{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UMDGL436SJ44OB2XZJPK57B4MW","short_pith_number":"pith:UMDGL436","canonical_record":{"source":{"id":"1508.01598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-07T04:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"1e0c6f57c84f1b798559113ef9c04e36bef05047cc57c68f18d3b1d26a2a3f45","abstract_canon_sha256":"8481bf0d7fea0ee8ec50f4f8dea5414795076d6c1c26fde5115152a9e9f1748a"},"schema_version":"1.0"},"canonical_sha256":"a30665f37e9279c70757ca5eaefc3c65b66c94fba2e3c95e4aad6309b561c35e","source":{"kind":"arxiv","id":"1508.01598","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01598","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01598v2","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01598","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"UMDGL436SJ44","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UMDGL436SJ44OB2X","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UMDGL436","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UMDGL436SJ44OB2XZJPK57B4MW","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-07T04:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"1e0c6f57c84f1b798559113ef9c04e36bef05047cc57c68f18d3b1d26a2a3f45","abstract_canon_sha256":"8481bf0d7fea0ee8ec50f4f8dea5414795076d6c1c26fde5115152a9e9f1748a"},"schema_version":"1.0"},"canonical_sha256":"a30665f37e9279c70757ca5eaefc3c65b66c94fba2e3c95e4aad6309b561c35e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:34.466246Z","signature_b64":"fuw9sfVaJKcd0ZOZhRS4O/NBh7sazldo0eCnuQFaqL+Jn4Jl9AKdZYKtzU/Sk4KRDj26C90wIySckGK/aGWRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a30665f37e9279c70757ca5eaefc3c65b66c94fba2e3c95e4aad6309b561c35e","last_reissued_at":"2026-05-18T00:55:34.465582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:34.465582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01598","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":"2026-05-18T00:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T0P8FsyMyqBlNDRHdoDoKid8KQZQ5IeflWAq/HxeqbhXDiMrUbjMZ6dNXJ69pnhP41NUGZvfeFMGx7/RBexlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:33:28.161098Z"},"content_sha256":"8943444f40b294a6a7f34c724a2dda1228195d8bc2acf7c26266131b8859318a","schema_version":"1.0","event_id":"sha256:8943444f40b294a6a7f34c724a2dda1228195d8bc2acf7c26266131b8859318a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UMDGL436SJ44OB2XZJPK57B4MW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Big image of Galois representations associated with finite slope $p$-adic families of modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian Iovita, Andrea Conti, Jacques Tilouine","submitted_at":"2015-08-07T04:16:02Z","abstract_excerpt":"We consider the Galois representation associated with a finite slope $p$-adic family of modular forms. We prove that the Lie algebra of its image contains a congruence Lie subalgebra of a non-trivial level. We describe the largest such level in terms of the congruences of the family with $p$-adic CM forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01598","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":"2026-05-18T00:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9T6g5KaxuBMv0aBbkFSip0Daf/K0iRMgesdt0F+y5FxXizoWppVWulZ8GEZ84oA7Vm6O9Q6u8EPhWDWoF3DVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:33:28.161752Z"},"content_sha256":"b85ef41aa10b76744f0eb7eb22843293e21921f0c6a9cc35196a6fee0417c43c","schema_version":"1.0","event_id":"sha256:b85ef41aa10b76744f0eb7eb22843293e21921f0c6a9cc35196a6fee0417c43c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMDGL436SJ44OB2XZJPK57B4MW/bundle.json","state_url":"https://pith.science/pith/UMDGL436SJ44OB2XZJPK57B4MW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMDGL436SJ44OB2XZJPK57B4MW/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":"2026-06-04T23:33:28Z","links":{"resolver":"https://pith.science/pith/UMDGL436SJ44OB2XZJPK57B4MW","bundle":"https://pith.science/pith/UMDGL436SJ44OB2XZJPK57B4MW/bundle.json","state":"https://pith.science/pith/UMDGL436SJ44OB2XZJPK57B4MW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMDGL436SJ44OB2XZJPK57B4MW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UMDGL436SJ44OB2XZJPK57B4MW","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":"8481bf0d7fea0ee8ec50f4f8dea5414795076d6c1c26fde5115152a9e9f1748a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-07T04:16:02Z","title_canon_sha256":"1e0c6f57c84f1b798559113ef9c04e36bef05047cc57c68f18d3b1d26a2a3f45"},"schema_version":"1.0","source":{"id":"1508.01598","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01598","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01598v2","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01598","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"UMDGL436SJ44","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UMDGL436SJ44OB2X","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UMDGL436","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:b85ef41aa10b76744f0eb7eb22843293e21921f0c6a9cc35196a6fee0417c43c","target":"graph","created_at":"2026-05-18T00:55:34Z","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":"We consider the Galois representation associated with a finite slope $p$-adic family of modular forms. We prove that the Lie algebra of its image contains a congruence Lie subalgebra of a non-trivial level. We describe the largest such level in terms of the congruences of the family with $p$-adic CM forms.","authors_text":"Adrian Iovita, Andrea Conti, Jacques Tilouine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-07T04:16:02Z","title":"Big image of Galois representations associated with finite slope $p$-adic families of modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01598","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":"sha256:8943444f40b294a6a7f34c724a2dda1228195d8bc2acf7c26266131b8859318a","target":"record","created_at":"2026-05-18T00:55:34Z","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":"8481bf0d7fea0ee8ec50f4f8dea5414795076d6c1c26fde5115152a9e9f1748a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-07T04:16:02Z","title_canon_sha256":"1e0c6f57c84f1b798559113ef9c04e36bef05047cc57c68f18d3b1d26a2a3f45"},"schema_version":"1.0","source":{"id":"1508.01598","kind":"arxiv","version":2}},"canonical_sha256":"a30665f37e9279c70757ca5eaefc3c65b66c94fba2e3c95e4aad6309b561c35e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a30665f37e9279c70757ca5eaefc3c65b66c94fba2e3c95e4aad6309b561c35e","first_computed_at":"2026-05-18T00:55:34.465582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:34.465582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fuw9sfVaJKcd0ZOZhRS4O/NBh7sazldo0eCnuQFaqL+Jn4Jl9AKdZYKtzU/Sk4KRDj26C90wIySckGK/aGWRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:34.466246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01598","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8943444f40b294a6a7f34c724a2dda1228195d8bc2acf7c26266131b8859318a","sha256:b85ef41aa10b76744f0eb7eb22843293e21921f0c6a9cc35196a6fee0417c43c"],"state_sha256":"5efab2d7c1cd20bfac4f39682df4ac7458e8df580853cbef32adea6b9ae8b7b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3XSxPjfOuw2ey5OiNsRnELr5mhOLkunrn35ANdA5SxUxycqWx8fA+owmfPxtaEdbjoNFTnWCTg024jWjLWesAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:33:28.166663Z","bundle_sha256":"47e280984aeb066c26c9f92117f7050ddbea69235b5876d013b02a3068a84623"}}