{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O7GIC6WAWIN7CDPJYZZGGXR555","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":"4e5e5db71b3add553f2db5bfeca491684754c61ed2850381f0ea41f01e1409b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2025-05-22T15:04:07Z","title_canon_sha256":"347d1c83fad71ec40586cf3f0f72eda74254164ddd3ce931d027c47fc7ba4225"},"schema_version":"1.0","source":{"id":"2505.16759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.16759","created_at":"2026-07-05T11:07:40Z"},{"alias_kind":"arxiv_version","alias_value":"2505.16759v1","created_at":"2026-07-05T11:07:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16759","created_at":"2026-07-05T11:07:40Z"},{"alias_kind":"pith_short_12","alias_value":"O7GIC6WAWIN7","created_at":"2026-07-05T11:07:40Z"},{"alias_kind":"pith_short_16","alias_value":"O7GIC6WAWIN7CDPJ","created_at":"2026-07-05T11:07:40Z"},{"alias_kind":"pith_short_8","alias_value":"O7GIC6WA","created_at":"2026-07-05T11:07:40Z"}],"graph_snapshots":[{"event_id":"sha256:92019b2ead46e2e2629dc667709d107349a78c6fdf8259c30ef6b35434cf0666","target":"graph","created_at":"2026-07-05T11:07:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.16759/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The diadic $C^*$-algebra $\\cQ_2$ contains canonically a copy of the Cuntz algebra $\\cO_2$. It is shown that the inclusion $\\cO_2 \\subset \\cQ_2$ is $C^*$-irreducible and rigid. It follows that the injective envelopes of these two $C^*$-algebras are $*$-isomorphic.","authors_text":"Jacopo Bassi, Roberto Conti","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2025-05-22T15:04:07Z","title":"On the inclusion $\\cO_2 \\subset \\cQ_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16759","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:e083921588afc8c6c0328ae761d1cd9673d137b977177021732befc414c07321","target":"record","created_at":"2026-07-05T11:07:40Z","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":"4e5e5db71b3add553f2db5bfeca491684754c61ed2850381f0ea41f01e1409b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2025-05-22T15:04:07Z","title_canon_sha256":"347d1c83fad71ec40586cf3f0f72eda74254164ddd3ce931d027c47fc7ba4225"},"schema_version":"1.0","source":{"id":"2505.16759","kind":"arxiv","version":1}},"canonical_sha256":"77cc817ac0b21bf10de9c672635e3def68057dc500abea3f4c8013d952544699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77cc817ac0b21bf10de9c672635e3def68057dc500abea3f4c8013d952544699","first_computed_at":"2026-07-05T11:07:40.567415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:07:40.567415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDEK7qxpO6qRGJa4N5mHWKRfVH42JLL62CdPgl+oiYsrdOivwBhiZGJgaZn4wINmLw/JI35l2Hf41Cl/Rez0Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:07:40.568032Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.16759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e083921588afc8c6c0328ae761d1cd9673d137b977177021732befc414c07321","sha256:92019b2ead46e2e2629dc667709d107349a78c6fdf8259c30ef6b35434cf0666"],"state_sha256":"d595dc0d09413c2ef44a5e64ccb90446d4486c7e2d5c0af6679a0dd3527d792e"}