{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VUFQENBAM2STXBJIPBODWO23NB","short_pith_number":"pith:VUFQENBA","canonical_record":{"source":{"id":"1207.3722","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-16T16:49:58Z","cross_cats_sorted":[],"title_canon_sha256":"25d8c375587af5ec9b65965c7c6722873cd461790254adb9fe73abde8b56c421","abstract_canon_sha256":"f33e5914fad7521a780392baec4db9eec1e85467bd583ba78160150211227feb"},"schema_version":"1.0"},"canonical_sha256":"ad0b02342066a53b8528785c3b3b5b686242822503e57d409344cf1fb209cc92","source":{"kind":"arxiv","id":"1207.3722","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3722","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3722v1","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3722","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"VUFQENBAM2ST","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VUFQENBAM2STXBJI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VUFQENBA","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VUFQENBAM2STXBJIPBODWO23NB","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3722","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-16T16:49:58Z","cross_cats_sorted":[],"title_canon_sha256":"25d8c375587af5ec9b65965c7c6722873cd461790254adb9fe73abde8b56c421","abstract_canon_sha256":"f33e5914fad7521a780392baec4db9eec1e85467bd583ba78160150211227feb"},"schema_version":"1.0"},"canonical_sha256":"ad0b02342066a53b8528785c3b3b5b686242822503e57d409344cf1fb209cc92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:42.808922Z","signature_b64":"I6OFEPGQOutxzNKndDTxJpa0eYKW/tVbgc03g6fGCjAximBicZ46AFK0OXhwwDBXFfUhxivox8PwBY0YSLK8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad0b02342066a53b8528785c3b3b5b686242822503e57d409344cf1fb209cc92","last_reissued_at":"2026-05-17T23:58:42.808374Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:42.808374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3722","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":"2026-05-17T23:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PF8ebg8xzlpDyUl93fBTs0nK12HgRh04zbEjE/c3o9yxBpDjVywUogGc++gvZklVl1Pa46Tp5ZXB48ZPCs2kCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:47:11.457417Z"},"content_sha256":"5774cdf83d7a4c2818b531970f3fc955f50baab4e8b99b762622fdcf346d0e2e","schema_version":"1.0","event_id":"sha256:5774cdf83d7a4c2818b531970f3fc955f50baab4e8b99b762622fdcf346d0e2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VUFQENBAM2STXBJIPBODWO23NB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some remarks on universality properties of $\\ell_\\infty / c_0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikolaj Krupski, Witold Marciszewski","submitted_at":"2012-07-16T16:49:58Z","abstract_excerpt":"We prove that if continuum is not a Kunen cardinal, then there is a uniform Eberlein compact space $K$ such that the Banach space $C(K)$ does not embed isometrically into $\\ell_\\infty/c_0$. We prove a similar result for isomorphic embeddings. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $\\ell_\\infty/c_0$, but fails to embed isometrically. As far as we know it is the first example of this kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3722","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":"2026-05-17T23:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5VUh+rKfWCIldQVEdXIp/PeBN/YUVqt8MreeTP4fMp8Y9Qe0FeELy6/CoW/gczBiAvn362uQR6RxWb4HSqzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:47:11.457773Z"},"content_sha256":"bad49bf4dfb56039f1c2fe5f032fc7a02a896414b74001ebe5ca0ac29eddf0ea","schema_version":"1.0","event_id":"sha256:bad49bf4dfb56039f1c2fe5f032fc7a02a896414b74001ebe5ca0ac29eddf0ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VUFQENBAM2STXBJIPBODWO23NB/bundle.json","state_url":"https://pith.science/pith/VUFQENBAM2STXBJIPBODWO23NB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VUFQENBAM2STXBJIPBODWO23NB/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":"2026-06-12T09:47:11Z","links":{"resolver":"https://pith.science/pith/VUFQENBAM2STXBJIPBODWO23NB","bundle":"https://pith.science/pith/VUFQENBAM2STXBJIPBODWO23NB/bundle.json","state":"https://pith.science/pith/VUFQENBAM2STXBJIPBODWO23NB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VUFQENBAM2STXBJIPBODWO23NB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VUFQENBAM2STXBJIPBODWO23NB","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":"f33e5914fad7521a780392baec4db9eec1e85467bd583ba78160150211227feb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-16T16:49:58Z","title_canon_sha256":"25d8c375587af5ec9b65965c7c6722873cd461790254adb9fe73abde8b56c421"},"schema_version":"1.0","source":{"id":"1207.3722","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3722","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3722v1","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3722","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"VUFQENBAM2ST","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VUFQENBAM2STXBJI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VUFQENBA","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:bad49bf4dfb56039f1c2fe5f032fc7a02a896414b74001ebe5ca0ac29eddf0ea","target":"graph","created_at":"2026-05-17T23:58:42Z","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 prove that if continuum is not a Kunen cardinal, then there is a uniform Eberlein compact space $K$ such that the Banach space $C(K)$ does not embed isometrically into $\\ell_\\infty/c_0$. We prove a similar result for isomorphic embeddings. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $\\ell_\\infty/c_0$, but fails to embed isometrically. As far as we know it is the first example of this kind.","authors_text":"Mikolaj Krupski, Witold Marciszewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-16T16:49:58Z","title":"Some remarks on universality properties of $\\ell_\\infty / c_0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3722","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":"sha256:5774cdf83d7a4c2818b531970f3fc955f50baab4e8b99b762622fdcf346d0e2e","target":"record","created_at":"2026-05-17T23:58:42Z","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":"f33e5914fad7521a780392baec4db9eec1e85467bd583ba78160150211227feb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-16T16:49:58Z","title_canon_sha256":"25d8c375587af5ec9b65965c7c6722873cd461790254adb9fe73abde8b56c421"},"schema_version":"1.0","source":{"id":"1207.3722","kind":"arxiv","version":1}},"canonical_sha256":"ad0b02342066a53b8528785c3b3b5b686242822503e57d409344cf1fb209cc92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad0b02342066a53b8528785c3b3b5b686242822503e57d409344cf1fb209cc92","first_computed_at":"2026-05-17T23:58:42.808374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:42.808374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I6OFEPGQOutxzNKndDTxJpa0eYKW/tVbgc03g6fGCjAximBicZ46AFK0OXhwwDBXFfUhxivox8PwBY0YSLK8DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:42.808922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3722","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5774cdf83d7a4c2818b531970f3fc955f50baab4e8b99b762622fdcf346d0e2e","sha256:bad49bf4dfb56039f1c2fe5f032fc7a02a896414b74001ebe5ca0ac29eddf0ea"],"state_sha256":"6f9388b4096039ebdedef617b2c46702d6a16fec7318bb554436ffe86183103c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cfCsZSm0Z5TcabN6fcHw7NRu28icKcMoAReugmReZEbh7AdmwDTmbray+jNQEzz6wWZpi18rGkOcX7rZkHOSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:47:11.459834Z","bundle_sha256":"28cf0c495b088987c0a77bf3063d0449b35f5806f32d0dd80721a63c02487010"}}