{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:2D37LYMWVTFUHZ4QOHAEWU3QTN","short_pith_number":"pith:2D37LYMW","canonical_record":{"source":{"id":"2302.08083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-02-16T04:42:40Z","cross_cats_sorted":["math.NT","math.QA","math.RT"],"title_canon_sha256":"f0c022f6e95714ba4cab7421a659e0e31f64134be4b4fa51780833d1da9719c4","abstract_canon_sha256":"dedca8a6bbcf479e040deaaff8727fc4415214fe0411ea8ad0d9890d7fa7200e"},"schema_version":"1.0"},"canonical_sha256":"d0f7f5e196accb43e79071c04b53709b6469f32894ec23fe27a24c005f1477e6","source":{"kind":"arxiv","id":"2302.08083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08083","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08083v1","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08083","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"2D37LYMWVTFU","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"pith_short_16","alias_value":"2D37LYMWVTFUHZ4Q","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"pith_short_8","alias_value":"2D37LYMW","created_at":"2026-07-05T05:42:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:2D37LYMWVTFUHZ4QOHAEWU3QTN","target":"record","payload":{"canonical_record":{"source":{"id":"2302.08083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-02-16T04:42:40Z","cross_cats_sorted":["math.NT","math.QA","math.RT"],"title_canon_sha256":"f0c022f6e95714ba4cab7421a659e0e31f64134be4b4fa51780833d1da9719c4","abstract_canon_sha256":"dedca8a6bbcf479e040deaaff8727fc4415214fe0411ea8ad0d9890d7fa7200e"},"schema_version":"1.0"},"canonical_sha256":"d0f7f5e196accb43e79071c04b53709b6469f32894ec23fe27a24c005f1477e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:42:33.990183Z","signature_b64":"Nj3rCXMpOvTO6yaV7BVomGFZAphT8xGVIFOtZ9G0fMVy1zbQwbfx3cJFQQrrocmJTzRpDI4+D+VsF1UAOg8yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0f7f5e196accb43e79071c04b53709b6469f32894ec23fe27a24c005f1477e6","last_reissued_at":"2026-07-05T05:42:33.989794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:42:33.989794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.08083","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":"2026-07-05T05:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tceTPeIllLijHzAMBvfMzX1rxOWjDeOObvM3DrsemryWdTlB+q6/LEhcj24AvlYHFsASZLf1EnTp7pvpypo1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:49:06.989417Z"},"content_sha256":"0e7bd109c37796a3d52cda706c5d830423f20c05385f7ab243cd696d6cf9d5a7","schema_version":"1.0","event_id":"sha256:0e7bd109c37796a3d52cda706c5d830423f20c05385f7ab243cd696d6cf9d5a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:2D37LYMWVTFUHZ4QOHAEWU3QTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Computational Complexity of Quantum Determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.QA","math.RT"],"primary_cat":"cs.CC","authors_text":"En-Jui Kuo, Shih-Han Hung","submitted_at":"2023-02-16T04:42:40Z","abstract_excerpt":"In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\\times n$ matrix $X$, the $q$-permanent of $X$ is defined as $$\\mathrm{Per}_q(X) = \\sum_{\\sigma\\in S_n} q^{\\ell(\\sigma)}X_{1,\\sigma(1)}\\ldots X_{n,\\sigma(n)},$$ where $\\ell(\\sigma)$ is the inversion number of permutation $\\sigma$ in the symmetric group $S_n$ on $n$ elements. The function family generalizes determinant and permanent, which correspond to the cases $q=-1$ and $q=1$ respectively.\n  For worst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08083","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/2302.08083/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":"2026-07-05T05:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SvxlvuX5GFS412/vDUlX7ewKuyFG1AKuKRktXmqlcSmxmEQw7HQ/hgwMrljCB4mZk8wng1N0b/gpvBB3rpvEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:49:06.989891Z"},"content_sha256":"b4b976963d5de4c2911c8b5cfe4b7b2ba32b293b466ff920fbab13354de73f90","schema_version":"1.0","event_id":"sha256:b4b976963d5de4c2911c8b5cfe4b7b2ba32b293b466ff920fbab13354de73f90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN/bundle.json","state_url":"https://pith.science/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN/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":"2026-08-18T15:49:06Z","links":{"resolver":"https://pith.science/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN","bundle":"https://pith.science/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN/bundle.json","state":"https://pith.science/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2D37LYMWVTFUHZ4QOHAEWU3QTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2D37LYMWVTFUHZ4QOHAEWU3QTN","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":"dedca8a6bbcf479e040deaaff8727fc4415214fe0411ea8ad0d9890d7fa7200e","cross_cats_sorted":["math.NT","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-02-16T04:42:40Z","title_canon_sha256":"f0c022f6e95714ba4cab7421a659e0e31f64134be4b4fa51780833d1da9719c4"},"schema_version":"1.0","source":{"id":"2302.08083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08083","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08083v1","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08083","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"2D37LYMWVTFU","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"pith_short_16","alias_value":"2D37LYMWVTFUHZ4Q","created_at":"2026-07-05T05:42:33Z"},{"alias_kind":"pith_short_8","alias_value":"2D37LYMW","created_at":"2026-07-05T05:42:33Z"}],"graph_snapshots":[{"event_id":"sha256:b4b976963d5de4c2911c8b5cfe4b7b2ba32b293b466ff920fbab13354de73f90","target":"graph","created_at":"2026-07-05T05:42:33Z","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/2302.08083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\\times n$ matrix $X$, the $q$-permanent of $X$ is defined as $$\\mathrm{Per}_q(X) = \\sum_{\\sigma\\in S_n} q^{\\ell(\\sigma)}X_{1,\\sigma(1)}\\ldots X_{n,\\sigma(n)},$$ where $\\ell(\\sigma)$ is the inversion number of permutation $\\sigma$ in the symmetric group $S_n$ on $n$ elements. The function family generalizes determinant and permanent, which correspond to the cases $q=-1$ and $q=1$ respectively.\n  For worst","authors_text":"En-Jui Kuo, Shih-Han Hung","cross_cats":["math.NT","math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-02-16T04:42:40Z","title":"The Computational Complexity of Quantum Determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08083","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":"sha256:0e7bd109c37796a3d52cda706c5d830423f20c05385f7ab243cd696d6cf9d5a7","target":"record","created_at":"2026-07-05T05:42:33Z","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":"dedca8a6bbcf479e040deaaff8727fc4415214fe0411ea8ad0d9890d7fa7200e","cross_cats_sorted":["math.NT","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2023-02-16T04:42:40Z","title_canon_sha256":"f0c022f6e95714ba4cab7421a659e0e31f64134be4b4fa51780833d1da9719c4"},"schema_version":"1.0","source":{"id":"2302.08083","kind":"arxiv","version":1}},"canonical_sha256":"d0f7f5e196accb43e79071c04b53709b6469f32894ec23fe27a24c005f1477e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0f7f5e196accb43e79071c04b53709b6469f32894ec23fe27a24c005f1477e6","first_computed_at":"2026-07-05T05:42:33.989794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:42:33.989794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nj3rCXMpOvTO6yaV7BVomGFZAphT8xGVIFOtZ9G0fMVy1zbQwbfx3cJFQQrrocmJTzRpDI4+D+VsF1UAOg8yDA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:42:33.990183Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.08083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e7bd109c37796a3d52cda706c5d830423f20c05385f7ab243cd696d6cf9d5a7","sha256:b4b976963d5de4c2911c8b5cfe4b7b2ba32b293b466ff920fbab13354de73f90"],"state_sha256":"c154f441c1f29416bb2231952b2c50dfec49303462e4c5234d5ab111b5d3609c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63BnU3pYuOJ3UCTpDaYIL3NJ/fAzVzGzlclwTYeuU4p/S/fOfTLTS70vG3M/U2eWSkjrd+1apMdQyU+orNQKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T15:49:06.993975Z","bundle_sha256":"a94144ff84ed292d13a12afed1ff0741b798d915050aa45c631177d2ef3d6eaa"}}