{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:RW7YGH2RNIMFOTQPDQTVSYHQHB","short_pith_number":"pith:RW7YGH2R","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"},"canonical_sha256":"8dbf831f516a18574e0f1c275960f0384b8b9194805401e05331bab22bfa83dd","source":{"kind":"arxiv","id":"0812.0778","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0778","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0778v2","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0778","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"pith_short_12","alias_value":"RW7YGH2RNIMF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RW7YGH2RNIMFOTQP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RW7YGH2R","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:RW7YGH2RNIMFOTQPDQTVSYHQHB","target":"record","payload":{"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"},"canonical_sha256":"8dbf831f516a18574e0f1c275960f0384b8b9194805401e05331bab22bfa83dd","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"},"source_kind":"arxiv","source_id":"0812.0778","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCK6ain3ClzRCCPmS008o7Bj6fXfF+Z+zDXwNyly0ogtl3KPJxcyWnsZ/O9wMjrDGLWy2miNQk3ouRlL08XXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:26:17.146566Z"},"content_sha256":"0f4964f5b9a534941e0ca307f1f5ffc24c97755764fb40901d6dbc3779cd250b","schema_version":"1.0","event_id":"sha256:0f4964f5b9a534941e0ca307f1f5ffc24c97755764fb40901d6dbc3779cd250b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:RW7YGH2RNIMFOTQPDQTVSYHQHB","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gboSjlHy+RsrVDUhC6JZ4QxOhy6GDYszlHPVRZcCBIeZ2rjsJYTs7+1DG5XBiqEQqxokddoZy4Naa9olkEZ/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:26:17.147298Z"},"content_sha256":"b3e1a22217ecb2d880c3beaa16a871a53384d561c4919244f81573112109c406","schema_version":"1.0","event_id":"sha256:b3e1a22217ecb2d880c3beaa16a871a53384d561c4919244f81573112109c406"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/bundle.json","state_url":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T07:26:17Z","links":{"resolver":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB","bundle":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/bundle.json","state":"https://pith.science/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RW7YGH2RNIMFOTQPDQTVSYHQHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RW7YGH2RNIMFOTQPDQTVSYHQHB","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":"36bf21b2901bdf4331142439e5d1ae7fe5a72a7d104b98f0edcc275c8463c68c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T18:53:16Z","title_canon_sha256":"fe2d50a0f442e3cef32713360a486fa06b98609c2d29e796adac938a14bd5cb1"},"schema_version":"1.0","source":{"id":"0812.0778","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0778","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0778v2","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0778","created_at":"2026-05-18T04:30:37Z"},{"alias_kind":"pith_short_12","alias_value":"RW7YGH2RNIMF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RW7YGH2RNIMFOTQP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RW7YGH2R","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:b3e1a22217ecb2d880c3beaa16a871a53384d561c4919244f81573112109c406","target":"graph","created_at":"2026-05-18T04:30:37Z","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"},"paper":{"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","authors_text":"David Swinarski, Valery Alexeev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T18:53:16Z","title":"Nef divisors on $\\bar{M}_{0,n}$ from GIT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0778","kind":"arxiv","version":2},"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":"sha256:0f4964f5b9a534941e0ca307f1f5ffc24c97755764fb40901d6dbc3779cd250b","target":"record","created_at":"2026-05-18T04:30:37Z","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":"36bf21b2901bdf4331142439e5d1ae7fe5a72a7d104b98f0edcc275c8463c68c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T18:53:16Z","title_canon_sha256":"fe2d50a0f442e3cef32713360a486fa06b98609c2d29e796adac938a14bd5cb1"},"schema_version":"1.0","source":{"id":"0812.0778","kind":"arxiv","version":2}},"canonical_sha256":"8dbf831f516a18574e0f1c275960f0384b8b9194805401e05331bab22bfa83dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dbf831f516a18574e0f1c275960f0384b8b9194805401e05331bab22bfa83dd","first_computed_at":"2026-05-18T04:30:37.099346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:37.099346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O69w874+nK38SkCbKTs0S+7GK1g+DFhUk83u5xPH8eobAMeB49Lmcjzrw9xvM/vU8h/IB4XDFfNXXbwDGxHTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:37.100669Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0778","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f4964f5b9a534941e0ca307f1f5ffc24c97755764fb40901d6dbc3779cd250b","sha256:b3e1a22217ecb2d880c3beaa16a871a53384d561c4919244f81573112109c406"],"state_sha256":"e33820fd369e381a5d2151161769f176ce8d3da8a60e4b16fd929e51642ea187"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNZ4m5ICdd5N2dpRa2VX8IpuBopiCyEqf3Xy8YEx7kpQy3EQRNH+3+Sv0It/iMVC21BsN8arU+H51o/2RSY4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:26:17.151250Z","bundle_sha256":"274b83b29378f55839b0301145903b3bb284e087cf2f37fd7bcc269c2d9e743e"}}