{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IYUX2RWW4EIJ326VXPCM5ZNZGK","short_pith_number":"pith:IYUX2RWW","canonical_record":{"source":{"id":"1311.1719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T15:51:44Z","cross_cats_sorted":[],"title_canon_sha256":"ca3c10b69298e474690b704a52be359e48dbbc05d403942fafe95f3333373c87","abstract_canon_sha256":"87c503f3775fc3f78f557c33d7a650c822eb9901d9b1ae3ba14da2e3c8d476a9"},"schema_version":"1.0"},"canonical_sha256":"46297d46d6e1109debd5bbc4cee5b932b87f7dfe63cb0cdd7f8c3d77244a69b3","source":{"kind":"arxiv","id":"1311.1719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1719","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1719v1","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1719","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"IYUX2RWW4EIJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IYUX2RWW4EIJ326V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IYUX2RWW","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IYUX2RWW4EIJ326VXPCM5ZNZGK","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T15:51:44Z","cross_cats_sorted":[],"title_canon_sha256":"ca3c10b69298e474690b704a52be359e48dbbc05d403942fafe95f3333373c87","abstract_canon_sha256":"87c503f3775fc3f78f557c33d7a650c822eb9901d9b1ae3ba14da2e3c8d476a9"},"schema_version":"1.0"},"canonical_sha256":"46297d46d6e1109debd5bbc4cee5b932b87f7dfe63cb0cdd7f8c3d77244a69b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:43.520643Z","signature_b64":"uanRmax1hdMTF4itpQ8lq88st6M9LSHbGz+dQAuar4kGbcVJoVAvZTIOyGyRXSdPRJvMF7pNJ1NgeVe6vjQkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46297d46d6e1109debd5bbc4cee5b932b87f7dfe63cb0cdd7f8c3d77244a69b3","last_reissued_at":"2026-05-18T03:07:43.519874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:43.519874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1719","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":"2026-05-18T03:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IRyb1tcMZrORvAF/fpVuMoBxohd5B1Fs0cdEAPDP6CTFq4GAwbN3GwO2zn3trOMVAxhWFb6pVIZza2SUu/ktCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:22:49.378421Z"},"content_sha256":"77d45f39174b4b744a4797a3877c86722912948332e8239bc16271970143cc82","schema_version":"1.0","event_id":"sha256:77d45f39174b4b744a4797a3877c86722912948332e8239bc16271970143cc82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IYUX2RWW4EIJ326VXPCM5ZNZGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular spaces of small extent are omega-resolvable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy","submitted_at":"2013-11-07T15:51:44Z","abstract_excerpt":"We improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character of X, is the smallest size of a non-empty open set in X and ext(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindel\\\"of spaces of uncountable dispersion character are omega-resolvable.\n  We also prove that any regular Lindel\\\"of space X with |X|=\\Delta(X)=omega_1 is even omega_1-resolvable. The questio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1719","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":"2026-05-18T03:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSVzpMrQLUh3/WkKfKyEmM6Wx/daaRkTzq5gk+yW6XJ4FElUoy9nuKGftGVDGe+9VjrdtkVVTQDezk62hNOLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:22:49.378770Z"},"content_sha256":"64bde2a80da63acaff44799719d7b933bf917b59d41cb9bee645d2bdb49ab93e","schema_version":"1.0","event_id":"sha256:64bde2a80da63acaff44799719d7b933bf917b59d41cb9bee645d2bdb49ab93e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK/bundle.json","state_url":"https://pith.science/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK/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":"2026-06-20T20:22:49Z","links":{"resolver":"https://pith.science/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK","bundle":"https://pith.science/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK/bundle.json","state":"https://pith.science/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYUX2RWW4EIJ326VXPCM5ZNZGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IYUX2RWW4EIJ326VXPCM5ZNZGK","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":"87c503f3775fc3f78f557c33d7a650c822eb9901d9b1ae3ba14da2e3c8d476a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T15:51:44Z","title_canon_sha256":"ca3c10b69298e474690b704a52be359e48dbbc05d403942fafe95f3333373c87"},"schema_version":"1.0","source":{"id":"1311.1719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1719","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1719v1","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1719","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"IYUX2RWW4EIJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IYUX2RWW4EIJ326V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IYUX2RWW","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:64bde2a80da63acaff44799719d7b933bf917b59d41cb9bee645d2bdb49ab93e","target":"graph","created_at":"2026-05-18T03:07:43Z","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 improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character of X, is the smallest size of a non-empty open set in X and ext(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindel\\\"of spaces of uncountable dispersion character are omega-resolvable.\n  We also prove that any regular Lindel\\\"of space X with |X|=\\Delta(X)=omega_1 is even omega_1-resolvable. The questio","authors_text":"Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T15:51:44Z","title":"Regular spaces of small extent are omega-resolvable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1719","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":"sha256:77d45f39174b4b744a4797a3877c86722912948332e8239bc16271970143cc82","target":"record","created_at":"2026-05-18T03:07:43Z","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":"87c503f3775fc3f78f557c33d7a650c822eb9901d9b1ae3ba14da2e3c8d476a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T15:51:44Z","title_canon_sha256":"ca3c10b69298e474690b704a52be359e48dbbc05d403942fafe95f3333373c87"},"schema_version":"1.0","source":{"id":"1311.1719","kind":"arxiv","version":1}},"canonical_sha256":"46297d46d6e1109debd5bbc4cee5b932b87f7dfe63cb0cdd7f8c3d77244a69b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46297d46d6e1109debd5bbc4cee5b932b87f7dfe63cb0cdd7f8c3d77244a69b3","first_computed_at":"2026-05-18T03:07:43.519874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:43.519874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uanRmax1hdMTF4itpQ8lq88st6M9LSHbGz+dQAuar4kGbcVJoVAvZTIOyGyRXSdPRJvMF7pNJ1NgeVe6vjQkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:43.520643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77d45f39174b4b744a4797a3877c86722912948332e8239bc16271970143cc82","sha256:64bde2a80da63acaff44799719d7b933bf917b59d41cb9bee645d2bdb49ab93e"],"state_sha256":"4bb0a2e0d14454f75f165c262a5382e814548c1daef28b2e55ef9f7345547201"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aeOGTF3t5Xzn9smzL7IgrXxoLBq+p13npinwhfRFwl2MfzHYCS86BCfpihixWkbZhX9kkHJcomflr6GqVswYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:22:49.380760Z","bundle_sha256":"fdb59c04804e8ee9fa05dcdbc1896da51af3bbf88d9ff6a905a8c5cef00ae806"}}