{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:D6W6Z7ZG6RRGQ5SCALB4DPKCND","short_pith_number":"pith:D6W6Z7ZG","schema_version":"1.0","canonical_sha256":"1fadecff26f46268764202c3c1bd4268eaf757c130ce1d72dee5ac03d54c16b3","source":{"kind":"arxiv","id":"1009.3089","version":4},"attestation_state":"computed","paper":{"title":"On the local structure and the homology of CAT$(\\kappa)$ spaces and euclidean buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Linus Kramer","submitted_at":"2010-09-16T05:13:40Z","abstract_excerpt":"We prove that every open subset of a euclidean building is a finite dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional simplicial complex. We also include a proof for the rigidity of homeomorphisms of euclidean buildings. A key step in our approach to this result is the following: the space of directions $\\Sigma_oX$ of a CAT$(\\kappa)$ space $X$ is homotopy quivalent to a small punctured disk $B_\\eps(X,o)\\setminus o$. The second ingredient is the local homology sheaf of $X$. Along the way, we prove some results abo"},"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":"1009.3089","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-16T05:13:40Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ad2f69f7aa83065a088fc574ec2ab3a8d2ea108bf85b9e48504f8a84098864d0","abstract_canon_sha256":"654d6bee3a6ea70dd5f6db32b09ba477e9fc7ba701c93ebbca82d11ef54dc53d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:58.026689Z","signature_b64":"0ttmDRpzfcZlF1s1l3j7RCQNvbMl3dVZPomxbOgZdu6RplFZPnFbDr2+E3W4Fzi6yx5j4U37gCvKvCFsOEP/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fadecff26f46268764202c3c1bd4268eaf757c130ce1d72dee5ac03d54c16b3","last_reissued_at":"2026-05-18T04:38:58.026274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:58.026274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the local structure and the homology of CAT$(\\kappa)$ spaces and euclidean buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Linus Kramer","submitted_at":"2010-09-16T05:13:40Z","abstract_excerpt":"We prove that every open subset of a euclidean building is a finite dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional simplicial complex. We also include a proof for the rigidity of homeomorphisms of euclidean buildings. A key step in our approach to this result is the following: the space of directions $\\Sigma_oX$ of a CAT$(\\kappa)$ space $X$ is homotopy quivalent to a small punctured disk $B_\\eps(X,o)\\setminus o$. The second ingredient is the local homology sheaf of $X$. Along the way, we prove some results abo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3089","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.3089","created_at":"2026-05-18T04:38:58.026342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3089v4","created_at":"2026-05-18T04:38:58.026342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3089","created_at":"2026-05-18T04:38:58.026342+00:00"},{"alias_kind":"pith_short_12","alias_value":"D6W6Z7ZG6RRG","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"D6W6Z7ZG6RRGQ5SC","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"D6W6Z7ZG","created_at":"2026-05-18T12:26:06.534383+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/D6W6Z7ZG6RRGQ5SCALB4DPKCND","json":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND.json","graph_json":"https://pith.science/api/pith-number/D6W6Z7ZG6RRGQ5SCALB4DPKCND/graph.json","events_json":"https://pith.science/api/pith-number/D6W6Z7ZG6RRGQ5SCALB4DPKCND/events.json","paper":"https://pith.science/paper/D6W6Z7ZG"},"agent_actions":{"view_html":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND","download_json":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND.json","view_paper":"https://pith.science/paper/D6W6Z7ZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3089&json=true","fetch_graph":"https://pith.science/api/pith-number/D6W6Z7ZG6RRGQ5SCALB4DPKCND/graph.json","fetch_events":"https://pith.science/api/pith-number/D6W6Z7ZG6RRGQ5SCALB4DPKCND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND/action/storage_attestation","attest_author":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND/action/author_attestation","sign_citation":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND/action/citation_signature","submit_replication":"https://pith.science/pith/D6W6Z7ZG6RRGQ5SCALB4DPKCND/action/replication_record"}},"created_at":"2026-05-18T04:38:58.026342+00:00","updated_at":"2026-05-18T04:38:58.026342+00:00"}