{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RYR43DUTKSNM4JCYQ6DL35KXZI","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":"7f3906b565f0b70f5ef13d9b6c202c11d6b3b18ce90737188ee166cc9d40c1f7","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-10-29T12:59:27Z","title_canon_sha256":"0a95bbefbe28e4dc5a1f2a881e953c5c7a8b5ae52f0c25dfcb9511eef78221ef"},"schema_version":"1.0","source":{"id":"0910.5632","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5632","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5632v3","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5632","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"RYR43DUTKSNM","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RYR43DUTKSNM4JCY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RYR43DUT","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:58c0b26cb22a145903219fc9e8725f82bf25c092f45edbc1439a6136f8f931b0","target":"graph","created_at":"2026-05-18T04:10:36Z","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":"In his 1992 article on generating functions Viterbo constructed a bi-invariant metric on the group of compactly supported Hamiltonian symplectomorphisms of R^2n. Using the set-up of arXiv:0901.3112 we extend the Viterbo metric to the group of compactly supported contactomorphisms of R^2n x S^1 isotopic to the identity. We also prove that the contactomorphism group is unbounded with respect to this metric.","authors_text":"Sheila Sandon","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-10-29T12:59:27Z","title":"An integer valued bi-invariant metric on the group of contactomorphisms of R^2n x S^1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5632","kind":"arxiv","version":3},"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":"sha256:6d3af94fb845d8f9a0c451f221723cd1143518950f5b2dc98221d24e5ac01103","target":"record","created_at":"2026-05-18T04:10:36Z","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":"7f3906b565f0b70f5ef13d9b6c202c11d6b3b18ce90737188ee166cc9d40c1f7","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-10-29T12:59:27Z","title_canon_sha256":"0a95bbefbe28e4dc5a1f2a881e953c5c7a8b5ae52f0c25dfcb9511eef78221ef"},"schema_version":"1.0","source":{"id":"0910.5632","kind":"arxiv","version":3}},"canonical_sha256":"8e23cd8e93549ace24588786bdf557ca095fbf7f6f5426f6c24aa4b489056df8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e23cd8e93549ace24588786bdf557ca095fbf7f6f5426f6c24aa4b489056df8","first_computed_at":"2026-05-18T04:10:36.104057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:36.104057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MgrUynZUdbRdnrLIjeZ57T51ffzadPMVneEykr5vEZdJy31FJre97hMxVWVwj/Xyss29vLKgf7TqAj8lmfs3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:36.104800Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5632","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d3af94fb845d8f9a0c451f221723cd1143518950f5b2dc98221d24e5ac01103","sha256:58c0b26cb22a145903219fc9e8725f82bf25c092f45edbc1439a6136f8f931b0"],"state_sha256":"a42108aad15786300c09d139a325615da9bfb5a07d127e3ba01e545d45a4b5d1"}