{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CC45RRWILQXUQXDUKAPTJTRAZB","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":"ec5da8f7e95069d5c6d060311c6c81238386eec912ab712a145b8c03ec671f69","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-19T08:11:05Z","title_canon_sha256":"3b0d06cf11433106e850fd3f229422b59b90afed99bb897f91f919a7b0e7fba5"},"schema_version":"1.0","source":{"id":"2605.19512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19512","created_at":"2026-05-20T01:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19512v1","created_at":"2026-05-20T01:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19512","created_at":"2026-05-20T01:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"CC45RRWILQXU","created_at":"2026-05-20T01:05:49Z"},{"alias_kind":"pith_short_16","alias_value":"CC45RRWILQXUQXDU","created_at":"2026-05-20T01:05:49Z"},{"alias_kind":"pith_short_8","alias_value":"CC45RRWI","created_at":"2026-05-20T01:05:49Z"}],"graph_snapshots":[{"event_id":"sha256:9b62ab6794546f81085ceef992a2b6f4a788c412e5f99c025a5879cf8a362c23","target":"graph","created_at":"2026-05-20T01:05:49Z","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/2605.19512/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Lie polynomial is an element of a free Lie algebra $\\mathcal F_k$ on $k$-generators, which defines a Lie map on a given Lie algebra $L$, by substituting $k$-elements of $L$. Similar to word maps on groups and polynomial maps on algebras, one studies here questions analogous to Waring-like problems, the L'vov-Kaplansky conjecture, etc. In this article, we would like to address a problem for Lie algebras parallel to the one Lubotzky solved (Images of word maps in finite simple groups, Glasg. Math. J., 56, no. 2, 465-469, 2014) for finite simple groups. It is easy to verify that the image of a ","authors_text":"Anupam Singh, Harish Kishnani","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-19T08:11:05Z","title":"Images of Lie Polynomials on simple Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19512","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:efb90c81c554769f6a4dc2e9b347b633ec0fbd3082adfbae2be4852f4b92f56c","target":"record","created_at":"2026-05-20T01:05:49Z","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":"ec5da8f7e95069d5c6d060311c6c81238386eec912ab712a145b8c03ec671f69","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-19T08:11:05Z","title_canon_sha256":"3b0d06cf11433106e850fd3f229422b59b90afed99bb897f91f919a7b0e7fba5"},"schema_version":"1.0","source":{"id":"2605.19512","kind":"arxiv","version":1}},"canonical_sha256":"10b9d8c6c85c2f485c74501f34ce20c87bcaa65f6e1dee912b010ffd86aa7b06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10b9d8c6c85c2f485c74501f34ce20c87bcaa65f6e1dee912b010ffd86aa7b06","first_computed_at":"2026-05-20T01:05:49.387082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:49.387082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lTGG03CzlsqRiAzQ57tYEQAsV4FKbpgOt1dokZeh7YFtfYK5jXdnt8/pHOOVF7tjoYLGD72t5hdIDna/PkRnBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:49.387876Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efb90c81c554769f6a4dc2e9b347b633ec0fbd3082adfbae2be4852f4b92f56c","sha256:9b62ab6794546f81085ceef992a2b6f4a788c412e5f99c025a5879cf8a362c23"],"state_sha256":"3ee78d8d9d1bc6e2102fbaf707d0993dae3fcba6dd1ffda1dc00e90f50066b79"}