{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3OAHU66XLLVHDK3SXCJJ2Z3LGT","short_pith_number":"pith:3OAHU66X","canonical_record":{"source":{"id":"1606.02136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"a65514411a256ebace1705c3a33bed476b9b8511d513c8d05ee6b7e92f2c8aef","abstract_canon_sha256":"bd08dd64561491ad97681ab4549186864418670466624a10ecc9422f71c1edd3"},"schema_version":"1.0"},"canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","source":{"kind":"arxiv","id":"1606.02136","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02136","created_at":"2026-05-18T00:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02136v3","created_at":"2026-05-18T00:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02136","created_at":"2026-05-18T00:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"3OAHU66XLLVH","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3OAHU66XLLVHDK3S","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3OAHU66X","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3OAHU66XLLVHDK3SXCJJ2Z3LGT","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"a65514411a256ebace1705c3a33bed476b9b8511d513c8d05ee6b7e92f2c8aef","abstract_canon_sha256":"bd08dd64561491ad97681ab4549186864418670466624a10ecc9422f71c1edd3"},"schema_version":"1.0"},"canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:36.254257Z","signature_b64":"xgst3TbyzBLN1NfJMWhAH1YCG9zKtK9hMtG7sth7IAR0YyKGezmWO8kYtFR9YZco40pQIQM5ydNGtGgRuERYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","last_reissued_at":"2026-05-18T00:54:36.253582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:36.253582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02136","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+z4ZPAjJ4i1+lM0zOKeEiFcY8KTvaax+DB1X5cocFco7w8cAizRwDqe42QE49/dnsQBBjVYNW+L3RaE2wPpYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:43:39.477673Z"},"content_sha256":"f377a2a4cb9c8be2befddc38cd42c29e543f1a303a8c3077fdc3953f3fca8d50","schema_version":"1.0","event_id":"sha256:f377a2a4cb9c8be2befddc38cd42c29e543f1a303a8c3077fdc3953f3fca8d50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3OAHU66XLLVHDK3SXCJJ2Z3LGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis, Thomas G. Wong","submitted_at":"2016-06-07T13:44:39Z","abstract_excerpt":"We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02136","kind":"arxiv","version":3},"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":"2026-05-18T00:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BHhNKRPvl63d4r+Pu+kej9E200tCdnFPpLA7agGcr58JYMH30RLZ12KTwZri7FQT8hHDMRRikKPwYal3Mp9ODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:43:39.478359Z"},"content_sha256":"bfda7cf4f3552a17b5247716e697e035d999471be5eafc686c1f670b80ecb455","schema_version":"1.0","event_id":"sha256:bfda7cf4f3552a17b5247716e697e035d999471be5eafc686c1f670b80ecb455"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/bundle.json","state_url":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/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":"2026-05-26T01:43:39Z","links":{"resolver":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT","bundle":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/bundle.json","state":"https://pith.science/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OAHU66XLLVHDK3SXCJJ2Z3LGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3OAHU66XLLVHDK3SXCJJ2Z3LGT","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":"bd08dd64561491ad97681ab4549186864418670466624a10ecc9422f71c1edd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:44:39Z","title_canon_sha256":"a65514411a256ebace1705c3a33bed476b9b8511d513c8d05ee6b7e92f2c8aef"},"schema_version":"1.0","source":{"id":"1606.02136","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02136","created_at":"2026-05-18T00:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02136v3","created_at":"2026-05-18T00:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02136","created_at":"2026-05-18T00:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"3OAHU66XLLVH","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3OAHU66XLLVHDK3S","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3OAHU66X","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:bfda7cf4f3552a17b5247716e697e035d999471be5eafc686c1f670b80ecb455","target":"graph","created_at":"2026-05-18T00:54:36Z","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":"We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance i","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis, Thomas G. Wong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:44:39Z","title":"Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02136","kind":"arxiv","version":3},"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:f377a2a4cb9c8be2befddc38cd42c29e543f1a303a8c3077fdc3953f3fca8d50","target":"record","created_at":"2026-05-18T00:54:36Z","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":"bd08dd64561491ad97681ab4549186864418670466624a10ecc9422f71c1edd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:44:39Z","title_canon_sha256":"a65514411a256ebace1705c3a33bed476b9b8511d513c8d05ee6b7e92f2c8aef"},"schema_version":"1.0","source":{"id":"1606.02136","kind":"arxiv","version":3}},"canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db807a7bd75aea71ab72b8929d676b34d4f02fd63f9a72a050c4076cb84b90fb","first_computed_at":"2026-05-18T00:54:36.253582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:36.253582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xgst3TbyzBLN1NfJMWhAH1YCG9zKtK9hMtG7sth7IAR0YyKGezmWO8kYtFR9YZco40pQIQM5ydNGtGgRuERYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:36.254257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02136","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f377a2a4cb9c8be2befddc38cd42c29e543f1a303a8c3077fdc3953f3fca8d50","sha256:bfda7cf4f3552a17b5247716e697e035d999471be5eafc686c1f670b80ecb455"],"state_sha256":"f6e9adcb4e23cf042296556d2e438b37a301bcbe62073f70b4adf520416f1bdf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USPYBtAltHM9oMroWSTQNqDTBtURO6IBgayrtCxDMJFHWi/YN8U3xCB8zdfLgdJDRETHQdcbl2YAN2SRs3IsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:43:39.482197Z","bundle_sha256":"622482c797930e51e7388183c7733b6cab4747445492953098f311d00e334aec"}}