{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AMF7BB7MQJYYT7CL2XH26J2EWX","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":"eb39057bd8511c73fe00144aa5a471a9c1bba74fe2fe5120ccc66ac9b5740f4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-09T15:27:51Z","title_canon_sha256":"ea7f2bc80c064dec55957077a043935208ea0adc1f6eaf6f5373192358390a4c"},"schema_version":"1.0","source":{"id":"2306.05961","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.05961","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"2306.05961v3","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.05961","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"AMF7BB7MQJYY","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"pith_short_16","alias_value":"AMF7BB7MQJYYT7CL","created_at":"2026-07-05T11:20:01Z"},{"alias_kind":"pith_short_8","alias_value":"AMF7BB7M","created_at":"2026-07-05T11:20:01Z"}],"graph_snapshots":[{"event_id":"sha256:72c2e137cdfed64b6e751713257c0a031128085bc00a430cbf1e887f230d0169","target":"graph","created_at":"2026-07-05T11:20:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.05961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the density of curves having squarefree discriminant in some families of curves that arise from Vinberg representations, showing that the global density is the product of the local densities. We do so using the framework of Thorne and Laga's PhD theses and Bhargava's orbit-counting techniques. This paper generalises a previous result by Bhargava, Shankar and Wang. As an application, we give an asymptotic for the number of reducible orbits of our representations.","authors_text":"Mart\\'i Oller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-09T15:27:51Z","title":"The density of ADE families of curves having squarefree discriminant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05961","kind":"arxiv","version":3},"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":"sha256:5d041aee5bd5a81ed42358b033bdd233e80805884b941ddc2a3ae48960fa64e1","target":"record","created_at":"2026-07-05T11:20:01Z","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":"eb39057bd8511c73fe00144aa5a471a9c1bba74fe2fe5120ccc66ac9b5740f4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-06-09T15:27:51Z","title_canon_sha256":"ea7f2bc80c064dec55957077a043935208ea0adc1f6eaf6f5373192358390a4c"},"schema_version":"1.0","source":{"id":"2306.05961","kind":"arxiv","version":3}},"canonical_sha256":"030bf087ec827189fc4bd5cfaf2744b5fa6bd37132e941fb3667fbd6925038b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"030bf087ec827189fc4bd5cfaf2744b5fa6bd37132e941fb3667fbd6925038b7","first_computed_at":"2026-07-05T11:20:01.349726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:01.349726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4wMqbMCaFuwjR0VEtHujBsKHz0HncJScJUgdLaGjWR5FHppSebHIiiYZQS0qwuvs3jjQtxg8yz7SBEfSzAKDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:01.350162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.05961","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d041aee5bd5a81ed42358b033bdd233e80805884b941ddc2a3ae48960fa64e1","sha256:72c2e137cdfed64b6e751713257c0a031128085bc00a430cbf1e887f230d0169"],"state_sha256":"fdd90c2a7d8c243568663b4ed34faf5fdb6b352a1e759bff71c348e36fab0a3e"}