{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UUAD7DN6OFACS7GTVFE2Z2W7PB","short_pith_number":"pith:UUAD7DN6","canonical_record":{"source":{"id":"1408.2137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-08-09T17:04:52Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"774fbb7bcd74069fb38b9fd564d6240bd9cbb9b45b8d439f6e3dddcbc4e71e09","abstract_canon_sha256":"69dd1bddb76c559cd739a185a690945f228d77cf9e6f92656fceb9397b6e8d2f"},"schema_version":"1.0"},"canonical_sha256":"a5003f8dbe7140297cd3a949aceadf787ddf9e359407c5e8e5888fc72297b47a","source":{"kind":"arxiv","id":"1408.2137","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2137","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2137v2","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2137","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"UUAD7DN6OFAC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UUAD7DN6OFACS7GT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UUAD7DN6","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UUAD7DN6OFACS7GTVFE2Z2W7PB","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-08-09T17:04:52Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"774fbb7bcd74069fb38b9fd564d6240bd9cbb9b45b8d439f6e3dddcbc4e71e09","abstract_canon_sha256":"69dd1bddb76c559cd739a185a690945f228d77cf9e6f92656fceb9397b6e8d2f"},"schema_version":"1.0"},"canonical_sha256":"a5003f8dbe7140297cd3a949aceadf787ddf9e359407c5e8e5888fc72297b47a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:51.966611Z","signature_b64":"wNeL92MWcnCw7fcP+LDfBKTRihb/GACBTgX6SCSAUB8KYa4KsPkLvN+11E8RO/PB4FpYuwYrxndPEg5gKBJBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5003f8dbe7140297cd3a949aceadf787ddf9e359407c5e8e5888fc72297b47a","last_reissued_at":"2026-05-18T02:17:51.965933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:51.965933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2137","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":"2026-05-18T02:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nSkcp6Bn0x+jE4Bb2Kd51lQ4UhCQ6rAw04Vmxr2/9Uf9FjlFwUP4iQ/ic9uLwvMP+hMcehJo5RLnTILKbgGjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:51:11.013799Z"},"content_sha256":"b9e3347e9b21c84d8b757b4bb47f3e5fb495fe992ef8a3a405436f654467ebe6","schema_version":"1.0","event_id":"sha256:b9e3347e9b21c84d8b757b4bb47f3e5fb495fe992ef8a3a405436f654467ebe6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UUAD7DN6OFACS7GTVFE2Z2W7PB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Countable dense homogeneity in powers of zero-dimensional definable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Andrea Medini","submitted_at":"2014-08-09T17:04:52Z","abstract_excerpt":"We show that, for a coanalytic subspace $X$ of $2^\\omega$, the countable dense homogeneity of $X^\\omega$ is equivalent to $X$ being Polish. This strengthens a result of Hru\\v{s}\\'ak and Zamora Avil\\'es. Then, inspired by results of Hern\\'andez-Guti\\'errez, Hru\\v{s}\\'ak and van Mill, using a technique of Medvedev, we construct a non-Polish subspace $X$ of $2^\\omega$ such that $X^\\omega$ is countable dense homogeneous. This gives the first $\\mathsf{ZFC}$ answer to a question of Hru\\v{s}\\'ak and Zamora Avil\\'es. Furthermore, since our example is consistently analytic, the equivalence result menti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2137","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":"2026-05-18T02:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a2BCV2zD8FyoYD+i7W9MxdGdn320kOrJqGYoNvZv9Fq6kz5xSC73iFMFM+porDhMj69cyVJq+rN13f+M7w9pDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:51:11.014142Z"},"content_sha256":"4eac7a4d492eb526bf913396e13f26b3f35c91958822885575cb75cc0b4d7a4c","schema_version":"1.0","event_id":"sha256:4eac7a4d492eb526bf913396e13f26b3f35c91958822885575cb75cc0b4d7a4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB/bundle.json","state_url":"https://pith.science/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB/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":"2026-06-27T15:51:11Z","links":{"resolver":"https://pith.science/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB","bundle":"https://pith.science/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB/bundle.json","state":"https://pith.science/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUAD7DN6OFACS7GTVFE2Z2W7PB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UUAD7DN6OFACS7GTVFE2Z2W7PB","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":"69dd1bddb76c559cd739a185a690945f228d77cf9e6f92656fceb9397b6e8d2f","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-08-09T17:04:52Z","title_canon_sha256":"774fbb7bcd74069fb38b9fd564d6240bd9cbb9b45b8d439f6e3dddcbc4e71e09"},"schema_version":"1.0","source":{"id":"1408.2137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2137","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2137v2","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2137","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"UUAD7DN6OFAC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UUAD7DN6OFACS7GT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UUAD7DN6","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:4eac7a4d492eb526bf913396e13f26b3f35c91958822885575cb75cc0b4d7a4c","target":"graph","created_at":"2026-05-18T02:17:51Z","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":"We show that, for a coanalytic subspace $X$ of $2^\\omega$, the countable dense homogeneity of $X^\\omega$ is equivalent to $X$ being Polish. This strengthens a result of Hru\\v{s}\\'ak and Zamora Avil\\'es. Then, inspired by results of Hern\\'andez-Guti\\'errez, Hru\\v{s}\\'ak and van Mill, using a technique of Medvedev, we construct a non-Polish subspace $X$ of $2^\\omega$ such that $X^\\omega$ is countable dense homogeneous. This gives the first $\\mathsf{ZFC}$ answer to a question of Hru\\v{s}\\'ak and Zamora Avil\\'es. Furthermore, since our example is consistently analytic, the equivalence result menti","authors_text":"Andrea Medini","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-08-09T17:04:52Z","title":"Countable dense homogeneity in powers of zero-dimensional definable spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2137","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:b9e3347e9b21c84d8b757b4bb47f3e5fb495fe992ef8a3a405436f654467ebe6","target":"record","created_at":"2026-05-18T02:17:51Z","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":"69dd1bddb76c559cd739a185a690945f228d77cf9e6f92656fceb9397b6e8d2f","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-08-09T17:04:52Z","title_canon_sha256":"774fbb7bcd74069fb38b9fd564d6240bd9cbb9b45b8d439f6e3dddcbc4e71e09"},"schema_version":"1.0","source":{"id":"1408.2137","kind":"arxiv","version":2}},"canonical_sha256":"a5003f8dbe7140297cd3a949aceadf787ddf9e359407c5e8e5888fc72297b47a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5003f8dbe7140297cd3a949aceadf787ddf9e359407c5e8e5888fc72297b47a","first_computed_at":"2026-05-18T02:17:51.965933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:51.965933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wNeL92MWcnCw7fcP+LDfBKTRihb/GACBTgX6SCSAUB8KYa4KsPkLvN+11E8RO/PB4FpYuwYrxndPEg5gKBJBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:51.966611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9e3347e9b21c84d8b757b4bb47f3e5fb495fe992ef8a3a405436f654467ebe6","sha256:4eac7a4d492eb526bf913396e13f26b3f35c91958822885575cb75cc0b4d7a4c"],"state_sha256":"5bfa9ee306ec8f7f46d6523e0c885c2b7121aedbb1cd9667f61e7107ce03f7a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CdIKIuPH0OCbaxcZGDk151o3kL5IrhAGS9h6U80Zb0VV5LkIamZsZ5xjCh+QOfNT4REH2wtIfzRYEBEdFV3ABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:51:11.016006Z","bundle_sha256":"53d72cd08fcb9bdf4422a6d77b46ccf22a91f8d76708c24a2bfb394133be6cc7"}}