{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:73CA5P2BPTDBTU6IK3DCMFNFFK","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":"5d8b9dde7794fad7e1844b464f39163444bbb10ffc6cdeb75eb291cab5e6979c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-22T14:21:09Z","title_canon_sha256":"724495b7d3917e6f580fc0706bb6222d5186a15c172fc9ec84c5fe6b850d1b39"},"schema_version":"1.0","source":{"id":"0812.4185","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4185","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4185v4","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4185","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"73CA5P2BPTDB","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"73CA5P2BPTDBTU6I","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"73CA5P2B","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:984bbcfc0f1c21b46ee80f99b78a36e67cdd917fdb4d9261b3d9979c128059c8","target":"graph","created_at":"2026-05-18T04:20:14Z","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":"Given a brane tiling on a torus, we provide a new way to prove and generalise the recent results of Szendroi, Mozgovoy and Reineke regarding the Donaldson-Thomas theory of the moduli space of framed cyclic representations of the associated algebra. Using only a natural cancellation-type consistency condition, we show that the algebras are 3-Calabi-Yau, and calculate Donaldson-Thomas type invariants of the moduli spaces. Two new ingredients to our proofs are a grading of the algebra by the path category of the associated quiver modulo relations, and a way of assigning winding numbers to pairs o","authors_text":"Ben Davison","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-22T14:21:09Z","title":"Consistency conditions for brane tilings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4185","kind":"arxiv","version":4},"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":"sha256:58258dce6b0aa0793e12193483ef6457a61033dc6c9487ddc64a418ba41b00b7","target":"record","created_at":"2026-05-18T04:20:14Z","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":"5d8b9dde7794fad7e1844b464f39163444bbb10ffc6cdeb75eb291cab5e6979c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-22T14:21:09Z","title_canon_sha256":"724495b7d3917e6f580fc0706bb6222d5186a15c172fc9ec84c5fe6b850d1b39"},"schema_version":"1.0","source":{"id":"0812.4185","kind":"arxiv","version":4}},"canonical_sha256":"fec40ebf417cc619d3c856c62615a52a928743e3dc3e83a1bd69a907cb825117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fec40ebf417cc619d3c856c62615a52a928743e3dc3e83a1bd69a907cb825117","first_computed_at":"2026-05-18T04:20:14.819050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:14.819050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ttb/nkWbqxoNY9gjI+2RE7rmB3o/CsAygS8Elx2FcJz+tcHLETnT9mMTqVzckk2A1LrMk9I/P41RYA2atafJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:14.819485Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4185","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58258dce6b0aa0793e12193483ef6457a61033dc6c9487ddc64a418ba41b00b7","sha256:984bbcfc0f1c21b46ee80f99b78a36e67cdd917fdb4d9261b3d9979c128059c8"],"state_sha256":"474e09c568203cc1e19b648e34bd4cd2806d75e165faf99daf277ddaab801f4e"}