{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YH7OIVTAFFPW2OEEWIVUXJ4LNB","short_pith_number":"pith:YH7OIVTA","schema_version":"1.0","canonical_sha256":"c1fee45660295f6d3884b22b4ba78b68663c4fd35cf07a289596973d5725f91a","source":{"kind":"arxiv","id":"1502.00819","version":1},"attestation_state":"computed","paper":{"title":"From reversible computation to quantum computation by Lagrange interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"quant-ph","authors_text":"Alexis De Vos, Stijn De Baerdemacker","submitted_at":"2015-02-03T11:34:18Z","abstract_excerpt":"Classical reversible circuits, acting on $w$~bits, are represented by permutation matrices of size $2^w \\times 2^w$. Those matrices form the group P($2^w$), isomorphic to the symmetric group {\\bf S}$_{2^w}$. The permutation group P($n$), isomorphic to {\\bf S}$_n$, contains cycles with length~$p$, ranging from~1 to $L(n)$, where $L(n)$ is the so-called Landau function. By Lagrange interpolation between the $p$~matrices of the cycle, we step from a finite cyclic group of order~$p$ to a 1-dimensional Lie group, subgroup of the unitary group U($n$). As U($2^w$) is the group of all possible quantum"},"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":"1502.00819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-03T11:34:18Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"94be89fd86ed91d433283cb1b66463a95f805cab944bcee2a7553734387fbae9","abstract_canon_sha256":"067f03ff83301ea62ba7c68923a57eb3f417daf3fb0b004171bcd6e5058b87a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:04.206700Z","signature_b64":"Eg7NBAUU5UfaGYgM8A4hJBT8NKV0o38JZfa/eNdH6X3HMyFyV+OkWynp5BZReHn3o8N0tn4nLZ/AZTr3ZoIUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1fee45660295f6d3884b22b4ba78b68663c4fd35cf07a289596973d5725f91a","last_reissued_at":"2026-05-18T02:28:04.206263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:04.206263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From reversible computation to quantum computation by Lagrange interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"quant-ph","authors_text":"Alexis De Vos, Stijn De Baerdemacker","submitted_at":"2015-02-03T11:34:18Z","abstract_excerpt":"Classical reversible circuits, acting on $w$~bits, are represented by permutation matrices of size $2^w \\times 2^w$. Those matrices form the group P($2^w$), isomorphic to the symmetric group {\\bf S}$_{2^w}$. The permutation group P($n$), isomorphic to {\\bf S}$_n$, contains cycles with length~$p$, ranging from~1 to $L(n)$, where $L(n)$ is the so-called Landau function. By Lagrange interpolation between the $p$~matrices of the cycle, we step from a finite cyclic group of order~$p$ to a 1-dimensional Lie group, subgroup of the unitary group U($n$). As U($2^w$) is the group of all possible quantum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00819","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":"1502.00819","created_at":"2026-05-18T02:28:04.206328+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.00819v1","created_at":"2026-05-18T02:28:04.206328+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00819","created_at":"2026-05-18T02:28:04.206328+00:00"},{"alias_kind":"pith_short_12","alias_value":"YH7OIVTAFFPW","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YH7OIVTAFFPW2OEE","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YH7OIVTA","created_at":"2026-05-18T12:29:50.041715+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/YH7OIVTAFFPW2OEEWIVUXJ4LNB","json":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB.json","graph_json":"https://pith.science/api/pith-number/YH7OIVTAFFPW2OEEWIVUXJ4LNB/graph.json","events_json":"https://pith.science/api/pith-number/YH7OIVTAFFPW2OEEWIVUXJ4LNB/events.json","paper":"https://pith.science/paper/YH7OIVTA"},"agent_actions":{"view_html":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB","download_json":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB.json","view_paper":"https://pith.science/paper/YH7OIVTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.00819&json=true","fetch_graph":"https://pith.science/api/pith-number/YH7OIVTAFFPW2OEEWIVUXJ4LNB/graph.json","fetch_events":"https://pith.science/api/pith-number/YH7OIVTAFFPW2OEEWIVUXJ4LNB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB/action/storage_attestation","attest_author":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB/action/author_attestation","sign_citation":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB/action/citation_signature","submit_replication":"https://pith.science/pith/YH7OIVTAFFPW2OEEWIVUXJ4LNB/action/replication_record"}},"created_at":"2026-05-18T02:28:04.206328+00:00","updated_at":"2026-05-18T02:28:04.206328+00:00"}