{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HAIEXG3MWL5ZRTWZ4ZUPFSVT4H","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":"2c83736643487498ba345667483e09686d3c40d73665636c8fc338bb9df0ac87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-21T18:14:44Z","title_canon_sha256":"f634663cc6fbdfae4a5f97dbe5badccbf525d88268f9364dc83bd8ae6785c1af"},"schema_version":"1.0","source":{"id":"1505.05817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05817","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05817v1","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05817","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"HAIEXG3MWL5Z","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HAIEXG3MWL5ZRTWZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HAIEXG3M","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f5a2b092693326daa6bf287d57449bb61aee62384472a29e40130ed7447033b3","target":"graph","created_at":"2026-05-18T02:03:53Z","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":"We construct examples of two convex bodies $K,L$ in $\\mathbb{R}^n$, such that every projection of $K$ onto a $(n-1)$-dimensional subspace can be rotated to be contained in the corresponding projection of $L$, but $K$ itself cannot be rotated to be contained in $L$. We also find necessary conditions on $K$ and $L$ to ensure that $K$ can be rotated to be contained in $L$ if all the $(n-1)$-dimensional projections have this property.","authors_text":"M.Angeles Alfonseca, Michelle Cordier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-21T18:14:44Z","title":"Counterexamples Related to Rotations of Shadows of Convex Bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05817","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:a88af2f2623c808ce4578417ce6f847a36b8cac158b0e58bffd6327794980338","target":"record","created_at":"2026-05-18T02:03:53Z","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":"2c83736643487498ba345667483e09686d3c40d73665636c8fc338bb9df0ac87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-21T18:14:44Z","title_canon_sha256":"f634663cc6fbdfae4a5f97dbe5badccbf525d88268f9364dc83bd8ae6785c1af"},"schema_version":"1.0","source":{"id":"1505.05817","kind":"arxiv","version":1}},"canonical_sha256":"38104b9b6cb2fb98ced9e668f2cab3e1d08cbbe568817fa4e95b4b4a6b7d22fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38104b9b6cb2fb98ced9e668f2cab3e1d08cbbe568817fa4e95b4b4a6b7d22fe","first_computed_at":"2026-05-18T02:03:53.409279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:53.409279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qF8NT2x23jdHCKea1uQeG6bFVgxgB+EXfEaSBuREdnlkcODD7ESwLRPlO78+tXXHj4Q8V0i5pCBP0YvUsB87Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:53.409825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a88af2f2623c808ce4578417ce6f847a36b8cac158b0e58bffd6327794980338","sha256:f5a2b092693326daa6bf287d57449bb61aee62384472a29e40130ed7447033b3"],"state_sha256":"9e8ba9cfd5e5b2201951e40f7521c33eea68457dcdd3f6f171557ce1e4446fec"}