{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:22MXFN7GRIQ4T23YDUCT7ZGRMD","short_pith_number":"pith:22MXFN7G","canonical_record":{"source":{"id":"quant-ph/0104137","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-29T00:28:03Z","cross_cats_sorted":[],"title_canon_sha256":"ef5035de46ac858f6870d7a1a0978eb3c2d983e899f399ff1185518a52826dd8","abstract_canon_sha256":"9fcb07867011628019fdd5e667801c32a53df611e11b7cf6219f5fea0617043a"},"schema_version":"1.0"},"canonical_sha256":"d69972b7e68a21c9eb781d053fe4d160e7de41eeb55fe17b163a1db805239df7","source":{"kind":"arxiv","id":"quant-ph/0104137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0104137","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0104137v1","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0104137","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"22MXFN7GRIQ4","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"pith_short_16","alias_value":"22MXFN7GRIQ4T23Y","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"pith_short_8","alias_value":"22MXFN7G","created_at":"2026-07-04T14:45:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:22MXFN7GRIQ4T23YDUCT7ZGRMD","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0104137","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-29T00:28:03Z","cross_cats_sorted":[],"title_canon_sha256":"ef5035de46ac858f6870d7a1a0978eb3c2d983e899f399ff1185518a52826dd8","abstract_canon_sha256":"9fcb07867011628019fdd5e667801c32a53df611e11b7cf6219f5fea0617043a"},"schema_version":"1.0"},"canonical_sha256":"d69972b7e68a21c9eb781d053fe4d160e7de41eeb55fe17b163a1db805239df7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:45:37.808605Z","signature_b64":"28SHR6SrOZF8gduQQQ8O/GLbdpXi9ZjEgWdsL0pgWGyDacxi5yqVc+JtUG7dZyWODof2fRVvIaNTVXH/TZ2uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d69972b7e68a21c9eb781d053fe4d160e7de41eeb55fe17b163a1db805239df7","last_reissued_at":"2026-07-04T14:45:37.808243Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:45:37.808243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0104137","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":"2026-07-04T14:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDL+z/8jQ/q21S+vHDJ0nsOqzeYRPernd6tK8cmLJ2FsDbqym1ug9Y9px0SkXeGFjj18Nahi0ww1Uoc4bueWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:32:33.520630Z"},"content_sha256":"e53f63b60e18db3a6c77b4750318369216308dfd7b2ef601fde08082c8a8a378","schema_version":"1.0","event_id":"sha256:e53f63b60e18db3a6c77b4750318369216308dfd7b2ef601fde08082c8a8a378"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:22MXFN7GRIQ4T23YDUCT7ZGRMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Walks on the Hypercube","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander Russell, Cristopher Moore","submitted_at":"2001-04-29T00:28:03Z","abstract_excerpt":"Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in continuous time. In both cases we show that the quantum walk mixes in (\\pi/4)n steps, faster than the O(n log n) steps required by the classical walk. In the continuous-time case, the probability distribution is {\\em exactly} uniform at this time. More importantly, these walks expose several subtleties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0104137","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0104137/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EygmlZXjvBEsOpqjESj80gMxJtYfWsLhj4wIsfupbvycW3o9vJKgnpliSvqn7kZFDYKSLpMOaU2UkMS6oRJ4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:32:33.521750Z"},"content_sha256":"75fea57d7bb7be9ede4212c9ef835bd2c3b2aac3c67a54cbdb45d0bd80b68626","schema_version":"1.0","event_id":"sha256:75fea57d7bb7be9ede4212c9ef835bd2c3b2aac3c67a54cbdb45d0bd80b68626"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD/bundle.json","state_url":"https://pith.science/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD/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":"2026-08-04T05:32:33Z","links":{"resolver":"https://pith.science/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD","bundle":"https://pith.science/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD/bundle.json","state":"https://pith.science/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22MXFN7GRIQ4T23YDUCT7ZGRMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:22MXFN7GRIQ4T23YDUCT7ZGRMD","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":"9fcb07867011628019fdd5e667801c32a53df611e11b7cf6219f5fea0617043a","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-29T00:28:03Z","title_canon_sha256":"ef5035de46ac858f6870d7a1a0978eb3c2d983e899f399ff1185518a52826dd8"},"schema_version":"1.0","source":{"id":"quant-ph/0104137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0104137","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0104137v1","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0104137","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"22MXFN7GRIQ4","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"pith_short_16","alias_value":"22MXFN7GRIQ4T23Y","created_at":"2026-07-04T14:45:37Z"},{"alias_kind":"pith_short_8","alias_value":"22MXFN7G","created_at":"2026-07-04T14:45:37Z"}],"graph_snapshots":[{"event_id":"sha256:75fea57d7bb7be9ede4212c9ef835bd2c3b2aac3c67a54cbdb45d0bd80b68626","target":"graph","created_at":"2026-07-04T14:45:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0104137/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in continuous time. In both cases we show that the quantum walk mixes in (\\pi/4)n steps, faster than the O(n log n) steps required by the classical walk. In the continuous-time case, the probability distribution is {\\em exactly} uniform at this time. More importantly, these walks expose several subtleties ","authors_text":"Alexander Russell, Cristopher Moore","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2001-04-29T00:28:03Z","title":"Quantum Walks on the Hypercube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0104137","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:e53f63b60e18db3a6c77b4750318369216308dfd7b2ef601fde08082c8a8a378","target":"record","created_at":"2026-07-04T14:45:37Z","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":"9fcb07867011628019fdd5e667801c32a53df611e11b7cf6219f5fea0617043a","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-29T00:28:03Z","title_canon_sha256":"ef5035de46ac858f6870d7a1a0978eb3c2d983e899f399ff1185518a52826dd8"},"schema_version":"1.0","source":{"id":"quant-ph/0104137","kind":"arxiv","version":1}},"canonical_sha256":"d69972b7e68a21c9eb781d053fe4d160e7de41eeb55fe17b163a1db805239df7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d69972b7e68a21c9eb781d053fe4d160e7de41eeb55fe17b163a1db805239df7","first_computed_at":"2026-07-04T14:45:37.808243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:45:37.808243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28SHR6SrOZF8gduQQQ8O/GLbdpXi9ZjEgWdsL0pgWGyDacxi5yqVc+JtUG7dZyWODof2fRVvIaNTVXH/TZ2uBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:45:37.808605Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0104137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e53f63b60e18db3a6c77b4750318369216308dfd7b2ef601fde08082c8a8a378","sha256:75fea57d7bb7be9ede4212c9ef835bd2c3b2aac3c67a54cbdb45d0bd80b68626"],"state_sha256":"7b817de7d8f0804c89a765a472267f7490f03f1fc17c4856722830206f525026"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2vi8YnY/IhWRR9SokKg+hhCTOlnUAnFezc/f/ZW1XbeTyOMWU/JkCF3VL6N9we9dWd3YcdwIOi+OipozNjNDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:32:33.529027Z","bundle_sha256":"5b8529d09188ea271380008870d26ace219a134e7c073f3c52b437701b392992"}}