{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7G4ZVQEPZV6THARRTLYTY74TVK","short_pith_number":"pith:7G4ZVQEP","canonical_record":{"source":{"id":"2402.07809","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-02-12T17:15:19Z","cross_cats_sorted":["cs.DS","math.PR"],"title_canon_sha256":"766794b00f16d92d4539e51e3175870ccb635c82cb5056e6dfaf251d1048e470","abstract_canon_sha256":"e8856a61404e7ad986513c6a88b3dc69f5670dc08711568b79b7e01aed4a02ed"},"schema_version":"1.0"},"canonical_sha256":"f9b99ac08fcd7d3382319af13c7f93aaa736aa46a0e84d4c1251ef3303cc4fbf","source":{"kind":"arxiv","id":"2402.07809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.07809","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"arxiv_version","alias_value":"2402.07809v1","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07809","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"pith_short_12","alias_value":"7G4ZVQEPZV6T","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"pith_short_16","alias_value":"7G4ZVQEPZV6THARR","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"pith_short_8","alias_value":"7G4ZVQEP","created_at":"2026-07-05T07:44:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7G4ZVQEPZV6THARRTLYTY74TVK","target":"record","payload":{"canonical_record":{"source":{"id":"2402.07809","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-02-12T17:15:19Z","cross_cats_sorted":["cs.DS","math.PR"],"title_canon_sha256":"766794b00f16d92d4539e51e3175870ccb635c82cb5056e6dfaf251d1048e470","abstract_canon_sha256":"e8856a61404e7ad986513c6a88b3dc69f5670dc08711568b79b7e01aed4a02ed"},"schema_version":"1.0"},"canonical_sha256":"f9b99ac08fcd7d3382319af13c7f93aaa736aa46a0e84d4c1251ef3303cc4fbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:12.761872Z","signature_b64":"xg0EjgUfKnPIHz1Y4/T6WL48POv5N7Y0PRP249pSApWKlO+yYjADRc3WYiYLQkfTBGna2TkgQv3IClnqzTgKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9b99ac08fcd7d3382319af13c7f93aaa736aa46a0e84d4c1251ef3303cc4fbf","last_reissued_at":"2026-07-05T07:44:12.761422Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:12.761422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.07809","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":"2026-07-05T07:44:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ba72CM7lXhIVMBosY8QrFVxEUsyDxdP4kejCkH7VqLf05nFYi93HlPgej2As0Fj/Qb/DPOcxbjYmnmozddtlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T05:04:43.597911Z"},"content_sha256":"43a694efafb71a4b20aa653cd98f127a3a78e469b1094ef8c3280528420545e0","schema_version":"1.0","event_id":"sha256:43a694efafb71a4b20aa653cd98f127a3a78e469b1094ef8c3280528420545e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7G4ZVQEPZV6THARRTLYTY74TVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum walks, the discrete wave equation and Chebyshev polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"quant-ph","authors_text":"Laurent Miclo, Simon Apers","submitted_at":"2024-02-12T17:15:19Z","abstract_excerpt":"A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the spreading or mixing rate of random walks on graphs. In this expository paper, inspired by a blog post by Terence Tao, we describe a particular perspective on this question that derives quantum walks from the discrete wave equation on graphs. This yields a description of the quantum walk dynamics as simply applying a Chebyshev polynomial to the random walk transi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07809","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/2402.07809/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":"2026-07-05T07:44:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x4M1K9cZezUjSzagVMFmFz8BycRr34r8eIO60qTNe5E5wu6nU5fp5Wi6cyTxfvMpCm1zUXorIflLw90h3Z96Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T05:04:43.598283Z"},"content_sha256":"79bd5ddc862a5a4f3b06cbd7bc7927b1168c8c7cbe14c8c839ae183dbf88e317","schema_version":"1.0","event_id":"sha256:79bd5ddc862a5a4f3b06cbd7bc7927b1168c8c7cbe14c8c839ae183dbf88e317"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7G4ZVQEPZV6THARRTLYTY74TVK/bundle.json","state_url":"https://pith.science/pith/7G4ZVQEPZV6THARRTLYTY74TVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7G4ZVQEPZV6THARRTLYTY74TVK/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":"2026-07-06T05:04:43Z","links":{"resolver":"https://pith.science/pith/7G4ZVQEPZV6THARRTLYTY74TVK","bundle":"https://pith.science/pith/7G4ZVQEPZV6THARRTLYTY74TVK/bundle.json","state":"https://pith.science/pith/7G4ZVQEPZV6THARRTLYTY74TVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7G4ZVQEPZV6THARRTLYTY74TVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7G4ZVQEPZV6THARRTLYTY74TVK","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":"e8856a61404e7ad986513c6a88b3dc69f5670dc08711568b79b7e01aed4a02ed","cross_cats_sorted":["cs.DS","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-02-12T17:15:19Z","title_canon_sha256":"766794b00f16d92d4539e51e3175870ccb635c82cb5056e6dfaf251d1048e470"},"schema_version":"1.0","source":{"id":"2402.07809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.07809","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"arxiv_version","alias_value":"2402.07809v1","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07809","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"pith_short_12","alias_value":"7G4ZVQEPZV6T","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"pith_short_16","alias_value":"7G4ZVQEPZV6THARR","created_at":"2026-07-05T07:44:12Z"},{"alias_kind":"pith_short_8","alias_value":"7G4ZVQEP","created_at":"2026-07-05T07:44:12Z"}],"graph_snapshots":[{"event_id":"sha256:79bd5ddc862a5a4f3b06cbd7bc7927b1168c8c7cbe14c8c839ae183dbf88e317","target":"graph","created_at":"2026-07-05T07:44:12Z","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/2402.07809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the spreading or mixing rate of random walks on graphs. In this expository paper, inspired by a blog post by Terence Tao, we describe a particular perspective on this question that derives quantum walks from the discrete wave equation on graphs. This yields a description of the quantum walk dynamics as simply applying a Chebyshev polynomial to the random walk transi","authors_text":"Laurent Miclo, Simon Apers","cross_cats":["cs.DS","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-02-12T17:15:19Z","title":"Quantum walks, the discrete wave equation and Chebyshev polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07809","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":"sha256:43a694efafb71a4b20aa653cd98f127a3a78e469b1094ef8c3280528420545e0","target":"record","created_at":"2026-07-05T07:44:12Z","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":"e8856a61404e7ad986513c6a88b3dc69f5670dc08711568b79b7e01aed4a02ed","cross_cats_sorted":["cs.DS","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-02-12T17:15:19Z","title_canon_sha256":"766794b00f16d92d4539e51e3175870ccb635c82cb5056e6dfaf251d1048e470"},"schema_version":"1.0","source":{"id":"2402.07809","kind":"arxiv","version":1}},"canonical_sha256":"f9b99ac08fcd7d3382319af13c7f93aaa736aa46a0e84d4c1251ef3303cc4fbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9b99ac08fcd7d3382319af13c7f93aaa736aa46a0e84d4c1251ef3303cc4fbf","first_computed_at":"2026-07-05T07:44:12.761422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:44:12.761422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xg0EjgUfKnPIHz1Y4/T6WL48POv5N7Y0PRP249pSApWKlO+yYjADRc3WYiYLQkfTBGna2TkgQv3IClnqzTgKDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:44:12.761872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.07809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43a694efafb71a4b20aa653cd98f127a3a78e469b1094ef8c3280528420545e0","sha256:79bd5ddc862a5a4f3b06cbd7bc7927b1168c8c7cbe14c8c839ae183dbf88e317"],"state_sha256":"687d30e9b024add2407ea081b89838f573e4462fa3c1976574790344854357af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVdptSKT8AAnW+bq/ZTnjUd85mpLJEraOVenPQE9Hj6KQeuZYUbewA+emtvFcUR4uw4URXV0fHEKXLr5DGqXAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T05:04:43.600961Z","bundle_sha256":"44e40df4878b8d43b3fef3703c9b94e896447198e0327bca9bb6c3c30ce9ac56"}}