{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:26OWHXOUVYO5ZTOC7ZNAURYEM5","short_pith_number":"pith:26OWHXOU","canonical_record":{"source":{"id":"1106.5586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-28T08:10:45Z","cross_cats_sorted":[],"title_canon_sha256":"8ae7c312850ed33c0de0ee73e981f6553e980511361dcc1672fea11454a53440","abstract_canon_sha256":"860db942eeddf494f0a345fd62ba3c424dae878435d4e6d1c48eab5707c63097"},"schema_version":"1.0"},"canonical_sha256":"d79d63ddd4ae1ddccdc2fe5a0a47046766a05935cac79e301e9965f5e903db7a","source":{"kind":"arxiv","id":"1106.5586","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5586","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5586v1","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5586","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"26OWHXOUVYO5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"26OWHXOUVYO5ZTOC","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"26OWHXOU","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:26OWHXOUVYO5ZTOC7ZNAURYEM5","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-28T08:10:45Z","cross_cats_sorted":[],"title_canon_sha256":"8ae7c312850ed33c0de0ee73e981f6553e980511361dcc1672fea11454a53440","abstract_canon_sha256":"860db942eeddf494f0a345fd62ba3c424dae878435d4e6d1c48eab5707c63097"},"schema_version":"1.0"},"canonical_sha256":"d79d63ddd4ae1ddccdc2fe5a0a47046766a05935cac79e301e9965f5e903db7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:12.888223Z","signature_b64":"Q9NE8Q2MxdNbkgTq23fUzXIPEaHFTNrb0TPZLxw195LjljTrgqncbSKrgq23cuoIvYuPeT/SBHmGjXpIdOi7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d79d63ddd4ae1ddccdc2fe5a0a47046766a05935cac79e301e9965f5e903db7a","last_reissued_at":"2026-05-18T04:19:12.887789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:12.887789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5586","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":"2026-05-18T04:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDf34Cm78V5UubvyfuMjDB1NPd0yXbDOcYDxSjUNTggWca1XMTahCCe/m+nzzXF5NymPgfjOIHsaD1wHsXekDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:39:49.943270Z"},"content_sha256":"7cb45dfcaf88a7078e86595676ae78a11d698eb18b5c8581a63be9ab793d1efd","schema_version":"1.0","event_id":"sha256:7cb45dfcaf88a7078e86595676ae78a11d698eb18b5c8581a63be9ab793d1efd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:26OWHXOUVYO5ZTOC7ZNAURYEM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Serre weights for rank two unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Geraghty, Thomas Barnet-Lamb, Toby Gee","submitted_at":"2011-06-28T08:10:45Z","abstract_excerpt":"We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights, agreeing with all conjectures in the literature, and under a mild assumption on the image of the mod l Galois representation we are able to show that any modular representation is modular of each conjectured weight. We make no assumptions on the ramification or inertial degrees of l. Our main innovation is to make use of the lifting techniques introduced in our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5586","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":""},"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":"2026-05-18T04:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BrIQlIVPRpxr6NOUw4W2x3Y9wNJLU2VI5X+58Cp9Gt+f1LOmJZF6sbhqEmEBH72rDtYVRh5HF19JozTrK3hcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:39:49.943672Z"},"content_sha256":"7f1dc73fb1f274d16db1637b8486a45b109c912e91096f8edd54280442b6331f","schema_version":"1.0","event_id":"sha256:7f1dc73fb1f274d16db1637b8486a45b109c912e91096f8edd54280442b6331f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5/bundle.json","state_url":"https://pith.science/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5/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":"2026-06-05T14:39:49Z","links":{"resolver":"https://pith.science/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5","bundle":"https://pith.science/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5/bundle.json","state":"https://pith.science/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/26OWHXOUVYO5ZTOC7ZNAURYEM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:26OWHXOUVYO5ZTOC7ZNAURYEM5","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":"860db942eeddf494f0a345fd62ba3c424dae878435d4e6d1c48eab5707c63097","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-28T08:10:45Z","title_canon_sha256":"8ae7c312850ed33c0de0ee73e981f6553e980511361dcc1672fea11454a53440"},"schema_version":"1.0","source":{"id":"1106.5586","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5586","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5586v1","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5586","created_at":"2026-05-18T04:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"26OWHXOUVYO5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"26OWHXOUVYO5ZTOC","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"26OWHXOU","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:7f1dc73fb1f274d16db1637b8486a45b109c912e91096f8edd54280442b6331f","target":"graph","created_at":"2026-05-18T04:19:12Z","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 study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights, agreeing with all conjectures in the literature, and under a mild assumption on the image of the mod l Galois representation we are able to show that any modular representation is modular of each conjectured weight. We make no assumptions on the ramification or inertial degrees of l. Our main innovation is to make use of the lifting techniques introduced in our ","authors_text":"David Geraghty, Thomas Barnet-Lamb, Toby Gee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-28T08:10:45Z","title":"Serre weights for rank two unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5586","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":"sha256:7cb45dfcaf88a7078e86595676ae78a11d698eb18b5c8581a63be9ab793d1efd","target":"record","created_at":"2026-05-18T04:19:12Z","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":"860db942eeddf494f0a345fd62ba3c424dae878435d4e6d1c48eab5707c63097","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-28T08:10:45Z","title_canon_sha256":"8ae7c312850ed33c0de0ee73e981f6553e980511361dcc1672fea11454a53440"},"schema_version":"1.0","source":{"id":"1106.5586","kind":"arxiv","version":1}},"canonical_sha256":"d79d63ddd4ae1ddccdc2fe5a0a47046766a05935cac79e301e9965f5e903db7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d79d63ddd4ae1ddccdc2fe5a0a47046766a05935cac79e301e9965f5e903db7a","first_computed_at":"2026-05-18T04:19:12.887789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:12.887789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q9NE8Q2MxdNbkgTq23fUzXIPEaHFTNrb0TPZLxw195LjljTrgqncbSKrgq23cuoIvYuPeT/SBHmGjXpIdOi7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:12.888223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5586","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cb45dfcaf88a7078e86595676ae78a11d698eb18b5c8581a63be9ab793d1efd","sha256:7f1dc73fb1f274d16db1637b8486a45b109c912e91096f8edd54280442b6331f"],"state_sha256":"81bcb54cffa0273ddf9cac7e08cfd0ba9e96cb9c9733b738c718b8f6a956b942"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGrMTd6JBN4+gffvyLgnOGVEdO4s1rkdQhJ7va13+LdMXvwOzMfQfgNQV/aITgL3hs1ydalvVFLq2NIdjKBPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:39:49.945636Z","bundle_sha256":"e883775beb9d6dad013ffbb5ae198b0e05498e3c0e83e9f3fcc2eed7cf7fb0f9"}}