{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NUAGZOOYNJQ3XFMSMRREIVBGZG","short_pith_number":"pith:NUAGZOOY","canonical_record":{"source":{"id":"1411.0178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-01T22:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"62aee3313e96fdb4c503a1344a8b413e33a684317f213b4537a29741135215ea","abstract_canon_sha256":"d4c63e4c16124598a91f59a1b522889cddd13f909e2a930dca32788fa1c70448"},"schema_version":"1.0"},"canonical_sha256":"6d006cb9d86a61bb95926462445426c9897f9969f36868adc38e3e81884ebb59","source":{"kind":"arxiv","id":"1411.0178","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0178","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0178v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0178","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"NUAGZOOYNJQ3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NUAGZOOYNJQ3XFMS","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NUAGZOOY","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NUAGZOOYNJQ3XFMSMRREIVBGZG","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-01T22:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"62aee3313e96fdb4c503a1344a8b413e33a684317f213b4537a29741135215ea","abstract_canon_sha256":"d4c63e4c16124598a91f59a1b522889cddd13f909e2a930dca32788fa1c70448"},"schema_version":"1.0"},"canonical_sha256":"6d006cb9d86a61bb95926462445426c9897f9969f36868adc38e3e81884ebb59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.359088Z","signature_b64":"EAe/nI6y7jpp5GeXerwrGlFZa9l1qK11RdWwy3xOEWy2OOxEbhKHwv6iGbrP2unrVdNYrhrIPcDpASZwaAvtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d006cb9d86a61bb95926462445426c9897f9969f36868adc38e3e81884ebb59","last_reissued_at":"2026-05-18T02:38:52.358531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.358531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0178","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":"2026-05-18T02:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5wUuiZ7dsSF9vRrlUHqzh2TZJdF8YSZ+etzh8DjLV4gvmdE9v/+ZoyGf6BpvSz7XrjByVQ1AjSuXaHuAgJRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:56:54.608670Z"},"content_sha256":"ac4e9d51327f130eee2840669f8cf38342ebb23b97b79b110aa499e290a2a302","schema_version":"1.0","event_id":"sha256:ac4e9d51327f130eee2840669f8cf38342ebb23b97b79b110aa499e290a2a302"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NUAGZOOYNJQ3XFMSMRREIVBGZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On regular CAT(0) cube complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Nir Lazarovich","submitted_at":"2014-11-01T22:44:49Z","abstract_excerpt":"We provide a necessary and sufficient condition on a finite flag simplicial complex, L, for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to L. We then find new examples of such CAT(0) cube complexes and prove that their automorphism groups are virtually simple. The latter uses a result, which we prove in the appendix, about the simplicity of certain subgroups of the automorphism group of a rank-one CAT(0) cube complex. This result generalizes previous results by Tits and by Haglund and Paulin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0178","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":"2026-05-18T02:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"voTmt2qduG67V/cC3q2iz+YD3LgvxawtUc32BG3PzazQO43T4OOjD0VewY7kaoDn04Q5d8lWYJfRLBCM05SQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:56:54.609013Z"},"content_sha256":"5a88ab063ea37c042232443b71ae065d487c86efd220a0129e792fbf3c66154c","schema_version":"1.0","event_id":"sha256:5a88ab063ea37c042232443b71ae065d487c86efd220a0129e792fbf3c66154c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG/bundle.json","state_url":"https://pith.science/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG/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":"2026-06-25T18:56:54Z","links":{"resolver":"https://pith.science/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG","bundle":"https://pith.science/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG/bundle.json","state":"https://pith.science/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUAGZOOYNJQ3XFMSMRREIVBGZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NUAGZOOYNJQ3XFMSMRREIVBGZG","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":"d4c63e4c16124598a91f59a1b522889cddd13f909e2a930dca32788fa1c70448","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-01T22:44:49Z","title_canon_sha256":"62aee3313e96fdb4c503a1344a8b413e33a684317f213b4537a29741135215ea"},"schema_version":"1.0","source":{"id":"1411.0178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0178","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0178v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0178","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"NUAGZOOYNJQ3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NUAGZOOYNJQ3XFMS","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NUAGZOOY","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:5a88ab063ea37c042232443b71ae065d487c86efd220a0129e792fbf3c66154c","target":"graph","created_at":"2026-05-18T02:38:52Z","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 provide a necessary and sufficient condition on a finite flag simplicial complex, L, for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to L. We then find new examples of such CAT(0) cube complexes and prove that their automorphism groups are virtually simple. The latter uses a result, which we prove in the appendix, about the simplicity of certain subgroups of the automorphism group of a rank-one CAT(0) cube complex. This result generalizes previous results by Tits and by Haglund and Paulin.","authors_text":"Nir Lazarovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-01T22:44:49Z","title":"On regular CAT(0) cube complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0178","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:ac4e9d51327f130eee2840669f8cf38342ebb23b97b79b110aa499e290a2a302","target":"record","created_at":"2026-05-18T02:38:52Z","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":"d4c63e4c16124598a91f59a1b522889cddd13f909e2a930dca32788fa1c70448","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-01T22:44:49Z","title_canon_sha256":"62aee3313e96fdb4c503a1344a8b413e33a684317f213b4537a29741135215ea"},"schema_version":"1.0","source":{"id":"1411.0178","kind":"arxiv","version":1}},"canonical_sha256":"6d006cb9d86a61bb95926462445426c9897f9969f36868adc38e3e81884ebb59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d006cb9d86a61bb95926462445426c9897f9969f36868adc38e3e81884ebb59","first_computed_at":"2026-05-18T02:38:52.358531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:52.358531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EAe/nI6y7jpp5GeXerwrGlFZa9l1qK11RdWwy3xOEWy2OOxEbhKHwv6iGbrP2unrVdNYrhrIPcDpASZwaAvtBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:52.359088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac4e9d51327f130eee2840669f8cf38342ebb23b97b79b110aa499e290a2a302","sha256:5a88ab063ea37c042232443b71ae065d487c86efd220a0129e792fbf3c66154c"],"state_sha256":"2d5f8773b723427f510a4f10e3e97094a0986a2fa9d676e0f892ad51f01b451d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N2lNT8NdVXEfm96E0ighFsd0k1pNp55ewONqbJg1TMJW1AXebpiD4K2PSJM58Z71kzN6AgZ6dNQ+Io/TMgT4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:56:54.610938Z","bundle_sha256":"a3090e59174814af3a62d6572f6922d42b411203951f971b5c5d45ce6fdea403"}}