{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QDQMP57OX4VY4U72OJ4G2UM5HN","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":"a6b8b25d3bfa5397dcfd59ff8efccf31c11a504408d9a9ed5de60941c7333c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-25T08:42:12Z","title_canon_sha256":"630a4e3a9119938b1c40dfd477c82e0cb67a31fc232ec587fcefc8f250a07aa2"},"schema_version":"1.0","source":{"id":"1602.07845","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07845","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07845v1","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07845","created_at":"2026-05-18T01:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"QDQMP57OX4VY","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QDQMP57OX4VY4U72","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QDQMP57O","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:034298d2ec3362008e07fd500b1b7cd4a3e6a0faf24e76fc166061681a793afd","target":"graph","created_at":"2026-05-18T01:19:58Z","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":"In this note we propose a version of the classical Stone-Weierstrass theorem in the context of quantum operations, by introducing a particular class of quantum operations, dubbed polynomial quantum operations. This result permits to interpret from a probabilistic point of view, and up to a certain approximation, any continuous function from the real cube [0; 1]^n to the real interval [0; 1] as a quantum operation.","authors_text":"Antonio Ledda, Giuseppe Sergioli, Hector Freytes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-25T08:42:12Z","title":"Continuous Functions as Quantum Operations: a probabilistic approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07845","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:d2350954ee3d89c6731f2818b592f013536ec5e5fc5f61da7f13aacf2e7bc95f","target":"record","created_at":"2026-05-18T01:19:58Z","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":"a6b8b25d3bfa5397dcfd59ff8efccf31c11a504408d9a9ed5de60941c7333c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-25T08:42:12Z","title_canon_sha256":"630a4e3a9119938b1c40dfd477c82e0cb67a31fc232ec587fcefc8f250a07aa2"},"schema_version":"1.0","source":{"id":"1602.07845","kind":"arxiv","version":1}},"canonical_sha256":"80e0c7f7eebf2b8e53fa72786d519d3b4c12367b8d8967c86f5fbb7181c62262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e0c7f7eebf2b8e53fa72786d519d3b4c12367b8d8967c86f5fbb7181c62262","first_computed_at":"2026-05-18T01:19:58.434725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:58.434725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVDTPfitPbAmQMdQo0hlAfj5JL07EAtpF3VEWzEPBGKMV5JBx1Ra7PrN4N2ncCUFzNHpq9CH2Ll493vHRuT2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:58.435304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07845","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2350954ee3d89c6731f2818b592f013536ec5e5fc5f61da7f13aacf2e7bc95f","sha256:034298d2ec3362008e07fd500b1b7cd4a3e6a0faf24e76fc166061681a793afd"],"state_sha256":"fb4f927b5293a7c1e52722c33a252d68185eb21597bc307660113f2d07e8eaeb"}