{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:R4O45GRUPGGZGZP35JBOQ2B2K5","short_pith_number":"pith:R4O45GRU","canonical_record":{"source":{"id":"2410.17905","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-23T14:25:56Z","cross_cats_sorted":["math.FA","math.GN"],"title_canon_sha256":"74e58c9713bb90b99f3b0ed4af597f803471384a364bf9f914bdee760c244960","abstract_canon_sha256":"3286f1d509156f8ba6ed63f346a2626ae5afb603e0ac3d3b71db015c760d24c5"},"schema_version":"1.0"},"canonical_sha256":"8f1dce9a34798d9365fbea42e8683a5752c5184a6cc74f8ddd5265e996115d5d","source":{"kind":"arxiv","id":"2410.17905","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17905","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17905v3","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17905","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"R4O45GRUPGGZ","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"pith_short_16","alias_value":"R4O45GRUPGGZGZP3","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"pith_short_8","alias_value":"R4O45GRU","created_at":"2026-05-29T02:05:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:R4O45GRUPGGZGZP35JBOQ2B2K5","target":"record","payload":{"canonical_record":{"source":{"id":"2410.17905","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-23T14:25:56Z","cross_cats_sorted":["math.FA","math.GN"],"title_canon_sha256":"74e58c9713bb90b99f3b0ed4af597f803471384a364bf9f914bdee760c244960","abstract_canon_sha256":"3286f1d509156f8ba6ed63f346a2626ae5afb603e0ac3d3b71db015c760d24c5"},"schema_version":"1.0"},"canonical_sha256":"8f1dce9a34798d9365fbea42e8683a5752c5184a6cc74f8ddd5265e996115d5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:33.626423Z","signature_b64":"fKaSj/oJJHnRd1DY1c33FXVSCO0VTT5o8GBfey5NIxH8dppXNHNBGkaO1GO0JkgALukdp9aiG51d1qm0wm3cDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f1dce9a34798d9365fbea42e8683a5752c5184a6cc74f8ddd5265e996115d5d","last_reissued_at":"2026-05-29T02:05:33.625389Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:33.625389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.17905","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PDYbwkdiRZPBjGtDtz4VZxzCA3N+/18yCoYbG6DIjR/ZrCE1hgfVCDT8GjOvxS+u+aHy/gs67pMtKafWshW3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:11:27.282075Z"},"content_sha256":"b5813da88537719a037588a60360514bad0230a8d0e17ad0e54644ed47789efb","schema_version":"1.0","event_id":"sha256:b5813da88537719a037588a60360514bad0230a8d0e17ad0e54644ed47789efb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:R4O45GRUPGGZGZP35JBOQ2B2K5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Key subgroups in the Polish group of all automorphisms of the rational circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GN"],"primary_cat":"math.DS","authors_text":"Michael Megrelishvili","submitted_at":"2024-10-23T14:25:56Z","abstract_excerpt":"Extending some results of a joint work with E. Glasner, we continue to study the Polish group $G:=\\mathrm{Aut}(\\mathbb{Q}_0)$ of all circular order preserving permutations of the rational circle $\\mathbb Q_0=\\mathbb Q/\\mathbb Z$, endowed with the pointwise topology. We show that the point stabilizers $H=G_q$ are extremely amenable inj-key subgroups of $G$ (that is, they distinguish coarser Hausdorff group topologies on $G$), but are not co-minimal in $G$. These examples answer a question posed in a joint work with M. Shlossberg and are inspired by a question of V. Pestov concerning Polish grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17905","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.17905/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-29T02:05:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/qk403M92Ine7RXO0BdeEouE97CxZjFT/wKjJo8VOKoWVjFH16SXQQZIKYZlog2p7XOqDh3AvGHuWlk28IH/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:11:27.282820Z"},"content_sha256":"7aea13e50fa60f348695c5f65a4cbd64649594a8b380b330c6a1bec8ede4a236","schema_version":"1.0","event_id":"sha256:7aea13e50fa60f348695c5f65a4cbd64649594a8b380b330c6a1bec8ede4a236"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4O45GRUPGGZGZP35JBOQ2B2K5/bundle.json","state_url":"https://pith.science/pith/R4O45GRUPGGZGZP35JBOQ2B2K5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4O45GRUPGGZGZP35JBOQ2B2K5/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":"2026-06-10T11:11:27Z","links":{"resolver":"https://pith.science/pith/R4O45GRUPGGZGZP35JBOQ2B2K5","bundle":"https://pith.science/pith/R4O45GRUPGGZGZP35JBOQ2B2K5/bundle.json","state":"https://pith.science/pith/R4O45GRUPGGZGZP35JBOQ2B2K5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4O45GRUPGGZGZP35JBOQ2B2K5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:R4O45GRUPGGZGZP35JBOQ2B2K5","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":"3286f1d509156f8ba6ed63f346a2626ae5afb603e0ac3d3b71db015c760d24c5","cross_cats_sorted":["math.FA","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-23T14:25:56Z","title_canon_sha256":"74e58c9713bb90b99f3b0ed4af597f803471384a364bf9f914bdee760c244960"},"schema_version":"1.0","source":{"id":"2410.17905","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17905","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17905v3","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17905","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"R4O45GRUPGGZ","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"pith_short_16","alias_value":"R4O45GRUPGGZGZP3","created_at":"2026-05-29T02:05:33Z"},{"alias_kind":"pith_short_8","alias_value":"R4O45GRU","created_at":"2026-05-29T02:05:33Z"}],"graph_snapshots":[{"event_id":"sha256:7aea13e50fa60f348695c5f65a4cbd64649594a8b380b330c6a1bec8ede4a236","target":"graph","created_at":"2026-05-29T02:05:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.17905/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Extending some results of a joint work with E. Glasner, we continue to study the Polish group $G:=\\mathrm{Aut}(\\mathbb{Q}_0)$ of all circular order preserving permutations of the rational circle $\\mathbb Q_0=\\mathbb Q/\\mathbb Z$, endowed with the pointwise topology. We show that the point stabilizers $H=G_q$ are extremely amenable inj-key subgroups of $G$ (that is, they distinguish coarser Hausdorff group topologies on $G$), but are not co-minimal in $G$. These examples answer a question posed in a joint work with M. Shlossberg and are inspired by a question of V. Pestov concerning Polish grou","authors_text":"Michael Megrelishvili","cross_cats":["math.FA","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-23T14:25:56Z","title":"Key subgroups in the Polish group of all automorphisms of the rational circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17905","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:b5813da88537719a037588a60360514bad0230a8d0e17ad0e54644ed47789efb","target":"record","created_at":"2026-05-29T02:05:33Z","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":"3286f1d509156f8ba6ed63f346a2626ae5afb603e0ac3d3b71db015c760d24c5","cross_cats_sorted":["math.FA","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-10-23T14:25:56Z","title_canon_sha256":"74e58c9713bb90b99f3b0ed4af597f803471384a364bf9f914bdee760c244960"},"schema_version":"1.0","source":{"id":"2410.17905","kind":"arxiv","version":3}},"canonical_sha256":"8f1dce9a34798d9365fbea42e8683a5752c5184a6cc74f8ddd5265e996115d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f1dce9a34798d9365fbea42e8683a5752c5184a6cc74f8ddd5265e996115d5d","first_computed_at":"2026-05-29T02:05:33.625389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:33.625389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fKaSj/oJJHnRd1DY1c33FXVSCO0VTT5o8GBfey5NIxH8dppXNHNBGkaO1GO0JkgALukdp9aiG51d1qm0wm3cDA==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:33.626423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.17905","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5813da88537719a037588a60360514bad0230a8d0e17ad0e54644ed47789efb","sha256:7aea13e50fa60f348695c5f65a4cbd64649594a8b380b330c6a1bec8ede4a236"],"state_sha256":"d5afed7960cbc3be580d1363065c07ab15022865125ec81f8c2fbb940ddd75e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7U83sPmzFF2Mp6+ZQ0NduYl4H8G/oqxS1EzjGfuuYG5qCxE/A4eDQ2YvQMkxDmHXdSxYLjrHOvh9yONCDvmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:11:27.286835Z","bundle_sha256":"4532fa6785bc137bc0aaf616da4aed99ec2d5f20ebbbb856fd01e96c04369bc7"}}