{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XZ4JEE6YIREY2D6DDNBMUGLETX","short_pith_number":"pith:XZ4JEE6Y","canonical_record":{"source":{"id":"1609.06414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-21T03:33:17Z","cross_cats_sorted":[],"title_canon_sha256":"ca1db047ed9bc98f101829aa45dc57bb957e1442bb1028dc0f806f2271a0a9e4","abstract_canon_sha256":"a23d2d81ca7f833d388c24c1af786903fc1328800b99eae61ed686d850b24832"},"schema_version":"1.0"},"canonical_sha256":"be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207","source":{"kind":"arxiv","id":"1609.06414","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06414","created_at":"2026-05-18T00:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06414v2","created_at":"2026-05-18T00:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06414","created_at":"2026-05-18T00:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"XZ4JEE6YIREY","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XZ4JEE6YIREY2D6D","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XZ4JEE6Y","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XZ4JEE6YIREY2D6DDNBMUGLETX","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-21T03:33:17Z","cross_cats_sorted":[],"title_canon_sha256":"ca1db047ed9bc98f101829aa45dc57bb957e1442bb1028dc0f806f2271a0a9e4","abstract_canon_sha256":"a23d2d81ca7f833d388c24c1af786903fc1328800b99eae61ed686d850b24832"},"schema_version":"1.0"},"canonical_sha256":"be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:21.221752Z","signature_b64":"vEKsdPQyCwJihG9N+/w8zG11RKFekeo8wri0+LEQO38JCqBpV184FwcBzoWqo7+BkknZlrtApuBhezaPOiifDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207","last_reissued_at":"2026-05-18T00:38:21.221085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:21.221085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06414","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":"2026-05-18T00:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqdjsbP3ZBLYhHYucmgP1P3t0Tg7BZ79J8kZeSTlOBL+mDvhDFkJHKoElsusUpHJ/0TfL6Fo8i/1Bay1t4d+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:05:34.324666Z"},"content_sha256":"ae158a9a6d2fb7b869f5c3ea480f5885e7726e36c0962de93bff1e2c4c364134","schema_version":"1.0","event_id":"sha256:ae158a9a6d2fb7b869f5c3ea480f5885e7726e36c0962de93bff1e2c4c364134"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XZ4JEE6YIREY2D6DDNBMUGLETX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Potentially $\\text{GL}_2$-type Galois representations associated to noncongruence modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ling Long, Tong Liu, Wen-Ching Winnie Li","submitted_at":"2016-09-21T03:33:17Z","abstract_excerpt":"In this paper, we consider Galois representations of the absolute Galois group $\\text{Gal}(\\overline {\\mathbb Q}/\\mathbb Q)$ attached to modular forms for noncongruence subgroups of $\\text{SL}_2(\\mathbb Z)$. When the underlying modular curves have a model over $\\mathbb Q$, these representations are constructed by Scholl and are referred to as Scholl representations, which form a large class of motivic Galois representations. In particular, by a result of Belyi, Scholl representations include the Galois actions on the Jacobian varieties of algebraic curves defined over $\\mathbb Q$. As Scholl re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06414","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":"2026-05-18T00:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"up4CiVsaey2rdfLkprfXP+2xF8Asz6DpvAXhIl7b3+AMxZo9LH4IcIyk3synF3qGVuPzGKhcjeFRqFufbEBmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:05:34.325027Z"},"content_sha256":"4fe60ce0a00fddf1e3f09c4c7f1ee016e4daa34e9c63e7f993ca6a12ce463255","schema_version":"1.0","event_id":"sha256:4fe60ce0a00fddf1e3f09c4c7f1ee016e4daa34e9c63e7f993ca6a12ce463255"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZ4JEE6YIREY2D6DDNBMUGLETX/bundle.json","state_url":"https://pith.science/pith/XZ4JEE6YIREY2D6DDNBMUGLETX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZ4JEE6YIREY2D6DDNBMUGLETX/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":"2026-05-28T04:05:34Z","links":{"resolver":"https://pith.science/pith/XZ4JEE6YIREY2D6DDNBMUGLETX","bundle":"https://pith.science/pith/XZ4JEE6YIREY2D6DDNBMUGLETX/bundle.json","state":"https://pith.science/pith/XZ4JEE6YIREY2D6DDNBMUGLETX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZ4JEE6YIREY2D6DDNBMUGLETX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XZ4JEE6YIREY2D6DDNBMUGLETX","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":"a23d2d81ca7f833d388c24c1af786903fc1328800b99eae61ed686d850b24832","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-21T03:33:17Z","title_canon_sha256":"ca1db047ed9bc98f101829aa45dc57bb957e1442bb1028dc0f806f2271a0a9e4"},"schema_version":"1.0","source":{"id":"1609.06414","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06414","created_at":"2026-05-18T00:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06414v2","created_at":"2026-05-18T00:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06414","created_at":"2026-05-18T00:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"XZ4JEE6YIREY","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XZ4JEE6YIREY2D6D","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XZ4JEE6Y","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:4fe60ce0a00fddf1e3f09c4c7f1ee016e4daa34e9c63e7f993ca6a12ce463255","target":"graph","created_at":"2026-05-18T00:38:21Z","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 consider Galois representations of the absolute Galois group $\\text{Gal}(\\overline {\\mathbb Q}/\\mathbb Q)$ attached to modular forms for noncongruence subgroups of $\\text{SL}_2(\\mathbb Z)$. When the underlying modular curves have a model over $\\mathbb Q$, these representations are constructed by Scholl and are referred to as Scholl representations, which form a large class of motivic Galois representations. In particular, by a result of Belyi, Scholl representations include the Galois actions on the Jacobian varieties of algebraic curves defined over $\\mathbb Q$. As Scholl re","authors_text":"Ling Long, Tong Liu, Wen-Ching Winnie Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-21T03:33:17Z","title":"Potentially $\\text{GL}_2$-type Galois representations associated to noncongruence modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06414","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:ae158a9a6d2fb7b869f5c3ea480f5885e7726e36c0962de93bff1e2c4c364134","target":"record","created_at":"2026-05-18T00:38:21Z","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":"a23d2d81ca7f833d388c24c1af786903fc1328800b99eae61ed686d850b24832","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-21T03:33:17Z","title_canon_sha256":"ca1db047ed9bc98f101829aa45dc57bb957e1442bb1028dc0f806f2271a0a9e4"},"schema_version":"1.0","source":{"id":"1609.06414","kind":"arxiv","version":2}},"canonical_sha256":"be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207","first_computed_at":"2026-05-18T00:38:21.221085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:21.221085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vEKsdPQyCwJihG9N+/w8zG11RKFekeo8wri0+LEQO38JCqBpV184FwcBzoWqo7+BkknZlrtApuBhezaPOiifDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:21.221752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06414","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae158a9a6d2fb7b869f5c3ea480f5885e7726e36c0962de93bff1e2c4c364134","sha256:4fe60ce0a00fddf1e3f09c4c7f1ee016e4daa34e9c63e7f993ca6a12ce463255"],"state_sha256":"214e27107868848198307a309d5a313d84b167d567a8185b63ed8d235fd5ead1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ypmMU14CZMO/h5xGq36L6Oz9i8C/7kiw3dewhmvE5yetDvDuzCVC5ldliXlN3PKFG74sG5q57hU1HL4+SdveAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:05:34.326954Z","bundle_sha256":"3e2cd951ab5937ab4ae58fff7fd354566074d3d0b10eedd5d4d31d9f79176c4e"}}