{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VINBQLMMBNBARDPVBYFXF2H5U2","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":"ff63f60688a90711a2fbd2b9db2b77911a2811ce7c03065f94f4246b3409595b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-05-23T20:12:08Z","title_canon_sha256":"8fd78a269fed5ef17b365558e028e1ebd8fb06220f7ef622865d569bb95259c5"},"schema_version":"1.0","source":{"id":"1205.5282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5282","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5282v1","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5282","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"VINBQLMMBNBA","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VINBQLMMBNBARDPV","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VINBQLMM","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:327a80a2b0ee56acbea08884d4bbc498e39da561a60ba76a591b1faf389f80bf","target":"graph","created_at":"2026-05-18T03:55:01Z","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 norm of a Boolean function $f:\\{0,1\\}^n \\to \\{-1,1\\}$ is the sum of the absolute values of its Fourier coefficients. This quantity provides useful upper and lower bounds on the complexity of a function in areas such as learning theory, circuit complexity, and communication complexity. In this paper, we give a combinatorial characterization for the spectral norm of symmetric functions. We show that the logarithm of the spectral norm is of the same order of magnitude as $r(f)\\log(n/r(f))$ where $r(f) = \\max\\{r_0,r_1\\}$, and $r_0$ and $r_1$ are the smallest integers less than $n/2$ s","authors_text":"Anil Ada, Hamed Hatami, Omar Fawzi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-05-23T20:12:08Z","title":"Spectral Norm of Symmetric Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5282","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":"sha256:6c4035d0791387ed23387eea5156c51f981e30998ba5e63a9c1f66f89aeb630b","target":"record","created_at":"2026-05-18T03:55:01Z","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":"ff63f60688a90711a2fbd2b9db2b77911a2811ce7c03065f94f4246b3409595b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-05-23T20:12:08Z","title_canon_sha256":"8fd78a269fed5ef17b365558e028e1ebd8fb06220f7ef622865d569bb95259c5"},"schema_version":"1.0","source":{"id":"1205.5282","kind":"arxiv","version":1}},"canonical_sha256":"aa1a182d8c0b42088df50e0b72e8fda685fc0802e8f89415fc37f4ecb595b6f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa1a182d8c0b42088df50e0b72e8fda685fc0802e8f89415fc37f4ecb595b6f7","first_computed_at":"2026-05-18T03:55:01.335080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:01.335080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4CHznyFqj1HwqVVTqYZ8g+seIxYJiAaHO7+AKnsvWs4N0UWBu2kEETTJKtgyXUZn17ed7im2I+Hjr8LBt5Q8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:01.335600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c4035d0791387ed23387eea5156c51f981e30998ba5e63a9c1f66f89aeb630b","sha256:327a80a2b0ee56acbea08884d4bbc498e39da561a60ba76a591b1faf389f80bf"],"state_sha256":"d3aa81c170b6f4e9acddf83c7aea9f1491cca9b7d4503df7d011a0cd9e665b2c"}