{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2FHZK6W3S2R7L7GRVYIKXTBYBW","short_pith_number":"pith:2FHZK6W3","canonical_record":{"source":{"id":"1106.1629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-08T19:31:33Z","cross_cats_sorted":[],"title_canon_sha256":"010fd27eba51bd23e7b99374551df2ee5a974a71e80890f32107d3a38a1ecdd2","abstract_canon_sha256":"9f0541640ec19f97521fa866e50f5d4ca70cb711bbee189432e994b5c8b8f223"},"schema_version":"1.0"},"canonical_sha256":"d14f957adb96a3f5fcd1ae10abcc380db3e0a70354493ef19d79f97806c91096","source":{"kind":"arxiv","id":"1106.1629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1629","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1629v1","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1629","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"2FHZK6W3S2R7","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2FHZK6W3S2R7L7GR","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2FHZK6W3","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2FHZK6W3S2R7L7GRVYIKXTBYBW","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-08T19:31:33Z","cross_cats_sorted":[],"title_canon_sha256":"010fd27eba51bd23e7b99374551df2ee5a974a71e80890f32107d3a38a1ecdd2","abstract_canon_sha256":"9f0541640ec19f97521fa866e50f5d4ca70cb711bbee189432e994b5c8b8f223"},"schema_version":"1.0"},"canonical_sha256":"d14f957adb96a3f5fcd1ae10abcc380db3e0a70354493ef19d79f97806c91096","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:22.626748Z","signature_b64":"O0Bd+/0aHKj6lvGaV1Ece3PM7YcVXK3ylZkM0C/mVGsvmO359MUrbDyTG0jkn8Cl/Rn4piKnbIFjVbn6aSX4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d14f957adb96a3f5fcd1ae10abcc380db3e0a70354493ef19d79f97806c91096","last_reissued_at":"2026-05-18T04:20:22.626156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:22.626156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1629","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":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMv8dYsQ8cytkDbfoF+DDXia5ZNTQ0nfFLzmb8mgwQyWoVR4kEfELrehNyTjgBVt82mHijJNQ5WFNlosQXeQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:54:03.331385Z"},"content_sha256":"649bd6a9e355becad24370a7683a57dd4fa07d8a6a6dd4d98dfeac5810074360","schema_version":"1.0","event_id":"sha256:649bd6a9e355becad24370a7683a57dd4fa07d8a6a6dd4d98dfeac5810074360"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2FHZK6W3S2R7L7GRVYIKXTBYBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniquely Universal Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Arnold W. Miller","submitted_at":"2011-06-08T19:31:33Z","abstract_excerpt":"We say that X x Y satisfies the Uniquely Universal property (UU) iff there exists a set U open in X x Y such that for every open set W in Y there is a unique cross section U_x of U with U_x=W. Michael Hrusak raised the question of when does X x Y satisfy UU and noted that if Y is compact then X must have an isolated point.\n  We prove the following:\n  1. If Y is a locally compact noncompact Polish space,\n  then C x Y has UU where C is the Cantor space.\n  2. If Y is Polish, then B x Y has UU iff Y is not compact\n  where B is the Baire space.\n  3. If Y is a sigma-compact subset of a Polish space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1629","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":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IDsQClcx5+3ZajzmpbAu1dhQN8Ext0QGHTzlE3kba+XV/cPUVpe0xTOFf+Fc0qL+d0QzOzlk1RIWprQoXhpzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:54:03.331726Z"},"content_sha256":"aef575387c8aed66fb176e20c5e74b932cfbac5694b54065f6e59ffdeb8f4267","schema_version":"1.0","event_id":"sha256:aef575387c8aed66fb176e20c5e74b932cfbac5694b54065f6e59ffdeb8f4267"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW/bundle.json","state_url":"https://pith.science/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW/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":"2026-06-20T06:54:03Z","links":{"resolver":"https://pith.science/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW","bundle":"https://pith.science/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW/bundle.json","state":"https://pith.science/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FHZK6W3S2R7L7GRVYIKXTBYBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2FHZK6W3S2R7L7GRVYIKXTBYBW","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":"9f0541640ec19f97521fa866e50f5d4ca70cb711bbee189432e994b5c8b8f223","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-08T19:31:33Z","title_canon_sha256":"010fd27eba51bd23e7b99374551df2ee5a974a71e80890f32107d3a38a1ecdd2"},"schema_version":"1.0","source":{"id":"1106.1629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1629","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1629v1","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1629","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"2FHZK6W3S2R7","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2FHZK6W3S2R7L7GR","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2FHZK6W3","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:aef575387c8aed66fb176e20c5e74b932cfbac5694b54065f6e59ffdeb8f4267","target":"graph","created_at":"2026-05-18T04:20:22Z","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 say that X x Y satisfies the Uniquely Universal property (UU) iff there exists a set U open in X x Y such that for every open set W in Y there is a unique cross section U_x of U with U_x=W. Michael Hrusak raised the question of when does X x Y satisfy UU and noted that if Y is compact then X must have an isolated point.\n  We prove the following:\n  1. If Y is a locally compact noncompact Polish space,\n  then C x Y has UU where C is the Cantor space.\n  2. If Y is Polish, then B x Y has UU iff Y is not compact\n  where B is the Baire space.\n  3. If Y is a sigma-compact subset of a Polish space ","authors_text":"Arnold W. Miller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-08T19:31:33Z","title":"Uniquely Universal Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1629","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":"sha256:649bd6a9e355becad24370a7683a57dd4fa07d8a6a6dd4d98dfeac5810074360","target":"record","created_at":"2026-05-18T04:20:22Z","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":"9f0541640ec19f97521fa866e50f5d4ca70cb711bbee189432e994b5c8b8f223","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-08T19:31:33Z","title_canon_sha256":"010fd27eba51bd23e7b99374551df2ee5a974a71e80890f32107d3a38a1ecdd2"},"schema_version":"1.0","source":{"id":"1106.1629","kind":"arxiv","version":1}},"canonical_sha256":"d14f957adb96a3f5fcd1ae10abcc380db3e0a70354493ef19d79f97806c91096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d14f957adb96a3f5fcd1ae10abcc380db3e0a70354493ef19d79f97806c91096","first_computed_at":"2026-05-18T04:20:22.626156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:22.626156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O0Bd+/0aHKj6lvGaV1Ece3PM7YcVXK3ylZkM0C/mVGsvmO359MUrbDyTG0jkn8Cl/Rn4piKnbIFjVbn6aSX4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:22.626748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:649bd6a9e355becad24370a7683a57dd4fa07d8a6a6dd4d98dfeac5810074360","sha256:aef575387c8aed66fb176e20c5e74b932cfbac5694b54065f6e59ffdeb8f4267"],"state_sha256":"ebdc2a586dff26c55560238cbaccf163478aaaaed94a06c335039dffd8a43a75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oyRBMtQkyE/6n6v4wvBcO6IElpJeAe+elzmGE17JxcpYCYkJoi7QtZEes3FT7kAHGsOZDA+4Jn3f2dlGjxFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:54:03.333514Z","bundle_sha256":"feadc30b58d26c25565cf57b7890d9204404c81524d78638205f952a32fec556"}}