{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PLKL2WVOC2CYE7QTCFMQJ6GCEW","short_pith_number":"pith:PLKL2WVO","canonical_record":{"source":{"id":"1901.08122","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-23T20:34:04Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"299b2f5773720c1506393b81494a2d4a0d73ae52866a66806d88af98df663fae","abstract_canon_sha256":"aafd3b5ee3c00f2f98de7972ed6e6c7790b0bd510caaaaefb90a0b9993d94b00"},"schema_version":"1.0"},"canonical_sha256":"7ad4bd5aae1685827e13115904f8c22599be4dc0177523ef5157705b9fe91309","source":{"kind":"arxiv","id":"1901.08122","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08122","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08122v2","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08122","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"PLKL2WVOC2CY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PLKL2WVOC2CYE7QT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PLKL2WVO","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PLKL2WVOC2CYE7QTCFMQJ6GCEW","target":"record","payload":{"canonical_record":{"source":{"id":"1901.08122","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-23T20:34:04Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"299b2f5773720c1506393b81494a2d4a0d73ae52866a66806d88af98df663fae","abstract_canon_sha256":"aafd3b5ee3c00f2f98de7972ed6e6c7790b0bd510caaaaefb90a0b9993d94b00"},"schema_version":"1.0"},"canonical_sha256":"7ad4bd5aae1685827e13115904f8c22599be4dc0177523ef5157705b9fe91309","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:19.118679Z","signature_b64":"upN6gralAZUBE/UMkgAhrWpFbX2gT/B7N5L8cOBAOp/f0aBovVqNrjcl9BdUj474k/KYvpZyLd3T9WxKDu3eBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ad4bd5aae1685827e13115904f8c22599be4dc0177523ef5157705b9fe91309","last_reissued_at":"2026-05-17T23:51:19.118052Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:19.118052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.08122","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":"2026-05-17T23:51:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtNPfg7zUMtkfoL5tmjzX3jhIHvVchwR/3G1kCXZxYSJUAzRdfZJ761Q1AZdheX1hzDaw9cBANbi0vo/3CMTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:59:28.649993Z"},"content_sha256":"413ea093f925f358b04e9cb1d2f6a8be7782173cc6f1a186e41d279881ba06cb","schema_version":"1.0","event_id":"sha256:413ea093f925f358b04e9cb1d2f6a8be7782173cc6f1a186e41d279881ba06cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PLKL2WVOC2CYE7QTCFMQJ6GCEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed subsets of root systems and regular subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Andrew Douglas, Willem A. de Graaf","submitted_at":"2019-01-23T20:34:04Z","abstract_excerpt":"We describe an algorithm for classifying the closed subsets of a root system, up to conjugation by the associated Weyl group. Such a classification of an irreducible root system is closely related to the classification of the regular subalgebras, up to inner automorphism, of the corresponding simple Lie algebra. We implement our algorithm to classify the closed subsets of the irreducible root systems of ranks 3 through 7. We present a complete description of the classification for the closed subsets of the rank 3 irreducible root system. We employ this root system classification to classify al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08122","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":"2026-05-17T23:51:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWatPLlcJ3oQU5gNoTrCwlCkO2Z8fN4TDvdFPMX6KbFIeAI4Qv+4UptzJXVahjkheNwfZcBq50nfCJ5br9OyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:59:28.650371Z"},"content_sha256":"2ef6c95783b8cce260130b15c253691b6289cc67355c89a62e3c986976f8f3fc","schema_version":"1.0","event_id":"sha256:2ef6c95783b8cce260130b15c253691b6289cc67355c89a62e3c986976f8f3fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW/bundle.json","state_url":"https://pith.science/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW/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":"2026-05-19T11:59:28Z","links":{"resolver":"https://pith.science/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW","bundle":"https://pith.science/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW/bundle.json","state":"https://pith.science/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLKL2WVOC2CYE7QTCFMQJ6GCEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PLKL2WVOC2CYE7QTCFMQJ6GCEW","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":"aafd3b5ee3c00f2f98de7972ed6e6c7790b0bd510caaaaefb90a0b9993d94b00","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-23T20:34:04Z","title_canon_sha256":"299b2f5773720c1506393b81494a2d4a0d73ae52866a66806d88af98df663fae"},"schema_version":"1.0","source":{"id":"1901.08122","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08122","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08122v2","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08122","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"PLKL2WVOC2CY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PLKL2WVOC2CYE7QT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PLKL2WVO","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:2ef6c95783b8cce260130b15c253691b6289cc67355c89a62e3c986976f8f3fc","target":"graph","created_at":"2026-05-17T23:51:19Z","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 describe an algorithm for classifying the closed subsets of a root system, up to conjugation by the associated Weyl group. Such a classification of an irreducible root system is closely related to the classification of the regular subalgebras, up to inner automorphism, of the corresponding simple Lie algebra. We implement our algorithm to classify the closed subsets of the irreducible root systems of ranks 3 through 7. We present a complete description of the classification for the closed subsets of the rank 3 irreducible root system. We employ this root system classification to classify al","authors_text":"Andrew Douglas, Willem A. de Graaf","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-23T20:34:04Z","title":"Closed subsets of root systems and regular subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08122","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":"sha256:413ea093f925f358b04e9cb1d2f6a8be7782173cc6f1a186e41d279881ba06cb","target":"record","created_at":"2026-05-17T23:51:19Z","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":"aafd3b5ee3c00f2f98de7972ed6e6c7790b0bd510caaaaefb90a0b9993d94b00","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-23T20:34:04Z","title_canon_sha256":"299b2f5773720c1506393b81494a2d4a0d73ae52866a66806d88af98df663fae"},"schema_version":"1.0","source":{"id":"1901.08122","kind":"arxiv","version":2}},"canonical_sha256":"7ad4bd5aae1685827e13115904f8c22599be4dc0177523ef5157705b9fe91309","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ad4bd5aae1685827e13115904f8c22599be4dc0177523ef5157705b9fe91309","first_computed_at":"2026-05-17T23:51:19.118052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:19.118052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"upN6gralAZUBE/UMkgAhrWpFbX2gT/B7N5L8cOBAOp/f0aBovVqNrjcl9BdUj474k/KYvpZyLd3T9WxKDu3eBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:19.118679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.08122","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:413ea093f925f358b04e9cb1d2f6a8be7782173cc6f1a186e41d279881ba06cb","sha256:2ef6c95783b8cce260130b15c253691b6289cc67355c89a62e3c986976f8f3fc"],"state_sha256":"4b131497fe5d732bcb97c4ae9d6af72f743ecc37dcea122d9896683e97626ce6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CqWHt4fb1JNemcOtkLHuF8OGTSAoaqVFLGgERJYfeXB9XFZimDClssu5yX2niPR+rdTA2PAReIqEdGgZ6ztfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T11:59:28.651980Z","bundle_sha256":"4ff22825dfa5f7d35baa580f82b5ac831bc87903f4f949b353d950f3abe1ec81"}}