{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GJPGVHFWW3QRIDEN2ZB5IATVGV","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":"48e1b4d21a4b6bcd9c35f8baf4d265589d0eb07d495957b42c72c3c2efafc44f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-18T15:08:14Z","title_canon_sha256":"bf736385972243f7cafc58aabe7f0720442424e6f546a9e676be753bac03645a"},"schema_version":"1.0","source":{"id":"1510.05256","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05256","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05256v7","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05256","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"GJPGVHFWW3QR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GJPGVHFWW3QRIDEN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GJPGVHFW","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:9dc542e264314f7daa0ba03b24b5165da19de26040937b8c419e3d025b0d85fc","target":"graph","created_at":"2026-05-17T23:55:01Z","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 $U$ be a horospherical subgroup of a noncompact simple Lie group $H$ and let $A$ be a maximal split torus in the normalizer of $U$. We define the expanding cone $A_U^+$ in $A$ with respect to $U$ and show that it can be explicitly calculated. We prove several dynamical results for translations of $U$-slices by elements of $A_U^+$ on finite volume homogeneous space $G/\\Gamma$ where $G$ is a Lie group containing $H$. More precisely, we prove quantitative nonescape of mass and equidistribution of a $U$-slice. If $H$ is a normal subgroup of $G$ and the $H$ action on $G/\\Gamma$ has a spectral g","authors_text":"Ronggang Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-18T15:08:14Z","title":"Expanding cone and applications to homogeneous dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05256","kind":"arxiv","version":7},"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":"sha256:7f06198cb4a948cd9e25f2401a28fcf681a0f6037df871415ce336a7cf27b029","target":"record","created_at":"2026-05-17T23:55:01Z","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":"48e1b4d21a4b6bcd9c35f8baf4d265589d0eb07d495957b42c72c3c2efafc44f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-18T15:08:14Z","title_canon_sha256":"bf736385972243f7cafc58aabe7f0720442424e6f546a9e676be753bac03645a"},"schema_version":"1.0","source":{"id":"1510.05256","kind":"arxiv","version":7}},"canonical_sha256":"325e6a9cb6b6e1140c8dd643d40275357088d21799653c6a1f89f8e1612e1d09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"325e6a9cb6b6e1140c8dd643d40275357088d21799653c6a1f89f8e1612e1d09","first_computed_at":"2026-05-17T23:55:01.467905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:01.467905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6VvCiQQxT/5rr7gZMaNSXDDPfFHjG9Jjuq3tzxI8M9N0GBdiSfsT/r6UUmL+kitg8YxMjqGQo4IZYz/Ac0DpCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:01.468393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05256","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f06198cb4a948cd9e25f2401a28fcf681a0f6037df871415ce336a7cf27b029","sha256:9dc542e264314f7daa0ba03b24b5165da19de26040937b8c419e3d025b0d85fc"],"state_sha256":"88febb3b41f2d0b1f69d22bfbc59640a95fd425df217e9e691f7e2d3c42301cc"}