{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CYCLAEIP6YOS3DVUBX6KHHFLVM","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":"e8d87abf853faa095f7b4069e766317a67ffb9a444877da7bf2475cd677566fd","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-08T23:09:36Z","title_canon_sha256":"b21b0259092cd2be5f4c051b3dcce4ac3fef4bf727b3d7db47c8828802985552"},"schema_version":"1.0","source":{"id":"2606.10242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10242","created_at":"2026-06-10T01:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10242v1","created_at":"2026-06-10T01:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10242","created_at":"2026-06-10T01:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"CYCLAEIP6YOS","created_at":"2026-06-10T01:09:01Z"},{"alias_kind":"pith_short_16","alias_value":"CYCLAEIP6YOS3DVU","created_at":"2026-06-10T01:09:01Z"},{"alias_kind":"pith_short_8","alias_value":"CYCLAEIP","created_at":"2026-06-10T01:09:01Z"}],"graph_snapshots":[{"event_id":"sha256:996102bb654752f4d8c4cf5b1c82a235e3a34f0e2e954cb1fa2bd906cfb8af81","target":"graph","created_at":"2026-06-10T01:09:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.10242/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Conditional on the Generalized Riemann Hypothesis for $L(s,\\chi)$, we prove the Selberg--Tsang high-moment bound for $X_\\chi(t) = \\operatorname{Im}\\log L(\\tfrac12+it,\\chi)$ at fixed squarefree odd conductor $q \\ge 3$ and primitive non-principal character $\\chi$. Writing $L_T = \\log\\log(qT)$: for every $K > 0$ there exist constants $C_K$ and $T_0$ such that $\\frac{1}{T}\\int_T^{2T} |X_\\chi(t)|^{2k}\\,dt \\le (C_K\\,k\\,L_T)^k$ for all $T \\ge T_0$ and every integer $1 \\le k \\le K L_T$. The proof ports Selberg's pointwise approximate formula for $S(t)$ to $L(s,\\chi)$ at fixed conductor under GRH, spli","authors_text":"Scott D. Hughes","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-08T23:09:36Z","title":"A Tsang-range high-moment bound for $\\operatorname{Im}\\log L(\\tfrac12+it,\\chi)$ under GRH"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10242","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":"sha256:4faf4c9058f9da3b25e0ea24d19aef3f6793a38d1152eb0cac932676a86c2c0d","target":"record","created_at":"2026-06-10T01:09:01Z","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":"e8d87abf853faa095f7b4069e766317a67ffb9a444877da7bf2475cd677566fd","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-08T23:09:36Z","title_canon_sha256":"b21b0259092cd2be5f4c051b3dcce4ac3fef4bf727b3d7db47c8828802985552"},"schema_version":"1.0","source":{"id":"2606.10242","kind":"arxiv","version":1}},"canonical_sha256":"1604b0110ff61d2d8eb40dfca39cabab07286759032817bb37ee3ce036454076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1604b0110ff61d2d8eb40dfca39cabab07286759032817bb37ee3ce036454076","first_computed_at":"2026-06-10T01:09:01.890006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:01.890006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jgv+qtZtlz5SsUqmRphJlpvKISugH2ug2DnFcspMcSz2pKtl2PYuD7QyrWMmTyP+Forj9gNp0zrr9vt+pEaPBg==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:01.891057Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4faf4c9058f9da3b25e0ea24d19aef3f6793a38d1152eb0cac932676a86c2c0d","sha256:996102bb654752f4d8c4cf5b1c82a235e3a34f0e2e954cb1fa2bd906cfb8af81"],"state_sha256":"e53bd37ac3e17f1647ea6dcb8b1c214a30e3cedd7291820ce5550f0ba0d9c22c"}