{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VO2WSJ2AOYXDDOFU4ASMFMWLS2","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":"ad69c7efd00ae5ccb6de3de754d4362f8c46469188d2b55ff71bbac6ac932253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-27T11:40:25Z","title_canon_sha256":"a72d170e5835303e56fc03ccda496b44ffd4a8d15d79c8b2c6eee36cf871a45d"},"schema_version":"1.0","source":{"id":"1202.5897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5897","created_at":"2026-05-18T04:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5897v2","created_at":"2026-05-18T04:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5897","created_at":"2026-05-18T04:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"VO2WSJ2AOYXD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VO2WSJ2AOYXDDOFU","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VO2WSJ2A","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:07f685c004aa50aee8a5da6b855c36fe18060e1f134fd9407908e1d845ad1221","target":"graph","created_at":"2026-05-18T04:00:28Z","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":"A right-invariant metric $\\rho_{\\alpha}$ on the compactly supported identity component $Cont_0(M,\\alpha)$ of the group of contactomorphisms of an arbitrary contact manifold $(M,\\alpha)$ is introduced in a similar way that the Hofer metric was defined on the group of Hamiltonian symplectomorphisms of a symplectic manifold. The restriction of $\\rho_{\\alpha}$ to the subgroup $G(M,\\alpha)$ of all strict contactomorphisms in $Cont_0(M,\\alpha)$ is bi-invariant.","authors_text":"Tomasz Rybicki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-27T11:40:25Z","title":"Bi-invariant metric on the strict contactomorphism group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5897","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":"sha256:99c62ff959ef4d54167a214f6ee8817776ab303c7fa00eff01bf112b6c533043","target":"record","created_at":"2026-05-18T04:00:28Z","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":"ad69c7efd00ae5ccb6de3de754d4362f8c46469188d2b55ff71bbac6ac932253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-27T11:40:25Z","title_canon_sha256":"a72d170e5835303e56fc03ccda496b44ffd4a8d15d79c8b2c6eee36cf871a45d"},"schema_version":"1.0","source":{"id":"1202.5897","kind":"arxiv","version":2}},"canonical_sha256":"abb5692740762e31b8b4e024c2b2cb96b44339e8de8c7bf2c4b933f4de82baab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abb5692740762e31b8b4e024c2b2cb96b44339e8de8c7bf2c4b933f4de82baab","first_computed_at":"2026-05-18T04:00:28.057257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:28.057257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TYoYGxbPhNbFtgQbHOHrP1XyHg+SdajNG8J++Kt2bsY3SqRuv1WH1PKhmEhhIwiLh2GwL1K+0Sn+L1Kem/aiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:28.057858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99c62ff959ef4d54167a214f6ee8817776ab303c7fa00eff01bf112b6c533043","sha256:07f685c004aa50aee8a5da6b855c36fe18060e1f134fd9407908e1d845ad1221"],"state_sha256":"2539e671a00865b1c72392fcbeffdafe074ace96728c272d662ceae9aa2c2c3e"}