{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6DC3IOODYO25B6STAWIUG63HT2","short_pith_number":"pith:6DC3IOOD","schema_version":"1.0","canonical_sha256":"f0c5b439c3c3b5d0fa530591437b679eb7e36957dc0abe1a474d3499edcccbc2","source":{"kind":"arxiv","id":"1305.6268","version":1},"attestation_state":"computed","paper":{"title":"A geometric definition of Gabrielov numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atsushi Takahashi, Wolfgang Ebeling","submitted_at":"2013-05-27T16:13:11Z","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"},"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":"1305.6268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-27T16:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"8f1c922e63674e7640502a9949a27cadb80bc2a818921b98ca017a846f332a9c","abstract_canon_sha256":"0f03e10692b34ff641f47e784ef115d15d2817aee0b5eb99ab671090b60a7db6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:51.715360Z","signature_b64":"dy9hZ2bjIH0iZJY/vuweYEWEl7KUzH57tLavNkg7kyHQxqFQO3S8DbkDY594MuXA/TRLsZUzShMX806l4OvrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0c5b439c3c3b5d0fa530591437b679eb7e36957dc0abe1a474d3499edcccbc2","last_reissued_at":"2026-05-18T03:24:51.714690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:51.714690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A geometric definition of Gabrielov numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atsushi Takahashi, Wolfgang Ebeling","submitted_at":"2013-05-27T16:13:11Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6268","kind":"arxiv","version":1},"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":"1305.6268","created_at":"2026-05-18T03:24:51.714796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6268v1","created_at":"2026-05-18T03:24:51.714796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6268","created_at":"2026-05-18T03:24:51.714796+00:00"},{"alias_kind":"pith_short_12","alias_value":"6DC3IOODYO25","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6DC3IOODYO25B6ST","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6DC3IOOD","created_at":"2026-05-18T12:27:36.564083+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/6DC3IOODYO25B6STAWIUG63HT2","json":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2.json","graph_json":"https://pith.science/api/pith-number/6DC3IOODYO25B6STAWIUG63HT2/graph.json","events_json":"https://pith.science/api/pith-number/6DC3IOODYO25B6STAWIUG63HT2/events.json","paper":"https://pith.science/paper/6DC3IOOD"},"agent_actions":{"view_html":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2","download_json":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2.json","view_paper":"https://pith.science/paper/6DC3IOOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6268&json=true","fetch_graph":"https://pith.science/api/pith-number/6DC3IOODYO25B6STAWIUG63HT2/graph.json","fetch_events":"https://pith.science/api/pith-number/6DC3IOODYO25B6STAWIUG63HT2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2/action/storage_attestation","attest_author":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2/action/author_attestation","sign_citation":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2/action/citation_signature","submit_replication":"https://pith.science/pith/6DC3IOODYO25B6STAWIUG63HT2/action/replication_record"}},"created_at":"2026-05-18T03:24:51.714796+00:00","updated_at":"2026-05-18T03:24:51.714796+00:00"}