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We show there are infinitely many quadruples $Q$ satisfying this condition. For every such $Q$, we consider $Z_Q\\subseteq M_g$ the locus in the moduli space of all smooth degree-$d$ curves embedded in $\\mathbb{P}^2(w_0,w_1,w_2)$. We show that, as $Q$ varies over all these quadruples, there are only finitely many different loci $Z_Q\\subseteq M_g$."},"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":"1803.07992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-21T16:23:12Z","cross_cats_sorted":[],"title_canon_sha256":"d026a206638f82c8c36aa5a79a15a0d9076679d856907850526216a925328fd9","abstract_canon_sha256":"9b71f33b1992dd5ccf0fb135d6cfca26b0b5c803232ff5e0f0a516b1cee1eca0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:06.652933Z","signature_b64":"sYFSRq5ewHf2oT2kFp9BlutjyowvsAMoJRNbZS/1ZRpgzA3aUrvNxr8KwQO9K4eOwxc6tuckADfBI/UtbSsVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"595fae17b3a665fa14ac0fc9363372ad7ee7b634d3261ae2ccfafd77a509cb04","last_reissued_at":"2026-05-17T23:53:06.652394Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:06.652394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the finiteness of loci of weighted plane curves in the moduli space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Monica Marinescu","submitted_at":"2018-03-21T16:23:12Z","abstract_excerpt":"For every fixed genus $g\\geq 1$, we consider all quadruples $Q=(w_0,w_1,w_2,d)\\in\\mathbb{Z}^4_{>0}$ with the property that any smooth degree-$d$ curve embedded in the weighted projective plane $\\mathbb{P}^2(w_0,w_1,w_2)$ has genus $g$. We show there are infinitely many quadruples $Q$ satisfying this condition. For every such $Q$, we consider $Z_Q\\subseteq M_g$ the locus in the moduli space of all smooth degree-$d$ curves embedded in $\\mathbb{P}^2(w_0,w_1,w_2)$. We show that, as $Q$ varies over all these quadruples, there are only finitely many different loci $Z_Q\\subseteq M_g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07992","kind":"arxiv","version":2},"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":"1803.07992","created_at":"2026-05-17T23:53:06.652484+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.07992v2","created_at":"2026-05-17T23:53:06.652484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07992","created_at":"2026-05-17T23:53:06.652484+00:00"},{"alias_kind":"pith_short_12","alias_value":"LFP24F5TUZS7","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LFP24F5TUZS7UFFM","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LFP24F5T","created_at":"2026-05-18T12:32:37.024351+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/LFP24F5TUZS7UFFMB7ETMM3SVV","json":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV.json","graph_json":"https://pith.science/api/pith-number/LFP24F5TUZS7UFFMB7ETMM3SVV/graph.json","events_json":"https://pith.science/api/pith-number/LFP24F5TUZS7UFFMB7ETMM3SVV/events.json","paper":"https://pith.science/paper/LFP24F5T"},"agent_actions":{"view_html":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV","download_json":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV.json","view_paper":"https://pith.science/paper/LFP24F5T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.07992&json=true","fetch_graph":"https://pith.science/api/pith-number/LFP24F5TUZS7UFFMB7ETMM3SVV/graph.json","fetch_events":"https://pith.science/api/pith-number/LFP24F5TUZS7UFFMB7ETMM3SVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV/action/storage_attestation","attest_author":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV/action/author_attestation","sign_citation":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV/action/citation_signature","submit_replication":"https://pith.science/pith/LFP24F5TUZS7UFFMB7ETMM3SVV/action/replication_record"}},"created_at":"2026-05-17T23:53:06.652484+00:00","updated_at":"2026-05-17T23:53:06.652484+00:00"}