{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J3EHFDNTR6S2JGTNVYPBKQ4U5S","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":"83605624b7c73413283c3e1b795b34c7746a45b815d5bd3ab9d095d108c47f59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-16T17:01:57Z","title_canon_sha256":"6ce92fc3dd0ec59753fbb670013e346a11ec89f5176ce9c61a65adec3a4588e0"},"schema_version":"1.0","source":{"id":"1309.4037","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4037","created_at":"2026-05-18T00:50:30Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4037v2","created_at":"2026-05-18T00:50:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4037","created_at":"2026-05-18T00:50:30Z"},{"alias_kind":"pith_short_12","alias_value":"J3EHFDNTR6S2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J3EHFDNTR6S2JGTN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J3EHFDNT","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:3767b864fb21d2523611661cfc7956c7fe3a5ecbcd738c608a1d499c8696f29f","target":"graph","created_at":"2026-05-18T00:50:30Z","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":"It is well known that most of the frequently used reversible logic gates (e.g., NOT, CNOT, SWAP, Toffoli, Fredkin) are self-inverse and are represented by square matrices that are unitary and Hermitian. However, with a simple minded argument, it is established that the most of the allowed reversible gates are non-self-inverse (unitary but non-Hermitian) in nature. It is also shown that the % of non-Hermitian gates increases with the dimension. For example, 58.33% of the 2-bit gates, 98.10% of the 3-bit gates and 99.99% of the 4-bit gates are non-Hermitian. As classical reversible gates are ess","authors_text":"Anirban Pathak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-16T17:01:57Z","title":"Statistical distribution of the reversible gates: what percentage of them are self-inverse?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4037","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":"sha256:3f74ecd8f2a5f2112c26c6d725791a3c9f8c6084ef8cb84d46bd1e7351817837","target":"record","created_at":"2026-05-18T00:50:30Z","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":"83605624b7c73413283c3e1b795b34c7746a45b815d5bd3ab9d095d108c47f59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-16T17:01:57Z","title_canon_sha256":"6ce92fc3dd0ec59753fbb670013e346a11ec89f5176ce9c61a65adec3a4588e0"},"schema_version":"1.0","source":{"id":"1309.4037","kind":"arxiv","version":2}},"canonical_sha256":"4ec8728db38fa5a49a6dae1e154394ecb8242fa0d720a91adc3d179cfb41e38e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ec8728db38fa5a49a6dae1e154394ecb8242fa0d720a91adc3d179cfb41e38e","first_computed_at":"2026-05-18T00:50:30.069720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:30.069720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A6WqrQtwqXW8vPSS7EsHwkp600b/R7+awT0QY7TF6XIiW2VJoMZ6v4hMnhD8VtK7akfPQg5vbhRKVw42rjZeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:30.070474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4037","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f74ecd8f2a5f2112c26c6d725791a3c9f8c6084ef8cb84d46bd1e7351817837","sha256:3767b864fb21d2523611661cfc7956c7fe3a5ecbcd738c608a1d499c8696f29f"],"state_sha256":"8886eb91a24129b51398576d97526181dbc59328fcc46c45629e62ea17bbdb47"}