{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:W7JTVQ57UTDB6EN5KPDLWMXXYD","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":"b241d8a36ed0fe6f2bbe5590cf03929ae12e3adbe920ffe27ed338b855b12a99","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-15T14:08:16Z","title_canon_sha256":"1497d89f28ed22644fa91a1360c4825d4b9d289fc590ba9ef78979a54d296e77"},"schema_version":"1.0","source":{"id":"0909.2808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2808","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2808v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2808","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"W7JTVQ57UTDB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"W7JTVQ57UTDB6EN5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"W7JTVQ57","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:38cddaeaa7dbabf4a26e499eb9e7bb4ac55519917ebb98e56c8433ab55cf0ec0","target":"graph","created_at":"2026-05-18T01:10:11Z","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":"In this paper, we generalise results obtained earlier by John Cremona and the author on the reduction theory of binary forms, which describe positive zero-cycles in P^1, to positive zero-cycles (or point clusters) in projective spaces of arbitrary dimension. This should have applications to more general projective varieties in P^n, by associating a suitable positive zero-cycle to them in an PGL(n+1)-invariant way. We discuss this in the case of (smooth) plane curves.","authors_text":"Michael Stoll","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-15T14:08:16Z","title":"Reduction theory of point clusters in projective space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2808","kind":"arxiv","version":1},"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":"sha256:65f60bb6078e42351e825408b49bf7a1a3053814b76cb73e674fdc31be12d1a4","target":"record","created_at":"2026-05-18T01:10:11Z","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":"b241d8a36ed0fe6f2bbe5590cf03929ae12e3adbe920ffe27ed338b855b12a99","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-15T14:08:16Z","title_canon_sha256":"1497d89f28ed22644fa91a1360c4825d4b9d289fc590ba9ef78979a54d296e77"},"schema_version":"1.0","source":{"id":"0909.2808","kind":"arxiv","version":1}},"canonical_sha256":"b7d33ac3bfa4c61f11bd53c6bb32f7c0d046f54d30979e194e02d22e01a4b70c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7d33ac3bfa4c61f11bd53c6bb32f7c0d046f54d30979e194e02d22e01a4b70c","first_computed_at":"2026-05-18T01:10:11.361171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:11.361171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WuC9SwmcaXEB/JIU5649EFi92IVLOCoXznEj2ET/kmfyu9/VrW+EuPZrH+9mAOk9CcUrj+S77LeIPNQzArpyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:11.361576Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65f60bb6078e42351e825408b49bf7a1a3053814b76cb73e674fdc31be12d1a4","sha256:38cddaeaa7dbabf4a26e499eb9e7bb4ac55519917ebb98e56c8433ab55cf0ec0"],"state_sha256":"833ea76667b6dd0c86510f6cbb1974350c3ef218a3340743b898b5574ada6fe1"}