{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MBZ6FUGT4FYHDI64IDOC2MVRMW","short_pith_number":"pith:MBZ6FUGT","canonical_record":{"source":{"id":"1707.09707","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T03:21:01Z","cross_cats_sorted":[],"title_canon_sha256":"69e1a0b611e3bd8ae91a0b1aed5dfbc6f19454f40b4b8b810903a7b8178c01a5","abstract_canon_sha256":"dd63e27c327aaa0dcd30e5bdf1ffc1fa48d5306d2857f8d30bed7faec8b5de8b"},"schema_version":"1.0"},"canonical_sha256":"6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f","source":{"kind":"arxiv","id":"1707.09707","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09707","created_at":"2026-05-18T00:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09707v5","created_at":"2026-05-18T00:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09707","created_at":"2026-05-18T00:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"MBZ6FUGT4FYH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MBZ6FUGT4FYHDI64","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MBZ6FUGT","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MBZ6FUGT4FYHDI64IDOC2MVRMW","target":"record","payload":{"canonical_record":{"source":{"id":"1707.09707","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T03:21:01Z","cross_cats_sorted":[],"title_canon_sha256":"69e1a0b611e3bd8ae91a0b1aed5dfbc6f19454f40b4b8b810903a7b8178c01a5","abstract_canon_sha256":"dd63e27c327aaa0dcd30e5bdf1ffc1fa48d5306d2857f8d30bed7faec8b5de8b"},"schema_version":"1.0"},"canonical_sha256":"6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:18.554349Z","signature_b64":"jK/wL4j6sQXf0KETWuIARik8IN+3gj/VDwCe6NFGEx54xd0LUUdIhkCIUq3c4P2g4tkkZhMXj0CDD+TxDz8JAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f","last_reissued_at":"2026-05-18T00:07:18.553777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:18.553777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.09707","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h0a5VFfnDaS7ukI8+WfLjgVRk9vj+EaOce3j9rFi6UlP4rHbcLS4oUcZZyHywDMDXQX6wqch13ZnbKRfgR6DAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:38:12.320595Z"},"content_sha256":"a64e5ce11cd60340142c0bfcdf524d14f46e2975519110ce6caa0f14aff26615","schema_version":"1.0","event_id":"sha256:a64e5ce11cd60340142c0bfcdf524d14f46e2975519110ce6caa0f14aff26615"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MBZ6FUGT4FYHDI64IDOC2MVRMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds of triple exponential sums with mixed exponential and linear terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kam Hung Yau","submitted_at":"2017-07-31T03:21:01Z","abstract_excerpt":"We establish bounds of triple exponential sums with mixed exponential and linear function. The method we use is by Shparlinski together with a bound of additive energy from Roche-Newton, Rudnev and Shkredov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09707","kind":"arxiv","version":5},"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":"2026-05-18T00:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4NTXZQ2a+bSdJBglRLo2osIVQf9cdp3VHV3PLukIN4AdAUfjgBExwGxmPaLMgt70ZXWVC3WvxXBmjNoqusKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:38:12.321299Z"},"content_sha256":"d93d8b537b6c4781710d5b1fe32221f00b16859b8569adad90472bba4959453e","schema_version":"1.0","event_id":"sha256:d93d8b537b6c4781710d5b1fe32221f00b16859b8569adad90472bba4959453e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW/bundle.json","state_url":"https://pith.science/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW/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":"2026-06-11T22:38:12Z","links":{"resolver":"https://pith.science/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW","bundle":"https://pith.science/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW/bundle.json","state":"https://pith.science/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MBZ6FUGT4FYHDI64IDOC2MVRMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MBZ6FUGT4FYHDI64IDOC2MVRMW","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":"dd63e27c327aaa0dcd30e5bdf1ffc1fa48d5306d2857f8d30bed7faec8b5de8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T03:21:01Z","title_canon_sha256":"69e1a0b611e3bd8ae91a0b1aed5dfbc6f19454f40b4b8b810903a7b8178c01a5"},"schema_version":"1.0","source":{"id":"1707.09707","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09707","created_at":"2026-05-18T00:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09707v5","created_at":"2026-05-18T00:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09707","created_at":"2026-05-18T00:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"MBZ6FUGT4FYH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MBZ6FUGT4FYHDI64","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MBZ6FUGT","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:d93d8b537b6c4781710d5b1fe32221f00b16859b8569adad90472bba4959453e","target":"graph","created_at":"2026-05-18T00:07:18Z","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 establish bounds of triple exponential sums with mixed exponential and linear function. The method we use is by Shparlinski together with a bound of additive energy from Roche-Newton, Rudnev and Shkredov.","authors_text":"Kam Hung Yau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T03:21:01Z","title":"Bounds of triple exponential sums with mixed exponential and linear terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09707","kind":"arxiv","version":5},"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:a64e5ce11cd60340142c0bfcdf524d14f46e2975519110ce6caa0f14aff26615","target":"record","created_at":"2026-05-18T00:07:18Z","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":"dd63e27c327aaa0dcd30e5bdf1ffc1fa48d5306d2857f8d30bed7faec8b5de8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T03:21:01Z","title_canon_sha256":"69e1a0b611e3bd8ae91a0b1aed5dfbc6f19454f40b4b8b810903a7b8178c01a5"},"schema_version":"1.0","source":{"id":"1707.09707","kind":"arxiv","version":5}},"canonical_sha256":"6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6073e2d0d3e17071a3dc40dc2d32b1659a0017fae51a56a0e88c6ce628dc7c9f","first_computed_at":"2026-05-18T00:07:18.553777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:18.553777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jK/wL4j6sQXf0KETWuIARik8IN+3gj/VDwCe6NFGEx54xd0LUUdIhkCIUq3c4P2g4tkkZhMXj0CDD+TxDz8JAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:18.554349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.09707","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a64e5ce11cd60340142c0bfcdf524d14f46e2975519110ce6caa0f14aff26615","sha256:d93d8b537b6c4781710d5b1fe32221f00b16859b8569adad90472bba4959453e"],"state_sha256":"1d58e722fc66a2fb5f52f114dac899b5e8f3e3e77a834a1ad795a4a1d3d1dfd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZbrZ7btgQIDC3Zyhdi+Czs/pS1U1OBkXTsRYelQTkoc6D5v4bKwj7ZEq+cv2JgR9NbUahbMi2nKKDY9jWWT8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:38:12.325595Z","bundle_sha256":"6ef87137d6d6daaf7afe956f58cff1e9b4513d00fd79add3351e4ddc083100e0"}}