{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MOFFAJ3K36ECI3GFOR55J53QZP","short_pith_number":"pith:MOFFAJ3K","canonical_record":{"source":{"id":"1904.02025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-03T14:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"11f5e281610ac2a834cd8474483a71ac18c60562d3d451f5b126c1bdcd0f1aaa","abstract_canon_sha256":"3a59133ec7dd39f2aeec032ff6ee273d3d1f2d8e7cf90031d0d2a8edc53cb1a2"},"schema_version":"1.0"},"canonical_sha256":"638a50276adf88246cc5747bd4f770cbf6f9f896358386b86a768a2b7635212c","source":{"kind":"arxiv","id":"1904.02025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02025","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02025v1","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02025","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"MOFFAJ3K36EC","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MOFFAJ3K36ECI3GF","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MOFFAJ3K","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MOFFAJ3K36ECI3GFOR55J53QZP","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-03T14:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"11f5e281610ac2a834cd8474483a71ac18c60562d3d451f5b126c1bdcd0f1aaa","abstract_canon_sha256":"3a59133ec7dd39f2aeec032ff6ee273d3d1f2d8e7cf90031d0d2a8edc53cb1a2"},"schema_version":"1.0"},"canonical_sha256":"638a50276adf88246cc5747bd4f770cbf6f9f896358386b86a768a2b7635212c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:28.953679Z","signature_b64":"gkYii1m3+isdilvHD1gOHjGOI0M6lfgrSpsDsbNwkobsx0zCaFl1WGq1jGw5f0uCwcqACFAAWAeHc6/tYR2PBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"638a50276adf88246cc5747bd4f770cbf6f9f896358386b86a768a2b7635212c","last_reissued_at":"2026-05-17T23:49:28.953043Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:28.953043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02025","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":"2026-05-17T23:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sD3artEdIeApMRFVacRbN1VQOnlGl4o34oqDzuremhglNZtu67jVJNd2juh8faOB1gQ4NqTHgFNMbHrK96bSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:05.143789Z"},"content_sha256":"387987a730f84d66ec2cddbd67519dce48e79919ca3730d12ed154cf39ecbb27","schema_version":"1.0","event_id":"sha256:387987a730f84d66ec2cddbd67519dce48e79919ca3730d12ed154cf39ecbb27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MOFFAJ3K36ECI3GFOR55J53QZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vorono\\\"{i} summation via switching cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Corbett, Edgar Assing","submitted_at":"2019-04-03T14:30:31Z","abstract_excerpt":"We consider the Fourier expansion of a Hecke (resp.\\ Hecke--Maa\\ss) cusp form of general level $N$ at the various cusps of $\\Gamma_{0}(N)\\bs\\Hb$. We explain how to compute these coefficients via the local theory of $p$-adic Whittaker functions and establish a classical Vorono\\\"i summation formula allowing an arbitrary additive twist. Our discussion has applications to bounding sums of Fourier coefficients and understanding the (generalised) Atkin--Lehner relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02025","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":"2026-05-17T23:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hngcq9fFbrON8Iy1oyg+BltEsHI3TuSNvA466OeTRiGYjpDnDtSQnpbnxh9okJiL+Fk69MF5wT07Eo/JIIowDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:05.144146Z"},"content_sha256":"1bcb4c8ff75dfc7a4b814849f98219f079592fe795cd5f48c2dfb0d3b5fe695c","schema_version":"1.0","event_id":"sha256:1bcb4c8ff75dfc7a4b814849f98219f079592fe795cd5f48c2dfb0d3b5fe695c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOFFAJ3K36ECI3GFOR55J53QZP/bundle.json","state_url":"https://pith.science/pith/MOFFAJ3K36ECI3GFOR55J53QZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOFFAJ3K36ECI3GFOR55J53QZP/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":"2026-06-02T19:26:05Z","links":{"resolver":"https://pith.science/pith/MOFFAJ3K36ECI3GFOR55J53QZP","bundle":"https://pith.science/pith/MOFFAJ3K36ECI3GFOR55J53QZP/bundle.json","state":"https://pith.science/pith/MOFFAJ3K36ECI3GFOR55J53QZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOFFAJ3K36ECI3GFOR55J53QZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MOFFAJ3K36ECI3GFOR55J53QZP","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":"3a59133ec7dd39f2aeec032ff6ee273d3d1f2d8e7cf90031d0d2a8edc53cb1a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-03T14:30:31Z","title_canon_sha256":"11f5e281610ac2a834cd8474483a71ac18c60562d3d451f5b126c1bdcd0f1aaa"},"schema_version":"1.0","source":{"id":"1904.02025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02025","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02025v1","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02025","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"MOFFAJ3K36EC","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MOFFAJ3K36ECI3GF","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MOFFAJ3K","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:1bcb4c8ff75dfc7a4b814849f98219f079592fe795cd5f48c2dfb0d3b5fe695c","target":"graph","created_at":"2026-05-17T23:49:28Z","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":"We consider the Fourier expansion of a Hecke (resp.\\ Hecke--Maa\\ss) cusp form of general level $N$ at the various cusps of $\\Gamma_{0}(N)\\bs\\Hb$. We explain how to compute these coefficients via the local theory of $p$-adic Whittaker functions and establish a classical Vorono\\\"i summation formula allowing an arbitrary additive twist. Our discussion has applications to bounding sums of Fourier coefficients and understanding the (generalised) Atkin--Lehner relations.","authors_text":"Andrew Corbett, Edgar Assing","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-03T14:30:31Z","title":"Vorono\\\"{i} summation via switching cusps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02025","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":"sha256:387987a730f84d66ec2cddbd67519dce48e79919ca3730d12ed154cf39ecbb27","target":"record","created_at":"2026-05-17T23:49:28Z","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":"3a59133ec7dd39f2aeec032ff6ee273d3d1f2d8e7cf90031d0d2a8edc53cb1a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-03T14:30:31Z","title_canon_sha256":"11f5e281610ac2a834cd8474483a71ac18c60562d3d451f5b126c1bdcd0f1aaa"},"schema_version":"1.0","source":{"id":"1904.02025","kind":"arxiv","version":1}},"canonical_sha256":"638a50276adf88246cc5747bd4f770cbf6f9f896358386b86a768a2b7635212c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"638a50276adf88246cc5747bd4f770cbf6f9f896358386b86a768a2b7635212c","first_computed_at":"2026-05-17T23:49:28.953043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:28.953043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gkYii1m3+isdilvHD1gOHjGOI0M6lfgrSpsDsbNwkobsx0zCaFl1WGq1jGw5f0uCwcqACFAAWAeHc6/tYR2PBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:28.953679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:387987a730f84d66ec2cddbd67519dce48e79919ca3730d12ed154cf39ecbb27","sha256:1bcb4c8ff75dfc7a4b814849f98219f079592fe795cd5f48c2dfb0d3b5fe695c"],"state_sha256":"52786c7e550f94dbb6f42766ef457a68d15b6d9d6daa448d1b39dfe04dba7c2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pHahJMebdteMojDNoUYh+ugkrr8WO7enUA9EZp/Dq8oWQqajU8Rg5F1CxyT6v2giSkZBjQeGShlAGHCgQABDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:26:05.146041Z","bundle_sha256":"6ef094981d420e363169b48f437d8bd8d208a36d3a53abf4ad1589395525fe2e"}}