{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MDBP3FZLJQPEHBCZKZGZXF4G4Y","short_pith_number":"pith:MDBP3FZL","canonical_record":{"source":{"id":"1010.0120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-01T10:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"869b46a2dd89866ac10c57c2a34cbae1038b993b6567948cdbbc7ec508615b9b","abstract_canon_sha256":"5f586cfead1a04c552468967bd0d58ea96a86709d4d7296c85442e7974420c09"},"schema_version":"1.0"},"canonical_sha256":"60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902","source":{"kind":"arxiv","id":"1010.0120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0120","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0120v1","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0120","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"MDBP3FZLJQPE","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MDBP3FZLJQPEHBCZ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MDBP3FZL","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MDBP3FZLJQPEHBCZKZGZXF4G4Y","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-01T10:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"869b46a2dd89866ac10c57c2a34cbae1038b993b6567948cdbbc7ec508615b9b","abstract_canon_sha256":"5f586cfead1a04c552468967bd0d58ea96a86709d4d7296c85442e7974420c09"},"schema_version":"1.0"},"canonical_sha256":"60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:00.248215Z","signature_b64":"GrUMBiSuQF87cdTzjK3XCdpd74kXI97neaUuGmvSs0jxawahKFWooOQ7RYnIwVPTf+14pxVqTfi8+tOgecOfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902","last_reissued_at":"2026-05-18T04:40:00.247818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:00.247818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0120","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":"2026-05-18T04:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Du8vS6v5tcFdDv91GkEvCx625yswh1hKhc1d8JGIs59KXG7WQGv4Izuus7Vusqx3S9m+VZ0ApQMFDIFaSVidAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:47:55.752477Z"},"content_sha256":"8fd49202cbab14f48e090796fa61e5ce0ee37acb89aff969705d90cac7647410","schema_version":"1.0","event_id":"sha256:8fd49202cbab14f48e090796fa61e5ce0ee37acb89aff969705d90cac7647410"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MDBP3FZLJQPEHBCZKZGZXF4G4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates for exponential sums with a large automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Rojas-Le\\'on","submitted_at":"2010-10-01T10:56:04Z","abstract_excerpt":"We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field $k=\\Fq$ for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line $\\AAA^1_k$: those invariant under translation by elements of $k$ and those invariant under homotheties with ratios in a large subgroup of the multiplicative group of $k$. In both cases, we are able to improve the bound by a factor of $\\sqrt{q}$ over an extension of $k$ of cardinality sufficiently large compared to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0120","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":"2026-05-18T04:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWrtFUk73n2AC/TWlyliy57RRkbkAhD65OCF4Ic2vRtp7rjyLlNWIe0GNN2fUYgJXZQBF0A2aC/NpeJta0XyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:47:55.752835Z"},"content_sha256":"4e6dfa0b4278438d1669d610a6181bcc3f1cf1ccda6bf964ea7972d2e78932de","schema_version":"1.0","event_id":"sha256:4e6dfa0b4278438d1669d610a6181bcc3f1cf1ccda6bf964ea7972d2e78932de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y/bundle.json","state_url":"https://pith.science/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y/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":"2026-06-22T10:47:55Z","links":{"resolver":"https://pith.science/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y","bundle":"https://pith.science/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y/bundle.json","state":"https://pith.science/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDBP3FZLJQPEHBCZKZGZXF4G4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MDBP3FZLJQPEHBCZKZGZXF4G4Y","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":"5f586cfead1a04c552468967bd0d58ea96a86709d4d7296c85442e7974420c09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-01T10:56:04Z","title_canon_sha256":"869b46a2dd89866ac10c57c2a34cbae1038b993b6567948cdbbc7ec508615b9b"},"schema_version":"1.0","source":{"id":"1010.0120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0120","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0120v1","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0120","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"MDBP3FZLJQPE","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MDBP3FZLJQPEHBCZ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MDBP3FZL","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:4e6dfa0b4278438d1669d610a6181bcc3f1cf1ccda6bf964ea7972d2e78932de","target":"graph","created_at":"2026-05-18T04:40:00Z","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 prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field $k=\\Fq$ for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line $\\AAA^1_k$: those invariant under translation by elements of $k$ and those invariant under homotheties with ratios in a large subgroup of the multiplicative group of $k$. In both cases, we are able to improve the bound by a factor of $\\sqrt{q}$ over an extension of $k$ of cardinality sufficiently large compared to","authors_text":"Antonio Rojas-Le\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-01T10:56:04Z","title":"Estimates for exponential sums with a large automorphism group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0120","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":"sha256:8fd49202cbab14f48e090796fa61e5ce0ee37acb89aff969705d90cac7647410","target":"record","created_at":"2026-05-18T04:40:00Z","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":"5f586cfead1a04c552468967bd0d58ea96a86709d4d7296c85442e7974420c09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-01T10:56:04Z","title_canon_sha256":"869b46a2dd89866ac10c57c2a34cbae1038b993b6567948cdbbc7ec508615b9b"},"schema_version":"1.0","source":{"id":"1010.0120","kind":"arxiv","version":1}},"canonical_sha256":"60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902","first_computed_at":"2026-05-18T04:40:00.247818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:00.247818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GrUMBiSuQF87cdTzjK3XCdpd74kXI97neaUuGmvSs0jxawahKFWooOQ7RYnIwVPTf+14pxVqTfi8+tOgecOfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:00.248215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fd49202cbab14f48e090796fa61e5ce0ee37acb89aff969705d90cac7647410","sha256:4e6dfa0b4278438d1669d610a6181bcc3f1cf1ccda6bf964ea7972d2e78932de"],"state_sha256":"bca59e1a8eee4f66dbf3d08623603363491c59dd2962c7bd3325939c645123bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"paAab48iMRTMKh1O4e8H1hYwV/Y+vaFQZxg9AYD/F5cvVdZTJRHp6fJv/n+coKvLZ0AyOZEvkD7aFImIjcczAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:47:55.754892Z","bundle_sha256":"15c79aa02bb08b06ccc7cd1cc8b74ef49ebf49fa862b71423137ad1b4a631c4e"}}