{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:RW7YGH2RNIMFOTQPDQTVSYHQHB","short_pith_number":"pith:RW7YGH2R","schema_version":"1.0","canonical_sha256":"8dbf831f516a18574e0f1c275960f0384b8b9194805401e05331bab22bfa83dd","source":{"kind":"arxiv","id":"0812.0778","version":2},"attestation_state":"computed","paper":{"title":"Nef divisors on $\\bar{M}_{0,n}$ from GIT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Swinarski, Valery Alexeev","submitted_at":"2008-12-03T18:53:16Z","abstract_excerpt":"We introduce and study the GIT CONE of $\\bar{M}_{0,n}$, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients $(\\mathbb P^1)^n//SL(2)$. We give an explicit formula for these line bundles and prove a number of basic results about the GIT cone.\n  As one application, we prove unconditionally that the log canonical models of $\\bar{M}_{0,n}$ with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson arXiv:0709.4037. (Cf. also a different proof by Fedorchuk and Smyt"},"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":"0812.0778","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T18:53:16Z","cross_cats_sorted":[],"title_canon_sha256":"fe2d50a0f442e3cef32713360a486fa06b98609c2d29e796adac938a14bd5cb1","abstract_canon_sha256":"36bf21b2901bdf4331142439e5d1ae7fe5a72a7d104b98f0edcc275c8463c68c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:37.100669Z","signature_b64":"O69w874+nK38SkCbKTs0S+7GK1g+DFhUk83u5xPH8eobAMeB49Lmcjzrw9xvM/vU8h/IB4XDFfNXXbwDGxHTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dbf831f516a18574e0f1c275960f0384b8b9194805401e05331bab22bfa83dd","last_reissued_at":"2026-05-18T04:30:37.099346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:37.099346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nef divisors on $\\bar{M}_{0,n}$ from GIT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Swinarski, Valery Alexeev","submitted_at":"2008-12-03T18:53:16Z","abstract_excerpt":"We introduce and study the GIT CONE of $\\bar{M}_{0,n}$, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients $(\\mathbb P^1)^n//SL(2)$. We give an explicit formula for these line bundles and prove a number of basic results about the GIT cone.\n  As one application, we prove unconditionally that the log canonical models of $\\bar{M}_{0,n}$ with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson arXiv:0709.4037. (Cf. also a different proof by Fedorchuk and Smyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0778","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":"0812.0778","created_at":"2026-05-18T04:30:37.099500+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.0778v2","created_at":"2026-05-18T04:30:37.099500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0778","created_at":"2026-05-18T04:30:37.099500+00:00"},{"alias_kind":"pith_short_12","alias_value":"RW7YGH2RNIMF","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"RW7YGH2RNIMFOTQP","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"RW7YGH2R","created_at":"2026-05-18T12:25:58.018023+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/RW7YGH2RNIMFOTQPDQTVSYHQHB","json":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB.json","graph_json":"https://pith.science/api/pith-number/RW7YGH2RNIMFOTQPDQTVSYHQHB/graph.json","events_json":"https://pith.science/api/pith-number/RW7YGH2RNIMFOTQPDQTVSYHQHB/events.json","paper":"https://pith.science/paper/RW7YGH2R"},"agent_actions":{"view_html":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB","download_json":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB.json","view_paper":"https://pith.science/paper/RW7YGH2R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.0778&json=true","fetch_graph":"https://pith.science/api/pith-number/RW7YGH2RNIMFOTQPDQTVSYHQHB/graph.json","fetch_events":"https://pith.science/api/pith-number/RW7YGH2RNIMFOTQPDQTVSYHQHB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/action/storage_attestation","attest_author":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/action/author_attestation","sign_citation":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/action/citation_signature","submit_replication":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/action/replication_record"}},"created_at":"2026-05-18T04:30:37.099500+00:00","updated_at":"2026-05-18T04:30:37.099500+00:00"}