{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:2RAP4QOMDFNWFBG4FC7QUAWGKM","short_pith_number":"pith:2RAP4QOM","schema_version":"1.0","canonical_sha256":"d440fe41cc195b6284dc28bf0a02c6530622abe5f688cfc45d8175aeb7d5f523","source":{"kind":"arxiv","id":"quant-ph/0610235","version":2},"attestation_state":"computed","paper":{"title":"BQP-complete Problems Concerning Mixing Properties of Classical Random Walks on Sparse Graphs","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dominik Janzing, Pawel Wocjan","submitted_at":"2006-10-27T10:44:55Z","abstract_excerpt":"We describe two BQP-complete problems concerning properties of sparse graphs having a certain symmetry. The graphs are specified by efficiently computable functions which output the adjacent vertices for each vertex. Let i and j be two given vertices. The first problem consists in estimating the difference between the number of paths of length m from j to j and those which from i to j, where m is polylogarithmic in the number of vertices. The scale of the estimation accuracy is specified by some a priori known upper bound on the growth of these differences with increasing m. The problem remain"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"quant-ph/0610235","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-10-27T10:44:55Z","cross_cats_sorted":[],"title_canon_sha256":"942f9c099631e2ba7942e38e9cf6ca22fe5b743facdffbe27609f28f24b7763a","abstract_canon_sha256":"de3c2b8cb26b2c0621d3c77f5596e77cfb97a19972d53d2d928e5b458fcf2469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:57:46.666152Z","signature_b64":"8qllb4ubyoG9+cgRcuiACQvC6P8ReQFHD87BOQwsdYOvuFfV7DAwKBqd5M6j5psFkpdSSNxyyGRtNfw28QvLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d440fe41cc195b6284dc28bf0a02c6530622abe5f688cfc45d8175aeb7d5f523","last_reissued_at":"2026-07-04T14:57:46.665787Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:57:46.665787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"BQP-complete Problems Concerning Mixing Properties of Classical Random Walks on Sparse Graphs","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dominik Janzing, Pawel Wocjan","submitted_at":"2006-10-27T10:44:55Z","abstract_excerpt":"We describe two BQP-complete problems concerning properties of sparse graphs having a certain symmetry. The graphs are specified by efficiently computable functions which output the adjacent vertices for each vertex. Let i and j be two given vertices. The first problem consists in estimating the difference between the number of paths of length m from j to j and those which from i to j, where m is polylogarithmic in the number of vertices. The scale of the estimation accuracy is specified by some a priori known upper bound on the growth of these differences with increasing m. The problem remain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0610235","kind":"arxiv","version":2},"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/0610235/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0610235","created_at":"2026-07-04T14:57:46.665844+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0610235v2","created_at":"2026-07-04T14:57:46.665844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0610235","created_at":"2026-07-04T14:57:46.665844+00:00"},{"alias_kind":"pith_short_12","alias_value":"2RAP4QOMDFNW","created_at":"2026-07-04T14:57:46.665844+00:00"},{"alias_kind":"pith_short_16","alias_value":"2RAP4QOMDFNWFBG4","created_at":"2026-07-04T14:57:46.665844+00:00"},{"alias_kind":"pith_short_8","alias_value":"2RAP4QOM","created_at":"2026-07-04T14:57:46.665844+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM","json":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM.json","graph_json":"https://pith.science/api/pith-number/2RAP4QOMDFNWFBG4FC7QUAWGKM/graph.json","events_json":"https://pith.science/api/pith-number/2RAP4QOMDFNWFBG4FC7QUAWGKM/events.json","paper":"https://pith.science/paper/2RAP4QOM"},"agent_actions":{"view_html":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM","download_json":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM.json","view_paper":"https://pith.science/paper/2RAP4QOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0610235&json=true","fetch_graph":"https://pith.science/api/pith-number/2RAP4QOMDFNWFBG4FC7QUAWGKM/graph.json","fetch_events":"https://pith.science/api/pith-number/2RAP4QOMDFNWFBG4FC7QUAWGKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM/action/storage_attestation","attest_author":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM/action/author_attestation","sign_citation":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM/action/citation_signature","submit_replication":"https://pith.science/pith/2RAP4QOMDFNWFBG4FC7QUAWGKM/action/replication_record"}},"created_at":"2026-07-04T14:57:46.665844+00:00","updated_at":"2026-07-04T14:57:46.665844+00:00"}