{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:62HL4HRIRX7Z5ITNYDM2MSOB4Q","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":"497f15c71287fc986c5ddb35a0a78ccbd40bf8254e31e2bf1863ccfcf168b8d7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-13T04:36:01Z","title_canon_sha256":"2c16e55017f8372b96c7c9988c8fb97877610fd6e9be7c4c08927036b0c29044"},"schema_version":"1.0","source":{"id":"1606.03807","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03807","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03807v2","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03807","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"pith_short_12","alias_value":"62HL4HRIRX7Z","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"62HL4HRIRX7Z5ITN","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"62HL4HRI","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:e8d9c40606a9dcf65548786afdedd3230e8d16384c42f1b6c3b307c6b6afb98b","target":"graph","created_at":"2026-05-18T00:48:42Z","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 construct an embedding $\\Phi$ of $[0,1]^{\\infty}$ into $Ham(M, \\omega)$, the group of Hamiltonian diffeomorphisms of a suitable closed symplectic manifold $(M, \\omega)$. We then prove that $\\Phi$ is in fact a quasi-isometry. After imposing further assumptions on $(M, \\omega)$, we adapt our methods to construct a similar embedding of $\\mathbb{R} \\oplus [0,1]^{\\infty}$ into either $Ham(M, \\omega)$ or $\\widetilde{Ham}(M, \\omega)$, the universal cover of $Ham(M, \\omega)$. Along the way, we prove results related to the filtered Floer chain complexes of radially symmetric Hamiltonians. Our proofs","authors_text":"Bret Stevenson","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-13T04:36:01Z","title":"A quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer's metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03807","kind":"arxiv","version":2},"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":"sha256:04eb0ee01c0a58337fda43d2da857cbdcc9e948d89b0e663d911e9f8fb7ebab0","target":"record","created_at":"2026-05-18T00:48:42Z","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":"497f15c71287fc986c5ddb35a0a78ccbd40bf8254e31e2bf1863ccfcf168b8d7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-06-13T04:36:01Z","title_canon_sha256":"2c16e55017f8372b96c7c9988c8fb97877610fd6e9be7c4c08927036b0c29044"},"schema_version":"1.0","source":{"id":"1606.03807","kind":"arxiv","version":2}},"canonical_sha256":"f68ebe1e288dff9ea26dc0d9a649c1e411e9724c9021eff323e5bc2ddf81bf00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f68ebe1e288dff9ea26dc0d9a649c1e411e9724c9021eff323e5bc2ddf81bf00","first_computed_at":"2026-05-18T00:48:42.661900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:42.661900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vFCVehv8k2v54mKQgR8CWZzzr89MzbMpeTl36xii1nQqnEwLmj6yOE7Z4sN/LaGKyJvzNmUtsWNF458MkZ0dCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:42.662446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03807","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04eb0ee01c0a58337fda43d2da857cbdcc9e948d89b0e663d911e9f8fb7ebab0","sha256:e8d9c40606a9dcf65548786afdedd3230e8d16384c42f1b6c3b307c6b6afb98b"],"state_sha256":"a438f06aa29fdcd86352d1f48ff4e3870340ac2f1de7743e85681559a9722317"}