{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XEBASOGK33HMFVIUUBW7GMCPDI","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":"d2b9184f4faccd27c271f3a200201a7c56ab7369f3bcde07f0b10c6b170280d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-16T22:39:03Z","title_canon_sha256":"2280c1d4ae12745761d8efcbdfa5f96fa7d0857455bf29d16d3c789283b2d31c"},"schema_version":"1.0","source":{"id":"1412.5219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5219","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5219v1","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5219","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"XEBASOGK33HM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XEBASOGK33HMFVIU","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XEBASOGK","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:9b59d760c8b161a93a8f344c49e2bf0a1f70646f911311b70847f8e355ac1f55","target":"graph","created_at":"2026-05-18T02:31:09Z","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":"Let $k$ be a field, $Q$ a finite directed graph, and $kQ$ its path algebra. Make $kQ$ an $\\NN$-graded algebra by assigning each arrow a positive degree. Let $I$ be a homogeneous ideal in $kQ$ and write $A=kQ/I$. Let $\\QGr A$ denote the quotient of the category of graded right $A$-modules modulo the Serre subcategory consisting of those graded modules that are the sum of their finite dimensional submodules. This paper shows there is a finite directed graph $Q'$ with all its arrows placed in degree 1 and a homogeneous ideal $I'\\subset kQ'$ such that $\\QGr A \\equiv \\QGr kQ'/I'$. This is an extens","authors_text":"Cody Holdaway","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-16T22:39:03Z","title":"Category equivalences involving graded modules over quotients of weighted path algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5219","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":"sha256:9bc884acac3b12ee1ceed6fed8633998bda1b6db3a559c61eab2779a560dff00","target":"record","created_at":"2026-05-18T02:31:09Z","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":"d2b9184f4faccd27c271f3a200201a7c56ab7369f3bcde07f0b10c6b170280d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-16T22:39:03Z","title_canon_sha256":"2280c1d4ae12745761d8efcbdfa5f96fa7d0857455bf29d16d3c789283b2d31c"},"schema_version":"1.0","source":{"id":"1412.5219","kind":"arxiv","version":1}},"canonical_sha256":"b9020938cadecec2d514a06df3304f1a134590db52f176f64556a88b9b022ec1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9020938cadecec2d514a06df3304f1a134590db52f176f64556a88b9b022ec1","first_computed_at":"2026-05-18T02:31:09.245428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:09.245428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zGwNJSnYnobgCTJqcJssnZ/QvziMhMzhOhEzbEG9kqwPyvksQNV9T0phMiXyfR5T03kDZqBDtgB6r0Zl3CtXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:09.246100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bc884acac3b12ee1ceed6fed8633998bda1b6db3a559c61eab2779a560dff00","sha256:9b59d760c8b161a93a8f344c49e2bf0a1f70646f911311b70847f8e355ac1f55"],"state_sha256":"33ffafb8b1896b8dee1552ae53cf941b595d4ebf7ab96de818f3a984124dbd21"}