{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:B645AUOIM6OMEUOQRYLTKVTZSO","short_pith_number":"pith:B645AUOI","canonical_record":{"source":{"id":"1105.6221","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-31T09:39:24Z","cross_cats_sorted":[],"title_canon_sha256":"199e5bc5c7024e5bb5c57d2f405c31c679ed7e67bee2cdbbbf548cd4e0dfeb73","abstract_canon_sha256":"80f0546ef4cacaba257644bacb533f53a8de8d5ae103b4d3f9250fbc9725fc41"},"schema_version":"1.0"},"canonical_sha256":"0fb9d051c8679cc251d08e173556799384e907c6e3cfbee732217e50d9d14208","source":{"kind":"arxiv","id":"1105.6221","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6221","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6221v5","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6221","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"B645AUOIM6OM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B645AUOIM6OMEUOQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B645AUOI","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:B645AUOIM6OMEUOQRYLTKVTZSO","target":"record","payload":{"canonical_record":{"source":{"id":"1105.6221","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-31T09:39:24Z","cross_cats_sorted":[],"title_canon_sha256":"199e5bc5c7024e5bb5c57d2f405c31c679ed7e67bee2cdbbbf548cd4e0dfeb73","abstract_canon_sha256":"80f0546ef4cacaba257644bacb533f53a8de8d5ae103b4d3f9250fbc9725fc41"},"schema_version":"1.0"},"canonical_sha256":"0fb9d051c8679cc251d08e173556799384e907c6e3cfbee732217e50d9d14208","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:53.494478Z","signature_b64":"LLm391P4aJn4jS++1RBin4nOiIbHUnKo/xoFzN72nAlTPLnKB77+l84V+7U3nSnQdqr226QYMhV6+TktC0aGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fb9d051c8679cc251d08e173556799384e907c6e3cfbee732217e50d9d14208","last_reissued_at":"2026-05-18T02:29:53.493615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:53.493615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.6221","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qOl+cR9qIwZyb1fUa2ABnIKBr0mG/snthV/AVIsydrtpTwYFpC9jBfLaoYUTvKoTn4zkZaDmV4JlmppgVXaSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:23:13.143578Z"},"content_sha256":"541289d57afb6976ebb989e78511d527626855d6398565240295a0577e26dbde","schema_version":"1.0","event_id":"sha256:541289d57afb6976ebb989e78511d527626855d6398565240295a0577e26dbde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:B645AUOIM6OMEUOQRYLTKVTZSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On relative extreme amenability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Lionel Nguyen Van Th\\'e, Yonatan Gutman","submitted_at":"2011-05-31T09:39:24Z","abstract_excerpt":"The purpose of this paper is to study the notion of relative extreme amenability for pairs of topological groups. We give a characterization by a fixed point property on universal spaces. In addition we introduce the concepts of an extremely amenable interpolant as well as maximally relatively extremely amenable pairs and give examples. It is shown that relative extreme amenability does not imply the existence of an extremely amenable interpolant. The theory is applied to generalize results of Kechris, Pestov and Todorcevic relating to the application of Fra\\\"{i}ss\\'e theory to the theory of D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6221","kind":"arxiv","version":5},"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":"2026-05-18T02:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0tqvOrR2iMle0svDALn3bxvm6lJETmaeOyUMOOXfFaLb1wG61T3epLMhZPfz5jDaMzLq8unNxXTHO4pTLOnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:23:13.144340Z"},"content_sha256":"9dffaccf310af33964891fea3c7ce881b4ef66b211eb9b0c54c6fd7c49d785bc","schema_version":"1.0","event_id":"sha256:9dffaccf310af33964891fea3c7ce881b4ef66b211eb9b0c54c6fd7c49d785bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B645AUOIM6OMEUOQRYLTKVTZSO/bundle.json","state_url":"https://pith.science/pith/B645AUOIM6OMEUOQRYLTKVTZSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B645AUOIM6OMEUOQRYLTKVTZSO/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":"2026-05-31T20:23:13Z","links":{"resolver":"https://pith.science/pith/B645AUOIM6OMEUOQRYLTKVTZSO","bundle":"https://pith.science/pith/B645AUOIM6OMEUOQRYLTKVTZSO/bundle.json","state":"https://pith.science/pith/B645AUOIM6OMEUOQRYLTKVTZSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B645AUOIM6OMEUOQRYLTKVTZSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:B645AUOIM6OMEUOQRYLTKVTZSO","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":"80f0546ef4cacaba257644bacb533f53a8de8d5ae103b4d3f9250fbc9725fc41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-31T09:39:24Z","title_canon_sha256":"199e5bc5c7024e5bb5c57d2f405c31c679ed7e67bee2cdbbbf548cd4e0dfeb73"},"schema_version":"1.0","source":{"id":"1105.6221","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6221","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6221v5","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6221","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"B645AUOIM6OM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B645AUOIM6OMEUOQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B645AUOI","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:9dffaccf310af33964891fea3c7ce881b4ef66b211eb9b0c54c6fd7c49d785bc","target":"graph","created_at":"2026-05-18T02:29:53Z","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":"The purpose of this paper is to study the notion of relative extreme amenability for pairs of topological groups. We give a characterization by a fixed point property on universal spaces. In addition we introduce the concepts of an extremely amenable interpolant as well as maximally relatively extremely amenable pairs and give examples. It is shown that relative extreme amenability does not imply the existence of an extremely amenable interpolant. The theory is applied to generalize results of Kechris, Pestov and Todorcevic relating to the application of Fra\\\"{i}ss\\'e theory to the theory of D","authors_text":"Lionel Nguyen Van Th\\'e, Yonatan Gutman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-31T09:39:24Z","title":"On relative extreme amenability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6221","kind":"arxiv","version":5},"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":"sha256:541289d57afb6976ebb989e78511d527626855d6398565240295a0577e26dbde","target":"record","created_at":"2026-05-18T02:29:53Z","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":"80f0546ef4cacaba257644bacb533f53a8de8d5ae103b4d3f9250fbc9725fc41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-31T09:39:24Z","title_canon_sha256":"199e5bc5c7024e5bb5c57d2f405c31c679ed7e67bee2cdbbbf548cd4e0dfeb73"},"schema_version":"1.0","source":{"id":"1105.6221","kind":"arxiv","version":5}},"canonical_sha256":"0fb9d051c8679cc251d08e173556799384e907c6e3cfbee732217e50d9d14208","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fb9d051c8679cc251d08e173556799384e907c6e3cfbee732217e50d9d14208","first_computed_at":"2026-05-18T02:29:53.493615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.493615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LLm391P4aJn4jS++1RBin4nOiIbHUnKo/xoFzN72nAlTPLnKB77+l84V+7U3nSnQdqr226QYMhV6+TktC0aGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.494478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.6221","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:541289d57afb6976ebb989e78511d527626855d6398565240295a0577e26dbde","sha256:9dffaccf310af33964891fea3c7ce881b4ef66b211eb9b0c54c6fd7c49d785bc"],"state_sha256":"11fa4043876c07fc80c07e51e53bfbe442683d304e386e71d9f4bc046062de5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7mEZGQSkZVj4eW34DtIbqfqrF08MawKUqpoQ416lhqNsY9p5zRCYY8dX0U8NgHQTIHE7z2sFXCsJq59/koNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:23:13.148961Z","bundle_sha256":"f1f2382c3999557cdcdcc0ae67178bf2dc689d4146d19bfd64b346b0d3ff449a"}}