{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VRUJ5ONZUYY3PSFCKRX2XGBCDO","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":"d58d06dd96cccfe279436e1233c79424fa149104eee3032508db10f2f8d0fa72","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:52:18Z","title_canon_sha256":"76495d3acb4a26e10a1f5f6e7a06b87e7de88493371307d6438e8513aa092ab0"},"schema_version":"1.0","source":{"id":"2606.30618","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30618","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30618v1","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30618","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"VRUJ5ONZUYY3","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_16","alias_value":"VRUJ5ONZUYY3PSFC","created_at":"2026-06-30T02:18:23Z"},{"alias_kind":"pith_short_8","alias_value":"VRUJ5ONZ","created_at":"2026-06-30T02:18:23Z"}],"graph_snapshots":[{"event_id":"sha256:b6faec753ec013832b12c358b20a9d6cd10f9b6760eb39335af328ae42cc8ad0","target":"graph","created_at":"2026-06-30T02:18:23Z","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/2606.30618/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $q$ be an integer and let $f$ be a normalised Hecke eigenform of integral weight for the full modular group. Let $L(s,\\mathrm{sym}^j f)$ denote the $j$-th symmetric power $L$-function associated to $f$, and let $\\lambda_{\\mathrm{sym}^j f}(n)$ denote its $n$-th coefficient. We study the behaviour of the partial sum of $\\lambda_{\\mathrm{sym}^j f}(n)$, and of its second moment, taken over those sums of $m$ squares that are congruent to $1$ modulo $q$. As an application, we investigate the shifted convolution sum of $\\lambda_{\\mathrm{sym}^j f}(n)$ against a $k$-full kernel function, for any $k","authors_text":"Arnab Mitra, Jewel Mahajan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:52:18Z","title":"Shifted convolution sums of coefficients of symmetric power $L$-functions with $k$-full kernels over sums of squares in arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30618","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":"sha256:92921e4920e73c6b5c42ff54a091f969c830193d72f45d95e458c562e5415a03","target":"record","created_at":"2026-06-30T02:18:23Z","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":"d58d06dd96cccfe279436e1233c79424fa149104eee3032508db10f2f8d0fa72","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:52:18Z","title_canon_sha256":"76495d3acb4a26e10a1f5f6e7a06b87e7de88493371307d6438e8513aa092ab0"},"schema_version":"1.0","source":{"id":"2606.30618","kind":"arxiv","version":1}},"canonical_sha256":"ac689eb9b9a631b7c8a2546fab98221b82d2b334823a6e7bb6366f5861245ea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac689eb9b9a631b7c8a2546fab98221b82d2b334823a6e7bb6366f5861245ea3","first_computed_at":"2026-06-30T02:18:23.033484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:18:23.033484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZOQkUESJttYUv+IXlMpQO85t09/FeaBLRq96cs3pFQiwBmLmL5RNnx8hqgC7RUDSwmjvQGY4BXAA0Ur6OnsqDg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:18:23.033935Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30618","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92921e4920e73c6b5c42ff54a091f969c830193d72f45d95e458c562e5415a03","sha256:b6faec753ec013832b12c358b20a9d6cd10f9b6760eb39335af328ae42cc8ad0"],"state_sha256":"0430dffa58721de48478327ef46a1e1446642f5041f68557c9bbe653070b992d"}