{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5RECAHMHADWFVY6E2UDSKDM4VZ","short_pith_number":"pith:5RECAHMH","canonical_record":{"source":{"id":"1510.00950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-04T16:38:48Z","cross_cats_sorted":[],"title_canon_sha256":"b9a2a2775de9410038ca2bc4e3e286a4d491538d3264acaccee83a2e226014bc","abstract_canon_sha256":"14e1c29d5585553b6e525964363c7fb74ccc32ca7e9ba6a1de1f1c76f2a8318a"},"schema_version":"1.0"},"canonical_sha256":"ec48201d8700ec5ae3c4d507250d9cae4599455144eceb874929142833f733db","source":{"kind":"arxiv","id":"1510.00950","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00950","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00950v2","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00950","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"5RECAHMHADWF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5RECAHMHADWFVY6E","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5RECAHMH","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5RECAHMHADWFVY6E2UDSKDM4VZ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-04T16:38:48Z","cross_cats_sorted":[],"title_canon_sha256":"b9a2a2775de9410038ca2bc4e3e286a4d491538d3264acaccee83a2e226014bc","abstract_canon_sha256":"14e1c29d5585553b6e525964363c7fb74ccc32ca7e9ba6a1de1f1c76f2a8318a"},"schema_version":"1.0"},"canonical_sha256":"ec48201d8700ec5ae3c4d507250d9cae4599455144eceb874929142833f733db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:25.251907Z","signature_b64":"wlz7dY/cUeV+c3Jnk3m1niUYE35HLl4rDkNxdecjz1pGb1MY+mLpWjoHeFAVQLs6pZfMaGfKSkwd5vLBIO1/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec48201d8700ec5ae3c4d507250d9cae4599455144eceb874929142833f733db","last_reissued_at":"2026-05-18T01:11:25.251376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:25.251376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00950","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9KsfO8sFrqMxNU8caB8/jzgD0SWIU9fANg5NCOUtQbywBb1373Pog/8y3KwFC1wQKJumPPvZ0PKyG6lGJIiZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:40:20.772444Z"},"content_sha256":"f3d1a88226b84dcae08116bfccdd139f8a9b7fb55b5993394f1e4de52a38f344","schema_version":"1.0","event_id":"sha256:f3d1a88226b84dcae08116bfccdd139f8a9b7fb55b5993394f1e4de52a38f344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5RECAHMHADWFVY6E2UDSKDM4VZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit hybrid estimate for $L(1/2+it,\\chi)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ghaith A. Hiary","submitted_at":"2015-10-04T16:38:48Z","abstract_excerpt":"An explicit hybrid estimate for $L(1/2+it,\\chi)$ is derived, where $\\chi$ is a Dirichlet character modulo $q$. The estimate applies when $t$ is bounded away from zero, and is most effective when $q$ is powerfull, yielding an explicit Weyl bound in this case. The estimate takes a particularly simple form if $q$ is a sixth power. Several hybrid lemmas of van der Corput--Weyl type are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00950","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UN62dXWELqrgVvfKTWb8V/vxD/gRjQL0Kdgc5MuiyH0IsmRrkBswWBHJWmI6kMK1yuiYfSl9FMdby00ngN/OCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:40:20.772777Z"},"content_sha256":"83661a1c0f153238d039cd8e8506438a4400f64e6d29b5c874bcf3ec494052da","schema_version":"1.0","event_id":"sha256:83661a1c0f153238d039cd8e8506438a4400f64e6d29b5c874bcf3ec494052da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RECAHMHADWFVY6E2UDSKDM4VZ/bundle.json","state_url":"https://pith.science/pith/5RECAHMHADWFVY6E2UDSKDM4VZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RECAHMHADWFVY6E2UDSKDM4VZ/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":"2026-06-27T13:40:20Z","links":{"resolver":"https://pith.science/pith/5RECAHMHADWFVY6E2UDSKDM4VZ","bundle":"https://pith.science/pith/5RECAHMHADWFVY6E2UDSKDM4VZ/bundle.json","state":"https://pith.science/pith/5RECAHMHADWFVY6E2UDSKDM4VZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RECAHMHADWFVY6E2UDSKDM4VZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5RECAHMHADWFVY6E2UDSKDM4VZ","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":"14e1c29d5585553b6e525964363c7fb74ccc32ca7e9ba6a1de1f1c76f2a8318a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-04T16:38:48Z","title_canon_sha256":"b9a2a2775de9410038ca2bc4e3e286a4d491538d3264acaccee83a2e226014bc"},"schema_version":"1.0","source":{"id":"1510.00950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00950","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00950v2","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00950","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"5RECAHMHADWF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5RECAHMHADWFVY6E","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5RECAHMH","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:83661a1c0f153238d039cd8e8506438a4400f64e6d29b5c874bcf3ec494052da","target":"graph","created_at":"2026-05-18T01:11:25Z","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":"An explicit hybrid estimate for $L(1/2+it,\\chi)$ is derived, where $\\chi$ is a Dirichlet character modulo $q$. The estimate applies when $t$ is bounded away from zero, and is most effective when $q$ is powerfull, yielding an explicit Weyl bound in this case. The estimate takes a particularly simple form if $q$ is a sixth power. Several hybrid lemmas of van der Corput--Weyl type are presented.","authors_text":"Ghaith A. Hiary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-04T16:38:48Z","title":"An explicit hybrid estimate for $L(1/2+it,\\chi)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00950","kind":"arxiv","version":2},"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:f3d1a88226b84dcae08116bfccdd139f8a9b7fb55b5993394f1e4de52a38f344","target":"record","created_at":"2026-05-18T01:11:25Z","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":"14e1c29d5585553b6e525964363c7fb74ccc32ca7e9ba6a1de1f1c76f2a8318a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-04T16:38:48Z","title_canon_sha256":"b9a2a2775de9410038ca2bc4e3e286a4d491538d3264acaccee83a2e226014bc"},"schema_version":"1.0","source":{"id":"1510.00950","kind":"arxiv","version":2}},"canonical_sha256":"ec48201d8700ec5ae3c4d507250d9cae4599455144eceb874929142833f733db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec48201d8700ec5ae3c4d507250d9cae4599455144eceb874929142833f733db","first_computed_at":"2026-05-18T01:11:25.251376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:25.251376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wlz7dY/cUeV+c3Jnk3m1niUYE35HLl4rDkNxdecjz1pGb1MY+mLpWjoHeFAVQLs6pZfMaGfKSkwd5vLBIO1/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:25.251907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3d1a88226b84dcae08116bfccdd139f8a9b7fb55b5993394f1e4de52a38f344","sha256:83661a1c0f153238d039cd8e8506438a4400f64e6d29b5c874bcf3ec494052da"],"state_sha256":"eae589ae6b00d2e70861ce2056c326e1ecc8e2360a1a6d50b2f87b646ac17f27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4g2HEL5877RZtmj3y6wlKd/LXItxA9ePGOpjMTuizUa22c7tCgEJH67VP8UFV+bTJSdp/hrqRN7bNgYIF6TdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:40:20.774784Z","bundle_sha256":"247b705cdf09d5988f137015f29f9cfbb38181be32351d7309776601bdce1bb6"}}