{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BTOCFNKA3H34R4U6BLGGTDISCH","short_pith_number":"pith:BTOCFNKA","schema_version":"1.0","canonical_sha256":"0cdc22b540d9f7c8f29e0acc698d1211cc3cc0d07187c743721f5fe36106c7ec","source":{"kind":"arxiv","id":"1805.09739","version":1},"attestation_state":"computed","paper":{"title":"Orders of bounded and strongly unbounded lattice type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alex Martsinkovsky, Fahimeh Sadat Fotouhi, Shokrollah Salarian","submitted_at":"2018-05-24T15:43:59Z","abstract_excerpt":"Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type has strongly unbounded representation type. These conjectures, now theorems, are our motivation for studying (generalized) orders of bounded and strongly unbounded lattice type. To each lattice over an order we assign a numerical invariant, $\\underline{\\h}$-length, measuring Hom modulo projectives. We show that an order of bounded lattice type is actually of"},"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":"1805.09739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-24T15:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"c472768d63d6bbf1a00d9e3c8072bebe4096c5120dea4629dba2c56f4261991a","abstract_canon_sha256":"9b504d235e6b3892d00ee8099a52153cc98d3e6be04845f6bf0bdc4576bb9500"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:02.963852Z","signature_b64":"Bfbbzki5La2QW5DqGWI+nTuEfiHsh2g7U+xkPrMKan7lvAWx11Zr9KUgKqNGZ7PgL4OQ5Az4vegp7HiucsQWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cdc22b540d9f7c8f29e0acc698d1211cc3cc0d07187c743721f5fe36106c7ec","last_reissued_at":"2026-05-18T00:15:02.963025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:02.963025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orders of bounded and strongly unbounded lattice type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alex Martsinkovsky, Fahimeh Sadat Fotouhi, Shokrollah Salarian","submitted_at":"2018-05-24T15:43:59Z","abstract_excerpt":"Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type has strongly unbounded representation type. These conjectures, now theorems, are our motivation for studying (generalized) orders of bounded and strongly unbounded lattice type. To each lattice over an order we assign a numerical invariant, $\\underline{\\h}$-length, measuring Hom modulo projectives. We show that an order of bounded lattice type is actually of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09739","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":"1805.09739","created_at":"2026-05-18T00:15:02.963174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.09739v1","created_at":"2026-05-18T00:15:02.963174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09739","created_at":"2026-05-18T00:15:02.963174+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTOCFNKA3H34","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTOCFNKA3H34R4U6","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTOCFNKA","created_at":"2026-05-18T12:32:16.446611+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/BTOCFNKA3H34R4U6BLGGTDISCH","json":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH.json","graph_json":"https://pith.science/api/pith-number/BTOCFNKA3H34R4U6BLGGTDISCH/graph.json","events_json":"https://pith.science/api/pith-number/BTOCFNKA3H34R4U6BLGGTDISCH/events.json","paper":"https://pith.science/paper/BTOCFNKA"},"agent_actions":{"view_html":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH","download_json":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH.json","view_paper":"https://pith.science/paper/BTOCFNKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.09739&json=true","fetch_graph":"https://pith.science/api/pith-number/BTOCFNKA3H34R4U6BLGGTDISCH/graph.json","fetch_events":"https://pith.science/api/pith-number/BTOCFNKA3H34R4U6BLGGTDISCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH/action/storage_attestation","attest_author":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH/action/author_attestation","sign_citation":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH/action/citation_signature","submit_replication":"https://pith.science/pith/BTOCFNKA3H34R4U6BLGGTDISCH/action/replication_record"}},"created_at":"2026-05-18T00:15:02.963174+00:00","updated_at":"2026-05-18T00:15:02.963174+00:00"}