{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3VZWVMQULMMZOXZXMVQGRN67XK","short_pith_number":"pith:3VZWVMQU","canonical_record":{"source":{"id":"2008.11773","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2020-08-26T19:32:13Z","cross_cats_sorted":[],"title_canon_sha256":"2bf0d4d6fdcc99b41cdcb74865f1a7b1e64bbfaca98c9be6a8a7a4489685c654","abstract_canon_sha256":"60cd772ad78d1a552be4c8ed7f1564201b3dd7982131fdbb2849c2ddfb16ce00"},"schema_version":"1.0"},"canonical_sha256":"dd736ab2145b19975f37656068b7dfba8e9b47461462c1f0c681e6a736718008","source":{"kind":"arxiv","id":"2008.11773","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.11773","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2008.11773v3","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.11773","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"3VZWVMQULMMZ","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"3VZWVMQULMMZOXZX","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"3VZWVMQU","created_at":"2026-07-05T06:14:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3VZWVMQULMMZOXZXMVQGRN67XK","target":"record","payload":{"canonical_record":{"source":{"id":"2008.11773","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2020-08-26T19:32:13Z","cross_cats_sorted":[],"title_canon_sha256":"2bf0d4d6fdcc99b41cdcb74865f1a7b1e64bbfaca98c9be6a8a7a4489685c654","abstract_canon_sha256":"60cd772ad78d1a552be4c8ed7f1564201b3dd7982131fdbb2849c2ddfb16ce00"},"schema_version":"1.0"},"canonical_sha256":"dd736ab2145b19975f37656068b7dfba8e9b47461462c1f0c681e6a736718008","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:14:21.972756Z","signature_b64":"3qeVzRUCR7K3iehcRCA3KojwE3InKstYIKphhMgPNBjlkxFY6k18DGiiNFSM7HedpdE48F8sf5VIJdD1iZ/KAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd736ab2145b19975f37656068b7dfba8e9b47461462c1f0c681e6a736718008","last_reissued_at":"2026-07-05T06:14:21.972389Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:14:21.972389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.11773","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":"2026-07-05T06:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2j9btYEjLC/6LQ5cz+cR40QOo8A7HVFCmVMew0/CtVH4/8AXXdizYFe2/9La2okUy2T7AFVYNGMGiDbOGLGvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T15:50:03.589956Z"},"content_sha256":"5b56ea11807f5f751f03eabfea25af42bb859f2042457b6d7c66715e0e199669","schema_version":"1.0","event_id":"sha256:5b56ea11807f5f751f03eabfea25af42bb859f2042457b6d7c66715e0e199669"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3VZWVMQULMMZOXZXMVQGRN67XK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutator lengths in general linear group over a skew-field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pavel Gvozdevsky","submitted_at":"2020-08-26T19:32:13Z","abstract_excerpt":"We give an upper and lower estimate for the maximal commutator length of a noncentral element of the elementary subgroup of the general linear group over a skew-field based on the maximal commutator length of an element of the multiplicative group of that skew-field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.11773","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.11773/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfYMfDduTQd7tBA/GT3wUkHjtMs2r7lwLZdVpwtdKhRwpfUGwiVHKrNhoiSDP1vrSFNzoevvAdHuyZwR0Kh6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T15:50:03.590278Z"},"content_sha256":"9eddd740da679c6a93fc6f07ff32f25d9939c67c46c9bed63954272e962d0382","schema_version":"1.0","event_id":"sha256:9eddd740da679c6a93fc6f07ff32f25d9939c67c46c9bed63954272e962d0382"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VZWVMQULMMZOXZXMVQGRN67XK/bundle.json","state_url":"https://pith.science/pith/3VZWVMQULMMZOXZXMVQGRN67XK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VZWVMQULMMZOXZXMVQGRN67XK/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":"2026-08-11T15:50:03Z","links":{"resolver":"https://pith.science/pith/3VZWVMQULMMZOXZXMVQGRN67XK","bundle":"https://pith.science/pith/3VZWVMQULMMZOXZXMVQGRN67XK/bundle.json","state":"https://pith.science/pith/3VZWVMQULMMZOXZXMVQGRN67XK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VZWVMQULMMZOXZXMVQGRN67XK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3VZWVMQULMMZOXZXMVQGRN67XK","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":"60cd772ad78d1a552be4c8ed7f1564201b3dd7982131fdbb2849c2ddfb16ce00","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2020-08-26T19:32:13Z","title_canon_sha256":"2bf0d4d6fdcc99b41cdcb74865f1a7b1e64bbfaca98c9be6a8a7a4489685c654"},"schema_version":"1.0","source":{"id":"2008.11773","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.11773","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2008.11773v3","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.11773","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"3VZWVMQULMMZ","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"3VZWVMQULMMZOXZX","created_at":"2026-07-05T06:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"3VZWVMQU","created_at":"2026-07-05T06:14:21Z"}],"graph_snapshots":[{"event_id":"sha256:9eddd740da679c6a93fc6f07ff32f25d9939c67c46c9bed63954272e962d0382","target":"graph","created_at":"2026-07-05T06:14:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.11773/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an upper and lower estimate for the maximal commutator length of a noncentral element of the elementary subgroup of the general linear group over a skew-field based on the maximal commutator length of an element of the multiplicative group of that skew-field.","authors_text":"Pavel Gvozdevsky","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2020-08-26T19:32:13Z","title":"Commutator lengths in general linear group over a skew-field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.11773","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":"sha256:5b56ea11807f5f751f03eabfea25af42bb859f2042457b6d7c66715e0e199669","target":"record","created_at":"2026-07-05T06:14:21Z","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":"60cd772ad78d1a552be4c8ed7f1564201b3dd7982131fdbb2849c2ddfb16ce00","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2020-08-26T19:32:13Z","title_canon_sha256":"2bf0d4d6fdcc99b41cdcb74865f1a7b1e64bbfaca98c9be6a8a7a4489685c654"},"schema_version":"1.0","source":{"id":"2008.11773","kind":"arxiv","version":3}},"canonical_sha256":"dd736ab2145b19975f37656068b7dfba8e9b47461462c1f0c681e6a736718008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd736ab2145b19975f37656068b7dfba8e9b47461462c1f0c681e6a736718008","first_computed_at":"2026-07-05T06:14:21.972389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:14:21.972389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3qeVzRUCR7K3iehcRCA3KojwE3InKstYIKphhMgPNBjlkxFY6k18DGiiNFSM7HedpdE48F8sf5VIJdD1iZ/KAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:14:21.972756Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.11773","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b56ea11807f5f751f03eabfea25af42bb859f2042457b6d7c66715e0e199669","sha256:9eddd740da679c6a93fc6f07ff32f25d9939c67c46c9bed63954272e962d0382"],"state_sha256":"409bd734c1c54788d3934040c2b86311874a0aa0a6190be29b19843daff805cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmKfUMih+Ek3tOOcGYTtMhTFuXo/OCdYgcqOTMNDGv12KiVyEIBLpfX9J0ppDm292aiQE4N0JeqKVmC+aa9ZDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T15:50:03.592650Z","bundle_sha256":"e9afbc955e1f06366fa3e468bb8dae6980f127a2b18f79334597675f9215499b"}}