{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GNASJVSYM2JDLBCBQ25KZYRNME","short_pith_number":"pith:GNASJVSY","canonical_record":{"source":{"id":"1409.5840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-20T01:38:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b49cf41e4138679d2864b26622f9f5992e48c79d2ba8109f9c75253df7119331","abstract_canon_sha256":"968b41331d73aeae86d4e8407f8dcb751ba1987f569273dad2e708420daf86d6"},"schema_version":"1.0"},"canonical_sha256":"334124d658669235844186baace22d61110e1501070012a27c655da11847820c","source":{"kind":"arxiv","id":"1409.5840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5840","created_at":"2026-05-18T01:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5840v1","created_at":"2026-05-18T01:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5840","created_at":"2026-05-18T01:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"GNASJVSYM2JD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNASJVSYM2JDLBCB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNASJVSY","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GNASJVSYM2JDLBCBQ25KZYRNME","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-20T01:38:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b49cf41e4138679d2864b26622f9f5992e48c79d2ba8109f9c75253df7119331","abstract_canon_sha256":"968b41331d73aeae86d4e8407f8dcb751ba1987f569273dad2e708420daf86d6"},"schema_version":"1.0"},"canonical_sha256":"334124d658669235844186baace22d61110e1501070012a27c655da11847820c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:23.930829Z","signature_b64":"IqkucMEVByz5PRwCbq+3psXtFR92DKKKPLLOqcSLqfpvZFGSzW6kb711qh4i2SCnbo+2MExvrmpsP5Hyi4EFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"334124d658669235844186baace22d61110e1501070012a27c655da11847820c","last_reissued_at":"2026-05-18T01:15:23.930131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:23.930131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5840","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MB+LM49gkf443WySgp1BkRD90Fk+1V0XwDINZP4lKL5+qCMhEbT4x80WWKgt5RO0W/J3SlGd1JGYK3wPu22oDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:31:24.815670Z"},"content_sha256":"06335bdc602feacb6dfd4197658234a88fa381ddfa8d0c32a67b330e78cd742a","schema_version":"1.0","event_id":"sha256:06335bdc602feacb6dfd4197658234a88fa381ddfa8d0c32a67b330e78cd742a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GNASJVSYM2JDLBCBQ25KZYRNME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect State Transfer in Laplacian Quantum Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"B Lovitz, C. Tamon, H. Zhan, J. Myer, R. Alvir, S. Dever, Y. Xu","submitted_at":"2014-09-20T01:38:16Z","abstract_excerpt":"For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \\exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between vertices $u$ and $v$ at time $\\tau$ if the $(u,v)$-entry of $U(\\tau)$ has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer:\n  (1) If a $n$-vertex graph has perfect state transfer at time $\\tau$ relative to the Laplacian, then so does its compleme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5840","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pP65fFm1JhzYqO0ACN8UQLVNsdrsdC4EnHv3qAldQu0OtmFoMZXC4B+i4PpI2OSWCrHpxRTttEJ5xEGtOAjXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:31:24.816234Z"},"content_sha256":"71244899a810b61d382346a71724fde7df9771d01374147263dff64d543e0a83","schema_version":"1.0","event_id":"sha256:71244899a810b61d382346a71724fde7df9771d01374147263dff64d543e0a83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNASJVSYM2JDLBCBQ25KZYRNME/bundle.json","state_url":"https://pith.science/pith/GNASJVSYM2JDLBCBQ25KZYRNME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNASJVSYM2JDLBCBQ25KZYRNME/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T16:31:24Z","links":{"resolver":"https://pith.science/pith/GNASJVSYM2JDLBCBQ25KZYRNME","bundle":"https://pith.science/pith/GNASJVSYM2JDLBCBQ25KZYRNME/bundle.json","state":"https://pith.science/pith/GNASJVSYM2JDLBCBQ25KZYRNME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNASJVSYM2JDLBCBQ25KZYRNME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GNASJVSYM2JDLBCBQ25KZYRNME","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":"968b41331d73aeae86d4e8407f8dcb751ba1987f569273dad2e708420daf86d6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-20T01:38:16Z","title_canon_sha256":"b49cf41e4138679d2864b26622f9f5992e48c79d2ba8109f9c75253df7119331"},"schema_version":"1.0","source":{"id":"1409.5840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5840","created_at":"2026-05-18T01:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5840v1","created_at":"2026-05-18T01:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5840","created_at":"2026-05-18T01:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"GNASJVSYM2JD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNASJVSYM2JDLBCB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNASJVSY","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:71244899a810b61d382346a71724fde7df9771d01374147263dff64d543e0a83","target":"graph","created_at":"2026-05-18T01:15:23Z","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":"For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \\exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between vertices $u$ and $v$ at time $\\tau$ if the $(u,v)$-entry of $U(\\tau)$ has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer:\n  (1) If a $n$-vertex graph has perfect state transfer at time $\\tau$ relative to the Laplacian, then so does its compleme","authors_text":"B Lovitz, C. Tamon, H. Zhan, J. Myer, R. Alvir, S. Dever, Y. Xu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-20T01:38:16Z","title":"Perfect State Transfer in Laplacian Quantum Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5840","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":"sha256:06335bdc602feacb6dfd4197658234a88fa381ddfa8d0c32a67b330e78cd742a","target":"record","created_at":"2026-05-18T01:15:23Z","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":"968b41331d73aeae86d4e8407f8dcb751ba1987f569273dad2e708420daf86d6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-20T01:38:16Z","title_canon_sha256":"b49cf41e4138679d2864b26622f9f5992e48c79d2ba8109f9c75253df7119331"},"schema_version":"1.0","source":{"id":"1409.5840","kind":"arxiv","version":1}},"canonical_sha256":"334124d658669235844186baace22d61110e1501070012a27c655da11847820c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"334124d658669235844186baace22d61110e1501070012a27c655da11847820c","first_computed_at":"2026-05-18T01:15:23.930131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:23.930131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IqkucMEVByz5PRwCbq+3psXtFR92DKKKPLLOqcSLqfpvZFGSzW6kb711qh4i2SCnbo+2MExvrmpsP5Hyi4EFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:23.930829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06335bdc602feacb6dfd4197658234a88fa381ddfa8d0c32a67b330e78cd742a","sha256:71244899a810b61d382346a71724fde7df9771d01374147263dff64d543e0a83"],"state_sha256":"e448892fc47acde41317716a02b3244210a53cbaa9c0582ec1c8e4f71c617d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"moUEOfwJg/zz+tLHWH2r988bqy+Xk3xut0xU5tDjinh3UlfCB5XJb5vJqRB5OdF3eSwgzbx1B0Lnqk5IMVUmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:31:24.820438Z","bundle_sha256":"f486d01688f66db8528c02325c20634bed036fb8ee93038334f3fb57852a8760"}}