{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EYI2UX2XYNQJZD4AZ6BMY5T5XG","short_pith_number":"pith:EYI2UX2X","canonical_record":{"source":{"id":"1110.3353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-14T22:40:23Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"0ee1b2aee393a209cc0613c93a44ea0f4af3c68a59fc35dbfe10f62427bac7a0","abstract_canon_sha256":"ef796c53775bd9ffabd43672da0ecc33958f80caa1c73fa0700b90570a2c9a98"},"schema_version":"1.0"},"canonical_sha256":"2611aa5f57c3609c8f80cf82cc767db9b7d96b6f0769a595396e76f91d4b6e05","source":{"kind":"arxiv","id":"1110.3353","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3353","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3353v2","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3353","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"EYI2UX2XYNQJ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EYI2UX2XYNQJZD4A","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EYI2UX2X","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EYI2UX2XYNQJZD4AZ6BMY5T5XG","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-14T22:40:23Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"0ee1b2aee393a209cc0613c93a44ea0f4af3c68a59fc35dbfe10f62427bac7a0","abstract_canon_sha256":"ef796c53775bd9ffabd43672da0ecc33958f80caa1c73fa0700b90570a2c9a98"},"schema_version":"1.0"},"canonical_sha256":"2611aa5f57c3609c8f80cf82cc767db9b7d96b6f0769a595396e76f91d4b6e05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:31.636269Z","signature_b64":"i1kk0pYZ2JBazJwFWr1AYP3+JN1BiVxjwP7i+Vl5JCWEZl3CrGN4n+uBvlRGmxyRfwnxGgvQpd3d4lWePo4bAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2611aa5f57c3609c8f80cf82cc767db9b7d96b6f0769a595396e76f91d4b6e05","last_reissued_at":"2026-05-18T03:46:31.635247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:31.635247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3353","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fysYthXz/4YSHiN9PHyUjqdQ3zocBa2BIVBLEJqlEmafDSBqJrb5IqJldj4CfCSq/H0YdzMjuk0NTbpSJTaQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:53:03.491043Z"},"content_sha256":"417cac8e9b51610a786db42b4e3ae8ffd265f999b0e441fd4676336e7dc2b3d2","schema_version":"1.0","event_id":"sha256:417cac8e9b51610a786db42b4e3ae8ffd265f999b0e441fd4676336e7dc2b3d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EYI2UX2XYNQJZD4AZ6BMY5T5XG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.GT","authors_text":"Michael Brandenbursky","submitted_at":"2011-10-14T22:40:23Z","abstract_excerpt":"Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component $Diff_0(M,vol)$ of the group of volume preserving diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental group, is Lipschitz with respect to the L^p-metric on the group $Diff_0(M,vol)$. As a consequence, assuming certain conditions on the fundamental group, we construct bi-Lipschitz embeddings of finite dimensional vector spaces into $Diff_0(M,vol)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3353","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4kEnFI0d2rmmz/C8JkWBWU7mzE/En/J9FCwXWIPHwD7y4CENuShT+D7tXnN4UcGqVL1nsZT/pJlyzLqPh59DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:53:03.491705Z"},"content_sha256":"4f4f4d523bc616aeb46578b7cd7e4480bb234a7ac8a21701cc23e4cd09dffd33","schema_version":"1.0","event_id":"sha256:4f4f4d523bc616aeb46578b7cd7e4480bb234a7ac8a21701cc23e4cd09dffd33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG/bundle.json","state_url":"https://pith.science/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T16:53:03Z","links":{"resolver":"https://pith.science/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG","bundle":"https://pith.science/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG/bundle.json","state":"https://pith.science/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYI2UX2XYNQJZD4AZ6BMY5T5XG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EYI2UX2XYNQJZD4AZ6BMY5T5XG","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":"ef796c53775bd9ffabd43672da0ecc33958f80caa1c73fa0700b90570a2c9a98","cross_cats_sorted":["math.DG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-14T22:40:23Z","title_canon_sha256":"0ee1b2aee393a209cc0613c93a44ea0f4af3c68a59fc35dbfe10f62427bac7a0"},"schema_version":"1.0","source":{"id":"1110.3353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3353","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3353v2","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3353","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"EYI2UX2XYNQJ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EYI2UX2XYNQJZD4A","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EYI2UX2X","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:4f4f4d523bc616aeb46578b7cd7e4480bb234a7ac8a21701cc23e4cd09dffd33","target":"graph","created_at":"2026-05-18T03:46:31Z","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":"Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component $Diff_0(M,vol)$ of the group of volume preserving diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental group, is Lipschitz with respect to the L^p-metric on the group $Diff_0(M,vol)$. As a consequence, assuming certain conditions on the fundamental group, we construct bi-Lipschitz embeddings of finite dimensional vector spaces into $Diff_0(M,vol)$.","authors_text":"Michael Brandenbursky","cross_cats":["math.DG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-14T22:40:23Z","title":"Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3353","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":"sha256:417cac8e9b51610a786db42b4e3ae8ffd265f999b0e441fd4676336e7dc2b3d2","target":"record","created_at":"2026-05-18T03:46:31Z","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":"ef796c53775bd9ffabd43672da0ecc33958f80caa1c73fa0700b90570a2c9a98","cross_cats_sorted":["math.DG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-14T22:40:23Z","title_canon_sha256":"0ee1b2aee393a209cc0613c93a44ea0f4af3c68a59fc35dbfe10f62427bac7a0"},"schema_version":"1.0","source":{"id":"1110.3353","kind":"arxiv","version":2}},"canonical_sha256":"2611aa5f57c3609c8f80cf82cc767db9b7d96b6f0769a595396e76f91d4b6e05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2611aa5f57c3609c8f80cf82cc767db9b7d96b6f0769a595396e76f91d4b6e05","first_computed_at":"2026-05-18T03:46:31.635247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:31.635247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i1kk0pYZ2JBazJwFWr1AYP3+JN1BiVxjwP7i+Vl5JCWEZl3CrGN4n+uBvlRGmxyRfwnxGgvQpd3d4lWePo4bAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:31.636269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:417cac8e9b51610a786db42b4e3ae8ffd265f999b0e441fd4676336e7dc2b3d2","sha256:4f4f4d523bc616aeb46578b7cd7e4480bb234a7ac8a21701cc23e4cd09dffd33"],"state_sha256":"4a5c507e30e95994c660481600a78655ab742e0d23eea27b90f667cd32109f2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tddf2COCDZFWINVlxVb9nM+y53k7DXWeac+T5bWaJRVrjmz68Po3H9DJgO+RN2LKevnyqckTGBL7KgAknetxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:53:03.494880Z","bundle_sha256":"ff85be5fdd818a1d1e47421b927ab9dda17ef04a4071e65ca28d626e75616a72"}}