{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T337XWSOWKPJY5XWAPZQIB2DPG","short_pith_number":"pith:T337XWSO","canonical_record":{"source":{"id":"1507.01261","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-05T19:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"a72ee8c1ce53cf9a7eacf4f09ad10ad1b63413dc4c39c54382f35ab0027a2a5c","abstract_canon_sha256":"decf8235914818449e58a0cc0a81256fabc969a713aa0190287576ac1ce0e861"},"schema_version":"1.0"},"canonical_sha256":"9ef7fbda4eb29e9c76f603f304074379979b910c621bb71e4c5cf556b5f78c1d","source":{"kind":"arxiv","id":"1507.01261","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01261","created_at":"2026-05-18T01:30:48Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01261v4","created_at":"2026-05-18T01:30:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01261","created_at":"2026-05-18T01:30:48Z"},{"alias_kind":"pith_short_12","alias_value":"T337XWSOWKPJ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T337XWSOWKPJY5XW","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T337XWSO","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T337XWSOWKPJY5XWAPZQIB2DPG","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01261","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-05T19:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"a72ee8c1ce53cf9a7eacf4f09ad10ad1b63413dc4c39c54382f35ab0027a2a5c","abstract_canon_sha256":"decf8235914818449e58a0cc0a81256fabc969a713aa0190287576ac1ce0e861"},"schema_version":"1.0"},"canonical_sha256":"9ef7fbda4eb29e9c76f603f304074379979b910c621bb71e4c5cf556b5f78c1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:48.741289Z","signature_b64":"VpvmVqAfRbtW9TFTX2LhRbE1uqnFLhEkLop2FSZRxpaaJ8iTlLQMLYobkdjj9zAbN1yMnGkmu2cXsVV7Ou3gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ef7fbda4eb29e9c76f603f304074379979b910c621bb71e4c5cf556b5f78c1d","last_reissued_at":"2026-05-18T01:30:48.740894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:48.740894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01261","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCdu9gt8CVWWOo/kdLbwxCfl1i+gdgrbLqM6GEIpEbJXaG5lgV5OYkyV9mUqSwGjooXQILD8X4xLJLuU0Xg3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:48:22.064009Z"},"content_sha256":"675c1ce06ac8cb06fa76d036d2ca5b0a4b2651af118b5d22d1ded62291b60e65","schema_version":"1.0","event_id":"sha256:675c1ce06ac8cb06fa76d036d2ca5b0a4b2651af118b5d22d1ded62291b60e65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T337XWSOWKPJY5XWAPZQIB2DPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit van der Corput estimate for $\\zeta(1/2+it)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ghaith A. Hiary","submitted_at":"2015-07-05T19:23:07Z","abstract_excerpt":"An explicit estimate for the Riemann zeta function on the critical line is derived using the van der Corput method. An explicit van der Corput lemma is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01261","kind":"arxiv","version":4},"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":"2026-05-18T01:30:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CDU+XU6XrIUfhmkT05rA3JkR85Ebn5YczSfz5uH6eRRYTb7BlAa5mkjt3euM7cHB1GA+QrmaeUcAZQPMsW9rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:48:22.064355Z"},"content_sha256":"d8418ed918c00624bae7867b96923cbe5f12b3d835f59b076b2917c51d043732","schema_version":"1.0","event_id":"sha256:d8418ed918c00624bae7867b96923cbe5f12b3d835f59b076b2917c51d043732"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T337XWSOWKPJY5XWAPZQIB2DPG/bundle.json","state_url":"https://pith.science/pith/T337XWSOWKPJY5XWAPZQIB2DPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T337XWSOWKPJY5XWAPZQIB2DPG/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":"2026-06-27T15:48:22Z","links":{"resolver":"https://pith.science/pith/T337XWSOWKPJY5XWAPZQIB2DPG","bundle":"https://pith.science/pith/T337XWSOWKPJY5XWAPZQIB2DPG/bundle.json","state":"https://pith.science/pith/T337XWSOWKPJY5XWAPZQIB2DPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T337XWSOWKPJY5XWAPZQIB2DPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T337XWSOWKPJY5XWAPZQIB2DPG","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":"decf8235914818449e58a0cc0a81256fabc969a713aa0190287576ac1ce0e861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-05T19:23:07Z","title_canon_sha256":"a72ee8c1ce53cf9a7eacf4f09ad10ad1b63413dc4c39c54382f35ab0027a2a5c"},"schema_version":"1.0","source":{"id":"1507.01261","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01261","created_at":"2026-05-18T01:30:48Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01261v4","created_at":"2026-05-18T01:30:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01261","created_at":"2026-05-18T01:30:48Z"},{"alias_kind":"pith_short_12","alias_value":"T337XWSOWKPJ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T337XWSOWKPJY5XW","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T337XWSO","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:d8418ed918c00624bae7867b96923cbe5f12b3d835f59b076b2917c51d043732","target":"graph","created_at":"2026-05-18T01:30:48Z","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 estimate for the Riemann zeta function on the critical line is derived using the van der Corput method. An explicit van der Corput lemma is presented.","authors_text":"Ghaith A. Hiary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-05T19:23:07Z","title":"An explicit van der Corput estimate for $\\zeta(1/2+it)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01261","kind":"arxiv","version":4},"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":"sha256:675c1ce06ac8cb06fa76d036d2ca5b0a4b2651af118b5d22d1ded62291b60e65","target":"record","created_at":"2026-05-18T01:30:48Z","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":"decf8235914818449e58a0cc0a81256fabc969a713aa0190287576ac1ce0e861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-05T19:23:07Z","title_canon_sha256":"a72ee8c1ce53cf9a7eacf4f09ad10ad1b63413dc4c39c54382f35ab0027a2a5c"},"schema_version":"1.0","source":{"id":"1507.01261","kind":"arxiv","version":4}},"canonical_sha256":"9ef7fbda4eb29e9c76f603f304074379979b910c621bb71e4c5cf556b5f78c1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ef7fbda4eb29e9c76f603f304074379979b910c621bb71e4c5cf556b5f78c1d","first_computed_at":"2026-05-18T01:30:48.740894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:48.740894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VpvmVqAfRbtW9TFTX2LhRbE1uqnFLhEkLop2FSZRxpaaJ8iTlLQMLYobkdjj9zAbN1yMnGkmu2cXsVV7Ou3gCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:48.741289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01261","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675c1ce06ac8cb06fa76d036d2ca5b0a4b2651af118b5d22d1ded62291b60e65","sha256:d8418ed918c00624bae7867b96923cbe5f12b3d835f59b076b2917c51d043732"],"state_sha256":"2ce1c70630e3debe940d1056959f26800be1034b5e9e64134305b63de4e6ee1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3+SjRKoU9ufFA9C5y8UUuK9VswuHzC/gHeA8xXkNoHhK6451A39TVb9xfHz5DDb+cC94OMMqnWEmVoqJcchDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:48:22.066179Z","bundle_sha256":"7720923696efa4803f123d516ad00ed7d3b110ac5ccf2fce91a7b20fa14d88e3"}}