{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FIXOIWMAGVWMHM7KVVSHQTMENQ","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":"7c05e8e7a5a3d311d2d75bd917af48f4b0b857068950dfc584d16b5a2b2806ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-06T12:59:13Z","title_canon_sha256":"620aebedaed99bbe8af4fb114250009f0863d21548ffd3ea14ed4db4b7aadb2d"},"schema_version":"1.0","source":{"id":"1507.01431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01431","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01431v1","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01431","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"FIXOIWMAGVWM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FIXOIWMAGVWMHM7K","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FIXOIWMA","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:416a328802a13d3e67c2d66ae3a49863eb2bb0c0447f0fd9fe6f7bf643b8353f","target":"graph","created_at":"2026-05-18T01:37:16Z","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":"In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for $2$-homogeneous polynomials on $\\ell_p^2$ spaces, $2<p\\leq\\infty$ and lower estimates for polynomials of higher degrees.","authors_text":"Gustavo A. Mu\\~noz-Fern\\'andez, Gustavo Ara\\'ujo, Juan B. Seoane-Sep\\'ulveda, Pablo Jim\\'enez-Rodr\\'iguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-06T12:59:13Z","title":"Estimates on the norm of polynomials and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01431","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":"sha256:2935fe7f2afa935a69fc58ddad0daa3ec26d3f08ecb63e7cdc68b90d289bd1d8","target":"record","created_at":"2026-05-18T01:37:16Z","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":"7c05e8e7a5a3d311d2d75bd917af48f4b0b857068950dfc584d16b5a2b2806ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-06T12:59:13Z","title_canon_sha256":"620aebedaed99bbe8af4fb114250009f0863d21548ffd3ea14ed4db4b7aadb2d"},"schema_version":"1.0","source":{"id":"1507.01431","kind":"arxiv","version":1}},"canonical_sha256":"2a2ee45980356cc3b3eaad64784d846c2e789c644b12a87e15becabee3e955d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a2ee45980356cc3b3eaad64784d846c2e789c644b12a87e15becabee3e955d0","first_computed_at":"2026-05-18T01:37:16.955362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:16.955362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mQqCjB7DvDvsRz88ETCDLo/bpuCGo3p/u1It0O+WK/cF7KzdDmNlrHnlOQn4Uibnsqewalxt7HrlKdMZ/xd9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:16.955960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2935fe7f2afa935a69fc58ddad0daa3ec26d3f08ecb63e7cdc68b90d289bd1d8","sha256:416a328802a13d3e67c2d66ae3a49863eb2bb0c0447f0fd9fe6f7bf643b8353f"],"state_sha256":"941f6072f17ec1f499232c101bfebf03554b497dfe3be5bfb58d29ad0501d3ae"}