{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JNQ3S3ZDIR6JZHKCTISVTFSMMF","short_pith_number":"pith:JNQ3S3ZD","canonical_record":{"source":{"id":"1711.05358","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-14T23:43:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3f933e772d170e4aa64e911b49e723cd92b127fa3b8962716d1703a21d15542a","abstract_canon_sha256":"eb161d9e05395fbf4dc3c4c7da78603ca17a5b9da287646cacbf63295bad54d1"},"schema_version":"1.0"},"canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","source":{"kind":"arxiv","id":"1711.05358","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05358","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05358v4","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05358","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"JNQ3S3ZDIR6J","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JNQ3S3ZDIR6JZHKC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JNQ3S3ZD","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JNQ3S3ZDIR6JZHKCTISVTFSMMF","target":"record","payload":{"canonical_record":{"source":{"id":"1711.05358","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-14T23:43:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3f933e772d170e4aa64e911b49e723cd92b127fa3b8962716d1703a21d15542a","abstract_canon_sha256":"eb161d9e05395fbf4dc3c4c7da78603ca17a5b9da287646cacbf63295bad54d1"},"schema_version":"1.0"},"canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:34.178782Z","signature_b64":"9FhSwtsDSKmC5+H6c2g3jV5WRoTssRMvV3+54/xYwlPitv/G29HOPqhN6DI67CAdcGMmeRxocG0X+kR/tz9mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","last_reissued_at":"2026-05-18T00:04:34.178012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:34.178012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.05358","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":"2026-05-18T00:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Luz1MlHT1pg0dwUSu3vTUq5cNaUGBUtsyFy7wTkzfJ0FowebAv0j7rfpHNkEN+ePKpi8H15cumCY65X1kjZyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:19.826469Z"},"content_sha256":"23b2203d5cba8b4e49ee3044b2dc68d46f2c81f6ee3aad819e62213f386056c9","schema_version":"1.0","event_id":"sha256:23b2203d5cba8b4e49ee3044b2dc68d46f2c81f6ee3aad819e62213f386056c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JNQ3S3ZDIR6JZHKCTISVTFSMMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear and quadratic uniformity of the M\\\"obius function over $\\mathbb{F}_q[t]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Pierre-Yves Bienvenu, Th\\'ai Ho\\`ang L\\^e","submitted_at":"2017-11-14T23:43:05Z","abstract_excerpt":"We examine correlations of the M\\\"obius function over $\\mathbb{F}_q[t]$ with linear or quadratic phases, that is, averages of the form \\begin{equation} \\label{eq:average} \\frac{1}{q^n}\\sum_{\\text{deg }f<n} \\mu(f)\\chi(Q(f)) \\end{equation} for an additive character $\\chi$ over $\\mathbb{F}_q$ and a polynomial $Q\\in\\mathbb{F}_q[x_0,\\ldots,x_{n-1}]$ of degree at most 2 in the coefficients $x_0,\\ldots, x_{n-1}$ of $f=\\sum_{i< n}x_i t^i$. Like in the integers, it is reasonable to expect that, due to the random-like behaviour of $\\mu$, such sums should exhibit considerable cancellation. In this paper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05358","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":"2026-05-18T00:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HMf1HHjPChS2a/atddaOHlYkyZ4XwUb8uEYA2ibYPC6mSW4EPVlaMZ0iS1LB26oemnT99GXhYG6B9XjNyc0NCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:02:19.826811Z"},"content_sha256":"6992b24eb3fc4aa7644d2ab5cdac3e4bb20669aaee86bf01c715746e34b658fe","schema_version":"1.0","event_id":"sha256:6992b24eb3fc4aa7644d2ab5cdac3e4bb20669aaee86bf01c715746e34b658fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/bundle.json","state_url":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/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":"2026-06-02T23:02:19Z","links":{"resolver":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF","bundle":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/bundle.json","state":"https://pith.science/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNQ3S3ZDIR6JZHKCTISVTFSMMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JNQ3S3ZDIR6JZHKCTISVTFSMMF","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":"eb161d9e05395fbf4dc3c4c7da78603ca17a5b9da287646cacbf63295bad54d1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-14T23:43:05Z","title_canon_sha256":"3f933e772d170e4aa64e911b49e723cd92b127fa3b8962716d1703a21d15542a"},"schema_version":"1.0","source":{"id":"1711.05358","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05358","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05358v4","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05358","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"JNQ3S3ZDIR6J","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JNQ3S3ZDIR6JZHKC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JNQ3S3ZD","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:6992b24eb3fc4aa7644d2ab5cdac3e4bb20669aaee86bf01c715746e34b658fe","target":"graph","created_at":"2026-05-18T00:04:34Z","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 examine correlations of the M\\\"obius function over $\\mathbb{F}_q[t]$ with linear or quadratic phases, that is, averages of the form \\begin{equation} \\label{eq:average} \\frac{1}{q^n}\\sum_{\\text{deg }f<n} \\mu(f)\\chi(Q(f)) \\end{equation} for an additive character $\\chi$ over $\\mathbb{F}_q$ and a polynomial $Q\\in\\mathbb{F}_q[x_0,\\ldots,x_{n-1}]$ of degree at most 2 in the coefficients $x_0,\\ldots, x_{n-1}$ of $f=\\sum_{i< n}x_i t^i$. Like in the integers, it is reasonable to expect that, due to the random-like behaviour of $\\mu$, such sums should exhibit considerable cancellation. In this paper ","authors_text":"Pierre-Yves Bienvenu, Th\\'ai Ho\\`ang L\\^e","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-14T23:43:05Z","title":"Linear and quadratic uniformity of the M\\\"obius function over $\\mathbb{F}_q[t]$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05358","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":"sha256:23b2203d5cba8b4e49ee3044b2dc68d46f2c81f6ee3aad819e62213f386056c9","target":"record","created_at":"2026-05-18T00:04:34Z","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":"eb161d9e05395fbf4dc3c4c7da78603ca17a5b9da287646cacbf63295bad54d1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-14T23:43:05Z","title_canon_sha256":"3f933e772d170e4aa64e911b49e723cd92b127fa3b8962716d1703a21d15542a"},"schema_version":"1.0","source":{"id":"1711.05358","kind":"arxiv","version":4}},"canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b61b96f23447c9c9d429a2559964c614091621fe8ef24f02409d61f8ba672c6","first_computed_at":"2026-05-18T00:04:34.178012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:34.178012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9FhSwtsDSKmC5+H6c2g3jV5WRoTssRMvV3+54/xYwlPitv/G29HOPqhN6DI67CAdcGMmeRxocG0X+kR/tz9mBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:34.178782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05358","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23b2203d5cba8b4e49ee3044b2dc68d46f2c81f6ee3aad819e62213f386056c9","sha256:6992b24eb3fc4aa7644d2ab5cdac3e4bb20669aaee86bf01c715746e34b658fe"],"state_sha256":"297c2adef43108bc24d61c4f56c4a823f6e37771e8866a57db9c7549aa5456ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvwsqBo9DJBTfQNp9u910ahzwnskNcZ24oiuna0fpER19H9M+nTEBd8ZiwX1lvOql6o3O02B4LzbHd3TNx/vDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:02:19.828916Z","bundle_sha256":"b55f2cf49f11f0adcd6e7b3c884ab9fda49dd2c4dfac355e561557f15d8b9106"}}