{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EY5JSVYSW6KHO4VPJUXSUBLC4I","short_pith_number":"pith:EY5JSVYS","canonical_record":{"source":{"id":"1306.3935","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T17:36:35Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"dd0a1b15f1f8974d62f7ae0c5f35e9129ccf808cf919d992ac64f49102e47c25","abstract_canon_sha256":"20d8ddb737cdb6ad1aa4270ac93c8c64df179bbf06f2cf15a0a2f03eadb94dc0"},"schema_version":"1.0"},"canonical_sha256":"263a995712b7947772af4d2f2a0562e2128a903b5c8d5112f8727614798b2e85","source":{"kind":"arxiv","id":"1306.3935","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3935","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3935v3","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3935","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"EY5JSVYSW6KH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EY5JSVYSW6KHO4VP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EY5JSVYS","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EY5JSVYSW6KHO4VPJUXSUBLC4I","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3935","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T17:36:35Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"dd0a1b15f1f8974d62f7ae0c5f35e9129ccf808cf919d992ac64f49102e47c25","abstract_canon_sha256":"20d8ddb737cdb6ad1aa4270ac93c8c64df179bbf06f2cf15a0a2f03eadb94dc0"},"schema_version":"1.0"},"canonical_sha256":"263a995712b7947772af4d2f2a0562e2128a903b5c8d5112f8727614798b2e85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:21.046692Z","signature_b64":"c3xyducSYBDsiM5iwssxHqL6mXYU+J5wlSoZup1P/onlDtQB72V56n6UIHfiiKIFq28PPqgeGaq3KCMYU/OLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"263a995712b7947772af4d2f2a0562e2128a903b5c8d5112f8727614798b2e85","last_reissued_at":"2026-05-18T01:23:21.046130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:21.046130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3935","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wk+FC4cf6MabLeDivyVZoDHJVoAWOEV93PFN04YwEr194P0hfv7elxGHuiTx+109Vn+ekQ3WAfZS+cfu0D8WCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:18.513705Z"},"content_sha256":"cf84675dbc78e3faf046447640955bd5879eccae640598f810e1fb5428c27f38","schema_version":"1.0","event_id":"sha256:cf84675dbc78e3faf046447640955bd5879eccae640598f810e1fb5428c27f38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EY5JSVYSW6KHO4VPJUXSUBLC4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tubular Jacobian Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Christof Geiss, Ra\\'ul Gonz\\'alez-Silva","submitted_at":"2013-06-17T17:36:35Z","abstract_excerpt":"We show that the endomorphism ring of each cluster tilting object in a tubular cluster category is a finite dimensional Jacobian algebra which is tame of polynomial growth. Moreover, these Jacobian algebras are given by a quiver with a non-degenerate potential and mutation of cluster tilting objects is compatible with mutation of QPs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3935","kind":"arxiv","version":3},"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":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+KcOYOvAQQI6blR8eyEOaiNwFR745Q8XgHlzu+/SZ9NAaGhnBCH/mYjlNGOg7qdvQz8iOD5xUQoSKyyZ6liDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:18.514054Z"},"content_sha256":"02e960570b6f51f3099d870f31d177e157850fc718f8c174dbf50d1e4ffdefcf","schema_version":"1.0","event_id":"sha256:02e960570b6f51f3099d870f31d177e157850fc718f8c174dbf50d1e4ffdefcf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I/bundle.json","state_url":"https://pith.science/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I/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":"2026-06-03T18:37:18Z","links":{"resolver":"https://pith.science/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I","bundle":"https://pith.science/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I/bundle.json","state":"https://pith.science/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EY5JSVYSW6KHO4VPJUXSUBLC4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EY5JSVYSW6KHO4VPJUXSUBLC4I","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":"20d8ddb737cdb6ad1aa4270ac93c8c64df179bbf06f2cf15a0a2f03eadb94dc0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T17:36:35Z","title_canon_sha256":"dd0a1b15f1f8974d62f7ae0c5f35e9129ccf808cf919d992ac64f49102e47c25"},"schema_version":"1.0","source":{"id":"1306.3935","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3935","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3935v3","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3935","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"EY5JSVYSW6KH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EY5JSVYSW6KHO4VP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EY5JSVYS","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:02e960570b6f51f3099d870f31d177e157850fc718f8c174dbf50d1e4ffdefcf","target":"graph","created_at":"2026-05-18T01:23:21Z","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 show that the endomorphism ring of each cluster tilting object in a tubular cluster category is a finite dimensional Jacobian algebra which is tame of polynomial growth. Moreover, these Jacobian algebras are given by a quiver with a non-degenerate potential and mutation of cluster tilting objects is compatible with mutation of QPs.","authors_text":"Christof Geiss, Ra\\'ul Gonz\\'alez-Silva","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T17:36:35Z","title":"Tubular Jacobian Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3935","kind":"arxiv","version":3},"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:cf84675dbc78e3faf046447640955bd5879eccae640598f810e1fb5428c27f38","target":"record","created_at":"2026-05-18T01:23:21Z","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":"20d8ddb737cdb6ad1aa4270ac93c8c64df179bbf06f2cf15a0a2f03eadb94dc0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T17:36:35Z","title_canon_sha256":"dd0a1b15f1f8974d62f7ae0c5f35e9129ccf808cf919d992ac64f49102e47c25"},"schema_version":"1.0","source":{"id":"1306.3935","kind":"arxiv","version":3}},"canonical_sha256":"263a995712b7947772af4d2f2a0562e2128a903b5c8d5112f8727614798b2e85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"263a995712b7947772af4d2f2a0562e2128a903b5c8d5112f8727614798b2e85","first_computed_at":"2026-05-18T01:23:21.046130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:21.046130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c3xyducSYBDsiM5iwssxHqL6mXYU+J5wlSoZup1P/onlDtQB72V56n6UIHfiiKIFq28PPqgeGaq3KCMYU/OLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:21.046692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3935","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf84675dbc78e3faf046447640955bd5879eccae640598f810e1fb5428c27f38","sha256:02e960570b6f51f3099d870f31d177e157850fc718f8c174dbf50d1e4ffdefcf"],"state_sha256":"0aa27148cfc30eb919bbd5d10d2557dd4775eba6532c07b05a0a7553aa11ab08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xe7+rxFvdVuxd9/wYkupkqcUmOwXQD2g3SEACPFBIIRONysIZoTl4/9Kqambd+mjcAXL/sraBSVDXGBQvcl8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:37:18.516049Z","bundle_sha256":"f2fd278774a8315a7df8d9686cb0de19583fa9ce62baa6f6732f993bcf35c90a"}}