{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B4RI2RZCOH6MXX2KBJRUIXDVEX","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":"af5e193d256fefd05aacfa4f18e6460e39903ddfd2ef38935a77b3b17bc81a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-24T18:00:03Z","title_canon_sha256":"48901bebd33f55cd1a76063ef88303f1b4700f07481680eca9a7d1be96762d9b"},"schema_version":"1.0","source":{"id":"1403.6064","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6064","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6064v4","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6064","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"B4RI2RZCOH6M","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4RI2RZCOH6MXX2K","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4RI2RZC","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f7ff461f5c6e749b566c298e2adb0e809dbb89d0d4de15357d37c37150bef64a","target":"graph","created_at":"2026-05-18T01:33:57Z","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 given a positive integer $m$, a real number $p\\in\\left[ 2,\\infty\\right)$ and $1\\leq s<p^{\\ast}$ the set of non--multiple $\\left( r;s\\right)$--summing $m$--linear forms on $\\ell_{p}\\times\\cdots\\times \\ell_{p}$ contains, except for the null vector, a closed subspace of maximal dimension whenever $r<\\frac{2ms}{s+2m-ms}$. This result is optimal since for $r\\geq\\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\\ell_{p}\\times \\cdots\\times\\ell_{p}$ are multiple $\\left( r;s\\right)$--summing. In particular, among other results, we generalize a result related to cotype (from 2010) due to Botel","authors_text":"Daniel Pellegrino, Gustavo Araujo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-24T18:00:03Z","title":"Optimal estimates for summing multilinear operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6064","kind":"arxiv","version":4},"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":"sha256:75f2a4d5df88926da250fe129e9bc2ef0c4cd3798c0c06e4896f522ccea5a085","target":"record","created_at":"2026-05-18T01:33:57Z","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":"af5e193d256fefd05aacfa4f18e6460e39903ddfd2ef38935a77b3b17bc81a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-24T18:00:03Z","title_canon_sha256":"48901bebd33f55cd1a76063ef88303f1b4700f07481680eca9a7d1be96762d9b"},"schema_version":"1.0","source":{"id":"1403.6064","kind":"arxiv","version":4}},"canonical_sha256":"0f228d472271fccbdf4a0a63445c7525c7f4b7bfefa0951faedf368de880035c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f228d472271fccbdf4a0a63445c7525c7f4b7bfefa0951faedf368de880035c","first_computed_at":"2026-05-18T01:33:57.102936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.102936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CTVB7BULieEpnyHJ5mvpB2pgStfiqXDba0N2CpqcEokBSKgNKBCWWugg0dgwqRSONqgfJt9kxniPx/6X5qgaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.103328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6064","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75f2a4d5df88926da250fe129e9bc2ef0c4cd3798c0c06e4896f522ccea5a085","sha256:f7ff461f5c6e749b566c298e2adb0e809dbb89d0d4de15357d37c37150bef64a"],"state_sha256":"464d87bf55f66f149d7ba179d6e4ed47d392f6afb5808b2ca0cca139e714f019"}