{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MWJ6VIOPDUNJ4S2GK2LDR2LISP","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":"a63d3224df4bb140f2cb93363b8bce14131c8ebaad8255027617ef4a03bea10f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-19T12:15:21Z","title_canon_sha256":"2fec12952bc32d2ebdf62db929b31d60315d10285599017a9621d4a3433f5c66"},"schema_version":"1.0","source":{"id":"1903.11384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11384","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11384v1","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11384","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"MWJ6VIOPDUNJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MWJ6VIOPDUNJ4S2G","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MWJ6VIOP","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:67e147017ffef1ae22f9951d8688d235288d31286cc14aa672310138946340d6","target":"graph","created_at":"2026-05-17T23:50:03Z","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":"By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \\le{n+1}$.","authors_text":"A. M. Perelomov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-19T12:15:21Z","title":"Euler's difference table and decomposition of tensor powers of adjoint representation of $A_n$ Lie algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11384","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:ffbc6a0f98dcacd2f7dc3bae2240f9bc0aa3474711ff84a8f37a12b1ebc8b06d","target":"record","created_at":"2026-05-17T23:50:03Z","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":"a63d3224df4bb140f2cb93363b8bce14131c8ebaad8255027617ef4a03bea10f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-19T12:15:21Z","title_canon_sha256":"2fec12952bc32d2ebdf62db929b31d60315d10285599017a9621d4a3433f5c66"},"schema_version":"1.0","source":{"id":"1903.11384","kind":"arxiv","version":1}},"canonical_sha256":"6593eaa1cf1d1a9e4b46569638e96893f95966648527ebf04a308b3dd3e9d8cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6593eaa1cf1d1a9e4b46569638e96893f95966648527ebf04a308b3dd3e9d8cc","first_computed_at":"2026-05-17T23:50:03.441623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:03.441623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G5TWZ1NG9moW6Q/hOowzTuAWA3XQ96/zx4VYMqiyzfIbhUNScQMG81KIO+Cy7/GKElbNIRrNn2MEIIi3ghRHCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:03.442146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffbc6a0f98dcacd2f7dc3bae2240f9bc0aa3474711ff84a8f37a12b1ebc8b06d","sha256:67e147017ffef1ae22f9951d8688d235288d31286cc14aa672310138946340d6"],"state_sha256":"7a5b46d49cd829cee50521b7f0d87d3b3eba6432e4650a05d6690667ec2f4e62"}