{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TCHYNZ6IWOWIASNBXV7GX6LSQG","short_pith_number":"pith:TCHYNZ6I","canonical_record":{"source":{"id":"1703.00616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-02T04:38:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c32bb319a5a706c871c378186b68dd98c146ba8232a38b2de5b0bc416aafb4a1","abstract_canon_sha256":"ff8edfc01e748dab24aee35197037033f2fb166056fd91f66eb613bde4bde9fe"},"schema_version":"1.0"},"canonical_sha256":"988f86e7c8b3ac8049a1bd7e6bf97281911c590f500afda174b4df1871419c61","source":{"kind":"arxiv","id":"1703.00616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00616","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00616v1","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00616","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"TCHYNZ6IWOWI","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TCHYNZ6IWOWIASNB","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TCHYNZ6I","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TCHYNZ6IWOWIASNBXV7GX6LSQG","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-02T04:38:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c32bb319a5a706c871c378186b68dd98c146ba8232a38b2de5b0bc416aafb4a1","abstract_canon_sha256":"ff8edfc01e748dab24aee35197037033f2fb166056fd91f66eb613bde4bde9fe"},"schema_version":"1.0"},"canonical_sha256":"988f86e7c8b3ac8049a1bd7e6bf97281911c590f500afda174b4df1871419c61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:36.533849Z","signature_b64":"T/IWa03wyWMRAHtrbpaUXW+gkN7/OK7znzU9a37U26LQB48Aad2f3wyrnt//sy4xpEwHzRtX0cQAdB0kCTEkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"988f86e7c8b3ac8049a1bd7e6bf97281911c590f500afda174b4df1871419c61","last_reissued_at":"2026-05-18T00:02:36.533224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:36.533224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00616","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":"2026-05-18T00:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2L6iyjMvHazLGJluZC61CFE+yooMJU7BTlUCh+vqBF3/kElW5uudVUZtWwv8DtJUmvfBMHhNXQypRhHwWGpOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:50:08.439088Z"},"content_sha256":"9db4c6538528723f142a2354bb3f2228ee399ac82149a7d2e98c110eaff2b2bc","schema_version":"1.0","event_id":"sha256:9db4c6538528723f142a2354bb3f2228ee399ac82149a7d2e98c110eaff2b2bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TCHYNZ6IWOWIASNBXV7GX6LSQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Action Dimension of Lattices in Euclidean Buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Kevin Schreve","submitted_at":"2017-03-02T04:38:20Z","abstract_excerpt":"The action dimension of a group G is the minimal dimension of a contractible manifold that G acts on properly discontinuously. We show that if G acts properly and cocompactly on a thick Euclidean building, then the action dimension is bounded below by twice the dimension of the building. We also compute the action dimension of S-arithmetic groups over number fields, partially answering a question of Bestvina, Kapovich, and Kleiner."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00616","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":"2026-05-18T00:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reUemITkU7/SQxHhNxtzfzz4l8mUSfK/BFX+wP2iBHiLEoldDlq2FAkgLzkfzPtidxhOQeO8oEKITFjxQdViDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:50:08.439441Z"},"content_sha256":"1ac6447e3b50438cea922b6b04e6fdd7b489f5cffc02e855dc409cbfbc75f1c0","schema_version":"1.0","event_id":"sha256:1ac6447e3b50438cea922b6b04e6fdd7b489f5cffc02e855dc409cbfbc75f1c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG/bundle.json","state_url":"https://pith.science/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG/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":"2026-06-08T14:50:08Z","links":{"resolver":"https://pith.science/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG","bundle":"https://pith.science/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG/bundle.json","state":"https://pith.science/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCHYNZ6IWOWIASNBXV7GX6LSQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TCHYNZ6IWOWIASNBXV7GX6LSQG","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":"ff8edfc01e748dab24aee35197037033f2fb166056fd91f66eb613bde4bde9fe","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-02T04:38:20Z","title_canon_sha256":"c32bb319a5a706c871c378186b68dd98c146ba8232a38b2de5b0bc416aafb4a1"},"schema_version":"1.0","source":{"id":"1703.00616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00616","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00616v1","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00616","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"TCHYNZ6IWOWI","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TCHYNZ6IWOWIASNB","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TCHYNZ6I","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:1ac6447e3b50438cea922b6b04e6fdd7b489f5cffc02e855dc409cbfbc75f1c0","target":"graph","created_at":"2026-05-18T00:02:36Z","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":"The action dimension of a group G is the minimal dimension of a contractible manifold that G acts on properly discontinuously. We show that if G acts properly and cocompactly on a thick Euclidean building, then the action dimension is bounded below by twice the dimension of the building. We also compute the action dimension of S-arithmetic groups over number fields, partially answering a question of Bestvina, Kapovich, and Kleiner.","authors_text":"Kevin Schreve","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-02T04:38:20Z","title":"Action Dimension of Lattices in Euclidean Buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00616","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":"sha256:9db4c6538528723f142a2354bb3f2228ee399ac82149a7d2e98c110eaff2b2bc","target":"record","created_at":"2026-05-18T00:02:36Z","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":"ff8edfc01e748dab24aee35197037033f2fb166056fd91f66eb613bde4bde9fe","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-02T04:38:20Z","title_canon_sha256":"c32bb319a5a706c871c378186b68dd98c146ba8232a38b2de5b0bc416aafb4a1"},"schema_version":"1.0","source":{"id":"1703.00616","kind":"arxiv","version":1}},"canonical_sha256":"988f86e7c8b3ac8049a1bd7e6bf97281911c590f500afda174b4df1871419c61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"988f86e7c8b3ac8049a1bd7e6bf97281911c590f500afda174b4df1871419c61","first_computed_at":"2026-05-18T00:02:36.533224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:36.533224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/IWa03wyWMRAHtrbpaUXW+gkN7/OK7znzU9a37U26LQB48Aad2f3wyrnt//sy4xpEwHzRtX0cQAdB0kCTEkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:36.533849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9db4c6538528723f142a2354bb3f2228ee399ac82149a7d2e98c110eaff2b2bc","sha256:1ac6447e3b50438cea922b6b04e6fdd7b489f5cffc02e855dc409cbfbc75f1c0"],"state_sha256":"5da971e9ac31d01fd5579832bf0e627f23d1b71719aef81a7ebe906326295958"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kn4hULtM2TMz0AMy+4tGT94vv/tTmdkoOHDm+EiS6SdK8IdGenOMyHLqFI0FHOwP0S/yW0cuhGfXeGKgieL6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:50:08.441400Z","bundle_sha256":"6782d94fd4d1df6ac483333b921b5fa3412c85d4b2751d190ee4162a04a1b553"}}