{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:S4T3O74LVNBGQCQEYT3DM6I4XF","short_pith_number":"pith:S4T3O74L","schema_version":"1.0","canonical_sha256":"9727b77f8bab42680a04c4f636791cb95260d4ec1d84e62cf45f34d4afee3abe","source":{"kind":"arxiv","id":"1506.00206","version":1},"attestation_state":"computed","paper":{"title":"Pinning Down versus Density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2015-05-31T09:06:57Z","abstract_excerpt":"The pinning down number $ {pd}(X)$ of a topological space $X$ is the smallest cardinal $\\kappa$ such that for any neighborhood assignment $U:X\\to \\tau_X$ there is a set $A\\in [X]^\\kappa$ with $A\\cap U(x)\\ne\\emptyset$ for all $x\\in X$. Clearly, c$(X) \\le {pd}(X) \\le {d}(X)$.\n  Here we prove that the following statements are equivalent:\n  (1) $2^\\kappa<\\kappa^{+\\omega}$ for each cardinal $\\kappa$;\n  (2) ${d}(X)={pd}(X)$ for each Hausdorff space $X$;\n  (3) ${d}(X)={pd}(X)$ for each 0-dimensional Hausdorff space $X$.\n  This answers two questions of Banakh and Ravsky.\n  The dispersion character $\\D"},"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":"1506.00206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-05-31T09:06:57Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"64dc6cf1d4c85732dab48aa8371dc16bb6588a65cf6a811a269c022d4c3c4615","abstract_canon_sha256":"2c6ed2a947262553808cd64226a0862fd84f35b0b332e8f21a9e264561601413"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:34.439370Z","signature_b64":"rKtEO/sIh5c0tz3HqrerLvTwElfjsF6SJxBFM5hkQyMz5dpqiMV2f4aZg6gykw+JFJbIAAqyepFyeB4P9XASCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9727b77f8bab42680a04c4f636791cb95260d4ec1d84e62cf45f34d4afee3abe","last_reissued_at":"2026-05-18T01:59:34.438657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:34.438657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pinning Down versus Density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2015-05-31T09:06:57Z","abstract_excerpt":"The pinning down number $ {pd}(X)$ of a topological space $X$ is the smallest cardinal $\\kappa$ such that for any neighborhood assignment $U:X\\to \\tau_X$ there is a set $A\\in [X]^\\kappa$ with $A\\cap U(x)\\ne\\emptyset$ for all $x\\in X$. Clearly, c$(X) \\le {pd}(X) \\le {d}(X)$.\n  Here we prove that the following statements are equivalent:\n  (1) $2^\\kappa<\\kappa^{+\\omega}$ for each cardinal $\\kappa$;\n  (2) ${d}(X)={pd}(X)$ for each Hausdorff space $X$;\n  (3) ${d}(X)={pd}(X)$ for each 0-dimensional Hausdorff space $X$.\n  This answers two questions of Banakh and Ravsky.\n  The dispersion character $\\D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00206","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":"1506.00206","created_at":"2026-05-18T01:59:34.438789+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00206v1","created_at":"2026-05-18T01:59:34.438789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00206","created_at":"2026-05-18T01:59:34.438789+00:00"},{"alias_kind":"pith_short_12","alias_value":"S4T3O74LVNBG","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S4T3O74LVNBGQCQE","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S4T3O74L","created_at":"2026-05-18T12:29:39.896362+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/S4T3O74LVNBGQCQEYT3DM6I4XF","json":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF.json","graph_json":"https://pith.science/api/pith-number/S4T3O74LVNBGQCQEYT3DM6I4XF/graph.json","events_json":"https://pith.science/api/pith-number/S4T3O74LVNBGQCQEYT3DM6I4XF/events.json","paper":"https://pith.science/paper/S4T3O74L"},"agent_actions":{"view_html":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF","download_json":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF.json","view_paper":"https://pith.science/paper/S4T3O74L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00206&json=true","fetch_graph":"https://pith.science/api/pith-number/S4T3O74LVNBGQCQEYT3DM6I4XF/graph.json","fetch_events":"https://pith.science/api/pith-number/S4T3O74LVNBGQCQEYT3DM6I4XF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF/action/storage_attestation","attest_author":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF/action/author_attestation","sign_citation":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF/action/citation_signature","submit_replication":"https://pith.science/pith/S4T3O74LVNBGQCQEYT3DM6I4XF/action/replication_record"}},"created_at":"2026-05-18T01:59:34.438789+00:00","updated_at":"2026-05-18T01:59:34.438789+00:00"}