{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UMO2BDABABWEFOFAGFLQIS72LG","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":"71d0911b9bc826450e1679e231bc9c866680f465e7837c5c882a6a13eeccd647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-30T18:57:57Z","title_canon_sha256":"ed0f396e18059fa9559bd2ebef2969f17bee72ebc60592d7fd28cedf95842a5d"},"schema_version":"1.0","source":{"id":"1710.11192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11192","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11192v1","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11192","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"UMO2BDABABWE","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UMO2BDABABWEFOFA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UMO2BDAB","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:a1e5eb429653d801d5336a70ac10e1c55fc5ae537c062da0afa8cf524b8365f6","target":"graph","created_at":"2026-05-18T00:31:44Z","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":"Let $X$ be a graph with adjacency matrix $A$. The \\textsl{continuous quantum walk} on $X$ is determined by the unitary matrices $U(t)=\\exp(itA)$. If $X$ is the complete graph $K_n$ and $a\\in V(X)$, then \\[1-|U(t)_{a,a}|\\le2/n. \\] In a sense, this means that a quantum walk on a complete graph stay home with high probability. In this paper we consider quantum walks on cones over an $\\ell$-regular graph on $n$ vertices. We prove that if $\\ell^2/n\\to\\infty$ as $n$ increases, than a quantum walk that starts on the apex of the cone will remain on it with probability tending to $1$ as $n$ increases. ","authors_text":"Chris Godsil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-30T18:57:57Z","title":"Sedentary quantum walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11192","kind":"arxiv","version":1},"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":"sha256:43ab639cdc24469af42b40fba1451af3aa699fc9b74fd4764963119bbbe48349","target":"record","created_at":"2026-05-18T00:31:44Z","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":"71d0911b9bc826450e1679e231bc9c866680f465e7837c5c882a6a13eeccd647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-30T18:57:57Z","title_canon_sha256":"ed0f396e18059fa9559bd2ebef2969f17bee72ebc60592d7fd28cedf95842a5d"},"schema_version":"1.0","source":{"id":"1710.11192","kind":"arxiv","version":1}},"canonical_sha256":"a31da08c01006c42b8a03157044bfa59a0b8a331a42228a458d1c8e469475905","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31da08c01006c42b8a03157044bfa59a0b8a331a42228a458d1c8e469475905","first_computed_at":"2026-05-18T00:31:44.625464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:44.625464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nwYuD9IH3ySQQIH7C21sgLBiidFy2jx1/GsmnIMVXzQ5Mcswe5FNAI4KIu7X/jF0N+MvvsmEiffaYEXtM04XDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:44.625938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43ab639cdc24469af42b40fba1451af3aa699fc9b74fd4764963119bbbe48349","sha256:a1e5eb429653d801d5336a70ac10e1c55fc5ae537c062da0afa8cf524b8365f6"],"state_sha256":"90decebf8f43af0773d56aae8f202a2082c27c4ac0b3f99400aa5c4c92f036b8"}