{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WPO4EK23QGVYSMLLGCB47BVF6Z","short_pith_number":"pith:WPO4EK23","canonical_record":{"source":{"id":"1111.1449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T20:15:54Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"632df8817752d636408aa58ef291f81295229e3648fbbc755c345b534ed6cc4c","abstract_canon_sha256":"6599bac843e0347e24eae7e8ff8dfa7a86bca16adc1481aff090d026459d48ec"},"schema_version":"1.0"},"canonical_sha256":"b3ddc22b5b81ab89316b3083cf86a5f65595008cf7b00f8e5bb3d68d21c2503c","source":{"kind":"arxiv","id":"1111.1449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1449","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1449v1","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1449","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"WPO4EK23QGVY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WPO4EK23QGVYSMLL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WPO4EK23","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WPO4EK23QGVYSMLLGCB47BVF6Z","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T20:15:54Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"632df8817752d636408aa58ef291f81295229e3648fbbc755c345b534ed6cc4c","abstract_canon_sha256":"6599bac843e0347e24eae7e8ff8dfa7a86bca16adc1481aff090d026459d48ec"},"schema_version":"1.0"},"canonical_sha256":"b3ddc22b5b81ab89316b3083cf86a5f65595008cf7b00f8e5bb3d68d21c2503c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:53.713824Z","signature_b64":"Cubtuc/rCFUuqKDhYAViDwF78aBC8Q91DZfQ/JIBFBHF/ST/VpfgutA75GHGWIoMhzJcV4qzycC8cxi5eBYdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3ddc22b5b81ab89316b3083cf86a5f65595008cf7b00f8e5bb3d68d21c2503c","last_reissued_at":"2026-05-18T04:07:53.713290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:53.713290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1449","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"diFCxu4p22LGkP+dnJfvcnamL3waMhr7RFUgvncor50gmgzQQp1MdxBlA1zsGRs6GfBUpudWNpQlLcQqcL7MDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:29:26.573855Z"},"content_sha256":"151ad795fca03389f41f9191a7c64f2768192c0162d14b4c809071a4d41a9ee6","schema_version":"1.0","event_id":"sha256:151ad795fca03389f41f9191a7c64f2768192c0162d14b4c809071a4d41a9ee6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WPO4EK23QGVYSMLLGCB47BVF6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On distortion in groups of homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.DS","authors_text":"Jarek K\\k{e}dra, \\'Swiatos{\\l}aw Gal","submitted_at":"2011-11-06T20:15:54Z","abstract_excerpt":"Let X be a path-connected topological space admitting a universal cover. Let Homeo(X,a) denote the group of homeomorphisms of X preserving degree one cohomology class a.\n  We investigate the distortion in Homeo(X,a). Let g be an element of Homeo(X,a). We define a Nielsen-type equivalence relation on the space of g-invariant Borel probability measures on X and prove that if a homeomorphism g admits two nonequivalent invariant measures then it is undistorted. We also define a local rotation number of a homeomorphism generalising the notion of the rotation of a homeomorphism of the circle. Then w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1449","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iYrJXdu/OTCl3d4yFv90mES9EuGeNpyC+LnCwYF4l2f8W8rmTJ+OFEh3kviPAPzu9LHCt7DwAkJjZaA2nVjrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:29:26.574184Z"},"content_sha256":"7fca279dfc9be3c7c47031596b8cca7375e9bd160c2dfbea19a1f452558ae928","schema_version":"1.0","event_id":"sha256:7fca279dfc9be3c7c47031596b8cca7375e9bd160c2dfbea19a1f452558ae928"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPO4EK23QGVYSMLLGCB47BVF6Z/bundle.json","state_url":"https://pith.science/pith/WPO4EK23QGVYSMLLGCB47BVF6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPO4EK23QGVYSMLLGCB47BVF6Z/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":"2026-06-20T06:29:26Z","links":{"resolver":"https://pith.science/pith/WPO4EK23QGVYSMLLGCB47BVF6Z","bundle":"https://pith.science/pith/WPO4EK23QGVYSMLLGCB47BVF6Z/bundle.json","state":"https://pith.science/pith/WPO4EK23QGVYSMLLGCB47BVF6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPO4EK23QGVYSMLLGCB47BVF6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WPO4EK23QGVYSMLLGCB47BVF6Z","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":"6599bac843e0347e24eae7e8ff8dfa7a86bca16adc1481aff090d026459d48ec","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T20:15:54Z","title_canon_sha256":"632df8817752d636408aa58ef291f81295229e3648fbbc755c345b534ed6cc4c"},"schema_version":"1.0","source":{"id":"1111.1449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1449","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1449v1","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1449","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"WPO4EK23QGVY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WPO4EK23QGVYSMLL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WPO4EK23","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:7fca279dfc9be3c7c47031596b8cca7375e9bd160c2dfbea19a1f452558ae928","target":"graph","created_at":"2026-05-18T04:07:53Z","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 X be a path-connected topological space admitting a universal cover. Let Homeo(X,a) denote the group of homeomorphisms of X preserving degree one cohomology class a.\n  We investigate the distortion in Homeo(X,a). Let g be an element of Homeo(X,a). We define a Nielsen-type equivalence relation on the space of g-invariant Borel probability measures on X and prove that if a homeomorphism g admits two nonequivalent invariant measures then it is undistorted. We also define a local rotation number of a homeomorphism generalising the notion of the rotation of a homeomorphism of the circle. Then w","authors_text":"Jarek K\\k{e}dra, \\'Swiatos{\\l}aw Gal","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T20:15:54Z","title":"On distortion in groups of homeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1449","kind":"arxiv","version":1},"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":"sha256:151ad795fca03389f41f9191a7c64f2768192c0162d14b4c809071a4d41a9ee6","target":"record","created_at":"2026-05-18T04:07:53Z","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":"6599bac843e0347e24eae7e8ff8dfa7a86bca16adc1481aff090d026459d48ec","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-06T20:15:54Z","title_canon_sha256":"632df8817752d636408aa58ef291f81295229e3648fbbc755c345b534ed6cc4c"},"schema_version":"1.0","source":{"id":"1111.1449","kind":"arxiv","version":1}},"canonical_sha256":"b3ddc22b5b81ab89316b3083cf86a5f65595008cf7b00f8e5bb3d68d21c2503c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3ddc22b5b81ab89316b3083cf86a5f65595008cf7b00f8e5bb3d68d21c2503c","first_computed_at":"2026-05-18T04:07:53.713290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:53.713290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cubtuc/rCFUuqKDhYAViDwF78aBC8Q91DZfQ/JIBFBHF/ST/VpfgutA75GHGWIoMhzJcV4qzycC8cxi5eBYdDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:53.713824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:151ad795fca03389f41f9191a7c64f2768192c0162d14b4c809071a4d41a9ee6","sha256:7fca279dfc9be3c7c47031596b8cca7375e9bd160c2dfbea19a1f452558ae928"],"state_sha256":"3330b64e3176d03cc1e01976cfce0adf3b33ab5bcad00993f685febbbd26454e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HIYiMq8LEOS+qQMAlLfttMcxfWDjdYLC/QttnwVd15xtN2tsgpu3KxOIntSmYFEivfEPHQ8fNhQ+fd6xCtPBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:29:26.576064Z","bundle_sha256":"0fb373907807eb2869c4991f05de2d2d1497e276c580bb59b675efeaa874846d"}}