{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WVSC74TUNHBSNNCXHI3SWAQVZU","short_pith_number":"pith:WVSC74TU","canonical_record":{"source":{"id":"2607.16893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T17:24:56Z","cross_cats_sorted":[],"title_canon_sha256":"d426cca60472824bf02f32bb7f409dcf55b21f11e9a880def54cc6871e1c5e45","abstract_canon_sha256":"f81a26262a38f1a50b2fbfb7921ea19bca307b246e5868fa2602d40d4d5311f6"},"schema_version":"1.0"},"canonical_sha256":"b5642ff27469c326b4573a372b0215cd148d3036e73db2018de4d824b2a4dbe5","source":{"kind":"arxiv","id":"2607.16893","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16893","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16893v1","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16893","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"pith_short_12","alias_value":"WVSC74TUNHBS","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"pith_short_16","alias_value":"WVSC74TUNHBSNNCX","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"pith_short_8","alias_value":"WVSC74TU","created_at":"2026-07-21T01:21:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WVSC74TUNHBSNNCXHI3SWAQVZU","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T17:24:56Z","cross_cats_sorted":[],"title_canon_sha256":"d426cca60472824bf02f32bb7f409dcf55b21f11e9a880def54cc6871e1c5e45","abstract_canon_sha256":"f81a26262a38f1a50b2fbfb7921ea19bca307b246e5868fa2602d40d4d5311f6"},"schema_version":"1.0"},"canonical_sha256":"b5642ff27469c326b4573a372b0215cd148d3036e73db2018de4d824b2a4dbe5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:21:04.221474Z","signature_b64":"1gamZOAZ3XaRExOGG/zz80vMzCVCwELbpnQx6u5Nn0peWtGBC5K0wMac3fsshLzThmaAxDtOE8Vbf0Kf0edcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5642ff27469c326b4573a372b0215cd148d3036e73db2018de4d824b2a4dbe5","last_reissued_at":"2026-07-21T01:21:04.220618Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:21:04.220618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16893","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":"2026-07-21T01:21:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWHMMurQR0J9Xfe7SVT/xc1bdQan6CzI03Aq4hNq9vrmzWzO9C8IX597yPE54BSWpcyUinvJUV7klqonqAnrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:57:23.181749Z"},"content_sha256":"8e70d289cccf7402e39c8110d86a5924d2a74023e0480d663fb98aba274d4ed0","schema_version":"1.0","event_id":"sha256:8e70d289cccf7402e39c8110d86a5924d2a74023e0480d663fb98aba274d4ed0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WVSC74TUNHBSNNCXHI3SWAQVZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Siegel-Weil formulas for $\\mathrm{GL}_2$ over non-Galois quartic CM fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mingkuan Zhang","submitted_at":"2026-07-18T17:24:56Z","abstract_excerpt":"We establish twisted Siegel-Weil formulas for non-Galois quartic CM fields, identifying the twisted theta integral against a quadratic character with the Doi-Naganuma lift of Hecke's integral. This implies the base change of Jacquet-Langlands correspondence for certain Hecke characters from $\\mathbb{Q}$ to real quadratic fields via Doi-Naganuma lift is an isomorphism. As an application, we prove that the twisted CM values of Borcherds forms are algebraic multiple of logarithm of units, explicitly described by the Fourier coefficients of twisted theta integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16893","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16893/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-21T01:21:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2n9T34p9A5xxPUX+VOkUXtCcggm9RLqaT7MN/jDHkcjigS1B7qaQGKOiQP3oFzinfsH+gi3naCEVQrjAWTDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:57:23.182558Z"},"content_sha256":"7c5a26f94025bc4b1687e2d712b295be1ddbcad3238c7cbe631a9a4ecf29533f","schema_version":"1.0","event_id":"sha256:7c5a26f94025bc4b1687e2d712b295be1ddbcad3238c7cbe631a9a4ecf29533f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVSC74TUNHBSNNCXHI3SWAQVZU/bundle.json","state_url":"https://pith.science/pith/WVSC74TUNHBSNNCXHI3SWAQVZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVSC74TUNHBSNNCXHI3SWAQVZU/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":"2026-08-09T04:57:23Z","links":{"resolver":"https://pith.science/pith/WVSC74TUNHBSNNCXHI3SWAQVZU","bundle":"https://pith.science/pith/WVSC74TUNHBSNNCXHI3SWAQVZU/bundle.json","state":"https://pith.science/pith/WVSC74TUNHBSNNCXHI3SWAQVZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVSC74TUNHBSNNCXHI3SWAQVZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WVSC74TUNHBSNNCXHI3SWAQVZU","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":"f81a26262a38f1a50b2fbfb7921ea19bca307b246e5868fa2602d40d4d5311f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T17:24:56Z","title_canon_sha256":"d426cca60472824bf02f32bb7f409dcf55b21f11e9a880def54cc6871e1c5e45"},"schema_version":"1.0","source":{"id":"2607.16893","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16893","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16893v1","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16893","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"pith_short_12","alias_value":"WVSC74TUNHBS","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"pith_short_16","alias_value":"WVSC74TUNHBSNNCX","created_at":"2026-07-21T01:21:04Z"},{"alias_kind":"pith_short_8","alias_value":"WVSC74TU","created_at":"2026-07-21T01:21:04Z"}],"graph_snapshots":[{"event_id":"sha256:7c5a26f94025bc4b1687e2d712b295be1ddbcad3238c7cbe631a9a4ecf29533f","target":"graph","created_at":"2026-07-21T01:21:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.16893/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish twisted Siegel-Weil formulas for non-Galois quartic CM fields, identifying the twisted theta integral against a quadratic character with the Doi-Naganuma lift of Hecke's integral. This implies the base change of Jacquet-Langlands correspondence for certain Hecke characters from $\\mathbb{Q}$ to real quadratic fields via Doi-Naganuma lift is an isomorphism. As an application, we prove that the twisted CM values of Borcherds forms are algebraic multiple of logarithm of units, explicitly described by the Fourier coefficients of twisted theta integrals.","authors_text":"Mingkuan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T17:24:56Z","title":"Twisted Siegel-Weil formulas for $\\mathrm{GL}_2$ over non-Galois quartic CM fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16893","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":"sha256:8e70d289cccf7402e39c8110d86a5924d2a74023e0480d663fb98aba274d4ed0","target":"record","created_at":"2026-07-21T01:21:04Z","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":"f81a26262a38f1a50b2fbfb7921ea19bca307b246e5868fa2602d40d4d5311f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-18T17:24:56Z","title_canon_sha256":"d426cca60472824bf02f32bb7f409dcf55b21f11e9a880def54cc6871e1c5e45"},"schema_version":"1.0","source":{"id":"2607.16893","kind":"arxiv","version":1}},"canonical_sha256":"b5642ff27469c326b4573a372b0215cd148d3036e73db2018de4d824b2a4dbe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5642ff27469c326b4573a372b0215cd148d3036e73db2018de4d824b2a4dbe5","first_computed_at":"2026-07-21T01:21:04.220618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:21:04.220618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1gamZOAZ3XaRExOGG/zz80vMzCVCwELbpnQx6u5Nn0peWtGBC5K0wMac3fsshLzThmaAxDtOE8Vbf0Kf0edcDA==","signature_status":"signed_v1","signed_at":"2026-07-21T01:21:04.221474Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16893","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e70d289cccf7402e39c8110d86a5924d2a74023e0480d663fb98aba274d4ed0","sha256:7c5a26f94025bc4b1687e2d712b295be1ddbcad3238c7cbe631a9a4ecf29533f"],"state_sha256":"651a3c408c9753ce6b5302ed345cadf83957f6300f4f1ef124c590d5bf9dbdc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3c/e+uDQdhcFU34pAVZFjg90meI/q0wBI+maumaSjiX6uEXZPNieih1aEfwlu8a+rY2aApz4TMHIxbNoOCr2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:57:23.189733Z","bundle_sha256":"4183a91db50e49bb1be053ffdc50c9fc71a5e8d56bd5993088330ab2fd2b1411"}}