{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:TKRJXLJLRLHIKYF5L6UF2SLMPT","short_pith_number":"pith:TKRJXLJL","canonical_record":{"source":{"id":"2606.29822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T06:00:15Z","cross_cats_sorted":[],"title_canon_sha256":"3446aff5e3432ad0e98ec973beeae78b2004aed0771525ee335ffae450059b51","abstract_canon_sha256":"45d991dfe6dc93a9aa8b8c9f20400a444a41786f13dcdeddba1311603a94e5b5"},"schema_version":"1.0"},"canonical_sha256":"9aa29bad2b8ace8560bd5fa85d496c7cf5a001a7f035cbb9bf6196576b5db13b","source":{"kind":"arxiv","id":"2606.29822","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29822","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29822v1","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29822","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"TKRJXLJLRLHI","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"pith_short_16","alias_value":"TKRJXLJLRLHIKYF5","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"pith_short_8","alias_value":"TKRJXLJL","created_at":"2026-06-30T02:17:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:TKRJXLJLRLHIKYF5L6UF2SLMPT","target":"record","payload":{"canonical_record":{"source":{"id":"2606.29822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T06:00:15Z","cross_cats_sorted":[],"title_canon_sha256":"3446aff5e3432ad0e98ec973beeae78b2004aed0771525ee335ffae450059b51","abstract_canon_sha256":"45d991dfe6dc93a9aa8b8c9f20400a444a41786f13dcdeddba1311603a94e5b5"},"schema_version":"1.0"},"canonical_sha256":"9aa29bad2b8ace8560bd5fa85d496c7cf5a001a7f035cbb9bf6196576b5db13b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:36.767054Z","signature_b64":"1OctYiq6ASpBeVxo346gE6G9e39aSJp0+oDzFn4Sbq+DiVsDWJEl5/lx/xGmuVRG/cpSMbpODzqnUE81+bBNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aa29bad2b8ace8560bd5fa85d496c7cf5a001a7f035cbb9bf6196576b5db13b","last_reissued_at":"2026-06-30T02:17:36.766594Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:36.766594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.29822","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":"2026-06-30T02:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d7iBKFxQzRqauj4PoONhyIJEOg3TD6TqgBAkgjG8DO9uetoVmPHghd5+oODPnzrRyLwOpCISe2+K2fqMqB/QAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:32:02.575366Z"},"content_sha256":"342cd2dc22c8d9a34cd0fb117bcdeefaca67339c8a130f5a417f3c273d4a5201","schema_version":"1.0","event_id":"sha256:342cd2dc22c8d9a34cd0fb117bcdeefaca67339c8a130f5a417f3c273d4a5201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:TKRJXLJLRLHIKYF5L6UF2SLMPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double weighted sum involving $\\mathrm{GL}(2)$ Fourier coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Himanshi Chanana, Mohd Harun","submitted_at":"2026-06-29T06:00:15Z","abstract_excerpt":"This article proves non-trivial estimates for a bilinear sum involving the Fourier coefficients of a Hecke-holomorphic or Hecke-Maass cusp form for $\\mathrm{SL}(2,\\mathbb{Z})$. As corollaries, we draw interesting results related to non-trivial bounds of different shifted convolution sums and summatory functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29822","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29822/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":"2026-06-30T02:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWSPdPdyCB0HoDBLOWYHIfNRvNajYVkSzc9PESJG0+OqSvR9CFN3zYDZgXBeLO2fks3Aj5raQfmKBSzHOsNYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:32:02.575729Z"},"content_sha256":"b0af84be9a87c2310b6fa3214fdba6eaad4c06f39bf70a681e6dbcc8de076e6d","schema_version":"1.0","event_id":"sha256:b0af84be9a87c2310b6fa3214fdba6eaad4c06f39bf70a681e6dbcc8de076e6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT/bundle.json","state_url":"https://pith.science/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT/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":"2026-07-03T18:32:02Z","links":{"resolver":"https://pith.science/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT","bundle":"https://pith.science/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT/bundle.json","state":"https://pith.science/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKRJXLJLRLHIKYF5L6UF2SLMPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TKRJXLJLRLHIKYF5L6UF2SLMPT","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":"45d991dfe6dc93a9aa8b8c9f20400a444a41786f13dcdeddba1311603a94e5b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T06:00:15Z","title_canon_sha256":"3446aff5e3432ad0e98ec973beeae78b2004aed0771525ee335ffae450059b51"},"schema_version":"1.0","source":{"id":"2606.29822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29822","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29822v1","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29822","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"TKRJXLJLRLHI","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"pith_short_16","alias_value":"TKRJXLJLRLHIKYF5","created_at":"2026-06-30T02:17:36Z"},{"alias_kind":"pith_short_8","alias_value":"TKRJXLJL","created_at":"2026-06-30T02:17:36Z"}],"graph_snapshots":[{"event_id":"sha256:b0af84be9a87c2310b6fa3214fdba6eaad4c06f39bf70a681e6dbcc8de076e6d","target":"graph","created_at":"2026-06-30T02:17:36Z","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/2606.29822/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article proves non-trivial estimates for a bilinear sum involving the Fourier coefficients of a Hecke-holomorphic or Hecke-Maass cusp form for $\\mathrm{SL}(2,\\mathbb{Z})$. As corollaries, we draw interesting results related to non-trivial bounds of different shifted convolution sums and summatory functions.","authors_text":"Himanshi Chanana, Mohd Harun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T06:00:15Z","title":"Double weighted sum involving $\\mathrm{GL}(2)$ Fourier coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29822","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":"sha256:342cd2dc22c8d9a34cd0fb117bcdeefaca67339c8a130f5a417f3c273d4a5201","target":"record","created_at":"2026-06-30T02:17:36Z","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":"45d991dfe6dc93a9aa8b8c9f20400a444a41786f13dcdeddba1311603a94e5b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T06:00:15Z","title_canon_sha256":"3446aff5e3432ad0e98ec973beeae78b2004aed0771525ee335ffae450059b51"},"schema_version":"1.0","source":{"id":"2606.29822","kind":"arxiv","version":1}},"canonical_sha256":"9aa29bad2b8ace8560bd5fa85d496c7cf5a001a7f035cbb9bf6196576b5db13b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aa29bad2b8ace8560bd5fa85d496c7cf5a001a7f035cbb9bf6196576b5db13b","first_computed_at":"2026-06-30T02:17:36.766594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:36.766594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1OctYiq6ASpBeVxo346gE6G9e39aSJp0+oDzFn4Sbq+DiVsDWJEl5/lx/xGmuVRG/cpSMbpODzqnUE81+bBNCg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:36.767054Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:342cd2dc22c8d9a34cd0fb117bcdeefaca67339c8a130f5a417f3c273d4a5201","sha256:b0af84be9a87c2310b6fa3214fdba6eaad4c06f39bf70a681e6dbcc8de076e6d"],"state_sha256":"30a2b18cbe00e53f126c6f4eabc61b594c1466bd052ab7d4fc4b187798bc3155"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onzt3zkc0eByBuPvjRN20hYJ/qmtMTXyL/6sjFU+omfhIH3JJyCWQWvJvzBkhQBK72WdqMuxiWE4aKatadyEAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T18:32:02.577614Z","bundle_sha256":"d33a59d7690e7e3fd323444dc43d57c9b26700beeb14be67e8cb441c9c20417a"}}