{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HUXPM747G42L6HXN7JSLEP653R","short_pith_number":"pith:HUXPM747","canonical_record":{"source":{"id":"1512.04711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T10:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"4ec09074a6c7ec416e143f75bb6fb40a30bf8475cbbd0dd5875ffcfbeeab6816","abstract_canon_sha256":"34e9f050e987ac3a37b5445371cf06d49c8fe34b4083a886600e2415a35f94e3"},"schema_version":"1.0"},"canonical_sha256":"3d2ef67f9f3734bf1eedfa64b23fdddc5536c322ac0106c7096d0d7b3a637f37","source":{"kind":"arxiv","id":"1512.04711","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04711","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04711v1","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04711","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"HUXPM747G42L","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HUXPM747G42L6HXN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HUXPM747","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HUXPM747G42L6HXN7JSLEP653R","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T10:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"4ec09074a6c7ec416e143f75bb6fb40a30bf8475cbbd0dd5875ffcfbeeab6816","abstract_canon_sha256":"34e9f050e987ac3a37b5445371cf06d49c8fe34b4083a886600e2415a35f94e3"},"schema_version":"1.0"},"canonical_sha256":"3d2ef67f9f3734bf1eedfa64b23fdddc5536c322ac0106c7096d0d7b3a637f37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:19.609807Z","signature_b64":"i7tXX8FjbUksJFLwANjeMeAVwOFbt8+i5tHT5vephZes2CPgv6y8wKYxexf4omWSHvPbjo8khnO/Xj5tQ7pyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d2ef67f9f3734bf1eedfa64b23fdddc5536c322ac0106c7096d0d7b3a637f37","last_reissued_at":"2026-05-18T01:24:19.609391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:19.609391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04711","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":"2026-05-18T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ry3rZk02aoQTkcm8Hwrr0QSoFeBSCy0Q3u0q29MdcZB1oRIgIsEy2IaVBO8FBU5Nofe6q2PYP4L+LtomkiD+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:13:49.980454Z"},"content_sha256":"11d977aa0d01072ad3cf90a47f4ccc38c37779d0261b1f9c51663162097c9983","schema_version":"1.0","event_id":"sha256:11d977aa0d01072ad3cf90a47f4ccc38c37779d0261b1f9c51663162097c9983"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HUXPM747G42L6HXN7JSLEP653R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A cotangent sum related to zeros of the Estermann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael Th. Rassias","submitted_at":"2015-12-15T10:32:22Z","abstract_excerpt":"We consider a cotangent sum related to Estermann's Zeta function. We provide an elementary and self-contained improvement of the error term in an asymptotic formula proved by V. I. Vasyunin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04711","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":""},"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":"2026-05-18T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lCs7at0t4ZODPQ3nFh1/QfZnRfJZRt/d4UWWWChhY27q19AgWn4L+G9rkg3WmP0hf4LxDh92+xy8tXP8usm1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:13:49.981091Z"},"content_sha256":"f48b28c9de6b4da92c022c6a6f266f6f25e5f51ecc4abc2576a77caedb8b50af","schema_version":"1.0","event_id":"sha256:f48b28c9de6b4da92c022c6a6f266f6f25e5f51ecc4abc2576a77caedb8b50af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUXPM747G42L6HXN7JSLEP653R/bundle.json","state_url":"https://pith.science/pith/HUXPM747G42L6HXN7JSLEP653R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUXPM747G42L6HXN7JSLEP653R/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":"2026-05-31T01:13:49Z","links":{"resolver":"https://pith.science/pith/HUXPM747G42L6HXN7JSLEP653R","bundle":"https://pith.science/pith/HUXPM747G42L6HXN7JSLEP653R/bundle.json","state":"https://pith.science/pith/HUXPM747G42L6HXN7JSLEP653R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUXPM747G42L6HXN7JSLEP653R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HUXPM747G42L6HXN7JSLEP653R","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":"34e9f050e987ac3a37b5445371cf06d49c8fe34b4083a886600e2415a35f94e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T10:32:22Z","title_canon_sha256":"4ec09074a6c7ec416e143f75bb6fb40a30bf8475cbbd0dd5875ffcfbeeab6816"},"schema_version":"1.0","source":{"id":"1512.04711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04711","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04711v1","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04711","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"HUXPM747G42L","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HUXPM747G42L6HXN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HUXPM747","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:f48b28c9de6b4da92c022c6a6f266f6f25e5f51ecc4abc2576a77caedb8b50af","target":"graph","created_at":"2026-05-18T01:24:19Z","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":"We consider a cotangent sum related to Estermann's Zeta function. We provide an elementary and self-contained improvement of the error term in an asymptotic formula proved by V. I. Vasyunin.","authors_text":"Michael Th. Rassias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T10:32:22Z","title":"A cotangent sum related to zeros of the Estermann zeta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04711","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":"sha256:11d977aa0d01072ad3cf90a47f4ccc38c37779d0261b1f9c51663162097c9983","target":"record","created_at":"2026-05-18T01:24:19Z","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":"34e9f050e987ac3a37b5445371cf06d49c8fe34b4083a886600e2415a35f94e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T10:32:22Z","title_canon_sha256":"4ec09074a6c7ec416e143f75bb6fb40a30bf8475cbbd0dd5875ffcfbeeab6816"},"schema_version":"1.0","source":{"id":"1512.04711","kind":"arxiv","version":1}},"canonical_sha256":"3d2ef67f9f3734bf1eedfa64b23fdddc5536c322ac0106c7096d0d7b3a637f37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d2ef67f9f3734bf1eedfa64b23fdddc5536c322ac0106c7096d0d7b3a637f37","first_computed_at":"2026-05-18T01:24:19.609391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:19.609391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7tXX8FjbUksJFLwANjeMeAVwOFbt8+i5tHT5vephZes2CPgv6y8wKYxexf4omWSHvPbjo8khnO/Xj5tQ7pyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:19.609807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11d977aa0d01072ad3cf90a47f4ccc38c37779d0261b1f9c51663162097c9983","sha256:f48b28c9de6b4da92c022c6a6f266f6f25e5f51ecc4abc2576a77caedb8b50af"],"state_sha256":"7402cbbe079cdc8bd2a924622ab81fc3307fa862a0afcdb7825d039c5fd272a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4E9l9H9I+xLPWMjsH5WIDIa5m7qvJHdHWmmTU/dAYibZnMEHbkg4+QoMPmXrVy0Mstr3vxoZDbpjl+GnkbpoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:13:49.984243Z","bundle_sha256":"de617b41079d4ef7a41bd1e70bcf1f8b9d3c172a770ae8e2d79aa04551563f9f"}}