{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6DC3IOODYO25B6STAWIUG63HT2","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":"0f03e10692b34ff641f47e784ef115d15d2817aee0b5eb99ab671090b60a7db6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-27T16:13:11Z","title_canon_sha256":"8f1c922e63674e7640502a9949a27cadb80bc2a818921b98ca017a846f332a9c"},"schema_version":"1.0","source":{"id":"1305.6268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6268","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6268v1","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6268","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"6DC3IOODYO25","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6DC3IOODYO25B6ST","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6DC3IOOD","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e1e0de78b2ee7862a66f87838d5b15f2f71592614a6c230d0d684304775ea980","target":"graph","created_at":"2026-05-18T03:24:51Z","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":"Gabrielov numbers describe certain Coxeter-Dynkin diagrams of the 14 exceptional unimodal singularities and play a role in Arnold's strange duality. In a previous paper, the authors defined Gabrielov numbers of a cusp singularity with an action of a finite abelian subgroup $G$ of ${\\rm SL}(3,\\CC)$ using the Gabrielov numbers of the cusp singularity and data of the group $G$. Here we consider a crepant resolution $Y \\to \\CC^3/G$ and the preimage $Z$ of the image of the Milnor fibre of the cusp singularity under the natural projection $\\CC^3 \\to \\CC^3/G$. Using the McKay correspondence, we compu","authors_text":"Atsushi Takahashi, Wolfgang Ebeling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-27T16:13:11Z","title":"A geometric definition of Gabrielov numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6268","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:fda96154f8f728a9d6c28b0a79c3a6854bbc5f6df1ee04bbfeef604218d25d67","target":"record","created_at":"2026-05-18T03:24:51Z","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":"0f03e10692b34ff641f47e784ef115d15d2817aee0b5eb99ab671090b60a7db6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-27T16:13:11Z","title_canon_sha256":"8f1c922e63674e7640502a9949a27cadb80bc2a818921b98ca017a846f332a9c"},"schema_version":"1.0","source":{"id":"1305.6268","kind":"arxiv","version":1}},"canonical_sha256":"f0c5b439c3c3b5d0fa530591437b679eb7e36957dc0abe1a474d3499edcccbc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0c5b439c3c3b5d0fa530591437b679eb7e36957dc0abe1a474d3499edcccbc2","first_computed_at":"2026-05-18T03:24:51.714690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:51.714690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dy9hZ2bjIH0iZJY/vuweYEWEl7KUzH57tLavNkg7kyHQxqFQO3S8DbkDY594MuXA/TRLsZUzShMX806l4OvrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:51.715360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fda96154f8f728a9d6c28b0a79c3a6854bbc5f6df1ee04bbfeef604218d25d67","sha256:e1e0de78b2ee7862a66f87838d5b15f2f71592614a6c230d0d684304775ea980"],"state_sha256":"8e0bea049b3782d16f9ff54c69507df5c28c2f0371e762fe458c700e9cd48369"}