{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:5VSXN27OWVIGWGVUBDGNTRNVPM","short_pith_number":"pith:5VSXN27O","schema_version":"1.0","canonical_sha256":"ed6576ebeeb5506b1ab408ccd9c5b57b29b63dcfdc91e6b298519a35d146fce7","source":{"kind":"arxiv","id":"2405.14658","version":1},"attestation_state":"computed","paper":{"title":"Proper affine deformations of positive representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Jean-Philippe Burelle, Ne\\v{z}a \\v{Z}ager Korenjak","submitted_at":"2024-05-23T14:56:48Z","abstract_excerpt":"We define for every positive Anosov representation of a nonabelian free group into $\\mathrm{SO}(2n,2n-1)$ a family of $\\mathbb{R}^{4n-1}$-valued cocycles which induce proper affine actions on $\\mathbb{R}^{4n-1}$. We construct fundamental domains in $\\mathbb{R}^{4n-1}$ bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2405.14658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-23T14:56:48Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"956b889338b0cb86f74e1b4b76bbb207f47155ddd139ab79e12d3ae64f02a106","abstract_canon_sha256":"b6b4bf125a6a181364edc00d8be3063a264adba875d420a6300210c19e174bcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:26.302026Z","signature_b64":"sW94p7nW+1TbRAu9bsEIafbRpExnQuArymd4Q0SJG3LkE5ELdVZ1XwtFVlp6T7mHJyI88XRAoPUVHIHNCFeZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed6576ebeeb5506b1ab408ccd9c5b57b29b63dcfdc91e6b298519a35d146fce7","last_reissued_at":"2026-07-05T08:22:26.301601Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:26.301601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proper affine deformations of positive representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Jean-Philippe Burelle, Ne\\v{z}a \\v{Z}ager Korenjak","submitted_at":"2024-05-23T14:56:48Z","abstract_excerpt":"We define for every positive Anosov representation of a nonabelian free group into $\\mathrm{SO}(2n,2n-1)$ a family of $\\mathbb{R}^{4n-1}$-valued cocycles which induce proper affine actions on $\\mathbb{R}^{4n-1}$. We construct fundamental domains in $\\mathbb{R}^{4n-1}$ bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14658","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.14658/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2405.14658","created_at":"2026-07-05T08:22:26.301664+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.14658v1","created_at":"2026-07-05T08:22:26.301664+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14658","created_at":"2026-07-05T08:22:26.301664+00:00"},{"alias_kind":"pith_short_12","alias_value":"5VSXN27OWVIG","created_at":"2026-07-05T08:22:26.301664+00:00"},{"alias_kind":"pith_short_16","alias_value":"5VSXN27OWVIGWGVU","created_at":"2026-07-05T08:22:26.301664+00:00"},{"alias_kind":"pith_short_8","alias_value":"5VSXN27O","created_at":"2026-07-05T08:22:26.301664+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.17422","citing_title":"Affine Anosov representations","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM","json":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM.json","graph_json":"https://pith.science/api/pith-number/5VSXN27OWVIGWGVUBDGNTRNVPM/graph.json","events_json":"https://pith.science/api/pith-number/5VSXN27OWVIGWGVUBDGNTRNVPM/events.json","paper":"https://pith.science/paper/5VSXN27O"},"agent_actions":{"view_html":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM","download_json":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM.json","view_paper":"https://pith.science/paper/5VSXN27O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.14658&json=true","fetch_graph":"https://pith.science/api/pith-number/5VSXN27OWVIGWGVUBDGNTRNVPM/graph.json","fetch_events":"https://pith.science/api/pith-number/5VSXN27OWVIGWGVUBDGNTRNVPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM/action/storage_attestation","attest_author":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM/action/author_attestation","sign_citation":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM/action/citation_signature","submit_replication":"https://pith.science/pith/5VSXN27OWVIGWGVUBDGNTRNVPM/action/replication_record"}},"created_at":"2026-07-05T08:22:26.301664+00:00","updated_at":"2026-07-05T08:22:26.301664+00:00"}