{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:N7LPW46JH5Y7KPEIRWQLDU54QK","short_pith_number":"pith:N7LPW46J","canonical_record":{"source":{"id":"2603.15197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-16T12:36:40Z","cross_cats_sorted":[],"title_canon_sha256":"421b7198b7fb2405553aaec80b49d2507e421342dd8b7a84dc2d88be1bb0d2c1","abstract_canon_sha256":"798b4247ed4fdd4b3a89b9ba062d86c55d6c81c89caa9869e0c94029db75b461"},"schema_version":"1.0"},"canonical_sha256":"6fd6fb73c93f71f53c888da0b1d3bc828b2b01e2792172014e088db632ee1c1b","source":{"kind":"arxiv","id":"2603.15197","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.15197","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2603.15197v2","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.15197","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"N7LPW46JH5Y7","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"N7LPW46JH5Y7KPEI","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"N7LPW46J","created_at":"2026-05-22T01:04:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:N7LPW46JH5Y7KPEIRWQLDU54QK","target":"record","payload":{"canonical_record":{"source":{"id":"2603.15197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-16T12:36:40Z","cross_cats_sorted":[],"title_canon_sha256":"421b7198b7fb2405553aaec80b49d2507e421342dd8b7a84dc2d88be1bb0d2c1","abstract_canon_sha256":"798b4247ed4fdd4b3a89b9ba062d86c55d6c81c89caa9869e0c94029db75b461"},"schema_version":"1.0"},"canonical_sha256":"6fd6fb73c93f71f53c888da0b1d3bc828b2b01e2792172014e088db632ee1c1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:00.248828Z","signature_b64":"EgGCD8VhBRlKGyrCH7YSihgM2EdNlMKzdJlnSDepHT3y2HPZZx4r7AihLYcuNJWHVyYYZmE1cI4m9AojKUwHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd6fb73c93f71f53c888da0b1d3bc828b2b01e2792172014e088db632ee1c1b","last_reissued_at":"2026-05-22T01:04:00.248167Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:00.248167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.15197","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"viGl/kbo8C5j/peEOFDQnpgYdYgBPHIq9WWtRfw//05XX+T+Qp+mvT62BxqhZMECk0XSYJ5Kke0dphYFRIV7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:03:06.163222Z"},"content_sha256":"32e18f3238eecc0dbe3d7b056a683d4c3b978202f6a4ae10cace70c61e7e54cb","schema_version":"1.0","event_id":"sha256:32e18f3238eecc0dbe3d7b056a683d4c3b978202f6a4ae10cace70c61e7e54cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:N7LPW46JH5Y7KPEIRWQLDU54QK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variance of GL(2) Fourier coefficients in arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Laurent Montaigu (UB)","submitted_at":"2026-03-16T12:36:40Z","abstract_excerpt":"We improve a result of Lau and Zhao on the variance of Fourier coefficients of primitive cuspidal modular forms for SL2(Z) in arithmetic progressions. This is achieved by using bounds on the first moment of Rankin-Selberg L-functions in the height aspect and non-trivial estimates for shifted convolution sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.15197","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.15197/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-22T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3MpBKrUrHsxGKia7jWYhvP59lxy+ZS20MkY67MFQT69b+ASTJbixUzXmOPC0noD+oqZpCZCypTAXSPATY4mDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:03:06.164032Z"},"content_sha256":"5420756a7890eea22d2f693faf35a0a62253b6621cc4c2c411dc27b035cbc717","schema_version":"1.0","event_id":"sha256:5420756a7890eea22d2f693faf35a0a62253b6621cc4c2c411dc27b035cbc717"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7LPW46JH5Y7KPEIRWQLDU54QK/bundle.json","state_url":"https://pith.science/pith/N7LPW46JH5Y7KPEIRWQLDU54QK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7LPW46JH5Y7KPEIRWQLDU54QK/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":"2026-06-11T06:03:06Z","links":{"resolver":"https://pith.science/pith/N7LPW46JH5Y7KPEIRWQLDU54QK","bundle":"https://pith.science/pith/N7LPW46JH5Y7KPEIRWQLDU54QK/bundle.json","state":"https://pith.science/pith/N7LPW46JH5Y7KPEIRWQLDU54QK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7LPW46JH5Y7KPEIRWQLDU54QK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:N7LPW46JH5Y7KPEIRWQLDU54QK","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":"798b4247ed4fdd4b3a89b9ba062d86c55d6c81c89caa9869e0c94029db75b461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-16T12:36:40Z","title_canon_sha256":"421b7198b7fb2405553aaec80b49d2507e421342dd8b7a84dc2d88be1bb0d2c1"},"schema_version":"1.0","source":{"id":"2603.15197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.15197","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2603.15197v2","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.15197","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"N7LPW46JH5Y7","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"N7LPW46JH5Y7KPEI","created_at":"2026-05-22T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"N7LPW46J","created_at":"2026-05-22T01:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:5420756a7890eea22d2f693faf35a0a62253b6621cc4c2c411dc27b035cbc717","target":"graph","created_at":"2026-05-22T01:04:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.15197/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We improve a result of Lau and Zhao on the variance of Fourier coefficients of primitive cuspidal modular forms for SL2(Z) in arithmetic progressions. This is achieved by using bounds on the first moment of Rankin-Selberg L-functions in the height aspect and non-trivial estimates for shifted convolution sums.","authors_text":"Laurent Montaigu (UB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-16T12:36:40Z","title":"Variance of GL(2) Fourier coefficients in arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.15197","kind":"arxiv","version":2},"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":"sha256:32e18f3238eecc0dbe3d7b056a683d4c3b978202f6a4ae10cace70c61e7e54cb","target":"record","created_at":"2026-05-22T01:04:00Z","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":"798b4247ed4fdd4b3a89b9ba062d86c55d6c81c89caa9869e0c94029db75b461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-16T12:36:40Z","title_canon_sha256":"421b7198b7fb2405553aaec80b49d2507e421342dd8b7a84dc2d88be1bb0d2c1"},"schema_version":"1.0","source":{"id":"2603.15197","kind":"arxiv","version":2}},"canonical_sha256":"6fd6fb73c93f71f53c888da0b1d3bc828b2b01e2792172014e088db632ee1c1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd6fb73c93f71f53c888da0b1d3bc828b2b01e2792172014e088db632ee1c1b","first_computed_at":"2026-05-22T01:04:00.248167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:00.248167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EgGCD8VhBRlKGyrCH7YSihgM2EdNlMKzdJlnSDepHT3y2HPZZx4r7AihLYcuNJWHVyYYZmE1cI4m9AojKUwHBg==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:00.248828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.15197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32e18f3238eecc0dbe3d7b056a683d4c3b978202f6a4ae10cace70c61e7e54cb","sha256:5420756a7890eea22d2f693faf35a0a62253b6621cc4c2c411dc27b035cbc717"],"state_sha256":"c3e960bef516e2b9a4a1311769ae27255fa18160d3415bde333e514b3343c24e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMdM0641rZdr8iKbp29/IUpqW07Br3+be1fb49HXfr8FLz2kvMhATiJ27+soX1JEmLUnvK0kbnWIZKBx7pfUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:03:06.168890Z","bundle_sha256":"11814d16f6039739fd234f3029bba198ee9ee65c585775799f2f08a797c9cf87"}}