{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZMGSFGJXFH4FZLO2QKBJXZWWQ5","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":"5f01078becdd822bb5826d098796eef05035265d3092d37b09b751ef3c0d8864","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-20T15:58:30Z","title_canon_sha256":"673c090cbc09870bc02fd4c51d1c32424aa4f26d5ade2b6877b10ae84f624cf4"},"schema_version":"1.0","source":{"id":"0910.3888","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3888","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3888v2","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3888","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZMGSFGJXFH4F","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZMGSFGJXFH4FZLO2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZMGSFGJX","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:113763307a19ac652ea1756439c0f17a9a0d045d244c9fa4427190dfc8a2cfba","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":"Given an homogeneous polynomial on a Banach space $E$ belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of $E$ and prove that this extension remains in the ideal and has the same ideal norm. As a consequence, we show that the Aron-Berner extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials. This allow us to obtain symmetric versions of some basic results of the metric theory of tensor products.","authors_text":"Daniel Carando, Daniel Galicer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-20T15:58:30Z","title":"Extending polynomials in maximal and minimal ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3888","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":"sha256:33766d4619955389ea62603dcee40d036b9615ec07d1ab4b57060813cd73d5d9","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":"5f01078becdd822bb5826d098796eef05035265d3092d37b09b751ef3c0d8864","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-20T15:58:30Z","title_canon_sha256":"673c090cbc09870bc02fd4c51d1c32424aa4f26d5ade2b6877b10ae84f624cf4"},"schema_version":"1.0","source":{"id":"0910.3888","kind":"arxiv","version":2}},"canonical_sha256":"cb0d22993729f85cadda82829be6d687439c58805026387b61499ced6740e838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb0d22993729f85cadda82829be6d687439c58805026387b61499ced6740e838","first_computed_at":"2026-05-18T04:04:31.372665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:31.372665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6seGGhvY6UmZM346X/2ZmuZcA+cxyk83nPFxDGuOYjOjcAfdEaGDgyVspSyGdjQrHlD8EQsJ02B+X9fl8gDKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:31.373278Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.3888","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33766d4619955389ea62603dcee40d036b9615ec07d1ab4b57060813cd73d5d9","sha256:113763307a19ac652ea1756439c0f17a9a0d045d244c9fa4427190dfc8a2cfba"],"state_sha256":"70eb16f8620f0ebf20f40b6338071778c848486441ab8a976c6fba744940d09f"}