{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BVYAH3VPO4RXJPKHWYK3YFZI7R","short_pith_number":"pith:BVYAH3VP","schema_version":"1.0","canonical_sha256":"0d7003eeaf772374bd47b615bc1728fc6e65d1b82c6d82921379af8a1cdfcbb4","source":{"kind":"arxiv","id":"1108.2352","version":3},"attestation_state":"computed","paper":{"title":"Flops and mutations for crepant resolutions of polyhedral singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alvaro Nolla de Celis, Yuhi Sekiya","submitted_at":"2011-08-11T09:04:36Z","abstract_excerpt":"Let $G$ be a polyhedral group $G\\subset SO(3)$ of types $\\mathbb{Z}/n\\mathbb{Z}$, $D_{2n}$ and $\\mathbb{T}$. We prove that there exists a one-to-one correspondence between flops of $G$-Hilb$\\mathbb{C}^3$ and mutations of the McKay quiver with potential which do not mutate the trivial vertex. This correspondence provides two equivalent methods to construct every projective crepant resolution for the singularities $\\mathbb{C}^3/G$, which are constructed as moduli spaces $\\mathcal{M}_C$ of quivers with potential for some chamber $C$ in the space $\\Theta$ of stability conditions. In addition, we s"},"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":"1108.2352","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-11T09:04:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"203f68e546fce27aafc5be065bfb0ea4a888647948f72c59590ebe758dd1c01a","abstract_canon_sha256":"f59087c74dd70410929d4fb6c717bf3bda1be04b4b535757c02ea72c51ef3d6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.314569Z","signature_b64":"0yEoMY8rEDX7bQpmSLgaYnqbjYnYuQW6CQIDczW6S+8uvAomwftRK5zFUG/yvhs7ruHaJSAJUyJ4eN5vTBe7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d7003eeaf772374bd47b615bc1728fc6e65d1b82c6d82921379af8a1cdfcbb4","last_reissued_at":"2026-05-18T01:36:21.314138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.314138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flops and mutations for crepant resolutions of polyhedral singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alvaro Nolla de Celis, Yuhi Sekiya","submitted_at":"2011-08-11T09:04:36Z","abstract_excerpt":"Let $G$ be a polyhedral group $G\\subset SO(3)$ of types $\\mathbb{Z}/n\\mathbb{Z}$, $D_{2n}$ and $\\mathbb{T}$. We prove that there exists a one-to-one correspondence between flops of $G$-Hilb$\\mathbb{C}^3$ and mutations of the McKay quiver with potential which do not mutate the trivial vertex. This correspondence provides two equivalent methods to construct every projective crepant resolution for the singularities $\\mathbb{C}^3/G$, which are constructed as moduli spaces $\\mathcal{M}_C$ of quivers with potential for some chamber $C$ in the space $\\Theta$ of stability conditions. In addition, we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2352","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.2352","created_at":"2026-05-18T01:36:21.314211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2352v3","created_at":"2026-05-18T01:36:21.314211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2352","created_at":"2026-05-18T01:36:21.314211+00:00"},{"alias_kind":"pith_short_12","alias_value":"BVYAH3VPO4RX","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BVYAH3VPO4RXJPKH","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BVYAH3VP","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.10698","citing_title":"On holographic duals of certain isolated weighted Gorenstein cDV singularities","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R","json":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R.json","graph_json":"https://pith.science/api/pith-number/BVYAH3VPO4RXJPKHWYK3YFZI7R/graph.json","events_json":"https://pith.science/api/pith-number/BVYAH3VPO4RXJPKHWYK3YFZI7R/events.json","paper":"https://pith.science/paper/BVYAH3VP"},"agent_actions":{"view_html":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R","download_json":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R.json","view_paper":"https://pith.science/paper/BVYAH3VP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2352&json=true","fetch_graph":"https://pith.science/api/pith-number/BVYAH3VPO4RXJPKHWYK3YFZI7R/graph.json","fetch_events":"https://pith.science/api/pith-number/BVYAH3VPO4RXJPKHWYK3YFZI7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R/action/storage_attestation","attest_author":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R/action/author_attestation","sign_citation":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R/action/citation_signature","submit_replication":"https://pith.science/pith/BVYAH3VPO4RXJPKHWYK3YFZI7R/action/replication_record"}},"created_at":"2026-05-18T01:36:21.314211+00:00","updated_at":"2026-05-18T01:36:21.314211+00:00"}