{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6HJ2P6JDIJSMXNTDPATRGE763W","short_pith_number":"pith:6HJ2P6JD","schema_version":"1.0","canonical_sha256":"f1d3a7f9234264cbb66378271313fedd854201fdf9b8829f53e15b11c7e13b1e","source":{"kind":"arxiv","id":"1211.3172","version":1},"attestation_state":"computed","paper":{"title":"Brauer-Thrall theory for maximal Cohen-Macaulay modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Graham J. Leuschke, Roger Wiegand","submitted_at":"2012-11-14T00:31:19Z","abstract_excerpt":"The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional $\\sk$-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large $\\sk$-dimension. These conjectures have natural interpretations in the context of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. This is a survey of progress on these transplanted conjectures."},"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":"1211.3172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-14T00:31:19Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a9b774abfbd08e1f881a087e672e79b3f3c71ce24f0e1167fb06959c7f354c3c","abstract_canon_sha256":"9567b1f399b2a6158527dbfaebe30056057b43b9fb340294602e1c3cfc574def"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:50.704390Z","signature_b64":"pO95HnmD4vtTCySPBFLBj1ap2uGGW/t8FeteVkDA/JECqbjfi5KI7ttpKgkgNo1PYr3UhYXj0sRhOJPgongxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d3a7f9234264cbb66378271313fedd854201fdf9b8829f53e15b11c7e13b1e","last_reissued_at":"2026-05-18T03:40:50.703641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:50.703641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brauer-Thrall theory for maximal Cohen-Macaulay modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Graham J. Leuschke, Roger Wiegand","submitted_at":"2012-11-14T00:31:19Z","abstract_excerpt":"The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional $\\sk$-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large $\\sk$-dimension. These conjectures have natural interpretations in the context of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. This is a survey of progress on these transplanted conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3172","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.3172","created_at":"2026-05-18T03:40:50.703761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.3172v1","created_at":"2026-05-18T03:40:50.703761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3172","created_at":"2026-05-18T03:40:50.703761+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HJ2P6JDIJSM","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HJ2P6JDIJSMXNTD","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HJ2P6JD","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W","json":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W.json","graph_json":"https://pith.science/api/pith-number/6HJ2P6JDIJSMXNTDPATRGE763W/graph.json","events_json":"https://pith.science/api/pith-number/6HJ2P6JDIJSMXNTDPATRGE763W/events.json","paper":"https://pith.science/paper/6HJ2P6JD"},"agent_actions":{"view_html":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W","download_json":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W.json","view_paper":"https://pith.science/paper/6HJ2P6JD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.3172&json=true","fetch_graph":"https://pith.science/api/pith-number/6HJ2P6JDIJSMXNTDPATRGE763W/graph.json","fetch_events":"https://pith.science/api/pith-number/6HJ2P6JDIJSMXNTDPATRGE763W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W/action/storage_attestation","attest_author":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W/action/author_attestation","sign_citation":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W/action/citation_signature","submit_replication":"https://pith.science/pith/6HJ2P6JDIJSMXNTDPATRGE763W/action/replication_record"}},"created_at":"2026-05-18T03:40:50.703761+00:00","updated_at":"2026-05-18T03:40:50.703761+00:00"}