{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ODQZEOW2RZOYYWU5BM6756TMRD","short_pith_number":"pith:ODQZEOW2","schema_version":"1.0","canonical_sha256":"70e1923ada8e5d8c5a9d0b3dfefa6c88cf0866d06dcf102d37b0767168aa2216","source":{"kind":"arxiv","id":"1504.05320","version":2},"attestation_state":"computed","paper":{"title":"Twists and braids for general 3-fold flops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Michael Wemyss, Will Donovan","submitted_at":"2015-04-21T07:04:05Z","abstract_excerpt":"Given a quasi-projective 3-fold X with only Gorenstein terminal singularities, we prove that the flop functors beginning at X satisfy higher degree braid relations, with the combinatorics controlled by a real hyperplane arrangement H. This leads to a general theory, incorporating known special cases with degree 3 braid relations, in which we show that higher degree relations can occur even for two smooth rational curves meeting at a point. This theory yields an action of the fundamental group of the complexified complement of H on the derived category of X, for any such 3-fold that admits indi"},"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":"1504.05320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T07:04:05Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"89e8b74b393986f74474b714506fe9a3fb51121fcb21c56306a581ded9cbdafe","abstract_canon_sha256":"97e4114229a25000d5eec16ca9b9e24fe5b4b2a0a177718def56ee1db98559cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.126544Z","signature_b64":"NhNdAYTUVBPyRZGsevPuB0ztRhlL+kf1OdLW6+S38+IF8ryW0Fu/IT7tw5F0b09AjGFtIDp1n95Gn0BYLnI+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70e1923ada8e5d8c5a9d0b3dfefa6c88cf0866d06dcf102d37b0767168aa2216","last_reissued_at":"2026-05-18T01:31:11.125870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.125870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twists and braids for general 3-fold flops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Michael Wemyss, Will Donovan","submitted_at":"2015-04-21T07:04:05Z","abstract_excerpt":"Given a quasi-projective 3-fold X with only Gorenstein terminal singularities, we prove that the flop functors beginning at X satisfy higher degree braid relations, with the combinatorics controlled by a real hyperplane arrangement H. This leads to a general theory, incorporating known special cases with degree 3 braid relations, in which we show that higher degree relations can occur even for two smooth rational curves meeting at a point. This theory yields an action of the fundamental group of the complexified complement of H on the derived category of X, for any such 3-fold that admits indi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05320","kind":"arxiv","version":2},"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":"1504.05320","created_at":"2026-05-18T01:31:11.125982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05320v2","created_at":"2026-05-18T01:31:11.125982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05320","created_at":"2026-05-18T01:31:11.125982+00:00"},{"alias_kind":"pith_short_12","alias_value":"ODQZEOW2RZOY","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"ODQZEOW2RZOYYWU5","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"ODQZEOW2","created_at":"2026-05-18T12:29:34.919912+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/ODQZEOW2RZOYYWU5BM6756TMRD","json":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD.json","graph_json":"https://pith.science/api/pith-number/ODQZEOW2RZOYYWU5BM6756TMRD/graph.json","events_json":"https://pith.science/api/pith-number/ODQZEOW2RZOYYWU5BM6756TMRD/events.json","paper":"https://pith.science/paper/ODQZEOW2"},"agent_actions":{"view_html":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD","download_json":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD.json","view_paper":"https://pith.science/paper/ODQZEOW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05320&json=true","fetch_graph":"https://pith.science/api/pith-number/ODQZEOW2RZOYYWU5BM6756TMRD/graph.json","fetch_events":"https://pith.science/api/pith-number/ODQZEOW2RZOYYWU5BM6756TMRD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD/action/storage_attestation","attest_author":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD/action/author_attestation","sign_citation":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD/action/citation_signature","submit_replication":"https://pith.science/pith/ODQZEOW2RZOYYWU5BM6756TMRD/action/replication_record"}},"created_at":"2026-05-18T01:31:11.125982+00:00","updated_at":"2026-05-18T01:31:11.125982+00:00"}