{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3BQGVATKUZDS3YRQ5CQMFKITDJ","short_pith_number":"pith:3BQGVATK","canonical_record":{"source":{"id":"2506.09334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-11T02:27:44Z","cross_cats_sorted":[],"title_canon_sha256":"d99522fa5a11e2c9ba54d01ba1fb6324e30aa49c9b613f79999804cb719617d7","abstract_canon_sha256":"b2743e3e0e664e597aa87820e20cbb6104f97875bfa1d7bbb3a244b76b8a0f1c"},"schema_version":"1.0"},"canonical_sha256":"d8606a826aa6472de230e8a0c2a9131a4172b3e45cf3969aa0b0ecf243ba9fa1","source":{"kind":"arxiv","id":"2506.09334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09334","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09334v1","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09334","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"3BQGVATKUZDS","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"pith_short_16","alias_value":"3BQGVATKUZDS3YRQ","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"pith_short_8","alias_value":"3BQGVATK","created_at":"2026-07-05T11:19:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3BQGVATKUZDS3YRQ5CQMFKITDJ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.09334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-11T02:27:44Z","cross_cats_sorted":[],"title_canon_sha256":"d99522fa5a11e2c9ba54d01ba1fb6324e30aa49c9b613f79999804cb719617d7","abstract_canon_sha256":"b2743e3e0e664e597aa87820e20cbb6104f97875bfa1d7bbb3a244b76b8a0f1c"},"schema_version":"1.0"},"canonical_sha256":"d8606a826aa6472de230e8a0c2a9131a4172b3e45cf3969aa0b0ecf243ba9fa1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:34.951009Z","signature_b64":"IjcQLzBD+gmT+ot+WgJP58Hlfpd0S1/Kb7swPrTeEdkSY22YAKe2+NaUFc2YvHMgv8Ok5YsGa4cijTU/Ds23Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8606a826aa6472de230e8a0c2a9131a4172b3e45cf3969aa0b0ecf243ba9fa1","last_reissued_at":"2026-07-05T11:19:34.950590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:34.950590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.09334","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:19:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+W17SW5faIFYFaTrF2VfZ048WD6WdaQuYYratyFUcQIQMTJqbHTXAe1SKYTVk+nk4igGHBYEPVkt3LpmuVmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:17:36.637332Z"},"content_sha256":"5f557ea4d19442607dd8f3c50ff1ea74c5ee09ef7deaaa97d7742c58ab82bbbf","schema_version":"1.0","event_id":"sha256:5f557ea4d19442607dd8f3c50ff1ea74c5ee09ef7deaaa97d7742c58ab82bbbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3BQGVATKUZDS3YRQ5CQMFKITDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bounds for high moments of zeta sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hao Zhang, Weijia Wang, Zikang Dong","submitted_at":"2025-06-11T02:27:44Z","abstract_excerpt":"In this article, we investigate high moments of zeta sums $\\sum_{n\\le x}n^{i t}$. We show unconditional lower bounds for them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09334","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.09334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:19:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PhJd+0L4WrF6S6RSxY4icQGxv7tWuoC6xMymWN0Bz8Fud/5zhBkKOH5bM5GInlt+qpxygqAJzFDADzACnEazAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:17:36.637817Z"},"content_sha256":"10261bd10923ec5a0bf352aa8fd6c7b0339c98cc1d5395dac241b66465536262","schema_version":"1.0","event_id":"sha256:10261bd10923ec5a0bf352aa8fd6c7b0339c98cc1d5395dac241b66465536262"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ/bundle.json","state_url":"https://pith.science/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T04:17:36Z","links":{"resolver":"https://pith.science/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ","bundle":"https://pith.science/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ/bundle.json","state":"https://pith.science/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BQGVATKUZDS3YRQ5CQMFKITDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3BQGVATKUZDS3YRQ5CQMFKITDJ","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":"b2743e3e0e664e597aa87820e20cbb6104f97875bfa1d7bbb3a244b76b8a0f1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-11T02:27:44Z","title_canon_sha256":"d99522fa5a11e2c9ba54d01ba1fb6324e30aa49c9b613f79999804cb719617d7"},"schema_version":"1.0","source":{"id":"2506.09334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09334","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09334v1","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09334","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"3BQGVATKUZDS","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"pith_short_16","alias_value":"3BQGVATKUZDS3YRQ","created_at":"2026-07-05T11:19:34Z"},{"alias_kind":"pith_short_8","alias_value":"3BQGVATK","created_at":"2026-07-05T11:19:34Z"}],"graph_snapshots":[{"event_id":"sha256:10261bd10923ec5a0bf352aa8fd6c7b0339c98cc1d5395dac241b66465536262","target":"graph","created_at":"2026-07-05T11:19:34Z","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/2506.09334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we investigate high moments of zeta sums $\\sum_{n\\le x}n^{i t}$. We show unconditional lower bounds for them.","authors_text":"Hao Zhang, Weijia Wang, Zikang Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-11T02:27:44Z","title":"Lower bounds for high moments of zeta sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09334","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":"sha256:5f557ea4d19442607dd8f3c50ff1ea74c5ee09ef7deaaa97d7742c58ab82bbbf","target":"record","created_at":"2026-07-05T11:19:34Z","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":"b2743e3e0e664e597aa87820e20cbb6104f97875bfa1d7bbb3a244b76b8a0f1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-06-11T02:27:44Z","title_canon_sha256":"d99522fa5a11e2c9ba54d01ba1fb6324e30aa49c9b613f79999804cb719617d7"},"schema_version":"1.0","source":{"id":"2506.09334","kind":"arxiv","version":1}},"canonical_sha256":"d8606a826aa6472de230e8a0c2a9131a4172b3e45cf3969aa0b0ecf243ba9fa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8606a826aa6472de230e8a0c2a9131a4172b3e45cf3969aa0b0ecf243ba9fa1","first_computed_at":"2026-07-05T11:19:34.950590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:34.950590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IjcQLzBD+gmT+ot+WgJP58Hlfpd0S1/Kb7swPrTeEdkSY22YAKe2+NaUFc2YvHMgv8Ok5YsGa4cijTU/Ds23Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:34.951009Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f557ea4d19442607dd8f3c50ff1ea74c5ee09ef7deaaa97d7742c58ab82bbbf","sha256:10261bd10923ec5a0bf352aa8fd6c7b0339c98cc1d5395dac241b66465536262"],"state_sha256":"e744970b366c36b4e60b432969c28387fc00f70284346f28f41f8506901320ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QAljs37sz46cE8azjtYxM/MiIO5dvi+B6g/FgRkZR81gH3a5AaMJqgmFvZp7ZquGaN6YK0VWd+nGUt+F/aLuCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:17:36.642567Z","bundle_sha256":"0f8516dc926852349a0b43659eddc5a5e8a705d3e535154e2af06f9735d4eecd"}}