{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:KBVZIGADGQKNDWW2HKQM4AY5OL","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":"a7882266ca8d6683d0faf9c36fed0b2ba39aa90c8bf0f03cdf2e67b0ba3dbaca","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2003-02-21T19:06:24Z","title_canon_sha256":"65d744a3e59fafbaf8c6ca94bdbb05174f061ec8bf9a2261e96cf64e9bfd1d59"},"schema_version":"1.0","source":{"id":"math/0302265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0302265","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0302265v2","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302265","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"KBVZIGADGQKN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KBVZIGADGQKNDWW2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KBVZIGAD","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:8b078d76bfb7d8aff22d1e95dbcbbec6b2134adcea67ddd8b6240b966c71f2e6","target":"graph","created_at":"2026-05-18T02:35:38Z","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":"Let M be a compact manifold with a Hamiltonian T action and moment map Phi. The restriction map in equivariant cohomology from M to a level set Phi^{-1}(p) is a surjection, and we denote the kernel by I_p. When T has isolated fixed points, we show that I_p distinguishes the chambers of the moment polytope for M. In particular, counting the number of distinct ideals I_p as p varies over different chambers is equivalent to counting the number of chambers.","authors_text":"Lisa C. Jeffrey, Rebecca F. Goldin, Tara S. Holm","cross_cats":[],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2003-02-21T19:06:24Z","title":"Distinguishing the Chambers of the Moment Polytope"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302265","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:bb85024b30d02247ec5bdf58019852842adb08237bc6fb5b9f19ccc55c7ae45d","target":"record","created_at":"2026-05-18T02:35:38Z","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":"a7882266ca8d6683d0faf9c36fed0b2ba39aa90c8bf0f03cdf2e67b0ba3dbaca","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2003-02-21T19:06:24Z","title_canon_sha256":"65d744a3e59fafbaf8c6ca94bdbb05174f061ec8bf9a2261e96cf64e9bfd1d59"},"schema_version":"1.0","source":{"id":"math/0302265","kind":"arxiv","version":2}},"canonical_sha256":"506b9418033414d1dada3aa0ce031d72f9c1e752486d5207712860e71aced9c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"506b9418033414d1dada3aa0ce031d72f9c1e752486d5207712860e71aced9c7","first_computed_at":"2026-05-18T02:35:38.585151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:38.585151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D5+nxgEzUFgq79xwlljQd7T9U0P2CBFlT17inwRN0aV4GUvlEgBS1jIzqjmKKUPITF9F7KnrL7NwYgA82iOmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:38.585707Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0302265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb85024b30d02247ec5bdf58019852842adb08237bc6fb5b9f19ccc55c7ae45d","sha256:8b078d76bfb7d8aff22d1e95dbcbbec6b2134adcea67ddd8b6240b966c71f2e6"],"state_sha256":"db8cfa3dfe02d2368f5e40fa767b922285304688c504ec0c9032bdc815e923e6"}