{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZE54MO5CCCNUBV6EASDFF26J7Z","short_pith_number":"pith:ZE54MO5C","canonical_record":{"source":{"id":"1502.00769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-03T07:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"839706935efbe6c3b0eee54fa9c39a1e103752c1552b92a6d63a5a71c544a0d2","abstract_canon_sha256":"ddfe03570272fa123a51166e86cbdfb2e449363769fb8f93292b970ed69dff5f"},"schema_version":"1.0"},"canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","source":{"kind":"arxiv","id":"1502.00769","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00769","created_at":"2026-05-18T00:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00769v1","created_at":"2026-05-18T00:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00769","created_at":"2026-05-18T00:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZE54MO5CCCNU","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZE54MO5CCCNUBV6E","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZE54MO5C","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZE54MO5CCCNUBV6EASDFF26J7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-03T07:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"839706935efbe6c3b0eee54fa9c39a1e103752c1552b92a6d63a5a71c544a0d2","abstract_canon_sha256":"ddfe03570272fa123a51166e86cbdfb2e449363769fb8f93292b970ed69dff5f"},"schema_version":"1.0"},"canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:52.679964Z","signature_b64":"TBLz2i1dEf0qJ/DxgWoKXl+CPtWb5pn5dy/b4C6DGNFwLDrz85i2XpC9GrvMcWkzJG+Xg5bPT6nJlMgIcJTeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","last_reissued_at":"2026-05-18T00:20:52.677957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:52.677957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00769","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":"2026-05-18T00:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNYGa3n/T0q+isl46YlpXJpkS4AMMZGguUa+YCVQY6YqXEXlU+rMmn2wmk9GJKnpIeXJz66XZJDdoUF/pYBLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:24:31.033081Z"},"content_sha256":"9fa53696d61f7698eaf9b52b8116cfeb7eefbe93a59c1669a801b3e5109b07b8","schema_version":"1.0","event_id":"sha256:9fa53696d61f7698eaf9b52b8116cfeb7eefbe93a59c1669a801b3e5109b07b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZE54MO5CCCNUBV6EASDFF26J7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trilinear forms with Kloosterman fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sandro Bettin, Vorrapan Chandee","submitted_at":"2015-02-03T07:57:21Z","abstract_excerpt":"We give new bounds for $\\sum_{{a, m ,n}}\\alpha_{m}\\beta_n\\nu_a {\\textrm e}\\left(\\frac{a\\overline m}{n}\\right)$ where $\\alpha_{m}$, $\\beta_n$ and $\\nu_a$ are arbitrary coefficients, improving upon a result of Duke, Friedlander and Iwaniec [DFI97]. We also apply these bounds to problems on representations by determinant equations and on the equidistribution of solutions to linear equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00769","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":"2026-05-18T00:20:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pT2l+aE9W9wciSZv1k8v3AEv7mQbZ/krpdP9mdjCk4SJiGcmCOQSV2Or6rD6N5pWhTAMtL7nMkrvaw9WLDTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:24:31.033433Z"},"content_sha256":"d4689de9582bb197aaa925d7cf98e42a824b86e7d8eff5686de89f22cef22dca","schema_version":"1.0","event_id":"sha256:d4689de9582bb197aaa925d7cf98e42a824b86e7d8eff5686de89f22cef22dca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/bundle.json","state_url":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/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":"2026-06-01T22:24:31Z","links":{"resolver":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z","bundle":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/bundle.json","state":"https://pith.science/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZE54MO5CCCNUBV6EASDFF26J7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZE54MO5CCCNUBV6EASDFF26J7Z","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":"ddfe03570272fa123a51166e86cbdfb2e449363769fb8f93292b970ed69dff5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-03T07:57:21Z","title_canon_sha256":"839706935efbe6c3b0eee54fa9c39a1e103752c1552b92a6d63a5a71c544a0d2"},"schema_version":"1.0","source":{"id":"1502.00769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00769","created_at":"2026-05-18T00:20:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00769v1","created_at":"2026-05-18T00:20:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00769","created_at":"2026-05-18T00:20:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZE54MO5CCCNU","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZE54MO5CCCNUBV6E","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZE54MO5C","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:d4689de9582bb197aaa925d7cf98e42a824b86e7d8eff5686de89f22cef22dca","target":"graph","created_at":"2026-05-18T00:20:52Z","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 give new bounds for $\\sum_{{a, m ,n}}\\alpha_{m}\\beta_n\\nu_a {\\textrm e}\\left(\\frac{a\\overline m}{n}\\right)$ where $\\alpha_{m}$, $\\beta_n$ and $\\nu_a$ are arbitrary coefficients, improving upon a result of Duke, Friedlander and Iwaniec [DFI97]. We also apply these bounds to problems on representations by determinant equations and on the equidistribution of solutions to linear equations.","authors_text":"Sandro Bettin, Vorrapan Chandee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-03T07:57:21Z","title":"Trilinear forms with Kloosterman fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00769","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":"sha256:9fa53696d61f7698eaf9b52b8116cfeb7eefbe93a59c1669a801b3e5109b07b8","target":"record","created_at":"2026-05-18T00:20:52Z","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":"ddfe03570272fa123a51166e86cbdfb2e449363769fb8f93292b970ed69dff5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-03T07:57:21Z","title_canon_sha256":"839706935efbe6c3b0eee54fa9c39a1e103752c1552b92a6d63a5a71c544a0d2"},"schema_version":"1.0","source":{"id":"1502.00769","kind":"arxiv","version":1}},"canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c93bc63ba2109b40d7c4048652ebc9fe71390141203ea6f16a9f64306f76508f","first_computed_at":"2026-05-18T00:20:52.677957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:52.677957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TBLz2i1dEf0qJ/DxgWoKXl+CPtWb5pn5dy/b4C6DGNFwLDrz85i2XpC9GrvMcWkzJG+Xg5bPT6nJlMgIcJTeDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:52.679964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fa53696d61f7698eaf9b52b8116cfeb7eefbe93a59c1669a801b3e5109b07b8","sha256:d4689de9582bb197aaa925d7cf98e42a824b86e7d8eff5686de89f22cef22dca"],"state_sha256":"481709d7403ac4682287b0197fc05ad947d63369ad3c63acb4394261be861144"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ji8/kHhq0ne4A7sKLlxMhqSm9A6IN7BCg7D86XB+TA0J4rR7LMogN1UE8hIj3inCdsjtcqkvejGHv50MN1MmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:24:31.035276Z","bundle_sha256":"e2fe6d6f6727af82c8c70b483a4834bef6be85c08266248bd23e798e29afca45"}}