{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RCDIUNX7LQ7TXEVVNZJHZ7SXNH","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":"272c6195078a2aea986ba559a079ad68484d8c5a55e6b276c7387e6cf1f73883","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-05T17:21:51Z","title_canon_sha256":"7b0d4bdc6d71e833b1df74eaa1c4ba41cfb24eb8467cc93e74868be11a88d274"},"schema_version":"1.0","source":{"id":"1610.01535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01535","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01535v1","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01535","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"RCDIUNX7LQ7T","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCDIUNX7LQ7TXEVV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCDIUNX7","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:fa3be27929754ac20aff7d61e55f312ea84baadb8f3ede59adb94c4345a26d29","target":"graph","created_at":"2026-05-18T01:03:06Z","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 $G= \\exp(\\g)$ be a connected, simply connected nilpotent Lie group. We show that for every $G$-invariant smooth sub-manifold $M$ of $g^*$, there exists an open relatively compact subset $\\mathcal{M}$ of $M$ such that for any smooth adapted field of operators $(F(l))_{l\\in M}$ supported in $G\\cdot \\mathcal{M}$ there exists a Schwartz function $f$ on $G$ such that $\\pi_l(f)= \\op_{F(l)}$ for all $l\\in M$. This retract theorem can then be used to show that for every Lie group $\\G$ of automorphisms of $G$ containing the inner automorphisms of $G$ with locally closed $\\G$-orbits in $\\g^*$, the p","authors_text":"Carine Molitor-Braun, Jean Ludwig, Ying-Fen Lin","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-05T17:21:51Z","title":"A retract theorem for nilpotent Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01535","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":"sha256:3ce0867ba0de29f90afcdf20f5ff78dfddbbae9164f02d5c60d4621f00882b71","target":"record","created_at":"2026-05-18T01:03:06Z","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":"272c6195078a2aea986ba559a079ad68484d8c5a55e6b276c7387e6cf1f73883","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-05T17:21:51Z","title_canon_sha256":"7b0d4bdc6d71e833b1df74eaa1c4ba41cfb24eb8467cc93e74868be11a88d274"},"schema_version":"1.0","source":{"id":"1610.01535","kind":"arxiv","version":1}},"canonical_sha256":"88868a36ff5c3f3b92b56e527cfe5769f633c7bde8869852ee36d515eb612288","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88868a36ff5c3f3b92b56e527cfe5769f633c7bde8869852ee36d515eb612288","first_computed_at":"2026-05-18T01:03:06.937073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:06.937073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49Sx6JpokS5IV5+dWyKdCCmoxBOOl+YFx4i7uzKGqRStHybWh/67D/GCfxxtzbeU5O281v9CuSCG1w5w4NU4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:06.937651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ce0867ba0de29f90afcdf20f5ff78dfddbbae9164f02d5c60d4621f00882b71","sha256:fa3be27929754ac20aff7d61e55f312ea84baadb8f3ede59adb94c4345a26d29"],"state_sha256":"6e3b44a62308ef813ffd8bb8b4a7acf748971b963495ddb1590fb8e571d99392"}