{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VYKDEGPCIQ3AMF4QWZVFA7H5XK","short_pith_number":"pith:VYKDEGPC","canonical_record":{"source":{"id":"1702.07917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-25T16:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"80f41d6712f8fdc225e7564732e4a8739f300ab3219fa5c2cd5e10f302d22f03","abstract_canon_sha256":"a0151e45bd8fdb6335716dadf04a77ad3ea2c2295f1fa83399641e67225b7428"},"schema_version":"1.0"},"canonical_sha256":"ae143219e24436061790b66a507cfdbab99659d01a79368dbe9257496e7fa06c","source":{"kind":"arxiv","id":"1702.07917","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07917","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07917v2","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07917","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"VYKDEGPCIQ3A","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VYKDEGPCIQ3AMF4Q","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VYKDEGPC","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VYKDEGPCIQ3AMF4QWZVFA7H5XK","target":"record","payload":{"canonical_record":{"source":{"id":"1702.07917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-25T16:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"80f41d6712f8fdc225e7564732e4a8739f300ab3219fa5c2cd5e10f302d22f03","abstract_canon_sha256":"a0151e45bd8fdb6335716dadf04a77ad3ea2c2295f1fa83399641e67225b7428"},"schema_version":"1.0"},"canonical_sha256":"ae143219e24436061790b66a507cfdbab99659d01a79368dbe9257496e7fa06c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:31.471599Z","signature_b64":"lGGPPw01cmm9UF5ZjgElHCDJm6SSraeJvGX1uOYk5Wulp42LKagSVk4vv+PFXk43m2wXaqZychCyWh4jo0FlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae143219e24436061790b66a507cfdbab99659d01a79368dbe9257496e7fa06c","last_reissued_at":"2026-05-18T00:24:31.470936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:31.470936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.07917","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zj/AtMNnONhzRnuWWKo+DK+Ipx71Jxcw8smNkbSI9XLgTFHmKtvYM8qyOwtX140jJURjnM/pUyUOeBlipx1MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:50:25.686040Z"},"content_sha256":"ce79668d19f3a8aed801762a4904f4b47ad66b868571adf9aa2513b6d742434a","schema_version":"1.0","event_id":"sha256:ce79668d19f3a8aed801762a4904f4b47ad66b868571adf9aa2513b6d742434a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VYKDEGPCIQ3AMF4QWZVFA7H5XK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic Siegel-Weil formula on $X_{0}(N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tonghai Yang, Tuoping Du","submitted_at":"2017-02-25T16:31:53Z","abstract_excerpt":"In this paper, we proved an arithmetic Siegel-Weil formula and the modularity of some arithmetic theta function on the modular curve $X_0(N)$ when $N$ is square free. In the process, we also construct some generalized Delta function for $\\Gamma_0(N)$ and proved some explicit Kronecker limit formula for Eisenstein series on $X_0(N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07917","kind":"arxiv","version":2},"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":"2026-05-18T00:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6TFbQ4ZmL5t9qfCs4JBg3RXXS0jfkLVOiDImEAvN24YK/V4rA/MqVI8UfkwE53C+Z3+DDP72f5zW2RTM+WdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:50:25.686401Z"},"content_sha256":"40b92cb0d8c354d265828a5f1d646437e10856a30873c0661831511e45527be1","schema_version":"1.0","event_id":"sha256:40b92cb0d8c354d265828a5f1d646437e10856a30873c0661831511e45527be1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK/bundle.json","state_url":"https://pith.science/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK/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":"2026-06-10T21:50:25Z","links":{"resolver":"https://pith.science/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK","bundle":"https://pith.science/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK/bundle.json","state":"https://pith.science/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYKDEGPCIQ3AMF4QWZVFA7H5XK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VYKDEGPCIQ3AMF4QWZVFA7H5XK","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":"a0151e45bd8fdb6335716dadf04a77ad3ea2c2295f1fa83399641e67225b7428","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-25T16:31:53Z","title_canon_sha256":"80f41d6712f8fdc225e7564732e4a8739f300ab3219fa5c2cd5e10f302d22f03"},"schema_version":"1.0","source":{"id":"1702.07917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07917","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07917v2","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07917","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"VYKDEGPCIQ3A","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VYKDEGPCIQ3AMF4Q","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VYKDEGPC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:40b92cb0d8c354d265828a5f1d646437e10856a30873c0661831511e45527be1","target":"graph","created_at":"2026-05-18T00:24:31Z","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 proved an arithmetic Siegel-Weil formula and the modularity of some arithmetic theta function on the modular curve $X_0(N)$ when $N$ is square free. In the process, we also construct some generalized Delta function for $\\Gamma_0(N)$ and proved some explicit Kronecker limit formula for Eisenstein series on $X_0(N)$.","authors_text":"Tonghai Yang, Tuoping Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-25T16:31:53Z","title":"Arithmetic Siegel-Weil formula on $X_{0}(N)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07917","kind":"arxiv","version":2},"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:ce79668d19f3a8aed801762a4904f4b47ad66b868571adf9aa2513b6d742434a","target":"record","created_at":"2026-05-18T00:24:31Z","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":"a0151e45bd8fdb6335716dadf04a77ad3ea2c2295f1fa83399641e67225b7428","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-25T16:31:53Z","title_canon_sha256":"80f41d6712f8fdc225e7564732e4a8739f300ab3219fa5c2cd5e10f302d22f03"},"schema_version":"1.0","source":{"id":"1702.07917","kind":"arxiv","version":2}},"canonical_sha256":"ae143219e24436061790b66a507cfdbab99659d01a79368dbe9257496e7fa06c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae143219e24436061790b66a507cfdbab99659d01a79368dbe9257496e7fa06c","first_computed_at":"2026-05-18T00:24:31.470936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:31.470936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGGPPw01cmm9UF5ZjgElHCDJm6SSraeJvGX1uOYk5Wulp42LKagSVk4vv+PFXk43m2wXaqZychCyWh4jo0FlAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:31.471599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce79668d19f3a8aed801762a4904f4b47ad66b868571adf9aa2513b6d742434a","sha256:40b92cb0d8c354d265828a5f1d646437e10856a30873c0661831511e45527be1"],"state_sha256":"10825b4a5ff98391f3f7b15392411c880c844b18ec741fe4d7b4fcd7f5d55427"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RAFx4emfRPK2cEjZKY4fMe6EuuGaHXuHPyYHrAmO6QxmtDbkoDbnh8zDpXsUj7HJgxbHF98dLxWy0VWC9LMaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:50:25.688282Z","bundle_sha256":"bbd5c7a3e0d1760cc382b07a938ff3a31dce076d3914cb86012011da02811763"}}