{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SLVKUR25AARQVXTRJB2VYEJEQH","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":"6fba979ae6ccfd61a7e579a8bf2f92a2912477827bfb8b9efdb907fb2b00fb67","cross_cats_sorted":["cs.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-07-09T02:47:50Z","title_canon_sha256":"73f69962d0ca1c5b212fe29c6913778cc163fd1c49443b957d778fbd2f26cbc6"},"schema_version":"1.0","source":{"id":"1507.02355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02355","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02355v1","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02355","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"SLVKUR25AARQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SLVKUR25AARQVXTR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SLVKUR25","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:546c99d2a98cd8c9863ac1c641e15f86004922d97de4fd6b8a901a7739d4b96f","target":"graph","created_at":"2026-05-18T01:37:06Z","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":"A \"shadow\" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three shadows of a cycle (i.e., a simple closed curve) in $\\mathbb R^3$ to be paths (i.e., simple open curves).\n  We also show two contrasting results: the three shadows of a path in $\\mathbb R^3$ can all be cycles (although not all convex) and, for every $d\\geq 1$, there exists a $d$-sphere embedded in $\\mathbb R^{d+2}$ whose $d+2$ shadows have no holes (i.e., they deformation-retract onto a point).","authors_text":"Giovanni Viglietta, Heuna Kim, Jean-Lou De Carufel, Michael G. Dobbins, Prosenjit Bose","cross_cats":["cs.CV","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-07-09T02:47:50Z","title":"The Shadows of a Cycle Cannot All Be Paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02355","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":"sha256:949a3ddd301170b13ea26a86e9b1bfd21c6a5203c4b90a9baa04b18c38dc464f","target":"record","created_at":"2026-05-18T01:37:06Z","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":"6fba979ae6ccfd61a7e579a8bf2f92a2912477827bfb8b9efdb907fb2b00fb67","cross_cats_sorted":["cs.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-07-09T02:47:50Z","title_canon_sha256":"73f69962d0ca1c5b212fe29c6913778cc163fd1c49443b957d778fbd2f26cbc6"},"schema_version":"1.0","source":{"id":"1507.02355","kind":"arxiv","version":1}},"canonical_sha256":"92eaaa475d00230ade7148755c112481cbf171c4e121b9c7ec4bf70d0d06cc79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92eaaa475d00230ade7148755c112481cbf171c4e121b9c7ec4bf70d0d06cc79","first_computed_at":"2026-05-18T01:37:06.917128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:06.917128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDSkFcocbXmzyYzGHXn/k8XDC7Qftl4hfhIqOjlr33OJXxbSORAcOY6S66i5NZtloCUML7kkc4MfEFAJiJ1CBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:06.917726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:949a3ddd301170b13ea26a86e9b1bfd21c6a5203c4b90a9baa04b18c38dc464f","sha256:546c99d2a98cd8c9863ac1c641e15f86004922d97de4fd6b8a901a7739d4b96f"],"state_sha256":"e37a0d4fa80805f120c22e1216b17ead4c164a51187a4f2da2e4c9e0f394b48a"}