{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:36DI2Y7WNCA7QOSYZOHOGRAHU5","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":"bac7b33b191bc96e0ca09d5e231f79ef3be002d54987d8de2ecacaedda553b3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-13T08:49:10Z","title_canon_sha256":"992bf12e190ce341e6fc8dbd24cae82431ced1102fc2f4a19d65880247538686"},"schema_version":"1.0","source":{"id":"1811.05781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05781","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05781v1","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05781","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"36DI2Y7WNCA7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"36DI2Y7WNCA7QOSY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"36DI2Y7W","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:6ef09ee8cdd2a95870391b6de487d9e21a7b2e15665c2a80ab8a0543f24eae51","target":"graph","created_at":"2026-05-18T00:00:42Z","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 the framework of constructing mirror symmetric pairs of Calabi-Yau manifolds, P. Berglund, T. H\\\"ubsch and M. Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and a finite abelian group $G$ of its diagonal symmetries and associated to this pair a dual pair $(\\widetilde{f}, \\widetilde{G})$. A. Takahashi suggested a generalization of this construction to pairs $(f, G)$ where $G$ is a non-abelian group generated by some diagonal symmetries and some permutations of variables. In a previous paper, the authors showed that some mirror symmetry phenomena appear only u","authors_text":"Sabir M. Gusein-Zade, Wolfgang Ebeling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-13T08:49:10Z","title":"On the orbifold Euler characteristics of dual invertible polynomials with non-abelian symmetry groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05781","kind":"arxiv","version":1},"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":"sha256:86d7bb7b4ef97a1c837dafe7c2f8dc2cb51e33422c97417df79414d7473ce7ef","target":"record","created_at":"2026-05-18T00:00:42Z","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":"bac7b33b191bc96e0ca09d5e231f79ef3be002d54987d8de2ecacaedda553b3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-13T08:49:10Z","title_canon_sha256":"992bf12e190ce341e6fc8dbd24cae82431ced1102fc2f4a19d65880247538686"},"schema_version":"1.0","source":{"id":"1811.05781","kind":"arxiv","version":1}},"canonical_sha256":"df868d63f66881f83a58cb8ee34407a771d3599f1a1e04f0f5268b7b18e2e2bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df868d63f66881f83a58cb8ee34407a771d3599f1a1e04f0f5268b7b18e2e2bc","first_computed_at":"2026-05-18T00:00:42.102559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:42.102559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+J5RGM2DtwTXVaFczYhcMVbx7jrnhu0+oAidKuvWMVNOst9kThoW+R5r6D1ck5dNBHj/i2jp/xGWKgS8fqWsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:42.103059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86d7bb7b4ef97a1c837dafe7c2f8dc2cb51e33422c97417df79414d7473ce7ef","sha256:6ef09ee8cdd2a95870391b6de487d9e21a7b2e15665c2a80ab8a0543f24eae51"],"state_sha256":"4db77852f147e95043ac04d9bc047be113f8e64199b3a41fc66a64a147c059c9"}