{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CKNZK5LKN3Z2RD4QKHT6HANEWC","short_pith_number":"pith:CKNZK5LK","canonical_record":{"source":{"id":"1411.3173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-11-12T13:42:44Z","cross_cats_sorted":[],"title_canon_sha256":"6bd74711800f441b95ce34169235f5892e2ecb55cd961515ed29e16746d712a2","abstract_canon_sha256":"c7baaf2663e4ab8370b3769ee192ac702962d5aa37a48fd80a1af186cad42677"},"schema_version":"1.0"},"canonical_sha256":"129b95756a6ef3a88f9051e7e381a4b08219e7994832a3d2e32ede56f154d1a2","source":{"kind":"arxiv","id":"1411.3173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3173","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3173v1","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3173","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"CKNZK5LKN3Z2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CKNZK5LKN3Z2RD4Q","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CKNZK5LK","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CKNZK5LKN3Z2RD4QKHT6HANEWC","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-11-12T13:42:44Z","cross_cats_sorted":[],"title_canon_sha256":"6bd74711800f441b95ce34169235f5892e2ecb55cd961515ed29e16746d712a2","abstract_canon_sha256":"c7baaf2663e4ab8370b3769ee192ac702962d5aa37a48fd80a1af186cad42677"},"schema_version":"1.0"},"canonical_sha256":"129b95756a6ef3a88f9051e7e381a4b08219e7994832a3d2e32ede56f154d1a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:07.732820Z","signature_b64":"t7Bl04wO2TMSrFfkPRLBdLMLtJY2b9P53QiM47LFdkK/7x9U4NttsMRDLc6m0cxw7P7xItusEbvFV4VNs4H3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"129b95756a6ef3a88f9051e7e381a4b08219e7994832a3d2e32ede56f154d1a2","last_reissued_at":"2026-05-18T02:30:07.732360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:07.732360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3173","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":"2026-05-18T02:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y04Mh8MXxPrBy84E955NYIwKPmueNZ8zgRwAA+42aXB7DMh9C5nF5ojGrrgRbrZfpRzPdoMjk5i8Ugb1FiCDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:57:57.003166Z"},"content_sha256":"9c90f0ab3225f6523dfcb5826a5150c77f57c8700cd3ca736292ba05cb4fe570","schema_version":"1.0","event_id":"sha256:9c90f0ab3225f6523dfcb5826a5150c77f57c8700cd3ca736292ba05cb4fe570"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CKNZK5LKN3Z2RD4QKHT6HANEWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $\\alpha$-embedded subsets of products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2014-11-12T13:42:44Z","abstract_excerpt":"We prove that every continuous function $f:E\\to Y$ depends on countably many coordinates, if $E$ is an $(\\aleph_1,\\aleph_0)$-invariant pseudo-$\\aleph_1$-compact subspace of a product of topological spaces and $Y$ is a space with a regular $G_\\delta$-diagonal. Using this fact for any $\\alpha<\\omega_1$ we construct an $(\\alpha+1)$-embedded subspace of a completely regular space which is not $\\alpha$-embedded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3173","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":"2026-05-18T02:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wq+a2VJ3r8IdpYY/TsdUuhfUj3BtSl5SoNXSAT//xUC/2cxQVJJ1QcRMZh9hk8QjyPu+NuIVCs/l1PReeksBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:57:57.003639Z"},"content_sha256":"13906058d8d0f01c82b33286bf455cec394a0c2392f03d97e12871fcd57fab46","schema_version":"1.0","event_id":"sha256:13906058d8d0f01c82b33286bf455cec394a0c2392f03d97e12871fcd57fab46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC/bundle.json","state_url":"https://pith.science/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC/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":"2026-06-25T18:57:57Z","links":{"resolver":"https://pith.science/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC","bundle":"https://pith.science/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC/bundle.json","state":"https://pith.science/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKNZK5LKN3Z2RD4QKHT6HANEWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CKNZK5LKN3Z2RD4QKHT6HANEWC","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":"c7baaf2663e4ab8370b3769ee192ac702962d5aa37a48fd80a1af186cad42677","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-11-12T13:42:44Z","title_canon_sha256":"6bd74711800f441b95ce34169235f5892e2ecb55cd961515ed29e16746d712a2"},"schema_version":"1.0","source":{"id":"1411.3173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3173","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3173v1","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3173","created_at":"2026-05-18T02:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"CKNZK5LKN3Z2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CKNZK5LKN3Z2RD4Q","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CKNZK5LK","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:13906058d8d0f01c82b33286bf455cec394a0c2392f03d97e12871fcd57fab46","target":"graph","created_at":"2026-05-18T02:30:07Z","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":"We prove that every continuous function $f:E\\to Y$ depends on countably many coordinates, if $E$ is an $(\\aleph_1,\\aleph_0)$-invariant pseudo-$\\aleph_1$-compact subspace of a product of topological spaces and $Y$ is a space with a regular $G_\\delta$-diagonal. Using this fact for any $\\alpha<\\omega_1$ we construct an $(\\alpha+1)$-embedded subspace of a completely regular space which is not $\\alpha$-embedded.","authors_text":"Olena Karlova, Volodymyr Mykhaylyuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-11-12T13:42:44Z","title":"On $\\alpha$-embedded subsets of products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3173","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":"sha256:9c90f0ab3225f6523dfcb5826a5150c77f57c8700cd3ca736292ba05cb4fe570","target":"record","created_at":"2026-05-18T02:30:07Z","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":"c7baaf2663e4ab8370b3769ee192ac702962d5aa37a48fd80a1af186cad42677","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-11-12T13:42:44Z","title_canon_sha256":"6bd74711800f441b95ce34169235f5892e2ecb55cd961515ed29e16746d712a2"},"schema_version":"1.0","source":{"id":"1411.3173","kind":"arxiv","version":1}},"canonical_sha256":"129b95756a6ef3a88f9051e7e381a4b08219e7994832a3d2e32ede56f154d1a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"129b95756a6ef3a88f9051e7e381a4b08219e7994832a3d2e32ede56f154d1a2","first_computed_at":"2026-05-18T02:30:07.732360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:07.732360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t7Bl04wO2TMSrFfkPRLBdLMLtJY2b9P53QiM47LFdkK/7x9U4NttsMRDLc6m0cxw7P7xItusEbvFV4VNs4H3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:07.732820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c90f0ab3225f6523dfcb5826a5150c77f57c8700cd3ca736292ba05cb4fe570","sha256:13906058d8d0f01c82b33286bf455cec394a0c2392f03d97e12871fcd57fab46"],"state_sha256":"f0591165f9762489635edf59724af66fbcef25de9fc798da46c93d23be9781ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvrmrIggxjGTsvt3kTlAoqn75iiDjz4TMLmsuH88vBMDyvytGadAgFSgR/99T8Jh90/z9aBlwcQbfOW63eoPCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:57:57.005947Z","bundle_sha256":"814d29bca0092b48cc042cb483d1738fa2758b80e6ae5482c1ea72d1ab4e377a"}}