{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DFJ4ZWMDAJZE4BKFBME735JH4G","short_pith_number":"pith:DFJ4ZWMD","canonical_record":{"source":{"id":"1112.2012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T03:24:19Z","cross_cats_sorted":["cs.DS","cs.SC","math.RT"],"title_canon_sha256":"3274b470878c410dde20d2bdc1e2a100ca6f3045b1dabfb5a8968174411d99e5","abstract_canon_sha256":"6401be1703583d348dfde45d180505c8e28a9fdc053200b89cdcc8d21b5cc1e5"},"schema_version":"1.0"},"canonical_sha256":"1953ccd98302724e05450b09fdf527e18316a0985948ac971042e9cf49a826f4","source":{"kind":"arxiv","id":"1112.2012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2012","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2012v1","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2012","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"DFJ4ZWMDAJZE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFJ4ZWMDAJZE4BKF","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFJ4ZWMD","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DFJ4ZWMDAJZE4BKFBME735JH4G","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T03:24:19Z","cross_cats_sorted":["cs.DS","cs.SC","math.RT"],"title_canon_sha256":"3274b470878c410dde20d2bdc1e2a100ca6f3045b1dabfb5a8968174411d99e5","abstract_canon_sha256":"6401be1703583d348dfde45d180505c8e28a9fdc053200b89cdcc8d21b5cc1e5"},"schema_version":"1.0"},"canonical_sha256":"1953ccd98302724e05450b09fdf527e18316a0985948ac971042e9cf49a826f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:44.376171Z","signature_b64":"FqYDuJqPpSeDS1YvV+Rgu23vHWUjU57yUFCG96CkzWSo43hVd9EIIycDYGP71r+JA51jfdp8A8lELlvyDtR8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1953ccd98302724e05450b09fdf527e18316a0985948ac971042e9cf49a826f4","last_reissued_at":"2026-05-18T04:06:44.375578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:44.375578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2012","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":"2026-05-18T04:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tr+p8Mzx7GpGENyGH/Jy2E9t/JyuBDZoAjGqVR+7XidikyxFtWQZULAQDIxJqS+jm33kfz4jzqR0Z/067jIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T00:28:44.688137Z"},"content_sha256":"baf35f00eb10a25a75a33d21030f12de5a1aaefeeae64744f09554f1c79cd221","schema_version":"1.0","event_id":"sha256:baf35f00eb10a25a75a33d21030f12de5a1aaefeeae64744f09554f1c79cd221"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DFJ4ZWMDAJZE4BKFBME735JH4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie algebra conjugacy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.SC","math.RT"],"primary_cat":"cs.CC","authors_text":"Joshua A. Grochow","submitted_at":"2011-12-09T03:24:19Z","abstract_excerpt":"We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that $A, B\\in L$ implies $AB - BA \\in L$. Two matrix Lie algebras are conjugate if there is an invertible matrix $M$ such that $L_1 = M L_2 M^{-1}$.\n  We show that certain cases of Lie algebra conjugacy are equivalent to graph isomorphism. On the other hand, we give polynomial-time algorithms for other cases of Lie algebra co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2012","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":"2026-05-18T04:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CyNoK5pMo9eCj8QMOED4XBIwgNGAau7kH6lWy+TPD8MOkVbP+NwnxEA4FAIVKuHtR9MmMd6MwLUL6cfvBQL7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T00:28:44.688502Z"},"content_sha256":"1d87e95007ca90d6b52236e8e000efdf6051544c687844251e3e664041502027","schema_version":"1.0","event_id":"sha256:1d87e95007ca90d6b52236e8e000efdf6051544c687844251e3e664041502027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFJ4ZWMDAJZE4BKFBME735JH4G/bundle.json","state_url":"https://pith.science/pith/DFJ4ZWMDAJZE4BKFBME735JH4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFJ4ZWMDAJZE4BKFBME735JH4G/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":"2026-07-01T00:28:44Z","links":{"resolver":"https://pith.science/pith/DFJ4ZWMDAJZE4BKFBME735JH4G","bundle":"https://pith.science/pith/DFJ4ZWMDAJZE4BKFBME735JH4G/bundle.json","state":"https://pith.science/pith/DFJ4ZWMDAJZE4BKFBME735JH4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFJ4ZWMDAJZE4BKFBME735JH4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DFJ4ZWMDAJZE4BKFBME735JH4G","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":"6401be1703583d348dfde45d180505c8e28a9fdc053200b89cdcc8d21b5cc1e5","cross_cats_sorted":["cs.DS","cs.SC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T03:24:19Z","title_canon_sha256":"3274b470878c410dde20d2bdc1e2a100ca6f3045b1dabfb5a8968174411d99e5"},"schema_version":"1.0","source":{"id":"1112.2012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2012","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2012v1","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2012","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"DFJ4ZWMDAJZE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFJ4ZWMDAJZE4BKF","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFJ4ZWMD","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:1d87e95007ca90d6b52236e8e000efdf6051544c687844251e3e664041502027","target":"graph","created_at":"2026-05-18T04:06:44Z","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 problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that $A, B\\in L$ implies $AB - BA \\in L$. Two matrix Lie algebras are conjugate if there is an invertible matrix $M$ such that $L_1 = M L_2 M^{-1}$.\n  We show that certain cases of Lie algebra conjugacy are equivalent to graph isomorphism. On the other hand, we give polynomial-time algorithms for other cases of Lie algebra co","authors_text":"Joshua A. Grochow","cross_cats":["cs.DS","cs.SC","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T03:24:19Z","title":"Lie algebra conjugacy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2012","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:baf35f00eb10a25a75a33d21030f12de5a1aaefeeae64744f09554f1c79cd221","target":"record","created_at":"2026-05-18T04:06:44Z","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":"6401be1703583d348dfde45d180505c8e28a9fdc053200b89cdcc8d21b5cc1e5","cross_cats_sorted":["cs.DS","cs.SC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T03:24:19Z","title_canon_sha256":"3274b470878c410dde20d2bdc1e2a100ca6f3045b1dabfb5a8968174411d99e5"},"schema_version":"1.0","source":{"id":"1112.2012","kind":"arxiv","version":1}},"canonical_sha256":"1953ccd98302724e05450b09fdf527e18316a0985948ac971042e9cf49a826f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1953ccd98302724e05450b09fdf527e18316a0985948ac971042e9cf49a826f4","first_computed_at":"2026-05-18T04:06:44.375578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:44.375578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FqYDuJqPpSeDS1YvV+Rgu23vHWUjU57yUFCG96CkzWSo43hVd9EIIycDYGP71r+JA51jfdp8A8lELlvyDtR8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:44.376171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baf35f00eb10a25a75a33d21030f12de5a1aaefeeae64744f09554f1c79cd221","sha256:1d87e95007ca90d6b52236e8e000efdf6051544c687844251e3e664041502027"],"state_sha256":"ea651d09cfc30d2fa8611335f46dbe128c9f95a0faead3d523194f542b565b9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFH41e/UmRbC8mECWuxCSAN/wyg6c1WAbHqEP9rjJpvV4kIr/Uo4G4pUAG7kE4xJ0MY++L30GSe+e5ZxhAUhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T00:28:44.690553Z","bundle_sha256":"f16635c10dba006332d42df316b1904194e68e2ee2dc19a4af2358ea0465f284"}}