{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RLURLLTICHZBPEQC7M55PL7ESE","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":"6cf2c26e68705c903031ab9361ddf68405190b5dea71ff30dd3d6fa36bcfe3e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-18T16:26:05Z","title_canon_sha256":"51380f59b32bf66f41459c1bf5f9af8031078fee2c0558bccfa0ed3db074f458"},"schema_version":"1.0","source":{"id":"1703.06316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06316","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06316v1","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06316","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"RLURLLTICHZB","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RLURLLTICHZBPEQC","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RLURLLTI","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:26cb7a57b0eb65fd61d7a9c3ce11cbc9bd8d66279548e5154773585f0a1aea9b","target":"graph","created_at":"2026-05-18T00:48:23Z","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 the linear polarization constants of finite dimensional Banach spaces. We obtain the correct asymptotic behaviour of these constants for the spaces $\\ell_p^d$: they behave as $\\sqrt[p]{d}$ if $1\\le p\\le 2$ and as $\\sqrt{d}$ if $2\\le p<\\infty$. For $p=\\infty$ we get the asymptotic behavior up to a logarithmic factor","authors_text":"Dami\\'an Pinasco, Daniel Carando, Jorge Tom\\'as Rodr\\'iguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-18T16:26:05Z","title":"On the linear polarization constants of finite dimensional spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06316","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":"sha256:0fa5feaf60fa819aabda6cd2c8a74641aa195e4004971386bd7d6e697ff42c69","target":"record","created_at":"2026-05-18T00:48:23Z","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":"6cf2c26e68705c903031ab9361ddf68405190b5dea71ff30dd3d6fa36bcfe3e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-18T16:26:05Z","title_canon_sha256":"51380f59b32bf66f41459c1bf5f9af8031078fee2c0558bccfa0ed3db074f458"},"schema_version":"1.0","source":{"id":"1703.06316","kind":"arxiv","version":1}},"canonical_sha256":"8ae915ae6811f2179202fb3bd7afe4912a720f91b0331a250c58fcb63c77bcfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae915ae6811f2179202fb3bd7afe4912a720f91b0331a250c58fcb63c77bcfd","first_computed_at":"2026-05-18T00:48:23.288410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:23.288410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gyzoHLlhsf1rEsYteLofUegIdLUw3YghCJAFHulxM42KAf5OxYmOeLpyHWPFu4Xsa3L2I/4bk7M1qw064kIiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:23.289020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fa5feaf60fa819aabda6cd2c8a74641aa195e4004971386bd7d6e697ff42c69","sha256:26cb7a57b0eb65fd61d7a9c3ce11cbc9bd8d66279548e5154773585f0a1aea9b"],"state_sha256":"9181b04d385b6a5ffd1d0828c06327026598c9951d27074af4f3359a421a3163"}