{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XPU65HLFRP6TF6YH5CEYNUIYBZ","short_pith_number":"pith:XPU65HLF","canonical_record":{"source":{"id":"1610.04670","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-15T00:03:32Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"543fc97fc6f944fe80119916ed4050e6d1d21e8b292dd1c5b56246260394db43","abstract_canon_sha256":"3dbf204a08f85b2a1c5c5b3cf04aed0375143e70b3149faa4e90d705fd19bd95"},"schema_version":"1.0"},"canonical_sha256":"bbe9ee9d658bfd32fb07e88986d1180e4fdb1d2d2dc1d41f0fb626e7a1593c6e","source":{"kind":"arxiv","id":"1610.04670","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04670","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04670v2","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04670","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"XPU65HLFRP6T","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XPU65HLFRP6TF6YH","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XPU65HLF","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XPU65HLFRP6TF6YH5CEYNUIYBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04670","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-15T00:03:32Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"543fc97fc6f944fe80119916ed4050e6d1d21e8b292dd1c5b56246260394db43","abstract_canon_sha256":"3dbf204a08f85b2a1c5c5b3cf04aed0375143e70b3149faa4e90d705fd19bd95"},"schema_version":"1.0"},"canonical_sha256":"bbe9ee9d658bfd32fb07e88986d1180e4fdb1d2d2dc1d41f0fb626e7a1593c6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:21.202557Z","signature_b64":"o/3DtHCdedfXoVCC2VqzzLssNYwbwuNEi31Oco40FIIZGoXDWEbZYUxNqrAIRr9PIlQSaV4aiIUNkyc/sFeYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbe9ee9d658bfd32fb07e88986d1180e4fdb1d2d2dc1d41f0fb626e7a1593c6e","last_reissued_at":"2026-05-18T00:22:21.202002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:21.202002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04670","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":"2026-05-18T00:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/XOUIoCKtwUCkq3EAhCtM6J2rOj0YGAM2KeL16ZUsa6wMQQFJhhKFq/UnLmM/6+syGQ6TdMRp2N8rWOl1csDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:11.457411Z"},"content_sha256":"6d2d7d51fba3377e0a63256b968f6b5741a24126875456b1fddfe79cab826e3f","schema_version":"1.0","event_id":"sha256:6d2d7d51fba3377e0a63256b968f6b5741a24126875456b1fddfe79cab826e3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XPU65HLFRP6TF6YH5CEYNUIYBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Hardness Results for the Permanent Using Linear Optics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Daniel Grier, Luke Schaeffer","submitted_at":"2016-10-15T00:03:32Z","abstract_excerpt":"In 2011, Aaronson gave a striking proof, based on quantum linear optics, showing that the problem of computing the permanent of a matrix is #P-hard. Aaronson's proof led naturally to hardness of approximation results for the permanent, and it was arguably simpler than Valiant's seminal proof of the same fact in 1979. Nevertheless, it did not prove that computing the permanent was #P-hard for any class of matrices which was not previously known. In this paper, we present a collection of new results about matrix permanents that are derived primarily via these linear optical techniques.\n  First, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04670","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":"2026-05-18T00:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27s4q6nWWzLGRPa2ORf72l6+zpgw6JlkOLW+gHvZyw6QlY4iW4CtXIM7uySFi3uJGgq85ENlQe2oB2MALaffAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:11.457756Z"},"content_sha256":"5464c3155aed2baabe9aebf68d1ede5b634b3f0da8da1434ac41245fbc312e7f","schema_version":"1.0","event_id":"sha256:5464c3155aed2baabe9aebf68d1ede5b634b3f0da8da1434ac41245fbc312e7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ/bundle.json","state_url":"https://pith.science/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ/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":"2026-06-04T20:24:11Z","links":{"resolver":"https://pith.science/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ","bundle":"https://pith.science/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ/bundle.json","state":"https://pith.science/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPU65HLFRP6TF6YH5CEYNUIYBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XPU65HLFRP6TF6YH5CEYNUIYBZ","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":"3dbf204a08f85b2a1c5c5b3cf04aed0375143e70b3149faa4e90d705fd19bd95","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-15T00:03:32Z","title_canon_sha256":"543fc97fc6f944fe80119916ed4050e6d1d21e8b292dd1c5b56246260394db43"},"schema_version":"1.0","source":{"id":"1610.04670","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04670","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04670v2","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04670","created_at":"2026-05-18T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"XPU65HLFRP6T","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XPU65HLFRP6TF6YH","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XPU65HLF","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:5464c3155aed2baabe9aebf68d1ede5b634b3f0da8da1434ac41245fbc312e7f","target":"graph","created_at":"2026-05-18T00:22:21Z","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 2011, Aaronson gave a striking proof, based on quantum linear optics, showing that the problem of computing the permanent of a matrix is #P-hard. Aaronson's proof led naturally to hardness of approximation results for the permanent, and it was arguably simpler than Valiant's seminal proof of the same fact in 1979. Nevertheless, it did not prove that computing the permanent was #P-hard for any class of matrices which was not previously known. In this paper, we present a collection of new results about matrix permanents that are derived primarily via these linear optical techniques.\n  First, ","authors_text":"Daniel Grier, Luke Schaeffer","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-15T00:03:32Z","title":"New Hardness Results for the Permanent Using Linear Optics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04670","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":"sha256:6d2d7d51fba3377e0a63256b968f6b5741a24126875456b1fddfe79cab826e3f","target":"record","created_at":"2026-05-18T00:22:21Z","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":"3dbf204a08f85b2a1c5c5b3cf04aed0375143e70b3149faa4e90d705fd19bd95","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-15T00:03:32Z","title_canon_sha256":"543fc97fc6f944fe80119916ed4050e6d1d21e8b292dd1c5b56246260394db43"},"schema_version":"1.0","source":{"id":"1610.04670","kind":"arxiv","version":2}},"canonical_sha256":"bbe9ee9d658bfd32fb07e88986d1180e4fdb1d2d2dc1d41f0fb626e7a1593c6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbe9ee9d658bfd32fb07e88986d1180e4fdb1d2d2dc1d41f0fb626e7a1593c6e","first_computed_at":"2026-05-18T00:22:21.202002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:21.202002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o/3DtHCdedfXoVCC2VqzzLssNYwbwuNEi31Oco40FIIZGoXDWEbZYUxNqrAIRr9PIlQSaV4aiIUNkyc/sFeYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:21.202557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04670","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d2d7d51fba3377e0a63256b968f6b5741a24126875456b1fddfe79cab826e3f","sha256:5464c3155aed2baabe9aebf68d1ede5b634b3f0da8da1434ac41245fbc312e7f"],"state_sha256":"e1242bf25c7f0c4b5997a626c5c4fcf28d2a955c3e6e420174f69b78717fb84c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDXbTT4IVLGjshb8SXIJbUVOYY3jclU4SutTrHRH4NfEcs+YajtcxKWma0hHzamwMor4oXmSvfo2LQJjRi2cBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:24:11.459881Z","bundle_sha256":"43f87d41f927a067aa2cbdf1536ba2b9be210f77bee7769a3ea1eeaa872a1b01"}}