{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BPPIVBFMZJ4BPJHTZFRHGGIXJW","short_pith_number":"pith:BPPIVBFM","schema_version":"1.0","canonical_sha256":"0bde8a84acca7817a4f3c9627319174db45007651ddc3aab6b0a149b0e7431e8","source":{"kind":"arxiv","id":"1502.05825","version":1},"attestation_state":"computed","paper":{"title":"Self-Inverse Functions and Palindromic Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","quant-ph"],"primary_cat":"cs.ET","authors_text":"D. Michael Miller, Gerhard W. Dueck, Mathias Soeken, Michael Kirkedal Thomsen","submitted_at":"2015-02-20T10:36:34Z","abstract_excerpt":"We investigate the subclass of reversible functions that are self-inverse and relate them to reversible circuits that are equal to their reverse circuit, which are called palindromic circuits. We precisely determine which self-inverse functions can be realized as a palindromic circuit. For those functions that cannot be realized as a palindromic circuit, we find alternative palindromic representations that require an extra circuit line or quantum gates in their construction. Our analyses make use of involutions in the symmetric group $S_{2^n}$ which are isomorphic to self-inverse reversible fu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.05825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.ET","submitted_at":"2015-02-20T10:36:34Z","cross_cats_sorted":["math.GR","quant-ph"],"title_canon_sha256":"9d5fea89b9d697d2097ecdfcf2339ed6e77fb986ed0ac99c0ea966003026e369","abstract_canon_sha256":"07d1f77a16d10e0323e92eb1a787b1a21111f021c4bdd5c910e5201baa02cedd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:44.700114Z","signature_b64":"t3Eicq8P4ZYs6CCs17CtT6lpBoZKm1jlHH1cfMro0O4gUu8LkmUE8gFeBTLe6FJR0q8CNfQnQ8Ke5HjpFhmVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bde8a84acca7817a4f3c9627319174db45007651ddc3aab6b0a149b0e7431e8","last_reissued_at":"2026-05-18T02:26:44.699715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:44.699715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-Inverse Functions and Palindromic Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","quant-ph"],"primary_cat":"cs.ET","authors_text":"D. Michael Miller, Gerhard W. Dueck, Mathias Soeken, Michael Kirkedal Thomsen","submitted_at":"2015-02-20T10:36:34Z","abstract_excerpt":"We investigate the subclass of reversible functions that are self-inverse and relate them to reversible circuits that are equal to their reverse circuit, which are called palindromic circuits. We precisely determine which self-inverse functions can be realized as a palindromic circuit. For those functions that cannot be realized as a palindromic circuit, we find alternative palindromic representations that require an extra circuit line or quantum gates in their construction. Our analyses make use of involutions in the symmetric group $S_{2^n}$ which are isomorphic to self-inverse reversible fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05825","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.05825","created_at":"2026-05-18T02:26:44.699770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05825v1","created_at":"2026-05-18T02:26:44.699770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05825","created_at":"2026-05-18T02:26:44.699770+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPPIVBFMZJ4B","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPPIVBFMZJ4BPJHT","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPPIVBFM","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW","json":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW.json","graph_json":"https://pith.science/api/pith-number/BPPIVBFMZJ4BPJHTZFRHGGIXJW/graph.json","events_json":"https://pith.science/api/pith-number/BPPIVBFMZJ4BPJHTZFRHGGIXJW/events.json","paper":"https://pith.science/paper/BPPIVBFM"},"agent_actions":{"view_html":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW","download_json":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW.json","view_paper":"https://pith.science/paper/BPPIVBFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05825&json=true","fetch_graph":"https://pith.science/api/pith-number/BPPIVBFMZJ4BPJHTZFRHGGIXJW/graph.json","fetch_events":"https://pith.science/api/pith-number/BPPIVBFMZJ4BPJHTZFRHGGIXJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW/action/storage_attestation","attest_author":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW/action/author_attestation","sign_citation":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW/action/citation_signature","submit_replication":"https://pith.science/pith/BPPIVBFMZJ4BPJHTZFRHGGIXJW/action/replication_record"}},"created_at":"2026-05-18T02:26:44.699770+00:00","updated_at":"2026-05-18T02:26:44.699770+00:00"}