{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JWGBXO3U3DFXZCI27A2MTNH5IH","short_pith_number":"pith:JWGBXO3U","canonical_record":{"source":{"id":"2606.30603","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"dded7c2e659b2b826f058e16d2003e4d43488403334f28eae55fdb325f40c8a8","abstract_canon_sha256":"a6951f9ec66be8911072f9267f9bdc0f09fbf496131f384f38b4f33eed974fa0"},"schema_version":"1.0"},"canonical_sha256":"4d8c1bbb74d8cb7c891af834c9b4fd41eda0ac7ca65c07e73364f80aca042503","source":{"kind":"arxiv","id":"2606.30603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30603","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30603v1","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30603","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"JWGBXO3U3DFX","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"pith_short_16","alias_value":"JWGBXO3U3DFXZCI2","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"pith_short_8","alias_value":"JWGBXO3U","created_at":"2026-06-30T02:18:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JWGBXO3U3DFXZCI27A2MTNH5IH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30603","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"dded7c2e659b2b826f058e16d2003e4d43488403334f28eae55fdb325f40c8a8","abstract_canon_sha256":"a6951f9ec66be8911072f9267f9bdc0f09fbf496131f384f38b4f33eed974fa0"},"schema_version":"1.0"},"canonical_sha256":"4d8c1bbb74d8cb7c891af834c9b4fd41eda0ac7ca65c07e73364f80aca042503","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:22.338037Z","signature_b64":"xmzxDBLo505WDhZabTWJ1+CPeWFpok0TfUJ1U8V4Sd5Nfl10VqFqXyjh+OwD1wpbgydcYGdCTF2DOgqfbSHGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d8c1bbb74d8cb7c891af834c9b4fd41eda0ac7ca65c07e73364f80aca042503","last_reissued_at":"2026-06-30T02:18:22.337395Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:22.337395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30603","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":"2026-06-30T02:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V1fl/JsC7gw4YcMuc0PCHGs0iUb9S0he3/39xdI5Hm+PO+Vz8aAJkjMyU4T2EDP9TFJVmqulhu+gM0q+/Rd1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:09:35.920975Z"},"content_sha256":"7e870404eed4ac0850ad241e3c271e524be25203b5c4496efbb0bf2205905816","schema_version":"1.0","event_id":"sha256:7e870404eed4ac0850ad241e3c271e524be25203b5c4496efbb0bf2205905816"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JWGBXO3U3DFXZCI27A2MTNH5IH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments and sign changes of symmetric power $L$-function coefficients over sums of squares","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arnab Mitra, Jewel Mahajan","submitted_at":"2026-06-29T17:41:18Z","abstract_excerpt":"Let $f$ be a normalised Hecke eigenform of even integral weight for the full modular group $\\mathrm{SL}(2,\\mathbb{Z})$, let $L(s,\\mathrm{sym}^{j}f)$ be the $j$th symmetric power $L$-function attached to $f$, and let $\\lambda_{\\mathrm{sym}^{j}f}(n)$ denote its $n$th Dirichlet coefficient. For each even integer $m$ with $2 \\le m \\le 12$, we establish upper bounds for the partial sums of $\\lambda_{\\mathrm{sym}^{j}f}(n)$ and asymptotic formulas for those of $\\lambda_{\\mathrm{sym}^{j}f}^{2}(n)$ taken over integers represented as a sum of $m$ squares. As an application, we obtain lower bounds for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30603","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/2606.30603/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":"2026-06-30T02:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2JJYj004qLr/3lhDukXe1naUeBbMdRekjX1pue2xfbWvrAx2myUM+u3b9tuekiWD2meMH6sf1JJV57xnzWKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:09:35.921633Z"},"content_sha256":"316e077a41ad92fb606cbe5231f5b3ab1c3a1b88cb6a9802098a03aed2bd7a67","schema_version":"1.0","event_id":"sha256:316e077a41ad92fb606cbe5231f5b3ab1c3a1b88cb6a9802098a03aed2bd7a67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWGBXO3U3DFXZCI27A2MTNH5IH/bundle.json","state_url":"https://pith.science/pith/JWGBXO3U3DFXZCI27A2MTNH5IH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWGBXO3U3DFXZCI27A2MTNH5IH/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":"2026-06-30T22:09:35Z","links":{"resolver":"https://pith.science/pith/JWGBXO3U3DFXZCI27A2MTNH5IH","bundle":"https://pith.science/pith/JWGBXO3U3DFXZCI27A2MTNH5IH/bundle.json","state":"https://pith.science/pith/JWGBXO3U3DFXZCI27A2MTNH5IH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWGBXO3U3DFXZCI27A2MTNH5IH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JWGBXO3U3DFXZCI27A2MTNH5IH","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":"a6951f9ec66be8911072f9267f9bdc0f09fbf496131f384f38b4f33eed974fa0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:41:18Z","title_canon_sha256":"dded7c2e659b2b826f058e16d2003e4d43488403334f28eae55fdb325f40c8a8"},"schema_version":"1.0","source":{"id":"2606.30603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30603","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30603v1","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30603","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"JWGBXO3U3DFX","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"pith_short_16","alias_value":"JWGBXO3U3DFXZCI2","created_at":"2026-06-30T02:18:22Z"},{"alias_kind":"pith_short_8","alias_value":"JWGBXO3U","created_at":"2026-06-30T02:18:22Z"}],"graph_snapshots":[{"event_id":"sha256:316e077a41ad92fb606cbe5231f5b3ab1c3a1b88cb6a9802098a03aed2bd7a67","target":"graph","created_at":"2026-06-30T02:18:22Z","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/2606.30603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f$ be a normalised Hecke eigenform of even integral weight for the full modular group $\\mathrm{SL}(2,\\mathbb{Z})$, let $L(s,\\mathrm{sym}^{j}f)$ be the $j$th symmetric power $L$-function attached to $f$, and let $\\lambda_{\\mathrm{sym}^{j}f}(n)$ denote its $n$th Dirichlet coefficient. For each even integer $m$ with $2 \\le m \\le 12$, we establish upper bounds for the partial sums of $\\lambda_{\\mathrm{sym}^{j}f}(n)$ and asymptotic formulas for those of $\\lambda_{\\mathrm{sym}^{j}f}^{2}(n)$ taken over integers represented as a sum of $m$ squares. As an application, we obtain lower bounds for th","authors_text":"Arnab Mitra, Jewel Mahajan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:41:18Z","title":"Moments and sign changes of symmetric power $L$-function coefficients over sums of squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30603","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":"sha256:7e870404eed4ac0850ad241e3c271e524be25203b5c4496efbb0bf2205905816","target":"record","created_at":"2026-06-30T02:18:22Z","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":"a6951f9ec66be8911072f9267f9bdc0f09fbf496131f384f38b4f33eed974fa0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:41:18Z","title_canon_sha256":"dded7c2e659b2b826f058e16d2003e4d43488403334f28eae55fdb325f40c8a8"},"schema_version":"1.0","source":{"id":"2606.30603","kind":"arxiv","version":1}},"canonical_sha256":"4d8c1bbb74d8cb7c891af834c9b4fd41eda0ac7ca65c07e73364f80aca042503","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d8c1bbb74d8cb7c891af834c9b4fd41eda0ac7ca65c07e73364f80aca042503","first_computed_at":"2026-06-30T02:18:22.337395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:18:22.337395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xmzxDBLo505WDhZabTWJ1+CPeWFpok0TfUJ1U8V4Sd5Nfl10VqFqXyjh+OwD1wpbgydcYGdCTF2DOgqfbSHGCQ==","signature_status":"signed_v1","signed_at":"2026-06-30T02:18:22.338037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e870404eed4ac0850ad241e3c271e524be25203b5c4496efbb0bf2205905816","sha256:316e077a41ad92fb606cbe5231f5b3ab1c3a1b88cb6a9802098a03aed2bd7a67"],"state_sha256":"9488f971c79acd1ea8ee9d155354109eebf11fd33de98f86c990aba3a5e8885d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bxq/SxbNp7lvCjWbZP09OeV1OxsolV1gpz3/CLuSlSz7XJ3RzMJJyiGL8ZUwfhI0+8qLFm7A4sog4OOwJcP7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:09:35.924516Z","bundle_sha256":"3a5490bc92b325061a3824a3806c58be6c37bc03e7faddb939bac0a0a17ca081"}}