{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WLYY5JHELB5FTFVA7YX7V67QAE","short_pith_number":"pith:WLYY5JHE","canonical_record":{"source":{"id":"1306.3965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-17T19:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"8ab7b2f7ca83f341c456044d7667326ed562f8e52fc12eb40c6ec6d47b57cf44","abstract_canon_sha256":"9f742375806e1594c3498883d12ac8c2c09990e37902eb38335aba64ccac6add"},"schema_version":"1.0"},"canonical_sha256":"b2f18ea4e4587a5996a0fe2ffafbf001185a498c803d9ce235e2e95c9811740d","source":{"kind":"arxiv","id":"1306.3965","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3965","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3965v1","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3965","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"WLYY5JHELB5F","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WLYY5JHELB5FTFVA","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WLYY5JHE","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WLYY5JHELB5FTFVA7YX7V67QAE","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-17T19:31:52Z","cross_cats_sorted":[],"title_canon_sha256":"8ab7b2f7ca83f341c456044d7667326ed562f8e52fc12eb40c6ec6d47b57cf44","abstract_canon_sha256":"9f742375806e1594c3498883d12ac8c2c09990e37902eb38335aba64ccac6add"},"schema_version":"1.0"},"canonical_sha256":"b2f18ea4e4587a5996a0fe2ffafbf001185a498c803d9ce235e2e95c9811740d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.905077Z","signature_b64":"O56hcelz3sfUZCVVbgd3tBKaWcAOO/51wT1NvfFD5oT2KTH3rN+KYmBNSBjqnbJR814ZFz5wMBbAJsLjw6uQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2f18ea4e4587a5996a0fe2ffafbf001185a498c803d9ce235e2e95c9811740d","last_reissued_at":"2026-05-18T03:20:45.904475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.904475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3965","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFVOzv7/45LLiPH5APPd4vL6C7b/XM59i0Ud1JNVOWN5kv7TF/BWM6G9FMZOtAMKnPZj12CK/zrnQEsPb1T3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:11:30.474382Z"},"content_sha256":"ed142219310435a04a2544757498d3473d643f95108f4a1690a98074d416c3ce","schema_version":"1.0","event_id":"sha256:ed142219310435a04a2544757498d3473d643f95108f4a1690a98074d416c3ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WLYY5JHELB5FTFVA7YX7V67QAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Szechtman, Leandro Cagliero","submitted_at":"2013-06-17T19:31:52Z","abstract_excerpt":"We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,y\\in K$. When is $F[x,y]=F[\\alpha x+\\beta y]$ for some non-zero elements $\\alpha,\\beta\\in F$?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3965","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UE2ZpQYkmWgQQWCLtEcQbi/nmwQdwO4S8EDNq694cfI4NjvfP/16oGsTr8O3RdUK++VdhxuFhRLeJrGD+kDUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:11:30.474855Z"},"content_sha256":"a29f863eef840c4994bee397a6e90aac026c213d371b9465ebf80b9054ceb47e","schema_version":"1.0","event_id":"sha256:a29f863eef840c4994bee397a6e90aac026c213d371b9465ebf80b9054ceb47e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WLYY5JHELB5FTFVA7YX7V67QAE/bundle.json","state_url":"https://pith.science/pith/WLYY5JHELB5FTFVA7YX7V67QAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WLYY5JHELB5FTFVA7YX7V67QAE/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":"2026-06-24T22:11:30Z","links":{"resolver":"https://pith.science/pith/WLYY5JHELB5FTFVA7YX7V67QAE","bundle":"https://pith.science/pith/WLYY5JHELB5FTFVA7YX7V67QAE/bundle.json","state":"https://pith.science/pith/WLYY5JHELB5FTFVA7YX7V67QAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WLYY5JHELB5FTFVA7YX7V67QAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WLYY5JHELB5FTFVA7YX7V67QAE","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":"9f742375806e1594c3498883d12ac8c2c09990e37902eb38335aba64ccac6add","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-17T19:31:52Z","title_canon_sha256":"8ab7b2f7ca83f341c456044d7667326ed562f8e52fc12eb40c6ec6d47b57cf44"},"schema_version":"1.0","source":{"id":"1306.3965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3965","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3965v1","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3965","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"WLYY5JHELB5F","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WLYY5JHELB5FTFVA","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WLYY5JHE","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:a29f863eef840c4994bee397a6e90aac026c213d371b9465ebf80b9054ceb47e","target":"graph","created_at":"2026-05-18T03:20:45Z","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 of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,y\\in K$. When is $F[x,y]=F[\\alpha x+\\beta y]$ for some non-zero elements $\\alpha,\\beta\\in F$?","authors_text":"Fernando Szechtman, Leandro Cagliero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-17T19:31:52Z","title":"On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3965","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:ed142219310435a04a2544757498d3473d643f95108f4a1690a98074d416c3ce","target":"record","created_at":"2026-05-18T03:20:45Z","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":"9f742375806e1594c3498883d12ac8c2c09990e37902eb38335aba64ccac6add","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-17T19:31:52Z","title_canon_sha256":"8ab7b2f7ca83f341c456044d7667326ed562f8e52fc12eb40c6ec6d47b57cf44"},"schema_version":"1.0","source":{"id":"1306.3965","kind":"arxiv","version":1}},"canonical_sha256":"b2f18ea4e4587a5996a0fe2ffafbf001185a498c803d9ce235e2e95c9811740d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2f18ea4e4587a5996a0fe2ffafbf001185a498c803d9ce235e2e95c9811740d","first_computed_at":"2026-05-18T03:20:45.904475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:45.904475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O56hcelz3sfUZCVVbgd3tBKaWcAOO/51wT1NvfFD5oT2KTH3rN+KYmBNSBjqnbJR814ZFz5wMBbAJsLjw6uQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:45.905077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed142219310435a04a2544757498d3473d643f95108f4a1690a98074d416c3ce","sha256:a29f863eef840c4994bee397a6e90aac026c213d371b9465ebf80b9054ceb47e"],"state_sha256":"e6c85fb9b8b179cf5515ec7fb3c1b31fc304baa18fd06290fea210d3b91045dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMH4J/UQav4/4RVr/8ScXDoFIjyOWBDj+/HwjMkcXbaPyEHeh8nXRA/VuL30t1LetfOhHqvrASgT/ZYQxdFgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:11:30.477206Z","bundle_sha256":"a9295843041295fc36961355d4b5ac72b401c9d1827df1d3635fa5ce27ec5fe8"}}