{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GO6Y5BRE2FRMA6NAZWKCOT5VAT","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":"85c16c493784e920920208b56a88ef1884299c6aa9b003f2e339ba337f7ee411","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-05T14:34:55Z","title_canon_sha256":"da84d024551f9fabfc811efedd8849cb286772517d9905c00ce2a1028fb06386"},"schema_version":"1.0","source":{"id":"1707.01420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01420","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01420v1","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01420","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"GO6Y5BRE2FRM","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GO6Y5BRE2FRMA6NA","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GO6Y5BRE","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:0f89a5353013a52f2c41f008889f6aed29e7c36696a2d157af21e721a3bdefb3","target":"graph","created_at":"2026-05-18T00:40:52Z","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":"Recently, considerable attention has been given to the study of the arithmetic sum of two planar sets. We focus on understanding the interior $\\left(A+\\Gamma\\right)^{\\circ}$, when $\\Gamma$ is a piecewise $\\mathcal{C}^2$ curve and $A\\subset \\mathbb{R}^2.$ To begin, we give an example of a very large (full-measure, dense, $G_\\delta$) set $A$ such that $\\left(A+S^1\\right)^{\\circ}=\\emptyset$, where $S^1$ denotes the unit circle. This suggests that merely the size of $A$ does not guarantee that $(A+S^1)^{\\circ }\\ne\\emptyset$. If, however, we assume that $A$ is a kind of generalized product of two r","authors_text":"K\\'aroly Simon, Krystal Taylor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-05T14:34:55Z","title":"Interior of sums of planar sets and curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01420","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":"sha256:32ac45164c67ca9d9d017c7cecc528878677495acb4dfec0fc184c5cdf1dbd9e","target":"record","created_at":"2026-05-18T00:40:52Z","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":"85c16c493784e920920208b56a88ef1884299c6aa9b003f2e339ba337f7ee411","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-05T14:34:55Z","title_canon_sha256":"da84d024551f9fabfc811efedd8849cb286772517d9905c00ce2a1028fb06386"},"schema_version":"1.0","source":{"id":"1707.01420","kind":"arxiv","version":1}},"canonical_sha256":"33bd8e8624d162c079a0cd94274fb504fa945248b5494b61b58163356cd2a19b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33bd8e8624d162c079a0cd94274fb504fa945248b5494b61b58163356cd2a19b","first_computed_at":"2026-05-18T00:40:52.382215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:52.382215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nXDdXCKuiysDmzOxcK/rH/yBwtwSgypJNVTO95CwYhjtAxiNqhZLszn+lSYOb1T9sP2xY9ySI+e2spwsFXfHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:52.382769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32ac45164c67ca9d9d017c7cecc528878677495acb4dfec0fc184c5cdf1dbd9e","sha256:0f89a5353013a52f2c41f008889f6aed29e7c36696a2d157af21e721a3bdefb3"],"state_sha256":"491f6224ad5168da73f6fca3f85172f97240fc998316aab0b0fac8f54a0cc776"}