{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PHYVP2XGVMBGVTAJNJOQE2ZUAJ","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":"07871ce1c23b5be2a92fe10547397df875b683c962d6f214bfd815e92a038ebf","cross_cats_sorted":["math.CO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-20T17:47:46Z","title_canon_sha256":"a142460aa9bf67b58a12ee97a1a78e01df2d243fb439348a546150be6e495b0d"},"schema_version":"1.0","source":{"id":"1111.4657","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4657","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4657v2","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4657","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"PHYVP2XGVMBG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PHYVP2XGVMBGVTAJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PHYVP2XG","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:50613ccd4b8443b8bc7416db9b63f68c20eb5faa168fe9769be3248406a7c7a3","target":"graph","created_at":"2026-05-18T03:53:44Z","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 determine some of the derived equivalences of a class of gentle algebras called surface algebras. These algebras are constructed from an unpunctured Riemann surface of genus 0 with boundary and marked points by introducing cuts in internal triangles of an arbitrary triangulation of the surface. In particular, we fix a triangulation of a surface and determine when different cuts produce derived equivalent algebras.","authors_text":"Lucas David-Roesler","cross_cats":["math.CO","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-20T17:47:46Z","title":"Derived Equivalence in Surface Algebras of Genus 0 via Graded Equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4657","kind":"arxiv","version":2},"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:fb945d5ae905853c476997024aeaa592f7dbcacd5b0d3532e6dff117c98c1c69","target":"record","created_at":"2026-05-18T03:53:44Z","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":"07871ce1c23b5be2a92fe10547397df875b683c962d6f214bfd815e92a038ebf","cross_cats_sorted":["math.CO","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-20T17:47:46Z","title_canon_sha256":"a142460aa9bf67b58a12ee97a1a78e01df2d243fb439348a546150be6e495b0d"},"schema_version":"1.0","source":{"id":"1111.4657","kind":"arxiv","version":2}},"canonical_sha256":"79f157eae6ab026acc096a5d026b340269f0e8dd19cabdc4257ea95ac15d1308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79f157eae6ab026acc096a5d026b340269f0e8dd19cabdc4257ea95ac15d1308","first_computed_at":"2026-05-18T03:53:44.979854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:44.979854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p6rcwTwKrA44uacdE9NBKYidmLTSeDRBAo4uwX25kTB9gvPW9qCA+XiPUW5FKEiVa06N5N7+5g/X9+1/JdgvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:44.980474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4657","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb945d5ae905853c476997024aeaa592f7dbcacd5b0d3532e6dff117c98c1c69","sha256:50613ccd4b8443b8bc7416db9b63f68c20eb5faa168fe9769be3248406a7c7a3"],"state_sha256":"dd9dedab5c6c06e4ccdcbe8d8a0fe1a81abd7d6ac70c69264bea2f62817dae49"}