{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KX2J5G7XLIFYEDFWTZSBQTMU5K","short_pith_number":"pith:KX2J5G7X","schema_version":"1.0","canonical_sha256":"55f49e9bf75a0b820cb69e64184d94eab2ae79f65a8de69c9360c17403f30ae5","source":{"kind":"arxiv","id":"1711.04336","version":1},"attestation_state":"computed","paper":{"title":"Fundamental bounded resolutions and quasi-$(DF)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"J.C. Ferrando, J. K\\c{a}kol, S. Gabriyelyan","submitted_at":"2017-11-12T18:39:57Z","abstract_excerpt":"We introduce a new class of locally convex spaces $E$, under the name quasi-$(DF)$-spaces, containing strictly the class of $(DF)$-spaces. A locally convex space $E$ is called a quasi-$(DF)$-space if (i) $E$ admits a fundamental bounded resolution, i.e. an $\\mathbb{N}^{\\mathbb{N}}$-increasing family of bounded sets in $E$ which swallows all bounded set in $E$, and (ii) $E$ belongs to the class $\\mathfrak{G}$ (in sense of Cascales--Orihuela). The class of quasi-$(DF)$-spaces is closed under taking subspaces, countable direct sums and countable products. Every regular $(LM)$-space (particularly,"},"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":"1711.04336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-12T18:39:57Z","cross_cats_sorted":[],"title_canon_sha256":"62c64f8634c1d57bb8daa41b17c93669975dd8957d2ef3fa951c846981d58965","abstract_canon_sha256":"524e78e09ae8407da030e0e1f8b8e5b419923ee88701840c30ab7c641509c076"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:39.380409Z","signature_b64":"bvlsfTXe272kHbY9Ade5RWQibnQer79z0Huy7wHPBQgT6Y2yqmBUJ9V2kCQ0mEvumgh4npHIl7GwjJy93lQtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55f49e9bf75a0b820cb69e64184d94eab2ae79f65a8de69c9360c17403f30ae5","last_reissued_at":"2026-05-18T00:30:39.379825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:39.379825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fundamental bounded resolutions and quasi-$(DF)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"J.C. Ferrando, J. K\\c{a}kol, S. Gabriyelyan","submitted_at":"2017-11-12T18:39:57Z","abstract_excerpt":"We introduce a new class of locally convex spaces $E$, under the name quasi-$(DF)$-spaces, containing strictly the class of $(DF)$-spaces. A locally convex space $E$ is called a quasi-$(DF)$-space if (i) $E$ admits a fundamental bounded resolution, i.e. an $\\mathbb{N}^{\\mathbb{N}}$-increasing family of bounded sets in $E$ which swallows all bounded set in $E$, and (ii) $E$ belongs to the class $\\mathfrak{G}$ (in sense of Cascales--Orihuela). The class of quasi-$(DF)$-spaces is closed under taking subspaces, countable direct sums and countable products. Every regular $(LM)$-space (particularly,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04336","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":"1711.04336","created_at":"2026-05-18T00:30:39.379911+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.04336v1","created_at":"2026-05-18T00:30:39.379911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04336","created_at":"2026-05-18T00:30:39.379911+00:00"},{"alias_kind":"pith_short_12","alias_value":"KX2J5G7XLIFY","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KX2J5G7XLIFYEDFW","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KX2J5G7X","created_at":"2026-05-18T12:31:28.150371+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/KX2J5G7XLIFYEDFWTZSBQTMU5K","json":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K.json","graph_json":"https://pith.science/api/pith-number/KX2J5G7XLIFYEDFWTZSBQTMU5K/graph.json","events_json":"https://pith.science/api/pith-number/KX2J5G7XLIFYEDFWTZSBQTMU5K/events.json","paper":"https://pith.science/paper/KX2J5G7X"},"agent_actions":{"view_html":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K","download_json":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K.json","view_paper":"https://pith.science/paper/KX2J5G7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.04336&json=true","fetch_graph":"https://pith.science/api/pith-number/KX2J5G7XLIFYEDFWTZSBQTMU5K/graph.json","fetch_events":"https://pith.science/api/pith-number/KX2J5G7XLIFYEDFWTZSBQTMU5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K/action/storage_attestation","attest_author":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K/action/author_attestation","sign_citation":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K/action/citation_signature","submit_replication":"https://pith.science/pith/KX2J5G7XLIFYEDFWTZSBQTMU5K/action/replication_record"}},"created_at":"2026-05-18T00:30:39.379911+00:00","updated_at":"2026-05-18T00:30:39.379911+00:00"}