{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H4XWIOJZ263OCENKB6WUDKIKKL","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":"ad3ad1a370247ff33c0a4dcad0171ec0b494fa157218c4f0ebdfff2f1ce668f5","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-05-29T19:31:02Z","title_canon_sha256":"ee637b61af0f43b5a89c1f0207af369193e3341a670ec9c143abd7d1a3b63530"},"schema_version":"1.0","source":{"id":"1805.11679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11679","created_at":"2026-05-18T00:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11679v1","created_at":"2026-05-18T00:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11679","created_at":"2026-05-18T00:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"H4XWIOJZ263O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H4XWIOJZ263OCENK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H4XWIOJZ","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:8772a831245843fb4f16741f00c6550f5e6f4a3298d8599c85daba3c884754d5","target":"graph","created_at":"2026-05-18T00:14:37Z","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":"This paper studies visibility problems in Euclidean spaces $\\mathbb{R}^d$ where the obstacles are the points of infinite discrete sets $Y\\subseteq\\mathbb{R}^d$. A point $x\\in\\mathbb{R}^d$ is called $\\varepsilon$-visible for $Y$ (notation: $x\\in\\mathbf{vis}(Y, \\varepsilon))$ if there exists a ray $L\\subseteq\\mathbb{R}^d$ emanating from $x$ such that $||y-z||\\geq\\varepsilon$, for all $y\\in Y\\setminus\\{x\\}$ and $z\\in L$. A point $x\\in\\mathbb{R}^d$ is called visible for $Y$ (notation: $x\\in\\mathbf{vis}(Y))$ if $x\\in\\mathbf{vis}(Y, \\varepsilon))$, for some $\\varepsilon>0$.\\\\ Our main result is the ","authors_text":"Michael Boshernitzan, Yaar Solomon","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-05-29T19:31:02Z","title":"On Visibility Problems with an Infinite Discrete, set of Obstacles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11679","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":"sha256:6ab0fa9eb4e03982e560238ce95e615175e1b0bfa0e934a7db2952fe2f523e39","target":"record","created_at":"2026-05-18T00:14:37Z","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":"ad3ad1a370247ff33c0a4dcad0171ec0b494fa157218c4f0ebdfff2f1ce668f5","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-05-29T19:31:02Z","title_canon_sha256":"ee637b61af0f43b5a89c1f0207af369193e3341a670ec9c143abd7d1a3b63530"},"schema_version":"1.0","source":{"id":"1805.11679","kind":"arxiv","version":1}},"canonical_sha256":"3f2f643939d7b6e111aa0fad41a90a52e8545ef7452bb72cffbeea3cef7393a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f2f643939d7b6e111aa0fad41a90a52e8545ef7452bb72cffbeea3cef7393a7","first_computed_at":"2026-05-18T00:14:37.004812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:37.004812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1wU1fPg2qXjyj/ip4CY41d7As46jcNJEx46hW8YAjNRMvvXBvs6Tdg1XrX07kIC3ZKSNwbJgozd4Gr8uwf5PDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:37.005575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ab0fa9eb4e03982e560238ce95e615175e1b0bfa0e934a7db2952fe2f523e39","sha256:8772a831245843fb4f16741f00c6550f5e6f4a3298d8599c85daba3c884754d5"],"state_sha256":"392ee3fe1b832f201802bedadfc7b0d43aa99501e7b24dd75af691c68fbe8347"}