{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R6RVGIPFM6P2KJKGJFKBDPTBEQ","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":"5bbc67378918f4f75cc48c723ef837e6745dcdca50bc4e4b14a35f3f81f880bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-07-06T19:13:40Z","title_canon_sha256":"c8b2b8bc2b3012bd96f5c0202cbfba491d4b4f6a31050aaf8f19c702c825bd1b"},"schema_version":"1.0","source":{"id":"1607.01748","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01748","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01748v2","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01748","created_at":"2026-05-18T00:49:04Z"},{"alias_kind":"pith_short_12","alias_value":"R6RVGIPFM6P2","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R6RVGIPFM6P2KJKG","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R6RVGIPF","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:5b8158eebde65f0d625da2bc73287f63c3e15311a4e6072a15865b8907b92e24","target":"graph","created_at":"2026-05-18T00:49:04Z","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":"In this paper we extend the classification scheme in [S] for $b^m$-symplectic surfaces and, more generally, $b^m$-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects for non-orientable surfaces. The paper also includes recipes to construct $b^m$-symplectic structures on surfaces. Feasibility of such constructions depends on orientability and on the colorability of an associated graph. The desingularization technique in [GMW] is revisited for surfaces and the compatibi","authors_text":"Arnau Planas, Eva Miranda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-07-06T19:13:40Z","title":"Equivariant classification of $b^m$-symplectic surfaces and Nambu structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01748","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":"sha256:3d335821ea48e4a41d5e899768d1ce98a40f7e905f7fdbd5b24fb0b9f99ab32e","target":"record","created_at":"2026-05-18T00:49:04Z","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":"5bbc67378918f4f75cc48c723ef837e6745dcdca50bc4e4b14a35f3f81f880bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-07-06T19:13:40Z","title_canon_sha256":"c8b2b8bc2b3012bd96f5c0202cbfba491d4b4f6a31050aaf8f19c702c825bd1b"},"schema_version":"1.0","source":{"id":"1607.01748","kind":"arxiv","version":2}},"canonical_sha256":"8fa35321e5679fa52546495411be612414e144b2e6f821907d3f8af3e1724413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fa35321e5679fa52546495411be612414e144b2e6f821907d3f8af3e1724413","first_computed_at":"2026-05-18T00:49:04.535152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:04.535152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hZZxr+ZPC2Pf3pTa8lkNwwcAtZhg+K1Hf2taemlPpen0hLdcB3U0u88cqeG7i/nRPwu+ii2QosmiTRTp/AfTDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:04.535663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01748","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d335821ea48e4a41d5e899768d1ce98a40f7e905f7fdbd5b24fb0b9f99ab32e","sha256:5b8158eebde65f0d625da2bc73287f63c3e15311a4e6072a15865b8907b92e24"],"state_sha256":"ac953241a84e431a3d15ebccfc6633d2bed0e866af01a9568ae97001377c315c"}