{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YXB2PCOTQG6TYUH7G6Z2COBALX","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":"b6467e842552997bc8e9ccfe52b4d4b6f63f7c5c3ed3b85d01ec4707a2208d97","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-09T08:14:21Z","title_canon_sha256":"87bdc3c7725cda095cb9369fa6f37e6cf366cdb4fe2d687e5954b391b0ee1acf"},"schema_version":"1.0","source":{"id":"1609.02685","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02685","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02685v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02685","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"YXB2PCOTQG6T","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YXB2PCOTQG6TYUH7","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YXB2PCOT","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:387ced3f01d363cb33698eb1334ffd44b2722b792c6e44246a5929358e635222","target":"graph","created_at":"2026-05-18T00:24:53Z","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 show that the problem whether every $1$-separably injective Banach space contains an isomorphic copy of $\\ell_\\infty$ is undecidable. Namely, unlike under the continuum hypothesis, assuming Martin's axiom and the negation of the continuum hypothesis, there is an $1$-separably injective Banach space of the form $C(K)$ (which means that $K$ is an $F$-space) without an isomorphic copy of $\\ell_\\infty$.\n  This result is a consequence of our study of $\\omega_2$-subsets of tightly $\\sigma$-filtered Boolean algebras introduced by Koppelberg for which we obtain some general principles useful when t","authors_text":"Antonio Avil\\'es, Piotr Koszmider","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-09T08:14:21Z","title":"A 1-separably injective space that does not contain $\\ell_\\infty$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02685","kind":"arxiv","version":3},"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":"sha256:0bd3807debb555eb6930f1e42fad5c9f2feacd803fc1e7473b24481efc4a9630","target":"record","created_at":"2026-05-18T00:24:53Z","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":"b6467e842552997bc8e9ccfe52b4d4b6f63f7c5c3ed3b85d01ec4707a2208d97","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-09T08:14:21Z","title_canon_sha256":"87bdc3c7725cda095cb9369fa6f37e6cf366cdb4fe2d687e5954b391b0ee1acf"},"schema_version":"1.0","source":{"id":"1609.02685","kind":"arxiv","version":3}},"canonical_sha256":"c5c3a789d381bd3c50ff37b3a138205dc330319489c317b94a584252ac031203","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5c3a789d381bd3c50ff37b3a138205dc330319489c317b94a584252ac031203","first_computed_at":"2026-05-18T00:24:53.244931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:53.244931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+aVrWMDJNTpVS1ylGmSQy1qTRB4mrWpBmPAvnF1Wg1ISHX1A/p5AbNvx+Xu2g4TtraNV8CmCdzp8ikj9bOyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:53.245728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02685","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bd3807debb555eb6930f1e42fad5c9f2feacd803fc1e7473b24481efc4a9630","sha256:387ced3f01d363cb33698eb1334ffd44b2722b792c6e44246a5929358e635222"],"state_sha256":"325bff625a6e083b83e03d5aab6295533fe75851973714f9da919bb7dbe8f06c"}