{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IWGGQENG4V5OCNIHWIHJ2NTN24","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":"d48bd54b2dfbe20bdfaae2955de683105d797cffcfa6ad396f5d0abc5e1663d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-26T16:33:01Z","title_canon_sha256":"b4691b45718476913d0c3461ea8a0de5e5b59420c35276dea64c4fc017407463"},"schema_version":"1.0","source":{"id":"1411.7291","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7291","created_at":"2026-05-18T00:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7291v1","created_at":"2026-05-18T00:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7291","created_at":"2026-05-18T00:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"IWGGQENG4V5O","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IWGGQENG4V5OCNIH","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IWGGQENG","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:99b4482845fa4c6b36a6653ff650c6e67cb3259d193abde6b4f3708d622611b2","target":"graph","created_at":"2026-05-18T00:39:58Z","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":"Let $J_n\\subset[1,n]$, $n=1,2,\\ldots$ be increasing sets of mutually coprime numbers. Under reasonable conditions on the coefficient sequence $\\{c^j_n\\}_{n,j}$, we show that $$ \\lim_{T\\to \\infty}\\frac{1}{T} \\int_{0}^T \\Big| \\sum_{j\\in J_n} c^j_n\\,j^{it}\\Big| \\dd t\\sim \\big(\\frac{\\pi} {2}\\sum_{j\\in J_n} (c^j_n)^2\\big)^{1/2} $$ as $n\\to \\infty$. We also show by means of an elementary device that for all $0<\\a<2$, \\begin{eqnarray*}\n  \\lim_{T\\to \\infty} \\Big(\\frac{1}{T} \\int_{0}^T \\big| \\sum_{n=1}^N n^{-it}\\big|^\\a\\dd t\\Big)^{1/\\a} \\ge C_\\a\\, \\frac{ N^{\\frac{1}{2}}} {\\big( \\log N\\big)^{{\\frac{1}{\\","authors_text":"Michel Weber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-26T16:33:01Z","title":"$\\boldsymbol L^{\\boldsymbol 1}$-Norm of Steinhaus chaose on the polydisc"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7291","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":"sha256:7a9eb4248790af82ea337cecfe0ef3b7a5bda4d8a38e67e0b8e93949d7097f06","target":"record","created_at":"2026-05-18T00:39:58Z","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":"d48bd54b2dfbe20bdfaae2955de683105d797cffcfa6ad396f5d0abc5e1663d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-26T16:33:01Z","title_canon_sha256":"b4691b45718476913d0c3461ea8a0de5e5b59420c35276dea64c4fc017407463"},"schema_version":"1.0","source":{"id":"1411.7291","kind":"arxiv","version":1}},"canonical_sha256":"458c6811a6e57ae13507b20e9d366dd7389760752e363a4c578b91c51624d93d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"458c6811a6e57ae13507b20e9d366dd7389760752e363a4c578b91c51624d93d","first_computed_at":"2026-05-18T00:39:58.713472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:58.713472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WMjeGT297CiNZ4cA1rFLMhtu1jWbrwUz8oXlTMXLy2fLvrw1UywQkC1/AWgjPCIwpbtppSN3NLubDun4m3cxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:58.713935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7291","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a9eb4248790af82ea337cecfe0ef3b7a5bda4d8a38e67e0b8e93949d7097f06","sha256:99b4482845fa4c6b36a6653ff650c6e67cb3259d193abde6b4f3708d622611b2"],"state_sha256":"002dda488ccc4aeeb5f67569321942d4b5e770d159a8838864504cf23b86c7df"}