{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q2YPLQ2Q2PTVU74RFVMZH3H43A","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":"408d3d8a9cf90ea150db2bc7d5b8387e236f5f411ef6fb043b9476d10c7e5386","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-13T02:06:56Z","title_canon_sha256":"e06bbeff2e322e937c44564056b39389502a42d96b4622fa317c258c49a163ba"},"schema_version":"1.0","source":{"id":"1702.03608","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03608","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03608v2","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03608","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"Q2YPLQ2Q2PTV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q2YPLQ2Q2PTVU74R","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q2YPLQ2Q","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:7e30fefb9b622782348f084fa68bc0520e436fc6851e3b8de87d6ac869904e5d","target":"graph","created_at":"2026-05-17T23:54:32Z","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":"A theorem of Hukuhara, Levelt, and Turrittin states that every formal differential operator has a Jordan decomposition. This theorem was generalised by Babbit and Varadarajan to the case of formal $G$-connections where $G$ is a semisimple group. In this paper, we provide straightforward proofs of these facts, highlighting the analogy between the linear and differential settings.","authors_text":"Masoud Kamgarpour, Samuel Weatherhog","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-13T02:06:56Z","title":"Jordan Decomposition for Formal G-Connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03608","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":"sha256:42a83282a202cba9e06fc3f293b748af66ee46c3916dd93a611facb45acf6c5f","target":"record","created_at":"2026-05-17T23:54:32Z","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":"408d3d8a9cf90ea150db2bc7d5b8387e236f5f411ef6fb043b9476d10c7e5386","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-13T02:06:56Z","title_canon_sha256":"e06bbeff2e322e937c44564056b39389502a42d96b4622fa317c258c49a163ba"},"schema_version":"1.0","source":{"id":"1702.03608","kind":"arxiv","version":2}},"canonical_sha256":"86b0f5c350d3e75a7f912d5993ecfcd81838a68ba31afa8c183fd0141eac85f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86b0f5c350d3e75a7f912d5993ecfcd81838a68ba31afa8c183fd0141eac85f1","first_computed_at":"2026-05-17T23:54:32.041909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:32.041909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vOEx720w2bDjdE58eEm5oHTlRbXIVHhKdkdVhvYMl+q4sc6nj8K/ryTFu5c8SxmOtJwqWH+37Ucj6FX8x7qDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:32.042446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03608","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42a83282a202cba9e06fc3f293b748af66ee46c3916dd93a611facb45acf6c5f","sha256:7e30fefb9b622782348f084fa68bc0520e436fc6851e3b8de87d6ac869904e5d"],"state_sha256":"df0b6862edbdd12470e7da43d2f058b8f89b56726e361e569d2d39f8699279d4"}