{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:C3X3BRY2AX3IJWGSSFORDALTNJ","short_pith_number":"pith:C3X3BRY2","canonical_record":{"source":{"id":"1408.3712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-16T06:57:47Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"f2a535df13f4b752848f1211e34ae56d9f3a92f2762200b02b597466fcf227a7","abstract_canon_sha256":"812c9a3d8aca674a0e0f9cd374d26f8c1502efbb978670379347aaae4c32bd25"},"schema_version":"1.0"},"canonical_sha256":"16efb0c71a05f684d8d2915d1181736a70b84eaf91b10ba986aa21c60989697f","source":{"kind":"arxiv","id":"1408.3712","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3712","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3712v2","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3712","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"C3X3BRY2AX3I","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C3X3BRY2AX3IJWGS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C3X3BRY2","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:C3X3BRY2AX3IJWGSSFORDALTNJ","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-16T06:57:47Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"f2a535df13f4b752848f1211e34ae56d9f3a92f2762200b02b597466fcf227a7","abstract_canon_sha256":"812c9a3d8aca674a0e0f9cd374d26f8c1502efbb978670379347aaae4c32bd25"},"schema_version":"1.0"},"canonical_sha256":"16efb0c71a05f684d8d2915d1181736a70b84eaf91b10ba986aa21c60989697f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:07.785874Z","signature_b64":"hTQESCp996+BlOe5rlq7kgOY5D358FZjFhvT9g2p6LfU+Dq6ZmM0dx5rse8boilfRwJikZ+DryPAXocwrpDlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16efb0c71a05f684d8d2915d1181736a70b84eaf91b10ba986aa21c60989697f","last_reissued_at":"2026-05-18T02:27:07.784926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:07.784926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3712","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HNSMz7PV6+KG6LN9qV8Ho3YKk2AJSpciNL3nYm17Pv4wLduADXxo0Y8Ea1VON2JgELFGK0edygt9o/aH3xECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:38:52.498483Z"},"content_sha256":"761bbbfd4d1f09fbde1568fddce234cd1a99de0c8a188f3baead68694558ec40","schema_version":"1.0","event_id":"sha256:761bbbfd4d1f09fbde1568fddce234cd1a99de0c8a188f3baead68694558ec40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:C3X3BRY2AX3IJWGSSFORDALTNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"What can quantum optics say about computational complexity theory?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Austin P. Lund, Saleh Rahimi-Keshari, Timothy C. Ralph","submitted_at":"2014-08-16T06:57:47Z","abstract_excerpt":"Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3712","kind":"arxiv","version":2},"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":"2026-05-18T02:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FfcL+QBFAH6Al1xj+PkWsmFWjHIbD5QTQCAdNTQryXqH9QZcC7UD4HgYcsw8P7/f3st/96sG6HbwkGgmrMD/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:38:52.498834Z"},"content_sha256":"f8727b7583b4d7c43ac95d9482ec33910748c9cb51c080fe5c0a66c817353c76","schema_version":"1.0","event_id":"sha256:f8727b7583b4d7c43ac95d9482ec33910748c9cb51c080fe5c0a66c817353c76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3X3BRY2AX3IJWGSSFORDALTNJ/bundle.json","state_url":"https://pith.science/pith/C3X3BRY2AX3IJWGSSFORDALTNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3X3BRY2AX3IJWGSSFORDALTNJ/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":"2026-05-30T08:38:52Z","links":{"resolver":"https://pith.science/pith/C3X3BRY2AX3IJWGSSFORDALTNJ","bundle":"https://pith.science/pith/C3X3BRY2AX3IJWGSSFORDALTNJ/bundle.json","state":"https://pith.science/pith/C3X3BRY2AX3IJWGSSFORDALTNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3X3BRY2AX3IJWGSSFORDALTNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C3X3BRY2AX3IJWGSSFORDALTNJ","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":"812c9a3d8aca674a0e0f9cd374d26f8c1502efbb978670379347aaae4c32bd25","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-16T06:57:47Z","title_canon_sha256":"f2a535df13f4b752848f1211e34ae56d9f3a92f2762200b02b597466fcf227a7"},"schema_version":"1.0","source":{"id":"1408.3712","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3712","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3712v2","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3712","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"C3X3BRY2AX3I","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C3X3BRY2AX3IJWGS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C3X3BRY2","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:f8727b7583b4d7c43ac95d9482ec33910748c9cb51c080fe5c0a66c817353c76","target":"graph","created_at":"2026-05-18T02:27:07Z","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":"Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, w","authors_text":"Austin P. Lund, Saleh Rahimi-Keshari, Timothy C. Ralph","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-16T06:57:47Z","title":"What can quantum optics say about computational complexity theory?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3712","kind":"arxiv","version":2},"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":"sha256:761bbbfd4d1f09fbde1568fddce234cd1a99de0c8a188f3baead68694558ec40","target":"record","created_at":"2026-05-18T02:27:07Z","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":"812c9a3d8aca674a0e0f9cd374d26f8c1502efbb978670379347aaae4c32bd25","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-16T06:57:47Z","title_canon_sha256":"f2a535df13f4b752848f1211e34ae56d9f3a92f2762200b02b597466fcf227a7"},"schema_version":"1.0","source":{"id":"1408.3712","kind":"arxiv","version":2}},"canonical_sha256":"16efb0c71a05f684d8d2915d1181736a70b84eaf91b10ba986aa21c60989697f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16efb0c71a05f684d8d2915d1181736a70b84eaf91b10ba986aa21c60989697f","first_computed_at":"2026-05-18T02:27:07.784926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:07.784926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTQESCp996+BlOe5rlq7kgOY5D358FZjFhvT9g2p6LfU+Dq6ZmM0dx5rse8boilfRwJikZ+DryPAXocwrpDlDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:07.785874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3712","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:761bbbfd4d1f09fbde1568fddce234cd1a99de0c8a188f3baead68694558ec40","sha256:f8727b7583b4d7c43ac95d9482ec33910748c9cb51c080fe5c0a66c817353c76"],"state_sha256":"0809317805efe74ef7f76e6c98adf291e11ca9bc838c282565e1cfbad9421ca7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vtDy7bWMB4ltHmsoLxvngmcZ8tlQLMCUH0s3tKfZq+lCqU+DnbRP+XeM8GiaG9qbgTVGiYfZrZjdz4q2gCXkAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:38:52.500835Z","bundle_sha256":"af443bdf5bfbc804827d92353e1bed63b701a28e6c6af1c10e0b14a036f43c5d"}}