{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:E753GTHLCDD33E7GJPXPCJOMAT","short_pith_number":"pith:E753GTHL","schema_version":"1.0","canonical_sha256":"27fbb34ceb10c7bd93e64beef125cc04fb250a8c71b281fe64638fdf94cb3e74","source":{"kind":"arxiv","id":"1411.7234","version":1},"attestation_state":"computed","paper":{"title":"Injective Metrics on Cube Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Benjamin Miesch","submitted_at":"2014-11-26T14:15:39Z","abstract_excerpt":"For locally finite CAT(0) cube complexes it is known that they are injectively metrizable choosing the $l_\\infty$-norm on each cube. In this paper we show that cube complexes which are injective with respect to this metric are always CAT(0). Moreover we give a criterion for finite dimensional CAT(0) cube complexes with finite width to posses an injective metric. As a side result we prove a modification of Bridson's Theorem for cube complexes saying that finite dimensional cube complexes with $l_p$-norms on the cubes are geodesic."},"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":"1411.7234","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-26T14:15:39Z","cross_cats_sorted":[],"title_canon_sha256":"734e2a74a71367fb2f9ba383690b3431d1d78d643e946bfec0722a71c92bf8a9","abstract_canon_sha256":"3fe50493b1ab8c5900c26d805a5de6462d4f532575e259a52e0b2974d8a6a795"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:44.952355Z","signature_b64":"2x6uxfrHznHNE66TF+Mu7mWpR0QlIE+A8k+IfW/U255V3VGGasneyWmZqTowVI2JvLooPK+1Yz9Tf4gc5h3uAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27fbb34ceb10c7bd93e64beef125cc04fb250a8c71b281fe64638fdf94cb3e74","last_reissued_at":"2026-05-18T02:32:44.951873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:44.951873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Injective Metrics on Cube Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Benjamin Miesch","submitted_at":"2014-11-26T14:15:39Z","abstract_excerpt":"For locally finite CAT(0) cube complexes it is known that they are injectively metrizable choosing the $l_\\infty$-norm on each cube. In this paper we show that cube complexes which are injective with respect to this metric are always CAT(0). Moreover we give a criterion for finite dimensional CAT(0) cube complexes with finite width to posses an injective metric. As a side result we prove a modification of Bridson's Theorem for cube complexes saying that finite dimensional cube complexes with $l_p$-norms on the cubes are geodesic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7234","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.7234","created_at":"2026-05-18T02:32:44.951939+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7234v1","created_at":"2026-05-18T02:32:44.951939+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7234","created_at":"2026-05-18T02:32:44.951939+00:00"},{"alias_kind":"pith_short_12","alias_value":"E753GTHLCDD3","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"E753GTHLCDD33E7G","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"E753GTHL","created_at":"2026-05-18T12:28:25.294606+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/E753GTHLCDD33E7GJPXPCJOMAT","json":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT.json","graph_json":"https://pith.science/api/pith-number/E753GTHLCDD33E7GJPXPCJOMAT/graph.json","events_json":"https://pith.science/api/pith-number/E753GTHLCDD33E7GJPXPCJOMAT/events.json","paper":"https://pith.science/paper/E753GTHL"},"agent_actions":{"view_html":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT","download_json":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT.json","view_paper":"https://pith.science/paper/E753GTHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7234&json=true","fetch_graph":"https://pith.science/api/pith-number/E753GTHLCDD33E7GJPXPCJOMAT/graph.json","fetch_events":"https://pith.science/api/pith-number/E753GTHLCDD33E7GJPXPCJOMAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT/action/storage_attestation","attest_author":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT/action/author_attestation","sign_citation":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT/action/citation_signature","submit_replication":"https://pith.science/pith/E753GTHLCDD33E7GJPXPCJOMAT/action/replication_record"}},"created_at":"2026-05-18T02:32:44.951939+00:00","updated_at":"2026-05-18T02:32:44.951939+00:00"}