{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GZTUMW36I6HF2QXIOVQ64INPJX","short_pith_number":"pith:GZTUMW36","canonical_record":{"source":{"id":"1810.11496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-26T18:43:01Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"26f9acd9408094f3c15482ba4f8072a381377940aa7b7be7a3b5690567ba3ae7","abstract_canon_sha256":"7a64d12a14fed9a168d49e5a34167c8ea1e97a0d14c9f5d30c50bb872daa0971"},"schema_version":"1.0"},"canonical_sha256":"3667465b7e478e5d42e87561ee21af4dc8ecdd58d532c013930acb565c66c08c","source":{"kind":"arxiv","id":"1810.11496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11496","created_at":"2026-05-18T00:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11496v1","created_at":"2026-05-18T00:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11496","created_at":"2026-05-18T00:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"GZTUMW36I6HF","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZTUMW36I6HF2QXI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZTUMW36","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GZTUMW36I6HF2QXIOVQ64INPJX","target":"record","payload":{"canonical_record":{"source":{"id":"1810.11496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-26T18:43:01Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"26f9acd9408094f3c15482ba4f8072a381377940aa7b7be7a3b5690567ba3ae7","abstract_canon_sha256":"7a64d12a14fed9a168d49e5a34167c8ea1e97a0d14c9f5d30c50bb872daa0971"},"schema_version":"1.0"},"canonical_sha256":"3667465b7e478e5d42e87561ee21af4dc8ecdd58d532c013930acb565c66c08c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:08.530028Z","signature_b64":"JNJ/hGSJ2m/ZyhHQ0P7DYoCMIKCBMWsT5kfZFPCjsErx7Uk2yXohglUIrudLAJ1qJDO+Xn2lYsWKdVt4cdgLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3667465b7e478e5d42e87561ee21af4dc8ecdd58d532c013930acb565c66c08c","last_reissued_at":"2026-05-18T00:02:08.529452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:08.529452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.11496","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WbQEzDMriruQAW0H10ke9cmQslXC6cAxgk1aV8Uq2SXzifQv8jM20hyhfTqQF2u614EzhgHfielw38yFEhRcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:00:11.591687Z"},"content_sha256":"d0b42b89ddbbe8f6e331b518448e5390de6812debb40fc41e8a998c1a9aefcb2","schema_version":"1.0","event_id":"sha256:d0b42b89ddbbe8f6e331b518448e5390de6812debb40fc41e8a998c1a9aefcb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GZTUMW36I6HF2QXIOVQ64INPJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Balanced ideals and domains of discontinuity of Anosov representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Florian Stecker","submitted_at":"2018-10-26T18:43:01Z","abstract_excerpt":"We consider the action of Anosov subgroups of a semi-simple Lie group on the associated flag manifolds. A systematic approach to construct cocompact domains of discontinuity for this action was given by Kapovich, Leeb and Porti in arXiv:1306.3837. For $\\Delta$-Anosov representations, we prove that every cocompact domain of discontinuity arises from this construction, up to a few exceptions in low rank. Then we compute which flag manifolds admit these domains and, in some cases, the number of domains. We also find a new compactification for locally symmetric spaces arising from maximal represen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11496","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9w1Weql5DlpON1IjO2JSsm22uwc8dHXrH0lBg9I0qvbyjTq+1cSNo+8/+spYA0smBd2idLB7JT6QUQxov/EmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:00:11.592159Z"},"content_sha256":"2aa2d214af1ade0c39853a9b6325b8bbc0c28014ec9354b294cbb1639a57d2c1","schema_version":"1.0","event_id":"sha256:2aa2d214af1ade0c39853a9b6325b8bbc0c28014ec9354b294cbb1639a57d2c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZTUMW36I6HF2QXIOVQ64INPJX/bundle.json","state_url":"https://pith.science/pith/GZTUMW36I6HF2QXIOVQ64INPJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZTUMW36I6HF2QXIOVQ64INPJX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T19:00:11Z","links":{"resolver":"https://pith.science/pith/GZTUMW36I6HF2QXIOVQ64INPJX","bundle":"https://pith.science/pith/GZTUMW36I6HF2QXIOVQ64INPJX/bundle.json","state":"https://pith.science/pith/GZTUMW36I6HF2QXIOVQ64INPJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZTUMW36I6HF2QXIOVQ64INPJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GZTUMW36I6HF2QXIOVQ64INPJX","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":"7a64d12a14fed9a168d49e5a34167c8ea1e97a0d14c9f5d30c50bb872daa0971","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-26T18:43:01Z","title_canon_sha256":"26f9acd9408094f3c15482ba4f8072a381377940aa7b7be7a3b5690567ba3ae7"},"schema_version":"1.0","source":{"id":"1810.11496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11496","created_at":"2026-05-18T00:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11496v1","created_at":"2026-05-18T00:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11496","created_at":"2026-05-18T00:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"GZTUMW36I6HF","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZTUMW36I6HF2QXI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZTUMW36","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:2aa2d214af1ade0c39853a9b6325b8bbc0c28014ec9354b294cbb1639a57d2c1","target":"graph","created_at":"2026-05-18T00:02:08Z","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 consider the action of Anosov subgroups of a semi-simple Lie group on the associated flag manifolds. A systematic approach to construct cocompact domains of discontinuity for this action was given by Kapovich, Leeb and Porti in arXiv:1306.3837. For $\\Delta$-Anosov representations, we prove that every cocompact domain of discontinuity arises from this construction, up to a few exceptions in low rank. Then we compute which flag manifolds admit these domains and, in some cases, the number of domains. We also find a new compactification for locally symmetric spaces arising from maximal represen","authors_text":"Florian Stecker","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-26T18:43:01Z","title":"Balanced ideals and domains of discontinuity of Anosov representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11496","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:d0b42b89ddbbe8f6e331b518448e5390de6812debb40fc41e8a998c1a9aefcb2","target":"record","created_at":"2026-05-18T00:02:08Z","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":"7a64d12a14fed9a168d49e5a34167c8ea1e97a0d14c9f5d30c50bb872daa0971","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-26T18:43:01Z","title_canon_sha256":"26f9acd9408094f3c15482ba4f8072a381377940aa7b7be7a3b5690567ba3ae7"},"schema_version":"1.0","source":{"id":"1810.11496","kind":"arxiv","version":1}},"canonical_sha256":"3667465b7e478e5d42e87561ee21af4dc8ecdd58d532c013930acb565c66c08c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3667465b7e478e5d42e87561ee21af4dc8ecdd58d532c013930acb565c66c08c","first_computed_at":"2026-05-18T00:02:08.529452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:08.529452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JNJ/hGSJ2m/ZyhHQ0P7DYoCMIKCBMWsT5kfZFPCjsErx7Uk2yXohglUIrudLAJ1qJDO+Xn2lYsWKdVt4cdgLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:08.530028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.11496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b42b89ddbbe8f6e331b518448e5390de6812debb40fc41e8a998c1a9aefcb2","sha256:2aa2d214af1ade0c39853a9b6325b8bbc0c28014ec9354b294cbb1639a57d2c1"],"state_sha256":"fa67124f4fa4661ba9e7c47a72b166d94d4173f391c631e378cffa374292ad1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKtdvJ/Mgc6nbd/UMvxcPFuHfgsYA9lD/8Q8Kf+ku3yJ/0v/lNrVPAn6SSS7RgYAYavCX5UfMIq24K1W4HKsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:00:11.594666Z","bundle_sha256":"96ff5bdc29b599d2b5561752cf8ea558be0e31f3ab1b6a17c8ae0ab411299628"}}