{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2RBCTDLVBAQUSWOZFIBSWKHBOP","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":"6dfd315ab115211099357fbf44616b00bef82d0608a10bfbf8c15820b0ee6511","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-17T17:33:30Z","title_canon_sha256":"54d2c04900688ad0fd497b96787126fe28ca3f405b0607fb37ff14659f8d6094"},"schema_version":"1.0","source":{"id":"0906.3253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3253","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3253v2","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3253","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"2RBCTDLVBAQU","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2RBCTDLVBAQUSWOZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2RBCTDLV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:dd4cb2353d13c408f68ed096ed1ef9660f11b1c1fa66601241789075ab01e9ba","target":"graph","created_at":"2026-05-18T04:04:31Z","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 study tensor norms that destroy unconditionality in the following sense: for every Banach space $E$ with unconditional basis, the $n$-fold tensor product of $E$ (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check weather a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from $\\varepsilon$ and $\\pi$ destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals n","authors_text":"Daniel Carando, Daniel Galicer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-17T17:33:30Z","title":"Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3253","kind":"arxiv","version":2},"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":"sha256:830ebda042e8ded82da3f3be280e096fd6ac1891ac454ec0e7f9c57b3daf4e78","target":"record","created_at":"2026-05-18T04:04:31Z","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":"6dfd315ab115211099357fbf44616b00bef82d0608a10bfbf8c15820b0ee6511","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-17T17:33:30Z","title_canon_sha256":"54d2c04900688ad0fd497b96787126fe28ca3f405b0607fb37ff14659f8d6094"},"schema_version":"1.0","source":{"id":"0906.3253","kind":"arxiv","version":2}},"canonical_sha256":"d442298d7508214959d92a032b28e173d8791c0c4967c677fdcbd7dc3ab2cc98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d442298d7508214959d92a032b28e173d8791c0c4967c677fdcbd7dc3ab2cc98","first_computed_at":"2026-05-18T04:04:31.396891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:31.396891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"do7yTXCaqpuoH8Q73PodbsGHaeeUvsF3PGlN3lhl/QXP8Qs1p61ReIiz+40Wtq8ktsQCQe+clLB/OSSlv5GFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:31.397859Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:830ebda042e8ded82da3f3be280e096fd6ac1891ac454ec0e7f9c57b3daf4e78","sha256:dd4cb2353d13c408f68ed096ed1ef9660f11b1c1fa66601241789075ab01e9ba"],"state_sha256":"2dad7374611fa2551bbb84e2edb6494755b90e7e948580cdc54f5808189b5868"}