{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DSKMG2QTCW6TWXDNKMYIMI4VGQ","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":"bc34070d1e59c966852f11bba2cab743feeec3c0ec8f04bf23ab23a59bca9ba4","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2012-06-25T13:28:18Z","title_canon_sha256":"31e70ff0f0f1775b09d21eecc626656f46bfa4d4e6fc32e7f3ef4b840460f64d"},"schema_version":"1.0","source":{"id":"1206.5675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5675","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5675v1","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5675","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"DSKMG2QTCW6T","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DSKMG2QTCW6TWXDN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DSKMG2QT","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:be2b2925fa092039b228321e9b44b879317d4806314df93b1bf9a13d8f07de89","target":"graph","created_at":"2026-05-18T03:52:39Z","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 work we construct an eigencurve for p-adic modular forms attached to an indefinite quaternion algebra over Q. Our theory includes the definition, both as rules on test objects and sections of line bundle, of p-adic modular forms, convergent and overconvergent, of any p-adic weight. We prove that our modular forms can be put in analytic families over the weight space and we introduce the Hecke operators U and T_l, that can also be put in families. We show that the U-operator acts compactly on the space of overconvergent modular forms. We finally construct the eigencurve, a rigid analyti","authors_text":"Riccardo Brasca","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2012-06-25T13:28:18Z","title":"Quaternionic modular forms of any weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5675","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":"sha256:09242e2fcc54f5877418ba41bdabf90a95db629d523129d188b1d4996c2233d5","target":"record","created_at":"2026-05-18T03:52:39Z","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":"bc34070d1e59c966852f11bba2cab743feeec3c0ec8f04bf23ab23a59bca9ba4","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2012-06-25T13:28:18Z","title_canon_sha256":"31e70ff0f0f1775b09d21eecc626656f46bfa4d4e6fc32e7f3ef4b840460f64d"},"schema_version":"1.0","source":{"id":"1206.5675","kind":"arxiv","version":1}},"canonical_sha256":"1c94c36a1315bd3b5c6d533086239534283bc18b63699f039a294cdc63690f76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c94c36a1315bd3b5c6d533086239534283bc18b63699f039a294cdc63690f76","first_computed_at":"2026-05-18T03:52:39.345052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:39.345052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"guSlmV2fPQLbu85xvVd62uNkkRpao1FINST5v8e6YbFwfRB14wb8DpLvHcdfOGq5jusRmVlnTEqcGQOyoQosAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:39.345676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09242e2fcc54f5877418ba41bdabf90a95db629d523129d188b1d4996c2233d5","sha256:be2b2925fa092039b228321e9b44b879317d4806314df93b1bf9a13d8f07de89"],"state_sha256":"2132e528055536efd75e9d555e57b057dcc864c89e2f6340bb271e4e721d2565"}