{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SS7P5JS7FV4J7SX3YKXTKAKGMG","short_pith_number":"pith:SS7P5JS7","canonical_record":{"source":{"id":"1409.0793","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-02T17:02:19Z","cross_cats_sorted":[],"title_canon_sha256":"8a7290cc04e4ac9a435bd39d264fcc39b35ffc2a4f4a6bcabe46f556e100a620","abstract_canon_sha256":"2c1362555446627ab52ee5f01fbc5265740657148f990792cf49f735be6b04fc"},"schema_version":"1.0"},"canonical_sha256":"94befea65f2d789fcafbc2af35014661a904a8cf8a0b2b52163d5e254acc1c97","source":{"kind":"arxiv","id":"1409.0793","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0793","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0793v4","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0793","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"pith_short_12","alias_value":"SS7P5JS7FV4J","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SS7P5JS7FV4J7SX3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SS7P5JS7","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SS7P5JS7FV4J7SX3YKXTKAKGMG","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0793","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-02T17:02:19Z","cross_cats_sorted":[],"title_canon_sha256":"8a7290cc04e4ac9a435bd39d264fcc39b35ffc2a4f4a6bcabe46f556e100a620","abstract_canon_sha256":"2c1362555446627ab52ee5f01fbc5265740657148f990792cf49f735be6b04fc"},"schema_version":"1.0"},"canonical_sha256":"94befea65f2d789fcafbc2af35014661a904a8cf8a0b2b52163d5e254acc1c97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:23.339920Z","signature_b64":"DZm2CL2oEdRT0GxLedsvErOO9ryz4LrnSCYNoi6B+uhhQstkKS8o3zL/wP9Z7qss9BBOXlwZ4FbL7bytF8jqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94befea65f2d789fcafbc2af35014661a904a8cf8a0b2b52163d5e254acc1c97","last_reissued_at":"2026-05-18T00:14:23.339235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:23.339235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0793","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vQlKWbZ+vpPaS3z7O+9cDE6onM3gy0Rg/3swxNH2iPOWQJjSq9mhRWyf3CIMnsyV4jWHorPvjfmTwafmqfnACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:37:39.006627Z"},"content_sha256":"9a4358937da5f6c89573d636e23ae28466f7eede69d420d9d8e23cd4aa9d1df6","schema_version":"1.0","event_id":"sha256:9a4358937da5f6c89573d636e23ae28466f7eede69d420d9d8e23cd4aa9d1df6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SS7P5JS7FV4J7SX3YKXTKAKGMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularized inner products of meromorphic modular forms and higher Green's functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna-Maria von Pippich, Ben Kane, Kathrin Bringmann","submitted_at":"2014-09-02T17:02:19Z","abstract_excerpt":"In this paper we study generalizations of quadratic form Poincar\\'e series, which naturally occur as outputs of theta lifts. Integrating against them yields evaluations of higher Green's functions. For this we require a new regularized inner product, which is of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0793","kind":"arxiv","version":4},"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":"2026-05-18T00:14:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9O0kIIzSqyya57EY5X9N/llvFKuoiwujaM2c8fp3L1JxnmjtXMD53QcKA8RSZdDlxmMGVpeIcn+JwzoQwZX0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:37:39.006978Z"},"content_sha256":"b8c9d00f92f93629fd43fa0ec1d0bd1080a587d1f7926b80e07d64e9b50ff679","schema_version":"1.0","event_id":"sha256:b8c9d00f92f93629fd43fa0ec1d0bd1080a587d1f7926b80e07d64e9b50ff679"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG/bundle.json","state_url":"https://pith.science/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG/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":"2026-05-22T18:37:39Z","links":{"resolver":"https://pith.science/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG","bundle":"https://pith.science/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG/bundle.json","state":"https://pith.science/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SS7P5JS7FV4J7SX3YKXTKAKGMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SS7P5JS7FV4J7SX3YKXTKAKGMG","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":"2c1362555446627ab52ee5f01fbc5265740657148f990792cf49f735be6b04fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-02T17:02:19Z","title_canon_sha256":"8a7290cc04e4ac9a435bd39d264fcc39b35ffc2a4f4a6bcabe46f556e100a620"},"schema_version":"1.0","source":{"id":"1409.0793","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0793","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0793v4","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0793","created_at":"2026-05-18T00:14:23Z"},{"alias_kind":"pith_short_12","alias_value":"SS7P5JS7FV4J","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SS7P5JS7FV4J7SX3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SS7P5JS7","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:b8c9d00f92f93629fd43fa0ec1d0bd1080a587d1f7926b80e07d64e9b50ff679","target":"graph","created_at":"2026-05-18T00:14:23Z","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"},"paper":{"abstract_excerpt":"In this paper we study generalizations of quadratic form Poincar\\'e series, which naturally occur as outputs of theta lifts. Integrating against them yields evaluations of higher Green's functions. For this we require a new regularized inner product, which is of independent interest.","authors_text":"Anna-Maria von Pippich, Ben Kane, Kathrin Bringmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-02T17:02:19Z","title":"Regularized inner products of meromorphic modular forms and higher Green's functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0793","kind":"arxiv","version":4},"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":"sha256:9a4358937da5f6c89573d636e23ae28466f7eede69d420d9d8e23cd4aa9d1df6","target":"record","created_at":"2026-05-18T00:14:23Z","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":"2c1362555446627ab52ee5f01fbc5265740657148f990792cf49f735be6b04fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-02T17:02:19Z","title_canon_sha256":"8a7290cc04e4ac9a435bd39d264fcc39b35ffc2a4f4a6bcabe46f556e100a620"},"schema_version":"1.0","source":{"id":"1409.0793","kind":"arxiv","version":4}},"canonical_sha256":"94befea65f2d789fcafbc2af35014661a904a8cf8a0b2b52163d5e254acc1c97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94befea65f2d789fcafbc2af35014661a904a8cf8a0b2b52163d5e254acc1c97","first_computed_at":"2026-05-18T00:14:23.339235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:23.339235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DZm2CL2oEdRT0GxLedsvErOO9ryz4LrnSCYNoi6B+uhhQstkKS8o3zL/wP9Z7qss9BBOXlwZ4FbL7bytF8jqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:23.339920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0793","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a4358937da5f6c89573d636e23ae28466f7eede69d420d9d8e23cd4aa9d1df6","sha256:b8c9d00f92f93629fd43fa0ec1d0bd1080a587d1f7926b80e07d64e9b50ff679"],"state_sha256":"f3a972c92217a30c7c0018e0152d1a99a58e802a448c58c004a5594d778a439b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mspiak7kpnDJxjfiIGllTYxkyyZnEqR7hnGGIzrI1xb028JBbYtyM1RT9RXS8w5nr4TXaC6m129Asiwe63KLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:37:39.009050Z","bundle_sha256":"2e5ce0ed885220540367c87d1d1de79c991f57ffe92bf532d2f0bd1a5ef79289"}}