{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QAR7OQFO2UZ23B7BLLRJIXBZEJ","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":"b34ca0fced3b1367f4cf5a5a15d14fef7ba129c4d62c00114b0b27d0d2df5d7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-17T01:21:36Z","title_canon_sha256":"4611edb13d4e662b1baf4abe102f06579f3e36c9cfc13002704d3a6629a14ab6"},"schema_version":"1.0","source":{"id":"1204.3681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3681","created_at":"2026-05-18T03:18:26Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3681v2","created_at":"2026-05-18T03:18:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3681","created_at":"2026-05-18T03:18:26Z"},{"alias_kind":"pith_short_12","alias_value":"QAR7OQFO2UZ2","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QAR7OQFO2UZ23B7B","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QAR7OQFO","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:6bb79870cd739f01a72d8de1c81f8796e775fa48ce4dfffa4b526c84543320b9","target":"graph","created_at":"2026-05-18T03:18:26Z","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":"Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005), 47--79], we call a quantum dynamics on a digraph \"saturated Z-local\" if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence with the directed edges (including loops) of the digraph. This idea appears recurrently in a variety of contexts including angular momentum, quantum chaos, and combinatorial matrix theory. Complete characterization of the digraph properties that allow such a process to exist is a long-standing open question that can also be formulated in terms of minimum ran","authors_text":"H. Tracy Hall, Simone Severini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-17T01:21:36Z","title":"Locality for quantum systems on graphs depends on the number field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3681","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":"sha256:2592564259be5e048519df2bcad0dafdd1a9400cecbecc4e616c3145c3f145f5","target":"record","created_at":"2026-05-18T03:18:26Z","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":"b34ca0fced3b1367f4cf5a5a15d14fef7ba129c4d62c00114b0b27d0d2df5d7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-17T01:21:36Z","title_canon_sha256":"4611edb13d4e662b1baf4abe102f06579f3e36c9cfc13002704d3a6629a14ab6"},"schema_version":"1.0","source":{"id":"1204.3681","kind":"arxiv","version":2}},"canonical_sha256":"8023f740aed533ad87e15ae2945c39224354e36412a3a02de421848aaffd2069","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8023f740aed533ad87e15ae2945c39224354e36412a3a02de421848aaffd2069","first_computed_at":"2026-05-18T03:18:26.800929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:26.800929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6YbWKJ/b3TVgrkYUcNSQodXehpI9Z88AQZAuiA9uPjTtn/VbyDc+z7XAlEqWQXabh+jXt/NPVtAz2cmNvXXYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:26.801536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2592564259be5e048519df2bcad0dafdd1a9400cecbecc4e616c3145c3f145f5","sha256:6bb79870cd739f01a72d8de1c81f8796e775fa48ce4dfffa4b526c84543320b9"],"state_sha256":"96d3d54720b4e56332ac74dc566a692b4e8a0d8f5ed0bca97e3b6f606ca55242"}