{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QPQUKKTRWD37B3YAVKA5N5OSQQ","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":"79129303ef85f71f8ef1c8ae175a15efb8bbb3da0c6ca2760de5e381f1b34137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-20T19:13:28Z","title_canon_sha256":"6e0a9998752b5b470567e4b27e8c6038d5d996c456dfb04413719c30b4036525"},"schema_version":"1.0","source":{"id":"1209.4619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4619","created_at":"2026-05-18T03:45:11Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4619v1","created_at":"2026-05-18T03:45:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4619","created_at":"2026-05-18T03:45:11Z"},{"alias_kind":"pith_short_12","alias_value":"QPQUKKTRWD37","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPQUKKTRWD37B3YA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPQUKKTR","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:f2481ef381307660dee908f2d9513b1ad3af7b818645ac3894e597daf187b4e4","target":"graph","created_at":"2026-05-18T03:45:11Z","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 a sequence $(f_i)_{i=1}^\\infty$ of translates of a fixed $f\\in L_p(R)$ cannot be an unconditional basis of $L_p(R)$ for any $1\\le p<\\infty$. In contrast to this, for every $2<p<\\infty$, $d\\in N$ and unbounded sequence $(\\lambda_n)_{n\\in N}\\subset R^d$ we establish the existence of a function $f\\in L_p(R^d)$ and sequence $(g^*_n)_{n\\in N}\\subset L_p^*(R^d)$ such that $(T_{\\lambda_n} f, g^*_n)_{n\\in N}$ forms an unconditional Schauder frame for $L_p(R^d)$. In particular, there exists a Schauder frame of integer translates for $L_p(R)$ if (and only if) $2<p<\\infty$.","authors_text":"A. Zs\\'ak, D. Freeman, E. Odell, Th. Schlumprecht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-20T19:13:28Z","title":"Unconditional structures of translates for $L_p(R^d)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4619","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:a43056d33af5bb0fa79c07e5b8f277bfa9edce7bd2a296513e936a08501de5d1","target":"record","created_at":"2026-05-18T03:45:11Z","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":"79129303ef85f71f8ef1c8ae175a15efb8bbb3da0c6ca2760de5e381f1b34137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-20T19:13:28Z","title_canon_sha256":"6e0a9998752b5b470567e4b27e8c6038d5d996c456dfb04413719c30b4036525"},"schema_version":"1.0","source":{"id":"1209.4619","kind":"arxiv","version":1}},"canonical_sha256":"83e1452a71b0f7f0ef00aa81d6f5d2842e798827a3ebc76a21ddac1798bf6839","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83e1452a71b0f7f0ef00aa81d6f5d2842e798827a3ebc76a21ddac1798bf6839","first_computed_at":"2026-05-18T03:45:11.153858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:11.153858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6aM+zhkE2MoL+B7hfI8ebeq0GyxuZiNFPxB07iYEEff/XO5iyVqR6M7+Ehh/zD9pjDm0UTyQTmnrpMB/YR1jCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:11.154687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a43056d33af5bb0fa79c07e5b8f277bfa9edce7bd2a296513e936a08501de5d1","sha256:f2481ef381307660dee908f2d9513b1ad3af7b818645ac3894e597daf187b4e4"],"state_sha256":"736cc8c12ea6b32c900e6cab0ff23d975e47cf38be494edf894b7bd6f283a60b"}