{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BWRRSV3FF25N77LPCC7QEOLKYR","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":"a0090216d4fe2c8f67a0f1291acd2323b1a1ff6ab5ab98a853183096fa23c6c1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-06T06:26:57Z","title_canon_sha256":"67a4a706ae45f3bcf48ca2d3e1d1b55b2c760e54ea7309450c12cc7de778e2e5"},"schema_version":"1.0","source":{"id":"1706.01618","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01618","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01618v1","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01618","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"BWRRSV3FF25N","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BWRRSV3FF25N77LP","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BWRRSV3F","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:9c328fd4f555a8e87fa0d37ebee3d32d8d9b08d3cc91ba2d0b0b204ac5a542ee","target":"graph","created_at":"2026-05-18T00:42:56Z","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 introduce the concept of $r$-equilateral $m$-gons. We prove the existence of $r$-equilateral $p$-gons in $\\mathbb R^d$ if $r<d$ and the existence of equilateral $p$-gons in the image of continuous injective maps $f:S^d\\to \\mathbb R^{d+1}$. Our ideas are based mainly in the paper of Y. Soibelman \\cite{soibelman}, in which the topological Borsuk number of $\\mathbb{R}^2$ is calculated by means of topological methods and the paper of P. Blagojevi\\'c and G. Ziegler \\cite{blagojevictetrahedra} where Fadell-Husseini index is used for solving a problem related to the topological Borsuk problem for ","authors_text":"Andr\\'es Angel, Jerson Borja","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-06T06:26:57Z","title":"Equilateral $p$-gons in $\\mathbb R^d$ and deformed spheres and mod $p$ Fadell-Husseini index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01618","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":"sha256:8ea89e4b2d244bbdaaba3803a438eca1732328727e044fef6365053a352802d7","target":"record","created_at":"2026-05-18T00:42:56Z","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":"a0090216d4fe2c8f67a0f1291acd2323b1a1ff6ab5ab98a853183096fa23c6c1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-06T06:26:57Z","title_canon_sha256":"67a4a706ae45f3bcf48ca2d3e1d1b55b2c760e54ea7309450c12cc7de778e2e5"},"schema_version":"1.0","source":{"id":"1706.01618","kind":"arxiv","version":1}},"canonical_sha256":"0da31957652ebadffd6f10bf02396ac47744cc5a651b6ce298eb728db4be1922","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0da31957652ebadffd6f10bf02396ac47744cc5a651b6ce298eb728db4be1922","first_computed_at":"2026-05-18T00:42:56.517127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:56.517127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ge5OoRZUc6kR/GL1kzGf0BWieag+pH4JrWAe92TWSGAARDkhUBjhJiBOsTK7xL0S6BDqyiF4SHHyMnUoG15ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:56.517830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.01618","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ea89e4b2d244bbdaaba3803a438eca1732328727e044fef6365053a352802d7","sha256:9c328fd4f555a8e87fa0d37ebee3d32d8d9b08d3cc91ba2d0b0b204ac5a542ee"],"state_sha256":"f9f35d46d9a2ef6ada7a21d0e1b97be3171033a440341f2df5ada496052c5955"}