{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:S3OUTCWS4T2E6EVYIGQO2ANTPD","short_pith_number":"pith:S3OUTCWS","schema_version":"1.0","canonical_sha256":"96dd498ad2e4f44f12b841a0ed01b378e457e1d939aee8c114f24f3972ab8831","source":{"kind":"arxiv","id":"1707.09171","version":1},"attestation_state":"computed","paper":{"title":"Inscribed Polygons that Characterize Inner Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carlos Ben\\'itez, Diego Y\\'a\\~nez, Pedro Mart\\'in","submitted_at":"2017-07-28T09:59:06Z","abstract_excerpt":"Let $X$ be a real normed space with unit sphere S. We prove that $X$ is an inner product space if and only if there exists a real number $\\rho=\\sqrt{(1+\\cos\\frac{2k\\pi}{2m+1})/2}$, $(k=1,2,\\ldots , m ;\\:m=1,2,\\ldots)$, such that every chord of $S$ that supports $\\rho S$ touches $\\rho S$ at its middle point. If this condition holds, then every point $u\\in S$ is a vertex of a regular polygon that is inscribed in $S$ and circumscribed about $\\rho S$."},"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":"1707.09171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-28T09:59:06Z","cross_cats_sorted":[],"title_canon_sha256":"60e9355b29cac1972488fedd280afcc691a7628f1cb2ed9ec5483f5a783fc9ff","abstract_canon_sha256":"dc3df84995a868995f435b686b16ef39e8f1444afbe476f6ebd620d25eb0f05f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:16.866827Z","signature_b64":"/jn+1dzmPf998pJ36eWYT32hBV1GoJAXseXdJmQy5jUNeZ2im/TXury63piCLZxo6jSRiaqXF9nL1TgJeQVgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96dd498ad2e4f44f12b841a0ed01b378e457e1d939aee8c114f24f3972ab8831","last_reissued_at":"2026-05-18T00:39:16.866302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:16.866302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inscribed Polygons that Characterize Inner Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carlos Ben\\'itez, Diego Y\\'a\\~nez, Pedro Mart\\'in","submitted_at":"2017-07-28T09:59:06Z","abstract_excerpt":"Let $X$ be a real normed space with unit sphere S. We prove that $X$ is an inner product space if and only if there exists a real number $\\rho=\\sqrt{(1+\\cos\\frac{2k\\pi}{2m+1})/2}$, $(k=1,2,\\ldots , m ;\\:m=1,2,\\ldots)$, such that every chord of $S$ that supports $\\rho S$ touches $\\rho S$ at its middle point. If this condition holds, then every point $u\\in S$ is a vertex of a regular polygon that is inscribed in $S$ and circumscribed about $\\rho S$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09171","kind":"arxiv","version":1},"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":"1707.09171","created_at":"2026-05-18T00:39:16.866400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.09171v1","created_at":"2026-05-18T00:39:16.866400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09171","created_at":"2026-05-18T00:39:16.866400+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3OUTCWS4T2E","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3OUTCWS4T2E6EVY","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3OUTCWS","created_at":"2026-05-18T12:31:43.269735+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/S3OUTCWS4T2E6EVYIGQO2ANTPD","json":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD.json","graph_json":"https://pith.science/api/pith-number/S3OUTCWS4T2E6EVYIGQO2ANTPD/graph.json","events_json":"https://pith.science/api/pith-number/S3OUTCWS4T2E6EVYIGQO2ANTPD/events.json","paper":"https://pith.science/paper/S3OUTCWS"},"agent_actions":{"view_html":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD","download_json":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD.json","view_paper":"https://pith.science/paper/S3OUTCWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.09171&json=true","fetch_graph":"https://pith.science/api/pith-number/S3OUTCWS4T2E6EVYIGQO2ANTPD/graph.json","fetch_events":"https://pith.science/api/pith-number/S3OUTCWS4T2E6EVYIGQO2ANTPD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD/action/storage_attestation","attest_author":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD/action/author_attestation","sign_citation":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD/action/citation_signature","submit_replication":"https://pith.science/pith/S3OUTCWS4T2E6EVYIGQO2ANTPD/action/replication_record"}},"created_at":"2026-05-18T00:39:16.866400+00:00","updated_at":"2026-05-18T00:39:16.866400+00:00"}