{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VGNKCOMXC5TGYSAKAKGNGAWAX7","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":"1162f5966b4b4f20723adbcfbbffca137b844368e57b3ecc166735c294edce83","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-03-27T17:11:15Z","title_canon_sha256":"8ad9e2448c209aad27148ca29968f36dda7554561e428242b367e2fca1082c19"},"schema_version":"1.0","source":{"id":"1703.09188","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09188","created_at":"2026-05-18T00:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09188v2","created_at":"2026-05-18T00:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09188","created_at":"2026-05-18T00:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"VGNKCOMXC5TG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VGNKCOMXC5TGYSAK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VGNKCOMX","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:f84116f91db1c521a0272472096c8be76a271971582ab86fa9493bb5ab9a8824","target":"graph","created_at":"2026-05-18T00:37:52Z","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":"Matrix Product Vectors form the appropriate framework to study and classify one-dimensional quantum systems. In this work, we develop the structure theory of Matrix Product Unitary operators (MPUs) which appear e.g. in the description of time evolutions of one-dimensional systems. We prove that all MPUs have a strict causal cone, making them Quantum Cellular Automata (QCAs), and derive a canonical form for MPUs which relates different MPU representations of the same unitary through a local gauge. We use this canonical form to prove an Index Theorem for MPUs which gives the precise conditions u","authors_text":"David Perez-Garcia, Frank Verstraete, J. Ignacio Cirac, Norbert Schuch","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-03-27T17:11:15Z","title":"Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09188","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:a15c5ab887be5eaafbd0d91b1e64de0cd22f46b797ddff942171183ecec2a952","target":"record","created_at":"2026-05-18T00:37:52Z","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":"1162f5966b4b4f20723adbcfbbffca137b844368e57b3ecc166735c294edce83","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-03-27T17:11:15Z","title_canon_sha256":"8ad9e2448c209aad27148ca29968f36dda7554561e428242b367e2fca1082c19"},"schema_version":"1.0","source":{"id":"1703.09188","kind":"arxiv","version":2}},"canonical_sha256":"a99aa1399717666c480a028cd302c0bfea655ab62a16fc965f9120e30159bfc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a99aa1399717666c480a028cd302c0bfea655ab62a16fc965f9120e30159bfc5","first_computed_at":"2026-05-18T00:37:52.559537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:52.559537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DEq/r88nvXbGHyvE+l5Ot2AKY7yYjuJ/YFIYxAKDaFnH3eiH45YvYsRAwE2DkcYuaDEDy9TQS7uLnrx4frd4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:52.560023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09188","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a15c5ab887be5eaafbd0d91b1e64de0cd22f46b797ddff942171183ecec2a952","sha256:f84116f91db1c521a0272472096c8be76a271971582ab86fa9493bb5ab9a8824"],"state_sha256":"029bb1d007f29782805e35b2fabcffe81f2d59b063c1d5b4cbbb994c441be456"}