{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N3Q6HFQLBUMYW3KLCGIBWKVLRN","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":"65e3b0cff61edd21d42920be16dd2d95a2b9c5f9c8a1ce793ec3dd130abcb66c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-20T07:27:09Z","title_canon_sha256":"c0d38ccb9c7eaf643534957d4c6370d89db5231aaa72f3183bc56271212ca9ee"},"schema_version":"1.0","source":{"id":"1505.05263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05263","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05263v2","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05263","created_at":"2026-05-18T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"N3Q6HFQLBUMY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N3Q6HFQLBUMYW3KL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N3Q6HFQL","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:491a6e9ecdf03adcab6f290dc4dbaed6400b1f2734f8cccf5fc27ccf9d08d4dc","target":"graph","created_at":"2026-05-18T01:17:37Z","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":"In this article we study the following question: What can be the measure of the minimal solid angle of a simplex in $\\mathbb{R}^d$? We show that in dimensions three it is not greater than the solid angle of the regular simplex. And in dimension four the same holds for simplices sufficiently close to the regular simplex. We also study a similar question for trihedral and dihedral angles of polyhedra compared to those of regular solids.","authors_text":"Arseniy Akopyan, Roman Karasev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-20T07:27:09Z","title":"Bounding minimal solid angles of polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05263","kind":"arxiv","version":2},"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":"sha256:34dee860c3e70d28d2b6aa315a5846fd7a19ee91ed94e3ed8d6822fb748d1e83","target":"record","created_at":"2026-05-18T01:17:37Z","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":"65e3b0cff61edd21d42920be16dd2d95a2b9c5f9c8a1ce793ec3dd130abcb66c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-20T07:27:09Z","title_canon_sha256":"c0d38ccb9c7eaf643534957d4c6370d89db5231aaa72f3183bc56271212ca9ee"},"schema_version":"1.0","source":{"id":"1505.05263","kind":"arxiv","version":2}},"canonical_sha256":"6ee1e3960b0d198b6d4b11901b2aab8b4f095142005e185113a11cede82c12d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ee1e3960b0d198b6d4b11901b2aab8b4f095142005e185113a11cede82c12d2","first_computed_at":"2026-05-18T01:17:37.523603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:37.523603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJ3eFB6hmVsVUamquYKG9B8STLskCeAdCwK9ytzCrYeCOCXyYn9a0f6cco522WLoNjOdiVYNxeoDeiaoyYTXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:37.524355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34dee860c3e70d28d2b6aa315a5846fd7a19ee91ed94e3ed8d6822fb748d1e83","sha256:491a6e9ecdf03adcab6f290dc4dbaed6400b1f2734f8cccf5fc27ccf9d08d4dc"],"state_sha256":"ae3ad7fca245911b2dddadab6287f7df82dfd1ee3d60863d48d60ac93f03682d"}