{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SM74AE5LASRBQSBI5EGQQCHKR6","short_pith_number":"pith:SM74AE5L","canonical_record":{"source":{"id":"1904.01037","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-01T18:03:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"2f95df6292294262f5c3fdea04f6cbdf4afe655eb77c2a793f6656daa5d2e46e","abstract_canon_sha256":"8bd624efa46ce37e3bbf82fcb72005244fca3ead490ca85b260ebfb86c10a0b0"},"schema_version":"1.0"},"canonical_sha256":"933fc013ab04a2184828e90d0808ea8f89ad36e07fa51f6ba5878aa4d3c025eb","source":{"kind":"arxiv","id":"1904.01037","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01037","created_at":"2026-05-17T23:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01037v3","created_at":"2026-05-17T23:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01037","created_at":"2026-05-17T23:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"SM74AE5LASRB","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SM74AE5LASRBQSBI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SM74AE5L","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SM74AE5LASRBQSBI5EGQQCHKR6","target":"record","payload":{"canonical_record":{"source":{"id":"1904.01037","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-01T18:03:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"2f95df6292294262f5c3fdea04f6cbdf4afe655eb77c2a793f6656daa5d2e46e","abstract_canon_sha256":"8bd624efa46ce37e3bbf82fcb72005244fca3ead490ca85b260ebfb86c10a0b0"},"schema_version":"1.0"},"canonical_sha256":"933fc013ab04a2184828e90d0808ea8f89ad36e07fa51f6ba5878aa4d3c025eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:24.512261Z","signature_b64":"zIXBbX6ojXp+K2MV1No2MoZc1yg4xRY+6KKvMxpfLVRTJJOUfnc+L+pblr0/Aa+SC3Oo7F703j2cWXCg3p0NAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"933fc013ab04a2184828e90d0808ea8f89ad36e07fa51f6ba5878aa4d3c025eb","last_reissued_at":"2026-05-17T23:39:24.511627Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:24.511627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.01037","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ew3PbmdwxNfpecNoX4HCebMt1d5sB4KnJhkbuHW3wA8+R0h/KMVzUQ1Ylzq3NCSHIyzCaeBr+8pcHUrY2s3OBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:46:11.309698Z"},"content_sha256":"a5906f88c7cb0106d2aee33dcdbd2f66eaee93b8711c747f453960d54993f503","schema_version":"1.0","event_id":"sha256:a5906f88c7cb0106d2aee33dcdbd2f66eaee93b8711c747f453960d54993f503"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SM74AE5LASRBQSBI5EGQQCHKR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An effective Lie--Kolchin theorem for quasi-unipotent matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Feng Luo, Hongbin Sun, Thomas Koberda","submitted_at":"2019-04-01T18:03:46Z","abstract_excerpt":"We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\\in\\mathrm{GL}_m(\\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for all $k\\geq0$ the matrix $AB^k$ is also quasi--unipotent. Then $A$ and $B$ have a common eigenvector. In particular, $\\langle A,B\\rangle<\\mathrm{GL}_m(\\mathbb{C})$ is a solvable subgroup. We give applications of this result to the representation theory of mapping class groups of orientable surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01037","kind":"arxiv","version":3},"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":"2026-05-17T23:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sndV4e1M8FiRDTHY5yqT+cAHBh8J1J2nSQziT2rewvdIazRqbIG44Nl3rNmXrc5UI64/gqxP3uHLodZECnCWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:46:11.310304Z"},"content_sha256":"01c4c201c1c115bb3542669fa788d4bbccc5f9b0f67376149fc80f5a931e0f25","schema_version":"1.0","event_id":"sha256:01c4c201c1c115bb3542669fa788d4bbccc5f9b0f67376149fc80f5a931e0f25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SM74AE5LASRBQSBI5EGQQCHKR6/bundle.json","state_url":"https://pith.science/pith/SM74AE5LASRBQSBI5EGQQCHKR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SM74AE5LASRBQSBI5EGQQCHKR6/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":"2026-05-25T20:46:11Z","links":{"resolver":"https://pith.science/pith/SM74AE5LASRBQSBI5EGQQCHKR6","bundle":"https://pith.science/pith/SM74AE5LASRBQSBI5EGQQCHKR6/bundle.json","state":"https://pith.science/pith/SM74AE5LASRBQSBI5EGQQCHKR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SM74AE5LASRBQSBI5EGQQCHKR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SM74AE5LASRBQSBI5EGQQCHKR6","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":"8bd624efa46ce37e3bbf82fcb72005244fca3ead490ca85b260ebfb86c10a0b0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-01T18:03:46Z","title_canon_sha256":"2f95df6292294262f5c3fdea04f6cbdf4afe655eb77c2a793f6656daa5d2e46e"},"schema_version":"1.0","source":{"id":"1904.01037","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01037","created_at":"2026-05-17T23:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01037v3","created_at":"2026-05-17T23:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01037","created_at":"2026-05-17T23:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"SM74AE5LASRB","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SM74AE5LASRBQSBI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SM74AE5L","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:01c4c201c1c115bb3542669fa788d4bbccc5f9b0f67376149fc80f5a931e0f25","target":"graph","created_at":"2026-05-17T23:39:24Z","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 establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\\in\\mathrm{GL}_m(\\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for all $k\\geq0$ the matrix $AB^k$ is also quasi--unipotent. Then $A$ and $B$ have a common eigenvector. In particular, $\\langle A,B\\rangle<\\mathrm{GL}_m(\\mathbb{C})$ is a solvable subgroup. We give applications of this result to the representation theory of mapping class groups of orientable surfaces.","authors_text":"Feng Luo, Hongbin Sun, Thomas Koberda","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-01T18:03:46Z","title":"An effective Lie--Kolchin theorem for quasi-unipotent matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01037","kind":"arxiv","version":3},"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:a5906f88c7cb0106d2aee33dcdbd2f66eaee93b8711c747f453960d54993f503","target":"record","created_at":"2026-05-17T23:39:24Z","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":"8bd624efa46ce37e3bbf82fcb72005244fca3ead490ca85b260ebfb86c10a0b0","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-01T18:03:46Z","title_canon_sha256":"2f95df6292294262f5c3fdea04f6cbdf4afe655eb77c2a793f6656daa5d2e46e"},"schema_version":"1.0","source":{"id":"1904.01037","kind":"arxiv","version":3}},"canonical_sha256":"933fc013ab04a2184828e90d0808ea8f89ad36e07fa51f6ba5878aa4d3c025eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"933fc013ab04a2184828e90d0808ea8f89ad36e07fa51f6ba5878aa4d3c025eb","first_computed_at":"2026-05-17T23:39:24.511627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:24.511627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zIXBbX6ojXp+K2MV1No2MoZc1yg4xRY+6KKvMxpfLVRTJJOUfnc+L+pblr0/Aa+SC3Oo7F703j2cWXCg3p0NAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:24.512261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01037","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5906f88c7cb0106d2aee33dcdbd2f66eaee93b8711c747f453960d54993f503","sha256:01c4c201c1c115bb3542669fa788d4bbccc5f9b0f67376149fc80f5a931e0f25"],"state_sha256":"f58a54d64ee84d2ba7136799e4136cbea0401c999ec6ed0f7c0594980039ffe7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"trd8FJQmNZtYH1/h+nm6k6E34jOCfmatVobpZuS/tGBF92Euv0WuOmvOFoYybu64mvcvZ9nDsqGo58yfFmVuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:46:11.313626Z","bundle_sha256":"31812f3038a8ddf22fc7e3651cbdfa30244363d57324e6669778d538a4da76c8"}}