{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FGQFZ37TOJB2I65THNUUAHCMWY","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":"aa75734282453c9557ce18687504aba63fdcf051cdb0f3f50578d1221c80d06e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-27T14:32:41Z","title_canon_sha256":"3246c846fd1452e9a350185fecc5c7c43a374ee1fc11ea51751058e2f09b76c7"},"schema_version":"1.0","source":{"id":"1605.08665","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08665","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08665v3","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08665","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"FGQFZ37TOJB2","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGQFZ37TOJB2I65T","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGQFZ37T","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:aed6ee740d9acc830d84fb50e7d93ef4cdb1a21c22bd235299f8025db5017c25","target":"graph","created_at":"2026-05-18T00:46:21Z","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 spectral $p$-norm of $r$-matrices generalizes the spectral $2$-norm of $2$-matrices. In 1911 Schur gave an upper bound on the spectral $2$-norm of $2$-matrices, which was extended in 1934 by Hardy, Littlewood, and Polya to $r$-matrices. Recently, Kolotilina, and independently the author, strengthened Schur's bound for $2$-matrices. The main result of this paper extends the latter result to $r$-matrices, thereby improving the result of Hardy, Littlewood, and Polya.\n  The proof is based on combinatorial concepts like $r$-partite $r$-matrix and symmetrant of a matrix, which appear to be instr","authors_text":"V. Nikiforov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-27T14:32:41Z","title":"Combinatorial methods for the spectral p-norm of hypermatrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08665","kind":"arxiv","version":3},"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:e0c184c3405d4710bf67f07e9b1871f9e5e2a907ad569951a2dc1669faa0245d","target":"record","created_at":"2026-05-18T00:46:21Z","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":"aa75734282453c9557ce18687504aba63fdcf051cdb0f3f50578d1221c80d06e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-27T14:32:41Z","title_canon_sha256":"3246c846fd1452e9a350185fecc5c7c43a374ee1fc11ea51751058e2f09b76c7"},"schema_version":"1.0","source":{"id":"1605.08665","kind":"arxiv","version":3}},"canonical_sha256":"29a05ceff37243a47bb33b69401c4cb6072d35513a301e6519c1760b74c133d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29a05ceff37243a47bb33b69401c4cb6072d35513a301e6519c1760b74c133d5","first_computed_at":"2026-05-18T00:46:21.001775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:21.001775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqYTTM5NkdSdChH4PInWpuY3+YGxFWZxpEsv7RA1nG3lm+OWOWeMJVpxUSCHx9z5d2FH1mxsOFJsM+Tr8ZTnDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:21.002231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08665","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0c184c3405d4710bf67f07e9b1871f9e5e2a907ad569951a2dc1669faa0245d","sha256:aed6ee740d9acc830d84fb50e7d93ef4cdb1a21c22bd235299f8025db5017c25"],"state_sha256":"59bfbc3ffc5fa30e5226d713319ffe5dbb486b53b7dfdd2c71a5e46d08998422"}