{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W5AIM6DT2VJIRDNM7ZC7DBRWBP","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":"d1aa0aea43f5c354fbbcf8654bc2c41305d5624a3d8fe090a541c6fd7e13e9c2","cross_cats_sorted":["math-ph","math.AC","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-20T04:15:30Z","title_canon_sha256":"f8bf1e453c46f273cbadc800bdaeb0c34c48ee9fad452f13fc1a988e1f4f3e6e"},"schema_version":"1.0","source":{"id":"1504.04933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04933","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04933v1","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04933","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"W5AIM6DT2VJI","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W5AIM6DT2VJIRDNM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W5AIM6DT","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:5a418858d6a580857fde655f1911dfea3699d7552e598e35592f113bb143563a","target":"graph","created_at":"2026-05-18T01:18:57Z","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 study the symplectic reduction of the phase space describing $k$ particles in $\\mathbb{R}^n$ with total angular momentum zero. This corresponds to the singular symplectic quotient associated to the diagonal action of $\\operatorname{O}_n$ on $k$ copies of $\\mathbb{C}^n$ at the zero value of the homogeneous quadratic moment map. We give a description of the ideal of relations of the ring of regular functions of the symplectic quotient. Using this description, we demonstrate $\\mathbb{Z}^+$-graded regular symplectomorphisms among the $\\operatorname{O}_n$- and $\\operatorname{SO}_n$-symplectic qu","authors_text":"Christopher Seaton, Hans-Christian Herbig, Joshua Cape","cross_cats":["math-ph","math.AC","math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-20T04:15:30Z","title":"Symplectic reduction at zero angular momentum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04933","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":"sha256:4f5d233d12c6ae653a9b329571b680720a7e2ff1294691b8f71aeeae504ecd70","target":"record","created_at":"2026-05-18T01:18:57Z","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":"d1aa0aea43f5c354fbbcf8654bc2c41305d5624a3d8fe090a541c6fd7e13e9c2","cross_cats_sorted":["math-ph","math.AC","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-20T04:15:30Z","title_canon_sha256":"f8bf1e453c46f273cbadc800bdaeb0c34c48ee9fad452f13fc1a988e1f4f3e6e"},"schema_version":"1.0","source":{"id":"1504.04933","kind":"arxiv","version":1}},"canonical_sha256":"b740867873d552888dacfe45f186360bfb34392bc76d3e776700a964fee42da3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b740867873d552888dacfe45f186360bfb34392bc76d3e776700a964fee42da3","first_computed_at":"2026-05-18T01:18:57.488297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:57.488297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZl70S70ahHxvIs7CMdBETS17Ei6ZplWfxRkAv6bWLS1fbhKPcYK4KU7nj8kfP6eys9MawzTLldAwKmC3INNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:57.488762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f5d233d12c6ae653a9b329571b680720a7e2ff1294691b8f71aeeae504ecd70","sha256:5a418858d6a580857fde655f1911dfea3699d7552e598e35592f113bb143563a"],"state_sha256":"a42382a722f1077f1e0ea72af355ff08a365b82f36a48de667f54e68bdeebb05"}