9a64d233043a5b7e5a1cdced2eb807736d20107abc6d277425fbc3cb6839e232"},"schema_version":"1.0","source":{"id":"2607.20416","kind":"arxiv","version":1}},"canonical_sha256":"944e472c968da06d87479fca475d478a065f918dd0a34b75c80cec474df3a5a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"944e472c968da06d87479fca475d478a065f918dd0a34b75c80cec474df3a5a5","first_computed_at":"2026-07-23T01:25:19.829167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:25:19.829167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TJg1ltz2xjg7m6k4Gr0wb55C+f1U5duQTySZ7ld/a+Upe1FYFKgrCuKNsyWF8m3C79BAFc6BP7GRuJ+Cvc2KCQ==","signature_status":"signed_v1","signed_at":"2026-07-23T01:25:19.830075Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08e3efecc3843b8445574e6ba26dd09bb358472113b871c60f0e15f3281d37f1","sha256:c4fec8d40558f1d36eb437fcb4cee9a3d65575bc4ff96180a7ef67b299e9b44b"],"state_sha256":"2f953d352311ab043808fb803e2a03d078eba381260e12d29a0b96b94a300bfb"}