{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZWAFGWKPEVTXWA645XT2YRMEU4","short_pith_number":"pith:ZWAFGWKP","canonical_record":{"source":{"id":"1308.5551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-26T12:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"79442ca67e5bd773691c760443e056a9fbb235c896515590e3174699d986cc5b","abstract_canon_sha256":"0c5e3d9ea9c92636ca015b271f47dfa5e25882ffc6790501a9f26defbf96f6e9"},"schema_version":"1.0"},"canonical_sha256":"cd8053594f25677b03dcede7ac4584a7029b254c2be3b263ef71e7f3b41fc2ab","source":{"kind":"arxiv","id":"1308.5551","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5551","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5551v1","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5551","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZWAFGWKPEVTX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZWAFGWKPEVTXWA64","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZWAFGWKP","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZWAFGWKPEVTXWA645XT2YRMEU4","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-26T12:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"79442ca67e5bd773691c760443e056a9fbb235c896515590e3174699d986cc5b","abstract_canon_sha256":"0c5e3d9ea9c92636ca015b271f47dfa5e25882ffc6790501a9f26defbf96f6e9"},"schema_version":"1.0"},"canonical_sha256":"cd8053594f25677b03dcede7ac4584a7029b254c2be3b263ef71e7f3b41fc2ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:04.149683Z","signature_b64":"yGrU3p9KOsgn6nea+aHDIX0mbjTO996Smp0sfPwW8R5yUUq6TpSEeOAhkm0HOgXb1a9yAn+XZNJHt/dT34fSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd8053594f25677b03dcede7ac4584a7029b254c2be3b263ef71e7f3b41fc2ab","last_reissued_at":"2026-05-18T03:15:04.148806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:04.148806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5551","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":"2026-05-18T03:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v+ywuTRMMS1qb/r7Gau1afbdfWrvn6HOMo+WP5HIZJjdjxV7GTkCUa7b+YgBQPg6oBO+Ekvzf4709s1QRLQkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:53:20.725274Z"},"content_sha256":"9dc1cd575e8c84b48b414e9360039f59ab8a0c5caef866d548b380f5b1ecb7d6","schema_version":"1.0","event_id":"sha256:9dc1cd575e8c84b48b414e9360039f59ab8a0c5caef866d548b380f5b1ecb7d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZWAFGWKPEVTXWA645XT2YRMEU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shifted convolution sums and Eisenstein series formed with modular symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nikolaos Diamantis, Roelof Bruggeman","submitted_at":"2013-08-26T12:03:56Z","abstract_excerpt":"The Fourier coefficient of a second order Eisenstein series is described as a shifted convolution sum. This description is used to obtain the spectral decomposition of and estimates for the shifted convolution sum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5551","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":"2026-05-18T03:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"39JdXo4x51sp+ZtcGekS/3NNhKFfpQOYxmP9Y/Ocr6jtzOVdku0KZz4BzYM514rlenti4TCsX6rwQ4oAWWwwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:53:20.726082Z"},"content_sha256":"50bc4dade0d331bc3e3bd57a095d052e63113334b2bf7de7ae85e4e0f798575b","schema_version":"1.0","event_id":"sha256:50bc4dade0d331bc3e3bd57a095d052e63113334b2bf7de7ae85e4e0f798575b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWAFGWKPEVTXWA645XT2YRMEU4/bundle.json","state_url":"https://pith.science/pith/ZWAFGWKPEVTXWA645XT2YRMEU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWAFGWKPEVTXWA645XT2YRMEU4/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":"2026-06-10T23:53:20Z","links":{"resolver":"https://pith.science/pith/ZWAFGWKPEVTXWA645XT2YRMEU4","bundle":"https://pith.science/pith/ZWAFGWKPEVTXWA645XT2YRMEU4/bundle.json","state":"https://pith.science/pith/ZWAFGWKPEVTXWA645XT2YRMEU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWAFGWKPEVTXWA645XT2YRMEU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZWAFGWKPEVTXWA645XT2YRMEU4","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":"0c5e3d9ea9c92636ca015b271f47dfa5e25882ffc6790501a9f26defbf96f6e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-26T12:03:56Z","title_canon_sha256":"79442ca67e5bd773691c760443e056a9fbb235c896515590e3174699d986cc5b"},"schema_version":"1.0","source":{"id":"1308.5551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5551","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5551v1","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5551","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZWAFGWKPEVTX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZWAFGWKPEVTXWA64","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZWAFGWKP","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:50bc4dade0d331bc3e3bd57a095d052e63113334b2bf7de7ae85e4e0f798575b","target":"graph","created_at":"2026-05-18T03:15:04Z","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":"The Fourier coefficient of a second order Eisenstein series is described as a shifted convolution sum. This description is used to obtain the spectral decomposition of and estimates for the shifted convolution sum.","authors_text":"Nikolaos Diamantis, Roelof Bruggeman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-26T12:03:56Z","title":"Shifted convolution sums and Eisenstein series formed with modular symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5551","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":"sha256:9dc1cd575e8c84b48b414e9360039f59ab8a0c5caef866d548b380f5b1ecb7d6","target":"record","created_at":"2026-05-18T03:15:04Z","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":"0c5e3d9ea9c92636ca015b271f47dfa5e25882ffc6790501a9f26defbf96f6e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-26T12:03:56Z","title_canon_sha256":"79442ca67e5bd773691c760443e056a9fbb235c896515590e3174699d986cc5b"},"schema_version":"1.0","source":{"id":"1308.5551","kind":"arxiv","version":1}},"canonical_sha256":"cd8053594f25677b03dcede7ac4584a7029b254c2be3b263ef71e7f3b41fc2ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd8053594f25677b03dcede7ac4584a7029b254c2be3b263ef71e7f3b41fc2ab","first_computed_at":"2026-05-18T03:15:04.148806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:04.148806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yGrU3p9KOsgn6nea+aHDIX0mbjTO996Smp0sfPwW8R5yUUq6TpSEeOAhkm0HOgXb1a9yAn+XZNJHt/dT34fSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:04.149683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dc1cd575e8c84b48b414e9360039f59ab8a0c5caef866d548b380f5b1ecb7d6","sha256:50bc4dade0d331bc3e3bd57a095d052e63113334b2bf7de7ae85e4e0f798575b"],"state_sha256":"b619d3d350567a866358be62a9a7490e1de18e6a5e8919bb1824cca860da946b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOXyiLjGtscRQyjroFEMUrfukV8mA5jDCOP8WmrXdz697LjQLhw2yUda0B+pTiBtbsz1xOuYWZOd3KQspJX1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:53:20.730853Z","bundle_sha256":"04fc9862d06135e62b63754188238847266cfefb43501b82be009c5b0f7b61ee"}}