{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7WEN6IT3C5ENC22EREF4BSYRQU","short_pith_number":"pith:7WEN6IT3","canonical_record":{"source":{"id":"1408.5546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-24T03:19:43Z","cross_cats_sorted":[],"title_canon_sha256":"94e674eb3b55000b97ae2311ab02f73a8fbe9e7b711dd34730dc190d7fa78d64","abstract_canon_sha256":"0ecf59bc3abd5558ba7e547defc3468fa0d555bd2dedc3532b06354b10a6abee"},"schema_version":"1.0"},"canonical_sha256":"fd88df227b1748d16b44890bc0cb1185305027b2eceb178cb3e130e37f0bed1b","source":{"kind":"arxiv","id":"1408.5546","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5546","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5546v1","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5546","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"7WEN6IT3C5EN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7WEN6IT3C5ENC22E","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7WEN6IT3","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7WEN6IT3C5ENC22EREF4BSYRQU","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-24T03:19:43Z","cross_cats_sorted":[],"title_canon_sha256":"94e674eb3b55000b97ae2311ab02f73a8fbe9e7b711dd34730dc190d7fa78d64","abstract_canon_sha256":"0ecf59bc3abd5558ba7e547defc3468fa0d555bd2dedc3532b06354b10a6abee"},"schema_version":"1.0"},"canonical_sha256":"fd88df227b1748d16b44890bc0cb1185305027b2eceb178cb3e130e37f0bed1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:24.874846Z","signature_b64":"qZQOfW8q2md2OWwM2WUJwclBdOw8EGGIyBJDtU/H4hyjA2rE+RuRfGnIlRJOP//q6wTJZ06ROBrrH+7z1xLIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd88df227b1748d16b44890bc0cb1185305027b2eceb178cb3e130e37f0bed1b","last_reissued_at":"2026-05-18T02:44:24.874504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:24.874504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5546","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":"2026-05-18T02:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NfN4CknmoQxTlVEjfKYFG1h4EIT/eC6JhQLaVMDS7WUmqmxRtbTe+GaAadLFPU6h16lBeUPPfrWHE+06JGi7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:00:48.388605Z"},"content_sha256":"2f66e87d732fa7bd89be8d057918d08058effce602db6786d68823c22bcff25c","schema_version":"1.0","event_id":"sha256:2f66e87d732fa7bd89be8d057918d08058effce602db6786d68823c22bcff25c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7WEN6IT3C5ENC22EREF4BSYRQU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"N. Christopher Phillips","submitted_at":"2014-08-24T03:19:43Z","abstract_excerpt":"We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal homeomorphism of X, and let Y be a closed subset of X. Let u be the standard unitary in C* (Z, X, h). The Y-orbit breaking subalgebra is the subalgebra of C* (Z, X, h) generated by C (X) and all elements f u for f in C (X) such that f vanishes on Y. If intersects each orbit of h at most once, then the Y-orbit breaking subalgebra is large in C* (Z, X, h). Large "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5546","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":"2026-05-18T02:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdAib6/bk+aVh6xwDzXOJZ6hE5GdLuEeX8IOjP3wIuTVKFaci/pl3tDmS+Gyi3Fmo1P/gTC/IcGS7Rwac7+mAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:00:48.389221Z"},"content_sha256":"b9d3630fc14fb7100b10097be37b2181a348daf8e35b9136a7289bf31b31f773","schema_version":"1.0","event_id":"sha256:b9d3630fc14fb7100b10097be37b2181a348daf8e35b9136a7289bf31b31f773"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7WEN6IT3C5ENC22EREF4BSYRQU/bundle.json","state_url":"https://pith.science/pith/7WEN6IT3C5ENC22EREF4BSYRQU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7WEN6IT3C5ENC22EREF4BSYRQU/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":"2026-05-25T12:00:48Z","links":{"resolver":"https://pith.science/pith/7WEN6IT3C5ENC22EREF4BSYRQU","bundle":"https://pith.science/pith/7WEN6IT3C5ENC22EREF4BSYRQU/bundle.json","state":"https://pith.science/pith/7WEN6IT3C5ENC22EREF4BSYRQU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7WEN6IT3C5ENC22EREF4BSYRQU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7WEN6IT3C5ENC22EREF4BSYRQU","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":"0ecf59bc3abd5558ba7e547defc3468fa0d555bd2dedc3532b06354b10a6abee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-24T03:19:43Z","title_canon_sha256":"94e674eb3b55000b97ae2311ab02f73a8fbe9e7b711dd34730dc190d7fa78d64"},"schema_version":"1.0","source":{"id":"1408.5546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5546","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5546v1","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5546","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"7WEN6IT3C5EN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7WEN6IT3C5ENC22E","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7WEN6IT3","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:b9d3630fc14fb7100b10097be37b2181a348daf8e35b9136a7289bf31b31f773","target":"graph","created_at":"2026-05-18T02:44:24Z","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 define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal homeomorphism of X, and let Y be a closed subset of X. Let u be the standard unitary in C* (Z, X, h). The Y-orbit breaking subalgebra is the subalgebra of C* (Z, X, h) generated by C (X) and all elements f u for f in C (X) such that f vanishes on Y. If intersects each orbit of h at most once, then the Y-orbit breaking subalgebra is large in C* (Z, X, h). Large ","authors_text":"N. Christopher Phillips","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-24T03:19:43Z","title":"Large subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5546","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":"sha256:2f66e87d732fa7bd89be8d057918d08058effce602db6786d68823c22bcff25c","target":"record","created_at":"2026-05-18T02:44:24Z","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":"0ecf59bc3abd5558ba7e547defc3468fa0d555bd2dedc3532b06354b10a6abee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-24T03:19:43Z","title_canon_sha256":"94e674eb3b55000b97ae2311ab02f73a8fbe9e7b711dd34730dc190d7fa78d64"},"schema_version":"1.0","source":{"id":"1408.5546","kind":"arxiv","version":1}},"canonical_sha256":"fd88df227b1748d16b44890bc0cb1185305027b2eceb178cb3e130e37f0bed1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd88df227b1748d16b44890bc0cb1185305027b2eceb178cb3e130e37f0bed1b","first_computed_at":"2026-05-18T02:44:24.874504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:24.874504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZQOfW8q2md2OWwM2WUJwclBdOw8EGGIyBJDtU/H4hyjA2rE+RuRfGnIlRJOP//q6wTJZ06ROBrrH+7z1xLIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:24.874846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f66e87d732fa7bd89be8d057918d08058effce602db6786d68823c22bcff25c","sha256:b9d3630fc14fb7100b10097be37b2181a348daf8e35b9136a7289bf31b31f773"],"state_sha256":"2af23bb87e69bfb23bea6c98ed5ef296dbfc237a0ae3d2a3c2c8eaa97c31cf00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dq1c2UjVWEvcR3Aq2JzM4RY12AMJEvsuR/YXVTczLgQmlcVCIHxOeQyb04D6OWsd6L2B/wgkrfZYWR0sbI8uDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:00:48.392621Z","bundle_sha256":"a2a5d4159da10c2d3677a6d480de5563cb9fed37b9a60c8e2a5552310dd49d66"}}