{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OOS4EIQTR6NXAZU3OWJEOUBMPW","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":"d4855f29a8106163ccbe1ed784cc72bd3f42a0b59c1e5f5e0d24f4bfb80d58b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-07-24T21:16:34Z","title_canon_sha256":"6b3fc841982a9f12bf00940189be99d60c12dad69296b2533f94a33ccf592afe"},"schema_version":"1.0","source":{"id":"2607.22920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.22920","created_at":"2026-07-28T00:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"2607.22920v1","created_at":"2026-07-28T00:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22920","created_at":"2026-07-28T00:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"OOS4EIQTR6NX","created_at":"2026-07-28T00:22:02Z"},{"alias_kind":"pith_short_16","alias_value":"OOS4EIQTR6NXAZU3","created_at":"2026-07-28T00:22:02Z"},{"alias_kind":"pith_short_8","alias_value":"OOS4EIQT","created_at":"2026-07-28T00:22:02Z"}],"graph_snapshots":[{"event_id":"sha256:f471ef08c7d58728646bbb0a01a957a5cda90e52484cfdf4a8af6d374bc085a8","target":"graph","created_at":"2026-07-28T00:22:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.22920/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the behavior of currents on flag-manifolds under actions of Anosov subgroups of complex semisimple Lie groups G. Given a current T of bidimension (k, k) on the full flag-manifold F = G/B, we average it under the group action via a construction analogous to the construction of Patterson-Sullivan measures. We show that under certain genericity conditions (in the case of currents of integration over subvarieties), the limiting current is a Gibbs current, i.e. is given by integration (with respect to a Gibbs measure) over the flag-limit set of suitable multiples of currents of integration","authors_text":"Michael Kapovich, Mikhail Lyubich, Nguyen-Bac Dang, Shengyuan Zhao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-07-24T21:16:34Z","title":"Equidistribution of currents under Anosov group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22920","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:fd08a2605e8626f66b717a118c72f160f110fb1df0f55b19a5d9c948570ad2eb","target":"record","created_at":"2026-07-28T00:22:02Z","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":"d4855f29a8106163ccbe1ed784cc72bd3f42a0b59c1e5f5e0d24f4bfb80d58b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-07-24T21:16:34Z","title_canon_sha256":"6b3fc841982a9f12bf00940189be99d60c12dad69296b2533f94a33ccf592afe"},"schema_version":"1.0","source":{"id":"2607.22920","kind":"arxiv","version":1}},"canonical_sha256":"73a5c222138f9b70669b759247502c7d895f2d5b35aef318e3fdf3294c9b82ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a5c222138f9b70669b759247502c7d895f2d5b35aef318e3fdf3294c9b82ea","first_computed_at":"2026-07-28T00:22:02.185280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T00:22:02.185280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PC4XCFN2aUGUtd6ShcjD/R3DL/ZH1uMYpnjSrh03Clk5d621fe52oDcb2k2vx5amIRM1tMTNda6YoNwTbtNTBg==","signature_status":"signed_v1","signed_at":"2026-07-28T00:22:02.186213Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.22920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd08a2605e8626f66b717a118c72f160f110fb1df0f55b19a5d9c948570ad2eb","sha256:f471ef08c7d58728646bbb0a01a957a5cda90e52484cfdf4a8af6d374bc085a8"],"state_sha256":"e6b4fef480c0651c91ec3beb65020b300006f5794482278f4583969f29bcb656"}