{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:DIQ5ODLS2XFWPOCSVBK6KPREJQ","short_pith_number":"pith:DIQ5ODLS","canonical_record":{"source":{"id":"math/0004052","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2000-04-10T10:15:16Z","cross_cats_sorted":[],"title_canon_sha256":"3be50db4867fb6a797a7a4814a60cc780ae562541cc7f76dbc193414676df7a8","abstract_canon_sha256":"89157fe89e9e4c2ac121c94038d7058528679694b0cf40ced544de4e634136bc"},"schema_version":"1.0"},"canonical_sha256":"1a21d70d72d5cb67b852a855e53e244c3a1cbff0436bf56ecc1ad6c8d24be13b","source":{"kind":"arxiv","id":"math/0004052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004052","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004052v1","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004052","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"DIQ5ODLS2XFW","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"DIQ5ODLS2XFWPOCS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"DIQ5ODLS","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:DIQ5ODLS2XFWPOCSVBK6KPREJQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0004052","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2000-04-10T10:15:16Z","cross_cats_sorted":[],"title_canon_sha256":"3be50db4867fb6a797a7a4814a60cc780ae562541cc7f76dbc193414676df7a8","abstract_canon_sha256":"89157fe89e9e4c2ac121c94038d7058528679694b0cf40ced544de4e634136bc"},"schema_version":"1.0"},"canonical_sha256":"1a21d70d72d5cb67b852a855e53e244c3a1cbff0436bf56ecc1ad6c8d24be13b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:45.999914Z","signature_b64":"PatvGZKhiFk1mA/UQ4m3Ru7eVnjTY2CAIOrgvwvVAxnYpj5g5K+tcIlverniFeLi9nT2tpukt3BHzOEJzFC2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a21d70d72d5cb67b852a855e53e244c3a1cbff0436bf56ecc1ad6c8d24be13b","last_reissued_at":"2026-05-18T03:32:45.999381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:45.999381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0004052","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":"2026-05-18T03:32:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bYbbJKQWb2ONf4Sw/vgeBdw2OeOnEbRD3mJLtVE6gmvMEDSHJT7be4kRt6iUi6we1FqXpMnqfxzcUEA/FjYxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:36:43.013958Z"},"content_sha256":"7c78443ce758779d7e844d07f277ef87b0f0e61999df1a93268a3069f8134aee","schema_version":"1.0","event_id":"sha256:7c78443ce758779d7e844d07f277ef87b0f0e61999df1a93268a3069f8134aee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:DIQ5ODLS2XFWPOCSVBK6KPREJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple purely infinite C*-algebras and n-filling actions","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"G. Robertson, P. Jolissaint","submitted_at":"2000-04-10T10:15:16Z","abstract_excerpt":"Let $n$ be a positive integer. We introduce a concept, which we call the $n$-filling property, for an action of a group on a separable unital $C^*$-algebra $A$. If $A=C(\\Omega)$ is a commutative unital $C^*$-algebra and the action is induced by a group of homeomorphisms of $\\Omega$ then the $n$-filling property reduces to a weak version of hyperbolicity. The $n$-filling property is used to prove that certain crossed product $C^*$-algebras are purely infinite and simple. A variety of group actions on boundaries of symmetric spaces and buildings have the $n$-filling property. An explicit example"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004052","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":"2026-05-18T03:32:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"llZJBy11Bn1IhNjhkaI48MGDBtekMh6fz91iwcoOCOEuoTy3gIgypOgL5y6hA7eD2Q5Nx6wHas/XTFEGoGsSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:36:43.014502Z"},"content_sha256":"216402010b202fa693ee4f6df46ebcd32901b150aea58fab8c502089a819b6e9","schema_version":"1.0","event_id":"sha256:216402010b202fa693ee4f6df46ebcd32901b150aea58fab8c502089a819b6e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ/bundle.json","state_url":"https://pith.science/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ/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":"2026-06-07T10:36:43Z","links":{"resolver":"https://pith.science/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ","bundle":"https://pith.science/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ/bundle.json","state":"https://pith.science/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DIQ5ODLS2XFWPOCSVBK6KPREJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:DIQ5ODLS2XFWPOCSVBK6KPREJQ","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":"89157fe89e9e4c2ac121c94038d7058528679694b0cf40ced544de4e634136bc","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2000-04-10T10:15:16Z","title_canon_sha256":"3be50db4867fb6a797a7a4814a60cc780ae562541cc7f76dbc193414676df7a8"},"schema_version":"1.0","source":{"id":"math/0004052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004052","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004052v1","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004052","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"DIQ5ODLS2XFW","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"DIQ5ODLS2XFWPOCS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"DIQ5ODLS","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:216402010b202fa693ee4f6df46ebcd32901b150aea58fab8c502089a819b6e9","target":"graph","created_at":"2026-05-18T03:32:45Z","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":"Let $n$ be a positive integer. We introduce a concept, which we call the $n$-filling property, for an action of a group on a separable unital $C^*$-algebra $A$. If $A=C(\\Omega)$ is a commutative unital $C^*$-algebra and the action is induced by a group of homeomorphisms of $\\Omega$ then the $n$-filling property reduces to a weak version of hyperbolicity. The $n$-filling property is used to prove that certain crossed product $C^*$-algebras are purely infinite and simple. A variety of group actions on boundaries of symmetric spaces and buildings have the $n$-filling property. An explicit example","authors_text":"G. Robertson, P. Jolissaint","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2000-04-10T10:15:16Z","title":"Simple purely infinite C*-algebras and n-filling actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004052","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":"sha256:7c78443ce758779d7e844d07f277ef87b0f0e61999df1a93268a3069f8134aee","target":"record","created_at":"2026-05-18T03:32:45Z","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":"89157fe89e9e4c2ac121c94038d7058528679694b0cf40ced544de4e634136bc","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2000-04-10T10:15:16Z","title_canon_sha256":"3be50db4867fb6a797a7a4814a60cc780ae562541cc7f76dbc193414676df7a8"},"schema_version":"1.0","source":{"id":"math/0004052","kind":"arxiv","version":1}},"canonical_sha256":"1a21d70d72d5cb67b852a855e53e244c3a1cbff0436bf56ecc1ad6c8d24be13b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a21d70d72d5cb67b852a855e53e244c3a1cbff0436bf56ecc1ad6c8d24be13b","first_computed_at":"2026-05-18T03:32:45.999381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:45.999381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PatvGZKhiFk1mA/UQ4m3Ru7eVnjTY2CAIOrgvwvVAxnYpj5g5K+tcIlverniFeLi9nT2tpukt3BHzOEJzFC2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:45.999914Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0004052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c78443ce758779d7e844d07f277ef87b0f0e61999df1a93268a3069f8134aee","sha256:216402010b202fa693ee4f6df46ebcd32901b150aea58fab8c502089a819b6e9"],"state_sha256":"2dcfbf4236ac2ac6032b33e33e3ceef42c21f8255ffd23dd05167ceac41dc6ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqyS7xhhP/pvAe9/rlq9DJW4HEjTSulsWDfMSCx2hqPY5JB0TJ/yan7rw+5zC+2Z8aKQQRIhm6sVl/ffrDD+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:36:43.017250Z","bundle_sha256":"f206c674e3a394ac316392d6b7bb985e14e3be7ec2edf1a780bc473c0988a31f"}}