{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WZMPUSC7EI3PYEHR4ESP3B2TZH","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":"4f7903d2790fa317db7cf210dcab06b1e38f934524d9a8823f8e3dd88dd4391e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-20T22:48:27Z","title_canon_sha256":"bfd161336360422c3398f6360045b0e91010f203c8fed5b78845bbd8c7477027"},"schema_version":"1.0","source":{"id":"1103.3899","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3899","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3899v4","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3899","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"WZMPUSC7EI3P","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WZMPUSC7EI3PYEHR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WZMPUSC7","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:beedff6a8ffe534e44c81a250cde08e55334fdbed03a531e8b066b693969a247","target":"graph","created_at":"2026-05-18T04:17:04Z","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":"We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given.","authors_text":"Clement Ampadu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-20T22:48:27Z","title":"Limit Theorems For Quantum Walks Associated with Hadamard Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3899","kind":"arxiv","version":4},"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":"sha256:8fe80aecf3ada047ae0024bacc69bf346ce9cff5da8d5b8f144ea9ea2bc9ef5f","target":"record","created_at":"2026-05-18T04:17:04Z","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":"4f7903d2790fa317db7cf210dcab06b1e38f934524d9a8823f8e3dd88dd4391e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-20T22:48:27Z","title_canon_sha256":"bfd161336360422c3398f6360045b0e91010f203c8fed5b78845bbd8c7477027"},"schema_version":"1.0","source":{"id":"1103.3899","kind":"arxiv","version":4}},"canonical_sha256":"b658fa485f2236fc10f1e124fd8753c9c5d5785404992ed6d20a366ff28fd530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b658fa485f2236fc10f1e124fd8753c9c5d5785404992ed6d20a366ff28fd530","first_computed_at":"2026-05-18T04:17:04.310201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:04.310201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yMXYerVawD+ut7PzRO1Hsuya6/IXMoprcZuwvqrZTzLLKE/mBgiGgwSOK+lAaUufyjVR7jaM9pXpBSXHy4xfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:04.310687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3899","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fe80aecf3ada047ae0024bacc69bf346ce9cff5da8d5b8f144ea9ea2bc9ef5f","sha256:beedff6a8ffe534e44c81a250cde08e55334fdbed03a531e8b066b693969a247"],"state_sha256":"bada6f072f9cc83549348d397dc5e73c30c66559eb68064839671f6f139d43cc"}