{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DWN45BIM6BVUYXDYJBOALLC2Q7","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":"6dfaa0c2c85351fdb5788b6d1c9f1d908ec92f38b5c4c3e5f59c0472d4b96af0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T19:40:53Z","title_canon_sha256":"024f25c0d0547b86f01bd26ce233c293dfc6e8a4887b614fbfeb923b46042fe4"},"schema_version":"1.0","source":{"id":"2607.01424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01424","created_at":"2026-07-03T00:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01424v1","created_at":"2026-07-03T00:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01424","created_at":"2026-07-03T00:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"DWN45BIM6BVU","created_at":"2026-07-03T00:16:59Z"},{"alias_kind":"pith_short_16","alias_value":"DWN45BIM6BVUYXDY","created_at":"2026-07-03T00:16:59Z"},{"alias_kind":"pith_short_8","alias_value":"DWN45BIM","created_at":"2026-07-03T00:16:59Z"}],"graph_snapshots":[{"event_id":"sha256:1e1c87fc26d2784733107f9893539c242bc07969747f8508b43adb07d0bdb22c","target":"graph","created_at":"2026-07-03T00:16:59Z","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/2607.01424/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We demonstrate an improved explicit upper bound of $|\\zeta(1+it)|$ for $3 \\leq t \\leq 10^9$ using smoothing techniques. Our method sharpens previous bounds relying on the Riemann--Siegel formula and the triangle inequality. In particular, we prove that for $t\\geq 3$, \\begin{align*}\n  |\\zeta(1+it)| \\leq \\frac{1}{2}\\log t + 1.57 \\end{align*} and for $t \\geq 10^8$, \\[ |\\zeta(1+it)|\\leq \\frac{1}{3}\\log t + 2\\log \\log t -1.16 . \\]","authors_text":"Andrew Christensen, Kyle Pratt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T19:40:53Z","title":"Utilizing Smoothing Techniques to Bound $|\\zeta(1+it)|$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01424","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:c24284ce7fa9a1024ae98ae190fc44af396355521afba2af52e55df4d482e136","target":"record","created_at":"2026-07-03T00:16:59Z","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":"6dfaa0c2c85351fdb5788b6d1c9f1d908ec92f38b5c4c3e5f59c0472d4b96af0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T19:40:53Z","title_canon_sha256":"024f25c0d0547b86f01bd26ce233c293dfc6e8a4887b614fbfeb923b46042fe4"},"schema_version":"1.0","source":{"id":"2607.01424","kind":"arxiv","version":1}},"canonical_sha256":"1d9bce850cf06b4c5c78485c05ac5a87d9254914b99f60236c5c3d2ed5bd2c6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d9bce850cf06b4c5c78485c05ac5a87d9254914b99f60236c5c3d2ed5bd2c6f","first_computed_at":"2026-07-03T00:16:59.926161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T00:16:59.926161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/ioWkgFANoZv+/Ait9cWS4lxg8hNKA0ISBODDWnpYnpV8eul8BYSTgxPuyIqw/xNVvvibIK7oZWp/Fs2nK3DA==","signature_status":"signed_v1","signed_at":"2026-07-03T00:16:59.926588Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c24284ce7fa9a1024ae98ae190fc44af396355521afba2af52e55df4d482e136","sha256:1e1c87fc26d2784733107f9893539c242bc07969747f8508b43adb07d0bdb22c"],"state_sha256":"2266e6d3a9d0d7f3b99279a0161ac6f561e36620886537d42ef70035fa03365b"}