{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HXHWYPYMH5OBLI3FBPSL4LA5TS","short_pith_number":"pith:HXHWYPYM","schema_version":"1.0","canonical_sha256":"3dcf6c3f0c3f5c15a3650be4be2c1d9ca1764a472d0006622b9578505adc658f","source":{"kind":"arxiv","id":"1611.02017","version":5},"attestation_state":"computed","paper":{"title":"Representation embeddings and the second Brauer-Thrall conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Klaus Bongartz","submitted_at":"2016-11-07T12:25:44Z","abstract_excerpt":"We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any representation-infinite finite-dimensional algebra. We also sharpen some known results on representation embeddings, we simplify some proofs and we construct a simultaneous orthogonal embedding for an infinite family of module categories. In the last section the minimal classes of representation-infinite algebras are determined. The result depends on the characteristic."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.02017","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-07T12:25:44Z","cross_cats_sorted":[],"title_canon_sha256":"01d10da06844d019bedc1fcc983eed3efc1a1479cf17104f0fdc70bc6bf8291d","abstract_canon_sha256":"5518082fb18719421dcbbb9615f1adb99961bd6292ee9ecfd9b345d3b03ed32f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:14:31.874586Z","signature_b64":"fkxMp4qGGK/D31vU9VWf+wdH+bCMotrvFk4Nd6goe/25ybSMJcSh/Q3azkL8ZsdIqcgk6ML7JQUThZ9A5unmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dcf6c3f0c3f5c15a3650be4be2c1d9ca1764a472d0006622b9578505adc658f","last_reissued_at":"2026-07-05T06:14:31.874214Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:14:31.874214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representation embeddings and the second Brauer-Thrall conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Klaus Bongartz","submitted_at":"2016-11-07T12:25:44Z","abstract_excerpt":"We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any representation-infinite finite-dimensional algebra. We also sharpen some known results on representation embeddings, we simplify some proofs and we construct a simultaneous orthogonal embedding for an infinite family of module categories. In the last section the minimal classes of representation-infinite algebras are determined. The result depends on the characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02017","kind":"arxiv","version":5},"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/1611.02017/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.02017","created_at":"2026-07-05T06:14:31.874270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.02017v5","created_at":"2026-07-05T06:14:31.874270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02017","created_at":"2026-07-05T06:14:31.874270+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXHWYPYMH5OB","created_at":"2026-07-05T06:14:31.874270+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXHWYPYMH5OBLI3F","created_at":"2026-07-05T06:14:31.874270+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXHWYPYM","created_at":"2026-07-05T06:14:31.874270+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2601.00379","citing_title":"Complete invariants for simultaneous similarity","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2601.00379","citing_title":"Complete invariants for simultaneous similarity","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS","json":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS.json","graph_json":"https://pith.science/api/pith-number/HXHWYPYMH5OBLI3FBPSL4LA5TS/graph.json","events_json":"https://pith.science/api/pith-number/HXHWYPYMH5OBLI3FBPSL4LA5TS/events.json","paper":"https://pith.science/paper/HXHWYPYM"},"agent_actions":{"view_html":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS","download_json":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS.json","view_paper":"https://pith.science/paper/HXHWYPYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.02017&json=true","fetch_graph":"https://pith.science/api/pith-number/HXHWYPYMH5OBLI3FBPSL4LA5TS/graph.json","fetch_events":"https://pith.science/api/pith-number/HXHWYPYMH5OBLI3FBPSL4LA5TS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS/action/storage_attestation","attest_author":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS/action/author_attestation","sign_citation":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS/action/citation_signature","submit_replication":"https://pith.science/pith/HXHWYPYMH5OBLI3FBPSL4LA5TS/action/replication_record"}},"created_at":"2026-07-05T06:14:31.874270+00:00","updated_at":"2026-07-05T06:14:31.874270+00:00"}