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We investigate its Gromov width and prove that the expression $$2\\pi \\min \\{2 r_j, (\\sum_{i \\neq j} r_i) - r_j\\,\\,|\\, j=1,\\ldots,n\\}$$ is the Gromov width of all (smooth) $5$--gon spaces and of $6$--gon spaces, under some condition on $r \\in \\mathbb{R}^6_+$. The same formula constitutes a lower bound for all (smooth) spaces of $6$--gons. Moreover, we prove that the Gromov width of $\\mathcal{M}(r)$ is given by the above express"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.00298","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-01T18:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"ecad7305764ea55fa6e10b87f056f4edb162c8ad9943487ddd53846f74a50310","abstract_canon_sha256":"5940d9656cb5ad789026755deeee043a123d27682c655c7faf2beca4e7a548e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:37.418615Z","signature_b64":"gtkVCnj8e1LD55svtFPW+e0VP3J9FuHMtMtX7gIyXQ04CwqiBFF1rp8FcT2KKvmDHmEFfxta7vsaObpkxZ3qAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8928672304102cda0e014889388176dabc128cf11d6d99e0d9a4e45f3e3b7b0d","last_reissued_at":"2026-05-18T00:44:37.418110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:37.418110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Gromov width of polygon spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Alessia Mandini, Milena Pabiniak","submitted_at":"2015-01-01T18:23:08Z","abstract_excerpt":"For generic $r=(r_1,\\ldots,r_n) \\in \\mathbb{R}^n_+$ the space $\\mathcal{M}(r)$ of $n$--gons in $\\mathbb{R}^3$ with edges of lengths $r$ is a smooth, symplectic manifold. We investigate its Gromov width and prove that the expression $$2\\pi \\min \\{2 r_j, (\\sum_{i \\neq j} r_i) - r_j\\,\\,|\\, j=1,\\ldots,n\\}$$ is the Gromov width of all (smooth) $5$--gon spaces and of $6$--gon spaces, under some condition on $r \\in \\mathbb{R}^6_+$. The same formula constitutes a lower bound for all (smooth) spaces of $6$--gons. Moreover, we prove that the Gromov width of $\\mathcal{M}(r)$ is given by the above express"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00298","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.00298","created_at":"2026-05-18T00:44:37.418174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00298v2","created_at":"2026-05-18T00:44:37.418174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00298","created_at":"2026-05-18T00:44:37.418174+00:00"},{"alias_kind":"pith_short_12","alias_value":"REUGOIYECAWN","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"REUGOIYECAWNUDQB","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"REUGOIYE","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K","json":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K.json","graph_json":"https://pith.science/api/pith-number/REUGOIYECAWNUDQBJCETRALW3K/graph.json","events_json":"https://pith.science/api/pith-number/REUGOIYECAWNUDQBJCETRALW3K/events.json","paper":"https://pith.science/paper/REUGOIYE"},"agent_actions":{"view_html":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K","download_json":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K.json","view_paper":"https://pith.science/paper/REUGOIYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00298&json=true","fetch_graph":"https://pith.science/api/pith-number/REUGOIYECAWNUDQBJCETRALW3K/graph.json","fetch_events":"https://pith.science/api/pith-number/REUGOIYECAWNUDQBJCETRALW3K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K/action/storage_attestation","attest_author":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K/action/author_attestation","sign_citation":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K/action/citation_signature","submit_replication":"https://pith.science/pith/REUGOIYECAWNUDQBJCETRALW3K/action/replication_record"}},"created_at":"2026-05-18T00:44:37.418174+00:00","updated_at":"2026-05-18T00:44:37.418174+00:00"}