{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:I7SMNOLITHYFYG5ART2CGAZLTD","short_pith_number":"pith:I7SMNOLI","canonical_record":{"source":{"id":"quant-ph/0412157","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-20T16:39:04Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"a483fbfcfa1310949040bd9079a7e609ad730b27f53a13e4b2dfd29a1f700ff6","abstract_canon_sha256":"3eb4b1b53ddf94f41ad91ab7e6a61e8fd9339d8188ebf3a3e58d3af7c09f6138"},"schema_version":"1.0"},"canonical_sha256":"47e4c6b96899f05c1ba08cf423032b98ccb2d2e99e5a970d8209ce21c8c770c3","source":{"kind":"arxiv","id":"quant-ph/0412157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0412157","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0412157v1","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0412157","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"I7SMNOLITHYF","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"I7SMNOLITHYFYG5A","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"I7SMNOLI","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:I7SMNOLITHYFYG5ART2CGAZLTD","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0412157","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-20T16:39:04Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"a483fbfcfa1310949040bd9079a7e609ad730b27f53a13e4b2dfd29a1f700ff6","abstract_canon_sha256":"3eb4b1b53ddf94f41ad91ab7e6a61e8fd9339d8188ebf3a3e58d3af7c09f6138"},"schema_version":"1.0"},"canonical_sha256":"47e4c6b96899f05c1ba08cf423032b98ccb2d2e99e5a970d8209ce21c8c770c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:58.111898Z","signature_b64":"17Hax9futPJC1UWNe98rCIVTpKQld2vVPS9bexFJEgSDNiDcSARB8gRHcLDz7gPmFJj1EvbLH3gj0L5tQDK+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47e4c6b96899f05c1ba08cf423032b98ccb2d2e99e5a970d8209ce21c8c770c3","last_reissued_at":"2026-05-18T01:37:58.111204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:58.111204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0412157","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":"2026-05-18T01:37:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+tV7ty2SW8KBs+VO/myx04o+Y09gvAT6M+otM6qL3jbXXMFwwXuFB4zS4zQwbLJwQK8jnHgAq8TQJ1SfOtgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:32:08.612816Z"},"content_sha256":"190086ed441a4f889e249d05fe7d840d2558cc18b6e6b884035c329b00399f6f","schema_version":"1.0","event_id":"sha256:190086ed441a4f889e249d05fe7d840d2558cc18b6e6b884035c329b00399f6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:I7SMNOLITHYFYG5ART2CGAZLTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A quantum version of Sanov's theorem","license":"","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"A. Szkola, I. Bjelakovic, J.-D. Deuschel, Ra. Siegmund-Schultze, R. Seiler, T. Krueger","submitted_at":"2004-12-20T16:39:04Z","abstract_excerpt":"We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\\Psi$ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the exponential separating rate is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set $\\Psi$. However, while in the classical case the separating subsets can be chosen universal, in the sense that they dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0412157","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":"2026-05-18T01:37:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4VRvtudj9OyhTk9dnoGgN8aBH3ajZaqBC5XANj1B501KVLRLoznfWOhQyc3DX/JBLU/WV8pDr7wnaHnLNvo+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:32:08.613162Z"},"content_sha256":"a4b9c6c6da5b68352978d59d4d129ac1ff04c3feb2bb748f8d41435704490c6b","schema_version":"1.0","event_id":"sha256:a4b9c6c6da5b68352978d59d4d129ac1ff04c3feb2bb748f8d41435704490c6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7SMNOLITHYFYG5ART2CGAZLTD/bundle.json","state_url":"https://pith.science/pith/I7SMNOLITHYFYG5ART2CGAZLTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7SMNOLITHYFYG5ART2CGAZLTD/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":"2026-06-02T21:32:08Z","links":{"resolver":"https://pith.science/pith/I7SMNOLITHYFYG5ART2CGAZLTD","bundle":"https://pith.science/pith/I7SMNOLITHYFYG5ART2CGAZLTD/bundle.json","state":"https://pith.science/pith/I7SMNOLITHYFYG5ART2CGAZLTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7SMNOLITHYFYG5ART2CGAZLTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:I7SMNOLITHYFYG5ART2CGAZLTD","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":"3eb4b1b53ddf94f41ad91ab7e6a61e8fd9339d8188ebf3a3e58d3af7c09f6138","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-20T16:39:04Z","title_canon_sha256":"a483fbfcfa1310949040bd9079a7e609ad730b27f53a13e4b2dfd29a1f700ff6"},"schema_version":"1.0","source":{"id":"quant-ph/0412157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0412157","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0412157v1","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0412157","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"I7SMNOLITHYF","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"I7SMNOLITHYFYG5A","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"I7SMNOLI","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a4b9c6c6da5b68352978d59d4d129ac1ff04c3feb2bb748f8d41435704490c6b","target":"graph","created_at":"2026-05-18T01:37:58Z","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":"We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\\Psi$ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the exponential separating rate is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set $\\Psi$. However, while in the classical case the separating subsets can be chosen universal, in the sense that they dep","authors_text":"A. Szkola, I. Bjelakovic, J.-D. Deuschel, Ra. Siegmund-Schultze, R. Seiler, T. Krueger","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-12-20T16:39:04Z","title":"A quantum version of Sanov's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0412157","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":"sha256:190086ed441a4f889e249d05fe7d840d2558cc18b6e6b884035c329b00399f6f","target":"record","created_at":"2026-05-18T01:37:58Z","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":"3eb4b1b53ddf94f41ad91ab7e6a61e8fd9339d8188ebf3a3e58d3af7c09f6138","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-20T16:39:04Z","title_canon_sha256":"a483fbfcfa1310949040bd9079a7e609ad730b27f53a13e4b2dfd29a1f700ff6"},"schema_version":"1.0","source":{"id":"quant-ph/0412157","kind":"arxiv","version":1}},"canonical_sha256":"47e4c6b96899f05c1ba08cf423032b98ccb2d2e99e5a970d8209ce21c8c770c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e4c6b96899f05c1ba08cf423032b98ccb2d2e99e5a970d8209ce21c8c770c3","first_computed_at":"2026-05-18T01:37:58.111204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:58.111204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"17Hax9futPJC1UWNe98rCIVTpKQld2vVPS9bexFJEgSDNiDcSARB8gRHcLDz7gPmFJj1EvbLH3gj0L5tQDK+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:58.111898Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0412157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:190086ed441a4f889e249d05fe7d840d2558cc18b6e6b884035c329b00399f6f","sha256:a4b9c6c6da5b68352978d59d4d129ac1ff04c3feb2bb748f8d41435704490c6b"],"state_sha256":"f0ffdb8ec13ae776b675a81e9e669c776fe9d0f06327a5fc830702f5a46b83ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uwR9G5mytBIfnB7SHTHFkRpSaD9UEIksZIXLrJQo/ECBMKRDuWeQCbGxB/ctyjYbQIYtsFxt7PdiYGJ6IlDzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:32:08.615133Z","bundle_sha256":"8c63bee06b9f0235712f07b79b56688e33d1ccb94f3bb06f0eb5a0c10e6f3916"}}