{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:IZQCILK6YIVGZ4C3LMKOJ5QJBM","short_pith_number":"pith:IZQCILK6","canonical_record":{"source":{"id":"2104.05822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-04-12T21:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"b926223971b3abf3cf6a93b4dd64496aeb5c936c2bf42faa7c18fd251511953b","abstract_canon_sha256":"34d53b0e3f99fae9f2bf637629fcfcff8359be08b998dee861b6d7bd5a193e86"},"schema_version":"1.0"},"canonical_sha256":"4660242d5ec22a6cf05b5b14e4f6090b06ee9f143b34c070e9a85161b84f7be7","source":{"kind":"arxiv","id":"2104.05822","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.05822","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2104.05822v1","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.05822","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"IZQCILK6YIVG","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"IZQCILK6YIVGZ4C3","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"IZQCILK6","created_at":"2026-07-05T05:06:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:IZQCILK6YIVGZ4C3LMKOJ5QJBM","target":"record","payload":{"canonical_record":{"source":{"id":"2104.05822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-04-12T21:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"b926223971b3abf3cf6a93b4dd64496aeb5c936c2bf42faa7c18fd251511953b","abstract_canon_sha256":"34d53b0e3f99fae9f2bf637629fcfcff8359be08b998dee861b6d7bd5a193e86"},"schema_version":"1.0"},"canonical_sha256":"4660242d5ec22a6cf05b5b14e4f6090b06ee9f143b34c070e9a85161b84f7be7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:50.745908Z","signature_b64":"VBK+QU3QgwyA1FjITzEuFaLbDccoPILxaYfWDwyVZkgiXaJ0n6+VMQKazXjw7itu6zZxNDL9fNSXOjuFpNGEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4660242d5ec22a6cf05b5b14e4f6090b06ee9f143b34c070e9a85161b84f7be7","last_reissued_at":"2026-07-05T05:06:50.745480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:50.745480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.05822","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":"2026-07-05T05:06:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yt2vxecgRynX/Z462uCMl3zghckiExfrBWZOA6rOCw8XOCvAY0Vje5vFPFq/JThSatpbgTGO3r9Di/Ak+/umDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:12:48.564403Z"},"content_sha256":"ec289e2f3f1685425b215f60786fe601f258ea7ec9ee22f2b7594a4a602af38d","schema_version":"1.0","event_id":"sha256:ec289e2f3f1685425b215f60786fe601f258ea7ec9ee22f2b7594a4a602af38d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:IZQCILK6YIVGZ4C3LMKOJ5QJBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the extremal points of the $\\Lambda$-polytopes and classical simulation of quantum computation with magic states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cihan Okay, Michael Zurel, Robert Raussendorf","submitted_at":"2021-04-12T21:12:45Z","abstract_excerpt":"We investigate the $\\Lambda$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $\\Lambda_n$, for every number $n$ of qubits. We establish two properties of the family $\\{\\Lambda_n, n\\in \\mathbb{N}\\}$, namely (i) Any extremal point (vertex) $A_\\alpha \\in \\Lambda_m$ can be used to construct vertices in $\\Lambda_n$, for all $n>m$. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.05822","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.05822/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:06:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lsIMB3PpGTxb43OWMt1QA0KlpaNXKhnvx65+sE44IR54+iPONZ2pKBOB/l4MBP4ft4OZKJoGgIYd4fkxnRP1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:12:48.565323Z"},"content_sha256":"b9141cad4110eb35c425ce507769c541fb7269f71dba6bd6acb1f8940e857ecd","schema_version":"1.0","event_id":"sha256:b9141cad4110eb35c425ce507769c541fb7269f71dba6bd6acb1f8940e857ecd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM/bundle.json","state_url":"https://pith.science/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM/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":"2026-08-17T21:12:48Z","links":{"resolver":"https://pith.science/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM","bundle":"https://pith.science/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM/bundle.json","state":"https://pith.science/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZQCILK6YIVGZ4C3LMKOJ5QJBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:IZQCILK6YIVGZ4C3LMKOJ5QJBM","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":"34d53b0e3f99fae9f2bf637629fcfcff8359be08b998dee861b6d7bd5a193e86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-04-12T21:12:45Z","title_canon_sha256":"b926223971b3abf3cf6a93b4dd64496aeb5c936c2bf42faa7c18fd251511953b"},"schema_version":"1.0","source":{"id":"2104.05822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.05822","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2104.05822v1","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.05822","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"IZQCILK6YIVG","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"IZQCILK6YIVGZ4C3","created_at":"2026-07-05T05:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"IZQCILK6","created_at":"2026-07-05T05:06:50Z"}],"graph_snapshots":[{"event_id":"sha256:b9141cad4110eb35c425ce507769c541fb7269f71dba6bd6acb1f8940e857ecd","target":"graph","created_at":"2026-07-05T05:06:50Z","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/2104.05822/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the $\\Lambda$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $\\Lambda_n$, for every number $n$ of qubits. We establish two properties of the family $\\{\\Lambda_n, n\\in \\mathbb{N}\\}$, namely (i) Any extremal point (vertex) $A_\\alpha \\in \\Lambda_m$ can be used to construct vertices in $\\Lambda_n$, for all $n>m$. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to ","authors_text":"Cihan Okay, Michael Zurel, Robert Raussendorf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-04-12T21:12:45Z","title":"On the extremal points of the $\\Lambda$-polytopes and classical simulation of quantum computation with magic states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.05822","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:ec289e2f3f1685425b215f60786fe601f258ea7ec9ee22f2b7594a4a602af38d","target":"record","created_at":"2026-07-05T05:06:50Z","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":"34d53b0e3f99fae9f2bf637629fcfcff8359be08b998dee861b6d7bd5a193e86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-04-12T21:12:45Z","title_canon_sha256":"b926223971b3abf3cf6a93b4dd64496aeb5c936c2bf42faa7c18fd251511953b"},"schema_version":"1.0","source":{"id":"2104.05822","kind":"arxiv","version":1}},"canonical_sha256":"4660242d5ec22a6cf05b5b14e4f6090b06ee9f143b34c070e9a85161b84f7be7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4660242d5ec22a6cf05b5b14e4f6090b06ee9f143b34c070e9a85161b84f7be7","first_computed_at":"2026-07-05T05:06:50.745480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:50.745480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VBK+QU3QgwyA1FjITzEuFaLbDccoPILxaYfWDwyVZkgiXaJ0n6+VMQKazXjw7itu6zZxNDL9fNSXOjuFpNGEAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:50.745908Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.05822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec289e2f3f1685425b215f60786fe601f258ea7ec9ee22f2b7594a4a602af38d","sha256:b9141cad4110eb35c425ce507769c541fb7269f71dba6bd6acb1f8940e857ecd"],"state_sha256":"50dde6962c5d68dd6255be7e1709ac95c5adca34378305d51d338495678c5417"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAm53YtAyjgoXfoExxCVZbYVOhlv9GpZsE+pW1V+A05rN2xnsc5H0/aRft9YKvWb+vmCe7mMOmgE0mr3IhK9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T21:12:48.736656Z","bundle_sha256":"5c2237911f71f5d0c58bf10824f82eba4f5172a6a27893e31d4107042e89a535"}}