{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FZ5YTKA4ICAV7GCBZ65JIZZSJC","short_pith_number":"pith:FZ5YTKA4","schema_version":"1.0","canonical_sha256":"2e7b89a81c40815f9841cfba94673248a0e2ac083af930e4e0e32cfaae293262","source":{"kind":"arxiv","id":"1202.6310","version":1},"attestation_state":"computed","paper":{"title":"Are Eberlein-Grothendieck scattered spaces $\\sigma$-discrete?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Antonio Avil\\'es, David Guerrero S\\'anchez","submitted_at":"2012-02-28T18:10:46Z","abstract_excerpt":"A space $X$ is Eberlein-Grothendieck if $X\\subset C_p(K)$ for some compact space $K.$ In this paper we address the problem of whether such a space $X$ is $\\sigma$-discrete whenever it is scattered. We show that if $w(K)\\leq\\omega_1$ then $X$ is $\\sigma$-dicrete whenever $X$ has height $\\omega_1$ and it is locally compact or locally countable. It is also proved that every Lindel\\\"of \\v{C}ech-complete scattered space is $\\sigma$-compact."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.6310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-02-28T18:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"a605ac90d17d7a0e0aca61069cc5bb84a8e2d01d999a25c34e15093db53950a4","abstract_canon_sha256":"f1f926ea0d92cb3edb4729e17735fd3f7041c7953a7b70b2967bbea762eadc98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:13.728286Z","signature_b64":"vfwZ9CPlSRk36vAHWwM8D3mHVAAC9A/H0RtlKkol5zCjOBBOiEkoZaUPnYSyNGfw8nG1zy7k4Z9n1rrKmo+7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e7b89a81c40815f9841cfba94673248a0e2ac083af930e4e0e32cfaae293262","last_reissued_at":"2026-05-18T04:01:13.727679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:13.727679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Are Eberlein-Grothendieck scattered spaces $\\sigma$-discrete?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Antonio Avil\\'es, David Guerrero S\\'anchez","submitted_at":"2012-02-28T18:10:46Z","abstract_excerpt":"A space $X$ is Eberlein-Grothendieck if $X\\subset C_p(K)$ for some compact space $K.$ In this paper we address the problem of whether such a space $X$ is $\\sigma$-discrete whenever it is scattered. We show that if $w(K)\\leq\\omega_1$ then $X$ is $\\sigma$-dicrete whenever $X$ has height $\\omega_1$ and it is locally compact or locally countable. It is also proved that every Lindel\\\"of \\v{C}ech-complete scattered space is $\\sigma$-compact."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6310","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.6310","created_at":"2026-05-18T04:01:13.727770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.6310v1","created_at":"2026-05-18T04:01:13.727770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6310","created_at":"2026-05-18T04:01:13.727770+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZ5YTKA4ICAV","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZ5YTKA4ICAV7GCB","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZ5YTKA4","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC","json":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC.json","graph_json":"https://pith.science/api/pith-number/FZ5YTKA4ICAV7GCBZ65JIZZSJC/graph.json","events_json":"https://pith.science/api/pith-number/FZ5YTKA4ICAV7GCBZ65JIZZSJC/events.json","paper":"https://pith.science/paper/FZ5YTKA4"},"agent_actions":{"view_html":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC","download_json":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC.json","view_paper":"https://pith.science/paper/FZ5YTKA4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.6310&json=true","fetch_graph":"https://pith.science/api/pith-number/FZ5YTKA4ICAV7GCBZ65JIZZSJC/graph.json","fetch_events":"https://pith.science/api/pith-number/FZ5YTKA4ICAV7GCBZ65JIZZSJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC/action/storage_attestation","attest_author":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC/action/author_attestation","sign_citation":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC/action/citation_signature","submit_replication":"https://pith.science/pith/FZ5YTKA4ICAV7GCBZ65JIZZSJC/action/replication_record"}},"created_at":"2026-05-18T04:01:13.727770+00:00","updated_at":"2026-05-18T04:01:13.727770+00:00"}