{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ISX4RVZ7ZNWHHVUZKEN3K7IMB3","short_pith_number":"pith:ISX4RVZ7","canonical_record":{"source":{"id":"1704.08147","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-26T14:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"901a0858e20fd4dbab6432944654ed7acfc7552fdafad3d2c362d954e36b4eeb","abstract_canon_sha256":"8f41f4a405571e49371f9df40ec4817a967e66ad260661f9c4ab9a475fc6f82c"},"schema_version":"1.0"},"canonical_sha256":"44afc8d73fcb6c73d699511bb57d0c0efabc190e90d058fab62cb1fa9a27a1ca","source":{"kind":"arxiv","id":"1704.08147","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08147","created_at":"2026-05-18T00:18:26Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08147v3","created_at":"2026-05-18T00:18:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08147","created_at":"2026-05-18T00:18:26Z"},{"alias_kind":"pith_short_12","alias_value":"ISX4RVZ7ZNWH","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ISX4RVZ7ZNWHHVUZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ISX4RVZ7","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ISX4RVZ7ZNWHHVUZKEN3K7IMB3","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08147","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-26T14:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"901a0858e20fd4dbab6432944654ed7acfc7552fdafad3d2c362d954e36b4eeb","abstract_canon_sha256":"8f41f4a405571e49371f9df40ec4817a967e66ad260661f9c4ab9a475fc6f82c"},"schema_version":"1.0"},"canonical_sha256":"44afc8d73fcb6c73d699511bb57d0c0efabc190e90d058fab62cb1fa9a27a1ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:26.832140Z","signature_b64":"aMj/5O7zywYjBYbRFeM7NPoLhp2TGb+kwfenmiSEateXNgYwIkmBd6tZqtyvhRonxQTFva4WbYYdjUVvJqOkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44afc8d73fcb6c73d699511bb57d0c0efabc190e90d058fab62cb1fa9a27a1ca","last_reissued_at":"2026-05-18T00:18:26.831351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:26.831351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08147","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W1Gzs+JJAg1Er1czBevMsV3PIRZAYyTEKRnqjwP/uERwsdzlTcUHGA23na7wJiSKj7txasOkbuZE0Tg2XXgrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:57:52.136349Z"},"content_sha256":"dc429fe6e8085aff389f2da0c5fe55290deed683f34e47964a3cc88d685252fd","schema_version":"1.0","event_id":"sha256:dc429fe6e8085aff389f2da0c5fe55290deed683f34e47964a3cc88d685252fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ISX4RVZ7ZNWHHVUZKEN3K7IMB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Niebur-Poincar\\'e Series and Traces of Singular Moduli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Steffen L\\\"obrich","submitted_at":"2017-04-26T14:51:57Z","abstract_excerpt":"We compute the Fourier coefficients of analogues of Kohnen and Zagier's modular forms $f_{k,D}$ of weight $2$ and negative discriminant. These functions can also be written as twisted traces of certain weight $2$ Poincar\\'e series with evaluations of Niebur-Poincar\\'e series as Fourier coefficients. This allows us to study twisted traces of singular moduli in an integral weight setting. In particular, we recover explicit series expressions for twisted traces of singular moduli and extend algebraicity results by Bengoechea to the weight $2$ case. We also compute regularized inner products of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08147","kind":"arxiv","version":3},"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":"2026-05-18T00:18:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYbU1120iA0o8YjZA8NkLQelwCKwV5wcT1Nb12BIdcsLnkdnwaI3vJwqWTavox9R0NUJXdCkyvSmHtIyqmMDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:57:52.136890Z"},"content_sha256":"2538377e23c44a730229ade7c0904f868c487a5db0bc7812508f434be2364110","schema_version":"1.0","event_id":"sha256:2538377e23c44a730229ade7c0904f868c487a5db0bc7812508f434be2364110"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3/bundle.json","state_url":"https://pith.science/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3/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":"2026-05-30T08:57:52Z","links":{"resolver":"https://pith.science/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3","bundle":"https://pith.science/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3/bundle.json","state":"https://pith.science/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ISX4RVZ7ZNWHHVUZKEN3K7IMB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ISX4RVZ7ZNWHHVUZKEN3K7IMB3","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":"8f41f4a405571e49371f9df40ec4817a967e66ad260661f9c4ab9a475fc6f82c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-26T14:51:57Z","title_canon_sha256":"901a0858e20fd4dbab6432944654ed7acfc7552fdafad3d2c362d954e36b4eeb"},"schema_version":"1.0","source":{"id":"1704.08147","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08147","created_at":"2026-05-18T00:18:26Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08147v3","created_at":"2026-05-18T00:18:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08147","created_at":"2026-05-18T00:18:26Z"},{"alias_kind":"pith_short_12","alias_value":"ISX4RVZ7ZNWH","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ISX4RVZ7ZNWHHVUZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ISX4RVZ7","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:2538377e23c44a730229ade7c0904f868c487a5db0bc7812508f434be2364110","target":"graph","created_at":"2026-05-18T00:18:26Z","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 compute the Fourier coefficients of analogues of Kohnen and Zagier's modular forms $f_{k,D}$ of weight $2$ and negative discriminant. These functions can also be written as twisted traces of certain weight $2$ Poincar\\'e series with evaluations of Niebur-Poincar\\'e series as Fourier coefficients. This allows us to study twisted traces of singular moduli in an integral weight setting. In particular, we recover explicit series expressions for twisted traces of singular moduli and extend algebraicity results by Bengoechea to the weight $2$ case. We also compute regularized inner products of th","authors_text":"Steffen L\\\"obrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-26T14:51:57Z","title":"Niebur-Poincar\\'e Series and Traces of Singular Moduli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08147","kind":"arxiv","version":3},"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:dc429fe6e8085aff389f2da0c5fe55290deed683f34e47964a3cc88d685252fd","target":"record","created_at":"2026-05-18T00:18:26Z","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":"8f41f4a405571e49371f9df40ec4817a967e66ad260661f9c4ab9a475fc6f82c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-26T14:51:57Z","title_canon_sha256":"901a0858e20fd4dbab6432944654ed7acfc7552fdafad3d2c362d954e36b4eeb"},"schema_version":"1.0","source":{"id":"1704.08147","kind":"arxiv","version":3}},"canonical_sha256":"44afc8d73fcb6c73d699511bb57d0c0efabc190e90d058fab62cb1fa9a27a1ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44afc8d73fcb6c73d699511bb57d0c0efabc190e90d058fab62cb1fa9a27a1ca","first_computed_at":"2026-05-18T00:18:26.831351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:26.831351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMj/5O7zywYjBYbRFeM7NPoLhp2TGb+kwfenmiSEateXNgYwIkmBd6tZqtyvhRonxQTFva4WbYYdjUVvJqOkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:26.832140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08147","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc429fe6e8085aff389f2da0c5fe55290deed683f34e47964a3cc88d685252fd","sha256:2538377e23c44a730229ade7c0904f868c487a5db0bc7812508f434be2364110"],"state_sha256":"3b7af48193533ea0c427b09addf678992957e181958c075a618db084c9d799a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzhoeiYNgvIQdo+nbACFPoTxjDzj7lhSVeXhDfdAuk6atJheIdtdFbhQGozSiDNbb72YJvuWkk28IEmSNwBuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:57:52.139618Z","bundle_sha256":"4b18b1b8c15e5445767f1718300ec464d258137309448147ecbd112b21a69bfa"}}