{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZUQ2RM725MB3OIGYQHBFRMQGBY","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":"6f9846b8667d6fc895403f1deff42dc547cb09ce8b4ffdd93fdbb9d214d17eea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-13T11:57:42Z","title_canon_sha256":"a4911bba36e5678bf5d799a977c85bb453a4bedaf9a708d6c33384b2475088ec"},"schema_version":"1.0","source":{"id":"0905.2079","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2079","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2079v2","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2079","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZUQ2RM725MB3","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZUQ2RM725MB3OIGY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZUQ2RM72","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:a2b22a798f9cb53c0e476036e4a87b25570a568a298bfb5d81c90a2ba99f9e3d","target":"graph","created_at":"2026-05-18T01:31:20Z","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":"The main goal of this note is to establish a connection between the cotype of the Banach space X and the parameters r for which every 2-homogeneous polynomial on X is r-dominated. Let cotX be the infimum of the cotypes assumed by X and (cotX)* be its conjugate. The main result of this note asserts that if cotX > 2, then for every 1<= r < (cotX)* there exists a non-r-dominated 2-homogeneous polynomial on X.","authors_text":"D. Pellegrino, G. Botelho, P. Rueda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-13T11:57:42Z","title":"Dominated bilinear forms and 2-homogeneous polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2079","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:efe0834dfe60d1217e4e2eee49bdb962dc36edecfcacd10793511907755f7264","target":"record","created_at":"2026-05-18T01:31:20Z","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":"6f9846b8667d6fc895403f1deff42dc547cb09ce8b4ffdd93fdbb9d214d17eea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-13T11:57:42Z","title_canon_sha256":"a4911bba36e5678bf5d799a977c85bb453a4bedaf9a708d6c33384b2475088ec"},"schema_version":"1.0","source":{"id":"0905.2079","kind":"arxiv","version":2}},"canonical_sha256":"cd21a8b3faeb03b720d881c258b2060e11dbfbd5e5c02ca9afb198b7e9f18f1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd21a8b3faeb03b720d881c258b2060e11dbfbd5e5c02ca9afb198b7e9f18f1a","first_computed_at":"2026-05-18T01:31:20.203128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:20.203128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"20IM2mSkk3QXp9gdFsa2vuCgaWUCUcl1JqPDM8ze5fzutfhooNSuNApY9CYbOMDxzY/ShbAH+NK9SY9H3gVHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:20.203731Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.2079","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efe0834dfe60d1217e4e2eee49bdb962dc36edecfcacd10793511907755f7264","sha256:a2b22a798f9cb53c0e476036e4a87b25570a568a298bfb5d81c90a2ba99f9e3d"],"state_sha256":"adc7c12e8a0cccbf3bf3f468e6b7e6c74335eef926ee9fd7769b19310e559d09"}