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We deduce that there are no intermediate capacities, between 1-capacities, first constructed by Gromov in 1985, and n-capacities, answering another question of Hofer. In 2008, Guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property."},"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":"1210.1537","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-10-04T18:54:21Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9c25941f06efc554c115c9d483cde166cf22e341b91983ce9d49562a433f7777","abstract_canon_sha256":"7aa0812998d920091906a07a0243503f092f9499c66d1148d66353b659410aeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:27.467597Z","signature_b64":"hnK8BrKYd/IgxwNK176+LRGU+ywZMUUaWCz0tH9zbMktJDdCFgUL06WpgyQqdgr+TNLX1d1mm8QjZerYf3HvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"319b14164022fcf4fd678b5f7eb26d67a22d804b7db02020e8450a9f96acae2a","last_reissued_at":"2026-05-18T01:53:27.466891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:27.466891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hofer question on intermediate symplectic capacities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Alvaro Pelayo, San Vu Ngoc","submitted_at":"2012-10-04T18:54:21Z","abstract_excerpt":"Roughly twenty five years ago Hofer asked: can the cylinder B^2(1) \\times \\mathbb{R}^{2(n-1)} be symplectically embedded into B^{2(n-1)}(R) \\times \\mathbb{R}^2 for some R>0? 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