{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MEDDFAV6ZVSZPELHRJOPDOQZU7","short_pith_number":"pith:MEDDFAV6","canonical_record":{"source":{"id":"1006.4791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-06-24T13:35:11Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"5c6dbe572ae4101bfa2009175b3aefad520aba1bf1437ba7b124a44389675d91","abstract_canon_sha256":"6f4bfc4738db65e534086b0d1804e5c140ad60a12e0d952d5a0822bb4e2b9252"},"schema_version":"1.0"},"canonical_sha256":"61063282becd659791678a5cf1ba19a7de6e7a6bf1c3cd232b3ca62e01414f2b","source":{"kind":"arxiv","id":"1006.4791","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4791","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4791v1","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4791","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"MEDDFAV6ZVSZ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MEDDFAV6ZVSZPELH","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MEDDFAV6","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MEDDFAV6ZVSZPELHRJOPDOQZU7","target":"record","payload":{"canonical_record":{"source":{"id":"1006.4791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-06-24T13:35:11Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"5c6dbe572ae4101bfa2009175b3aefad520aba1bf1437ba7b124a44389675d91","abstract_canon_sha256":"6f4bfc4738db65e534086b0d1804e5c140ad60a12e0d952d5a0822bb4e2b9252"},"schema_version":"1.0"},"canonical_sha256":"61063282becd659791678a5cf1ba19a7de6e7a6bf1c3cd232b3ca62e01414f2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:46.721698Z","signature_b64":"dSsKDzrnMmN6N8rIshmHgtz0vCY1b5r6dm5N+3Voq451GV9PCkqma4QZ/ZodUEihkwcGR0eEAaGSDD7uZ9MBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61063282becd659791678a5cf1ba19a7de6e7a6bf1c3cd232b3ca62e01414f2b","last_reissued_at":"2026-05-18T03:48:46.720983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:46.720983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.4791","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":"2026-05-18T03:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZotLKEj5Vfa6rWjJNEQbLw0YaqcML7EqpOyWI5TnhOXMe8qTrk/6C72CUWfr+XK/mG5RGgYuysS63WSGs7JzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:36.035661Z"},"content_sha256":"ab7cfad2fb033604d786519dd7597c8998db28089ace6e0974020905fccd5429","schema_version":"1.0","event_id":"sha256:ab7cfad2fb033604d786519dd7597c8998db28089ace6e0974020905fccd5429"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MEDDFAV6ZVSZPELHRJOPDOQZU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.OA","authors_text":"Jeong Hee Hong, Roberto Conti, Wojciech Szymanski","submitted_at":"2010-06-24T13:35:11Z","abstract_excerpt":"It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of the Cuntz algebra O_n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via restriction, with the group of those homeomorphisms of the full one-sided n-shift space which eventually commute along with their inverses with the shift transformation. The image of this group in the outer automorphism group of O_n can be embedded into the quotient of the automorphism group of the full two-sided n-shift by its center, generated by the shift"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4791","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":"2026-05-18T03:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwYsINtkDBgugdZvDRvr6D/956735j8DmXX95Y1xpejyJDyPQK+HFtp58+6yL53TqpjTUA4RL7YSbmBn/+2UDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:36.036008Z"},"content_sha256":"2cba334ca98e41d24b16bd4ec0368bdb77229858074c24263026844bebafe759","schema_version":"1.0","event_id":"sha256:2cba334ca98e41d24b16bd4ec0368bdb77229858074c24263026844bebafe759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7/bundle.json","state_url":"https://pith.science/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7/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":"2026-05-28T10:30:36Z","links":{"resolver":"https://pith.science/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7","bundle":"https://pith.science/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7/bundle.json","state":"https://pith.science/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEDDFAV6ZVSZPELHRJOPDOQZU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MEDDFAV6ZVSZPELHRJOPDOQZU7","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":"6f4bfc4738db65e534086b0d1804e5c140ad60a12e0d952d5a0822bb4e2b9252","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-06-24T13:35:11Z","title_canon_sha256":"5c6dbe572ae4101bfa2009175b3aefad520aba1bf1437ba7b124a44389675d91"},"schema_version":"1.0","source":{"id":"1006.4791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4791","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4791v1","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4791","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"MEDDFAV6ZVSZ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MEDDFAV6ZVSZPELH","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MEDDFAV6","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:2cba334ca98e41d24b16bd4ec0368bdb77229858074c24263026844bebafe759","target":"graph","created_at":"2026-05-18T03:48:46Z","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":"It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of the Cuntz algebra O_n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via restriction, with the group of those homeomorphisms of the full one-sided n-shift space which eventually commute along with their inverses with the shift transformation. The image of this group in the outer automorphism group of O_n can be embedded into the quotient of the automorphism group of the full two-sided n-shift by its center, generated by the shift","authors_text":"Jeong Hee Hong, Roberto Conti, Wojciech Szymanski","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-06-24T13:35:11Z","title":"The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4791","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:ab7cfad2fb033604d786519dd7597c8998db28089ace6e0974020905fccd5429","target":"record","created_at":"2026-05-18T03:48:46Z","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":"6f4bfc4738db65e534086b0d1804e5c140ad60a12e0d952d5a0822bb4e2b9252","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-06-24T13:35:11Z","title_canon_sha256":"5c6dbe572ae4101bfa2009175b3aefad520aba1bf1437ba7b124a44389675d91"},"schema_version":"1.0","source":{"id":"1006.4791","kind":"arxiv","version":1}},"canonical_sha256":"61063282becd659791678a5cf1ba19a7de6e7a6bf1c3cd232b3ca62e01414f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61063282becd659791678a5cf1ba19a7de6e7a6bf1c3cd232b3ca62e01414f2b","first_computed_at":"2026-05-18T03:48:46.720983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:46.720983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSsKDzrnMmN6N8rIshmHgtz0vCY1b5r6dm5N+3Voq451GV9PCkqma4QZ/ZodUEihkwcGR0eEAaGSDD7uZ9MBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:46.721698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.4791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab7cfad2fb033604d786519dd7597c8998db28089ace6e0974020905fccd5429","sha256:2cba334ca98e41d24b16bd4ec0368bdb77229858074c24263026844bebafe759"],"state_sha256":"0f861ed900928e493276d3d773f3b55264ebd125f15654f346682c8d866e5a70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPW1+hAxBeO5BGcAW1sbSJLOGNCdl5Fc0REWz7z1z9pccpMnFewNrX59LIy8r2BqRpOuWDcJVDx7sfaGcq8GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:30:36.038022Z","bundle_sha256":"085930c231a79bab2d53004cea0e1b24990983b37cd9215020e482aaec1368c1"}}