{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FDDJKIG6O6ZJS77YVD6NNIMSTR","short_pith_number":"pith:FDDJKIG6","schema_version":"1.0","canonical_sha256":"28c69520de77b2997ff8a8fcd6a1929c424b3649f8fdf2543245793445ff0927","source":{"kind":"arxiv","id":"1102.4889","version":1},"attestation_state":"computed","paper":{"title":"Hofer Geometry of a Subset of a Symplectic Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Fabian Ziltener, Jan Swoboda","submitted_at":"2011-02-24T01:20:17Z","abstract_excerpt":"To every closed subset $X$ of a symplectic manifold $(M,\\omega)$ we associate a natural group of Hamiltonian diffeomorphisms $Ham(X,\\omega)$. We equip this group with a semi-norm $\\Vert\\cdot\\Vert^{X,\\omega}$, generalizing the Hofer norm. We discuss $Ham(X,\\omega)$ and $\\Vert\\cdot\\Vert^{X,\\omega}$ if $X$ is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of $X$ in $M$. Its first part states that for the unit sphere in $R^{2n}$ this diameter is bounded below by $\\frac\\pi2$, if $n\\geq2$. Its second part states that for $n\\geq2$ and $d\\geq n+1$ there exi"},"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":"1102.4889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-02-24T01:20:17Z","cross_cats_sorted":[],"title_canon_sha256":"5a6e9bb40ab9f56db37914940fc06d5b6d10e2cedd0cc93e37aecd4612d187d2","abstract_canon_sha256":"8e64641fbc8ba8ddb84c9de504875be69dc63279bfeadd43921302c03a94cec4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:58.519897Z","signature_b64":"UC+b3qQw4pPZxfNL55RNfqpnCSkt9uppU1Vn70Q06r2Hf7CzfXTonRG1jr1pBl5JO3vcReyurehlUIYDW+UBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28c69520de77b2997ff8a8fcd6a1929c424b3649f8fdf2543245793445ff0927","last_reissued_at":"2026-05-18T04:27:58.519424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:58.519424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hofer Geometry of a Subset of a Symplectic Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Fabian Ziltener, Jan Swoboda","submitted_at":"2011-02-24T01:20:17Z","abstract_excerpt":"To every closed subset $X$ of a symplectic manifold $(M,\\omega)$ we associate a natural group of Hamiltonian diffeomorphisms $Ham(X,\\omega)$. We equip this group with a semi-norm $\\Vert\\cdot\\Vert^{X,\\omega}$, generalizing the Hofer norm. We discuss $Ham(X,\\omega)$ and $\\Vert\\cdot\\Vert^{X,\\omega}$ if $X$ is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of $X$ in $M$. Its first part states that for the unit sphere in $R^{2n}$ this diameter is bounded below by $\\frac\\pi2$, if $n\\geq2$. Its second part states that for $n\\geq2$ and $d\\geq n+1$ there exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4889","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":"1102.4889","created_at":"2026-05-18T04:27:58.519500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4889v1","created_at":"2026-05-18T04:27:58.519500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4889","created_at":"2026-05-18T04:27:58.519500+00:00"},{"alias_kind":"pith_short_12","alias_value":"FDDJKIG6O6ZJ","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FDDJKIG6O6ZJS77Y","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FDDJKIG6","created_at":"2026-05-18T12:26:28.662955+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/FDDJKIG6O6ZJS77YVD6NNIMSTR","json":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR.json","graph_json":"https://pith.science/api/pith-number/FDDJKIG6O6ZJS77YVD6NNIMSTR/graph.json","events_json":"https://pith.science/api/pith-number/FDDJKIG6O6ZJS77YVD6NNIMSTR/events.json","paper":"https://pith.science/paper/FDDJKIG6"},"agent_actions":{"view_html":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR","download_json":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR.json","view_paper":"https://pith.science/paper/FDDJKIG6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4889&json=true","fetch_graph":"https://pith.science/api/pith-number/FDDJKIG6O6ZJS77YVD6NNIMSTR/graph.json","fetch_events":"https://pith.science/api/pith-number/FDDJKIG6O6ZJS77YVD6NNIMSTR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR/action/storage_attestation","attest_author":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR/action/author_attestation","sign_citation":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR/action/citation_signature","submit_replication":"https://pith.science/pith/FDDJKIG6O6ZJS77YVD6NNIMSTR/action/replication_record"}},"created_at":"2026-05-18T04:27:58.519500+00:00","updated_at":"2026-05-18T04:27:58.519500+00:00"}