{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HRA6SVMRGUBW3OHKLUT3YCPUNK","short_pith_number":"pith:HRA6SVMR","schema_version":"1.0","canonical_sha256":"3c41e9559135036db8ea5d27bc09f46a966d77ad6f6a254c93cf465fc9903145","source":{"kind":"arxiv","id":"1808.03539","version":2},"attestation_state":"computed","paper":{"title":"Moduli of Weierstrass fibrations with marked section","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Inchiostro","submitted_at":"2018-08-10T13:47:01Z","abstract_excerpt":"We study the the moduli space of KSBA stable pairs $(X,sS+\\sum a_i F_i)$, consisting of a Weierstrass fibration $X$, its section $S$, and some fibers $F_i$. We find a compactification which is a DM stack, and we describe the objects on the boundary. We show that the fibration in the definition of Weierstrass fibration extends to the boundary, and it is equidimensional when $s \\ll 1$. We prove that there are wall-crossing morphisms when the weights $s$ and $a_i$ change. When $s=1$, this recovers the work of La Nave (arXiv:math/0205035); and a special case of the work of Ascher-Bejleri (arXiv:17"},"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":"1808.03539","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-10T13:47:01Z","cross_cats_sorted":[],"title_canon_sha256":"d0f1e2c5e30ddbef28305e58ac715d77439742ed36630dd82a74bc23f480c8b1","abstract_canon_sha256":"4efcb80bc23215cf1b01a34b6ad9c81c16f42605ed7c7d2e4bea83763aa9089a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:55.114234Z","signature_b64":"o1Mk9GwGNaWg1H2FIc+/lyEgtFhnFYMb/Nqq+Bx+epKz4QJzrguQ2hYgwXE2ev7zym0IlVchwFA072T+ofOvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c41e9559135036db8ea5d27bc09f46a966d77ad6f6a254c93cf465fc9903145","last_reissued_at":"2026-05-18T00:04:55.113719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:55.113719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli of Weierstrass fibrations with marked section","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Inchiostro","submitted_at":"2018-08-10T13:47:01Z","abstract_excerpt":"We study the the moduli space of KSBA stable pairs $(X,sS+\\sum a_i F_i)$, consisting of a Weierstrass fibration $X$, its section $S$, and some fibers $F_i$. We find a compactification which is a DM stack, and we describe the objects on the boundary. We show that the fibration in the definition of Weierstrass fibration extends to the boundary, and it is equidimensional when $s \\ll 1$. We prove that there are wall-crossing morphisms when the weights $s$ and $a_i$ change. When $s=1$, this recovers the work of La Nave (arXiv:math/0205035); and a special case of the work of Ascher-Bejleri (arXiv:17"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03539","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":"1808.03539","created_at":"2026-05-18T00:04:55.113806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.03539v2","created_at":"2026-05-18T00:04:55.113806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03539","created_at":"2026-05-18T00:04:55.113806+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRA6SVMRGUBW","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRA6SVMRGUBW3OHK","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRA6SVMR","created_at":"2026-05-18T12:32:28.185984+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/HRA6SVMRGUBW3OHKLUT3YCPUNK","json":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK.json","graph_json":"https://pith.science/api/pith-number/HRA6SVMRGUBW3OHKLUT3YCPUNK/graph.json","events_json":"https://pith.science/api/pith-number/HRA6SVMRGUBW3OHKLUT3YCPUNK/events.json","paper":"https://pith.science/paper/HRA6SVMR"},"agent_actions":{"view_html":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK","download_json":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK.json","view_paper":"https://pith.science/paper/HRA6SVMR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.03539&json=true","fetch_graph":"https://pith.science/api/pith-number/HRA6SVMRGUBW3OHKLUT3YCPUNK/graph.json","fetch_events":"https://pith.science/api/pith-number/HRA6SVMRGUBW3OHKLUT3YCPUNK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK/action/storage_attestation","attest_author":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK/action/author_attestation","sign_citation":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK/action/citation_signature","submit_replication":"https://pith.science/pith/HRA6SVMRGUBW3OHKLUT3YCPUNK/action/replication_record"}},"created_at":"2026-05-18T00:04:55.113806+00:00","updated_at":"2026-05-18T00:04:55.113806+00:00"}