{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TJ6CIM6JP3ORGYSBEZ2PXJTYKS","short_pith_number":"pith:TJ6CIM6J","schema_version":"1.0","canonical_sha256":"9a7c2433c97edd1362412674fba67854ae95deffdbc73b83d56ae70f337e74e0","source":{"kind":"arxiv","id":"2608.04520","version":1},"attestation_state":"computed","paper":{"title":"The geometry of triples of antipodal ideal chambers of affine buildings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.GR","authors_text":"Corentin Le Bars, Corina Ciobotaru","submitted_at":"2026-08-05T06:53:50Z","abstract_excerpt":"In this article, we investigate two notions of genericity for triples of antipodal ideal chambers in a locally finite affine building $X$: one defined at the ideal boundary $X^{\\infty}$, which we call ideal-genericity, and the other defined from within the affine building \\(X\\), which we call affine-genericity. While ideal-genericity implies affine-genericity, the latter is the more suitable notion for constructing a barycenter map associated with affine-generic triples of antipodal ideal chambers. This perspective also allows us to establish that this barycenter map is locally constant, and h"},"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":"2608.04520","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-08-05T06:53:50Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"75f2ac9367e055ace24eda1eb41d0b3d896e08fc77b36ec513a57fb799720423","abstract_canon_sha256":"a0d31dd27f8fe194c89f6d1357a3a19a488c7a3209298d0ce55fabdd411adcd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:35:46.360481Z","signature_b64":"s4gi/98GNpV9kzMJ7tve3O8MCBg7yzRL+yy1GJTwSllxkEtoc8ZRS6KY73pS5K2PUmm4RfMjsZL11v6mR01wCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a7c2433c97edd1362412674fba67854ae95deffdbc73b83d56ae70f337e74e0","last_reissued_at":"2026-08-06T01:35:46.358978Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:35:46.358978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The geometry of triples of antipodal ideal chambers of affine buildings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.GR","authors_text":"Corentin Le Bars, Corina Ciobotaru","submitted_at":"2026-08-05T06:53:50Z","abstract_excerpt":"In this article, we investigate two notions of genericity for triples of antipodal ideal chambers in a locally finite affine building $X$: one defined at the ideal boundary $X^{\\infty}$, which we call ideal-genericity, and the other defined from within the affine building \\(X\\), which we call affine-genericity. While ideal-genericity implies affine-genericity, the latter is the more suitable notion for constructing a barycenter map associated with affine-generic triples of antipodal ideal chambers. This perspective also allows us to establish that this barycenter map is locally constant, and h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04520","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/2608.04520/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":"2608.04520","created_at":"2026-08-06T01:35:46.360806+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04520v1","created_at":"2026-08-06T01:35:46.360806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04520","created_at":"2026-08-06T01:35:46.360806+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJ6CIM6JP3OR","created_at":"2026-08-06T01:35:46.360806+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJ6CIM6JP3ORGYSB","created_at":"2026-08-06T01:35:46.360806+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJ6CIM6J","created_at":"2026-08-06T01:35:46.360806+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS","json":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS.json","graph_json":"https://pith.science/api/pith-number/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/graph.json","events_json":"https://pith.science/api/pith-number/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/events.json","paper":"https://pith.science/paper/TJ6CIM6J"},"agent_actions":{"view_html":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS","download_json":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS.json","view_paper":"https://pith.science/paper/TJ6CIM6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04520&json=true","fetch_graph":"https://pith.science/api/pith-number/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/graph.json","fetch_events":"https://pith.science/api/pith-number/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/action/storage_attestation","attest_author":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/action/author_attestation","sign_citation":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/action/citation_signature","submit_replication":"https://pith.science/pith/TJ6CIM6JP3ORGYSBEZ2PXJTYKS/action/replication_record"}},"created_at":"2026-08-06T01:35:46.360806+00:00","updated_at":"2026-08-06T01:35:46.360806+00:00"}