{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DDTSIKU5MWPL3R2HSLO4TXKEKG","short_pith_number":"pith:DDTSIKU5","canonical_record":{"source":{"id":"1703.06214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-17T23:09:18Z","cross_cats_sorted":[],"title_canon_sha256":"b311eda65cbab3137956d3629ffaa11d74f016c20b5e04307d55faf2079f6e93","abstract_canon_sha256":"031d1654a00cab31d732c14368a049dd7e4cdf38b557f03787c88644eaea18f0"},"schema_version":"1.0"},"canonical_sha256":"18e7242a9d659ebdc74792ddc9dd4451a9eeaca4ccf8c9a1d845c68ba7bdbee1","source":{"kind":"arxiv","id":"1703.06214","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06214","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06214v1","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06214","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"DDTSIKU5MWPL","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DDTSIKU5MWPL3R2H","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DDTSIKU5","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DDTSIKU5MWPL3R2HSLO4TXKEKG","target":"record","payload":{"canonical_record":{"source":{"id":"1703.06214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-17T23:09:18Z","cross_cats_sorted":[],"title_canon_sha256":"b311eda65cbab3137956d3629ffaa11d74f016c20b5e04307d55faf2079f6e93","abstract_canon_sha256":"031d1654a00cab31d732c14368a049dd7e4cdf38b557f03787c88644eaea18f0"},"schema_version":"1.0"},"canonical_sha256":"18e7242a9d659ebdc74792ddc9dd4451a9eeaca4ccf8c9a1d845c68ba7bdbee1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:23.580641Z","signature_b64":"3k3J0dipdMJzs/UBRzmOCiueq9b/IyD2DtmREV7yP1qox9eUbv36vEzf1sst0NSpQNpNqelcldWLwBWHcYhJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18e7242a9d659ebdc74792ddc9dd4451a9eeaca4ccf8c9a1d845c68ba7bdbee1","last_reissued_at":"2026-05-18T00:48:23.579973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:23.579973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.06214","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":"2026-05-18T00:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDL5DmDQ8KVIZKTkK43fW5vtGtpmvp5XkCmS4q8DmJImRB/uiylt4WOErszVu+mmSovc4oAEaMijzzxf/PkKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:50:03.642532Z"},"content_sha256":"b51bf0c7d95869fdf064ffbbbd4b9b2b5eea5fbbffb46b4bc43ed46fbf8b8522","schema_version":"1.0","event_id":"sha256:b51bf0c7d95869fdf064ffbbbd4b9b2b5eea5fbbffb46b4bc43ed46fbf8b8522"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DDTSIKU5MWPL3R2HSLO4TXKEKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free 2-step nilpotent Lie algebras and indecomposable modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Szechtman, Leandro Cagliero, Luis Gutierrez","submitted_at":"2017-03-17T23:09:18Z","abstract_excerpt":"Given an algebraically closed field $F$ of characteristic 0 and an $F$-vector space $V$, let $L(V)=V\\oplus\\Lambda^2(V)$ denote the free 2-step nilpotent Lie algebra associated to $V$. In this paper, we classify all uniserial representations of the solvable Lie algebra $\\mathfrak g=\\langle x\\rangle\\ltimes L(V)$, where $x$ acts on $V$ via an arbitrary invertible Jordan block."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06214","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":"2026-05-18T00:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRTWZD4tx1OQubrVeYNDJwDChyRiAkUCk6yzZOnePZsA+yu5TKoaJn4hhYVfndIEdtJ9VZllb/brEjexNSb2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:50:03.642889Z"},"content_sha256":"2c7937a60480de53e257d30b96709cb10b5aae56ca4c7657561238e223d87e1d","schema_version":"1.0","event_id":"sha256:2c7937a60480de53e257d30b96709cb10b5aae56ca4c7657561238e223d87e1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG/bundle.json","state_url":"https://pith.science/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG/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":"2026-06-24T17:50:03Z","links":{"resolver":"https://pith.science/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG","bundle":"https://pith.science/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG/bundle.json","state":"https://pith.science/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DDTSIKU5MWPL3R2HSLO4TXKEKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DDTSIKU5MWPL3R2HSLO4TXKEKG","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":"031d1654a00cab31d732c14368a049dd7e4cdf38b557f03787c88644eaea18f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-17T23:09:18Z","title_canon_sha256":"b311eda65cbab3137956d3629ffaa11d74f016c20b5e04307d55faf2079f6e93"},"schema_version":"1.0","source":{"id":"1703.06214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06214","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06214v1","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06214","created_at":"2026-05-18T00:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"DDTSIKU5MWPL","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DDTSIKU5MWPL3R2H","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DDTSIKU5","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:2c7937a60480de53e257d30b96709cb10b5aae56ca4c7657561238e223d87e1d","target":"graph","created_at":"2026-05-18T00:48:23Z","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":"Given an algebraically closed field $F$ of characteristic 0 and an $F$-vector space $V$, let $L(V)=V\\oplus\\Lambda^2(V)$ denote the free 2-step nilpotent Lie algebra associated to $V$. In this paper, we classify all uniserial representations of the solvable Lie algebra $\\mathfrak g=\\langle x\\rangle\\ltimes L(V)$, where $x$ acts on $V$ via an arbitrary invertible Jordan block.","authors_text":"Fernando Szechtman, Leandro Cagliero, Luis Gutierrez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-17T23:09:18Z","title":"Free 2-step nilpotent Lie algebras and indecomposable modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06214","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:b51bf0c7d95869fdf064ffbbbd4b9b2b5eea5fbbffb46b4bc43ed46fbf8b8522","target":"record","created_at":"2026-05-18T00:48:23Z","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":"031d1654a00cab31d732c14368a049dd7e4cdf38b557f03787c88644eaea18f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-17T23:09:18Z","title_canon_sha256":"b311eda65cbab3137956d3629ffaa11d74f016c20b5e04307d55faf2079f6e93"},"schema_version":"1.0","source":{"id":"1703.06214","kind":"arxiv","version":1}},"canonical_sha256":"18e7242a9d659ebdc74792ddc9dd4451a9eeaca4ccf8c9a1d845c68ba7bdbee1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18e7242a9d659ebdc74792ddc9dd4451a9eeaca4ccf8c9a1d845c68ba7bdbee1","first_computed_at":"2026-05-18T00:48:23.579973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:23.579973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3k3J0dipdMJzs/UBRzmOCiueq9b/IyD2DtmREV7yP1qox9eUbv36vEzf1sst0NSpQNpNqelcldWLwBWHcYhJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:23.580641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b51bf0c7d95869fdf064ffbbbd4b9b2b5eea5fbbffb46b4bc43ed46fbf8b8522","sha256:2c7937a60480de53e257d30b96709cb10b5aae56ca4c7657561238e223d87e1d"],"state_sha256":"d3a0ca562750c24b6a45a1509f176cc7ca8c865242d27ae85c555231c6cf54ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MPBodTxk0IGYhhu5kPuM+Xw/vfLg1MCKT4jq3I2Euwx4wlotE+vSN1sFrTOB8/0789VYUIb+jxrxK9ZuF42KBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:50:03.644810Z","bundle_sha256":"08088831601cf4a45e51d9813fdcf587fdd8d50cdd922adf453480a6e20ba957"}}