{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VEIIBIOPBWDP72IRPO3CHQ6ZT7","short_pith_number":"pith:VEIIBIOP","canonical_record":{"source":{"id":"1106.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-01T08:47:07Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f6f8d335dc100a148027377f1ef584b52cc7e9251d0f216dfdfafbe7e7356025","abstract_canon_sha256":"5987386e114a3dd5b0daed14e391202b012e71d71372432edb167a5063979e09"},"schema_version":"1.0"},"canonical_sha256":"a91080a1cf0d86ffe9117bb623c3d99fe894231e4f29add39f6c8523b550e83e","source":{"kind":"arxiv","id":"1106.0121","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0121","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0121v2","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0121","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"VEIIBIOPBWDP","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VEIIBIOPBWDP72IR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VEIIBIOP","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VEIIBIOPBWDP72IRPO3CHQ6ZT7","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-01T08:47:07Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f6f8d335dc100a148027377f1ef584b52cc7e9251d0f216dfdfafbe7e7356025","abstract_canon_sha256":"5987386e114a3dd5b0daed14e391202b012e71d71372432edb167a5063979e09"},"schema_version":"1.0"},"canonical_sha256":"a91080a1cf0d86ffe9117bb623c3d99fe894231e4f29add39f6c8523b550e83e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:07.258173Z","signature_b64":"tuLp71aHnqlNpWJAEMA60eQ/XOxQ0ru/OoXFXSTKAJQ3Yz7CEZBveOD2v+kcFT9plH4kTdWLg8QPuZa38XukBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a91080a1cf0d86ffe9117bb623c3d99fe894231e4f29add39f6c8523b550e83e","last_reissued_at":"2026-05-18T04:11:07.257669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:07.257669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0121","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":"2026-05-18T04:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ct6+HD/gyZJi1yQQu79+UGEZklwPG8PdnJNlyTdPUP13tdIh4SXdtZwB87y10OLZ++TQn0acy+zk30juycj9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:20:41.836020Z"},"content_sha256":"cfc4ec368ae359de2f0cfebc08d37670d71edd73847f30f362c1c50e79ba7072","schema_version":"1.0","event_id":"sha256:cfc4ec368ae359de2f0cfebc08d37670d71edd73847f30f362c1c50e79ba7072"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VEIIBIOPBWDP72IRPO3CHQ6ZT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The universal minimal space for groups of homeomorphisms of h-homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Eli Glasner, Yonatan Gutman","submitted_at":"2011-06-01T08:47:07Z","abstract_excerpt":"Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. It is shown that the universal minimal space M(G) of the topological group G=Homeo(X), is the space of maximal chains on X introduced by Uspenskij. If X is metrizable then clearly X is homeomorphic to the Cantor set and the result was already known (Glasner-Weiss 2003). However many new examples arise for non-metrizable spaces. These include, among others, the generalized Cantor sets X={0,1}^{kappa} for non-countable cardinals kappa, and the corona or remainder of omega, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0121","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":"2026-05-18T04:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ApHToNNE5+JlfMKfrQQLmvszS3kWa0HGPDwYGyXaYLzxqWhJDa+yTY6GDJr1KwDg+MGVkQ2x9fMbx2W0/T0cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:20:41.836401Z"},"content_sha256":"67ab74bef8d4b03ed487bf2a97927e3fb423320d8a9fdd2bed56531c70874d4d","schema_version":"1.0","event_id":"sha256:67ab74bef8d4b03ed487bf2a97927e3fb423320d8a9fdd2bed56531c70874d4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7/bundle.json","state_url":"https://pith.science/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7/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":"2026-05-31T20:20:41Z","links":{"resolver":"https://pith.science/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7","bundle":"https://pith.science/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7/bundle.json","state":"https://pith.science/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VEIIBIOPBWDP72IRPO3CHQ6ZT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VEIIBIOPBWDP72IRPO3CHQ6ZT7","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":"5987386e114a3dd5b0daed14e391202b012e71d71372432edb167a5063979e09","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-01T08:47:07Z","title_canon_sha256":"f6f8d335dc100a148027377f1ef584b52cc7e9251d0f216dfdfafbe7e7356025"},"schema_version":"1.0","source":{"id":"1106.0121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0121","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0121v2","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0121","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"VEIIBIOPBWDP","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VEIIBIOPBWDP72IR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VEIIBIOP","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:67ab74bef8d4b03ed487bf2a97927e3fb423320d8a9fdd2bed56531c70874d4d","target":"graph","created_at":"2026-05-18T04:11:07Z","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 h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. It is shown that the universal minimal space M(G) of the topological group G=Homeo(X), is the space of maximal chains on X introduced by Uspenskij. If X is metrizable then clearly X is homeomorphic to the Cantor set and the result was already known (Glasner-Weiss 2003). However many new examples arise for non-metrizable spaces. These include, among others, the generalized Cantor sets X={0,1}^{kappa} for non-countable cardinals kappa, and the corona or remainder of omega, ","authors_text":"Eli Glasner, Yonatan Gutman","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-01T08:47:07Z","title":"The universal minimal space for groups of homeomorphisms of h-homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0121","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:cfc4ec368ae359de2f0cfebc08d37670d71edd73847f30f362c1c50e79ba7072","target":"record","created_at":"2026-05-18T04:11:07Z","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":"5987386e114a3dd5b0daed14e391202b012e71d71372432edb167a5063979e09","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-01T08:47:07Z","title_canon_sha256":"f6f8d335dc100a148027377f1ef584b52cc7e9251d0f216dfdfafbe7e7356025"},"schema_version":"1.0","source":{"id":"1106.0121","kind":"arxiv","version":2}},"canonical_sha256":"a91080a1cf0d86ffe9117bb623c3d99fe894231e4f29add39f6c8523b550e83e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a91080a1cf0d86ffe9117bb623c3d99fe894231e4f29add39f6c8523b550e83e","first_computed_at":"2026-05-18T04:11:07.257669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:07.257669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tuLp71aHnqlNpWJAEMA60eQ/XOxQ0ru/OoXFXSTKAJQ3Yz7CEZBveOD2v+kcFT9plH4kTdWLg8QPuZa38XukBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:07.258173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfc4ec368ae359de2f0cfebc08d37670d71edd73847f30f362c1c50e79ba7072","sha256:67ab74bef8d4b03ed487bf2a97927e3fb423320d8a9fdd2bed56531c70874d4d"],"state_sha256":"f9551b62b931f8270cb63164c161acf65d12f402251b0a4c1acba2739f8e36e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzl+waNRoxPChBbwsfOMVP5KUc59XRzj0B0rIcJM2M7tBcJF+Oqi7VKNFxv5UB0ONDrFQX+ehQBeHaw7qN7fAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:20:41.839091Z","bundle_sha256":"b618a45299823338fc556770ac6ca4f3aa7bce6526d1d979ba6b83247b397799"}}