{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TCWUQRMBAR7WFLYFMZX7L4HGS2","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":"47662194dc315c878ac7b69139d21b93b7ae56efd4ee94fff3babb884e4c5e8d","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-30T15:33:37Z","title_canon_sha256":"e17aba763bf9bd7c8504c96e891daa470c61f462686740863f88337b73dad709"},"schema_version":"1.0","source":{"id":"1401.7883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7883","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7883v2","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7883","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"TCWUQRMBAR7W","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TCWUQRMBAR7WFLYF","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TCWUQRMB","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:c3c6f674f48d7ab56175cdd36adaf9a4f15e13cf624bb372668254626fa6a8be","target":"graph","created_at":"2026-05-18T02:27:51Z","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":"The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all line sums equal to 1. We conjecture that a similar procedure exists, which allows, starting from an arbitrary unitary matrix, to find a scaled matrix which is unitary and has all line sums equal to 1. The existence of such algorithm guarantees a powerful decomposition of an arbitrary quantum circuit.","authors_text":"Alexis De Vos, Stijn De Baerdemacker","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-30T15:33:37Z","title":"Scaling a unitary matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7883","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":"sha256:93030b667e69a766ae456137148659968687c47053b239cd8aa298e55eec38b0","target":"record","created_at":"2026-05-18T02:27:51Z","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":"47662194dc315c878ac7b69139d21b93b7ae56efd4ee94fff3babb884e4c5e8d","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-30T15:33:37Z","title_canon_sha256":"e17aba763bf9bd7c8504c96e891daa470c61f462686740863f88337b73dad709"},"schema_version":"1.0","source":{"id":"1401.7883","kind":"arxiv","version":2}},"canonical_sha256":"98ad484581047f62af05666ff5f0e696a0f90ea1fb7b9beda4797bd4a091dccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98ad484581047f62af05666ff5f0e696a0f90ea1fb7b9beda4797bd4a091dccd","first_computed_at":"2026-05-18T02:27:51.226869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:51.226869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UYBaP00q+DX3cEpGc/iJhb3TuMkkJoTxOvzHiwulWjEV6qYjAaQEhb01F8Xz3fViXpX7gQx5kd/FLr7s+aNGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:51.227385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93030b667e69a766ae456137148659968687c47053b239cd8aa298e55eec38b0","sha256:c3c6f674f48d7ab56175cdd36adaf9a4f15e13cf624bb372668254626fa6a8be"],"state_sha256":"c33c11abe15b12630c02c230caa3399f78db565128e218868e6c6e0270a1f378"}