{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RHNN2WS6XBRMOZQBS7EKYJKBRP","short_pith_number":"pith:RHNN2WS6","canonical_record":{"source":{"id":"1804.09950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-26T09:18:52Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"e544ca35e9e5bc82f9facb7b7afcdbf03f693ab4c5a4ffe24f185b14809852de","abstract_canon_sha256":"7ded1c17a4584ae31c5467ce845bf445982aab8d7e6e40bbd977c9be0326cab5"},"schema_version":"1.0"},"canonical_sha256":"89dadd5a5eb862c7660197c8ac25418bfc7e19b84ed18bb522d23c9f13d3ddcb","source":{"kind":"arxiv","id":"1804.09950","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09950","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09950v2","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09950","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"RHNN2WS6XBRM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RHNN2WS6XBRMOZQB","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RHNN2WS6","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RHNN2WS6XBRMOZQBS7EKYJKBRP","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-26T09:18:52Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"e544ca35e9e5bc82f9facb7b7afcdbf03f693ab4c5a4ffe24f185b14809852de","abstract_canon_sha256":"7ded1c17a4584ae31c5467ce845bf445982aab8d7e6e40bbd977c9be0326cab5"},"schema_version":"1.0"},"canonical_sha256":"89dadd5a5eb862c7660197c8ac25418bfc7e19b84ed18bb522d23c9f13d3ddcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:53.878534Z","signature_b64":"deBF3j6jhC5FeJ50wMSiOLmW9u+/WexgiWckEJNI3CyTq8hi8HOv8Vz9JS2gPD4nabZidsBNP5rSqJvvNxEHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89dadd5a5eb862c7660197c8ac25418bfc7e19b84ed18bb522d23c9f13d3ddcb","last_reissued_at":"2026-05-17T23:42:53.877872Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:53.877872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09950","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enxbcNDPaJZhM6DrdsVhrL+dCKTCnEZ9faFkXLgJ9JIVvDqLq4ZybccvDi4oM9LxwytlW9aC9yZPrPA7mOQGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:03:05.072707Z"},"content_sha256":"498092ec6f116a63c4e637b2324d4a73d4057cb581a48b0aad13d70106220afa","schema_version":"1.0","event_id":"sha256:498092ec6f116a63c4e637b2324d4a73d4057cb581a48b0aad13d70106220afa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RHNN2WS6XBRMOZQBS7EKYJKBRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.DS","authors_text":"Kamil Khadiev, Liliya Safina","submitted_at":"2018-04-26T09:18:52Z","abstract_excerpt":"In this paper, we present a quantum algorithm for dynamic programming approach for problems on directed acyclic graphs (DAGs). The running time of the algorithm is $O(\\sqrt{\\hat{n}m}\\log \\hat{n})$, and the running time of the best known deterministic algorithm is $O(n+m)$, where $n$ is the number of vertices, $\\hat{n}$ is the number of vertices with at least one outgoing edge; $m$ is the number of edges. We show that we can solve problems that use OR, AND, NAND, MAX and MIN functions as the main transition steps. The approach is useful for a couple of problems. One of them is computing a Boole"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09950","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":""},"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":"2026-05-17T23:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRowaEKheOGXQZIRbs2ANgPnq0QWJqnK4XUq2F/GXElWjx3eoM8x+Zlit5jCLk1DCLLqZlVXbbBjbYXqDHNrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:03:05.073457Z"},"content_sha256":"a4268000d0a6e7c9f2d50c7beb14cfec32cc6b0e01d5cd150a29025c3c2e446e","schema_version":"1.0","event_id":"sha256:a4268000d0a6e7c9f2d50c7beb14cfec32cc6b0e01d5cd150a29025c3c2e446e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP/bundle.json","state_url":"https://pith.science/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP/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":"2026-06-08T20:03:05Z","links":{"resolver":"https://pith.science/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP","bundle":"https://pith.science/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP/bundle.json","state":"https://pith.science/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHNN2WS6XBRMOZQBS7EKYJKBRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RHNN2WS6XBRMOZQBS7EKYJKBRP","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":"7ded1c17a4584ae31c5467ce845bf445982aab8d7e6e40bbd977c9be0326cab5","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-26T09:18:52Z","title_canon_sha256":"e544ca35e9e5bc82f9facb7b7afcdbf03f693ab4c5a4ffe24f185b14809852de"},"schema_version":"1.0","source":{"id":"1804.09950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09950","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09950v2","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09950","created_at":"2026-05-17T23:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"RHNN2WS6XBRM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RHNN2WS6XBRMOZQB","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RHNN2WS6","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:a4268000d0a6e7c9f2d50c7beb14cfec32cc6b0e01d5cd150a29025c3c2e446e","target":"graph","created_at":"2026-05-17T23:42:53Z","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":"In this paper, we present a quantum algorithm for dynamic programming approach for problems on directed acyclic graphs (DAGs). The running time of the algorithm is $O(\\sqrt{\\hat{n}m}\\log \\hat{n})$, and the running time of the best known deterministic algorithm is $O(n+m)$, where $n$ is the number of vertices, $\\hat{n}$ is the number of vertices with at least one outgoing edge; $m$ is the number of edges. We show that we can solve problems that use OR, AND, NAND, MAX and MIN functions as the main transition steps. The approach is useful for a couple of problems. One of them is computing a Boole","authors_text":"Kamil Khadiev, Liliya Safina","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-26T09:18:52Z","title":"Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09950","kind":"arxiv","version":2},"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":"sha256:498092ec6f116a63c4e637b2324d4a73d4057cb581a48b0aad13d70106220afa","target":"record","created_at":"2026-05-17T23:42:53Z","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":"7ded1c17a4584ae31c5467ce845bf445982aab8d7e6e40bbd977c9be0326cab5","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-26T09:18:52Z","title_canon_sha256":"e544ca35e9e5bc82f9facb7b7afcdbf03f693ab4c5a4ffe24f185b14809852de"},"schema_version":"1.0","source":{"id":"1804.09950","kind":"arxiv","version":2}},"canonical_sha256":"89dadd5a5eb862c7660197c8ac25418bfc7e19b84ed18bb522d23c9f13d3ddcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89dadd5a5eb862c7660197c8ac25418bfc7e19b84ed18bb522d23c9f13d3ddcb","first_computed_at":"2026-05-17T23:42:53.877872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:53.877872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"deBF3j6jhC5FeJ50wMSiOLmW9u+/WexgiWckEJNI3CyTq8hi8HOv8Vz9JS2gPD4nabZidsBNP5rSqJvvNxEHAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:53.878534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:498092ec6f116a63c4e637b2324d4a73d4057cb581a48b0aad13d70106220afa","sha256:a4268000d0a6e7c9f2d50c7beb14cfec32cc6b0e01d5cd150a29025c3c2e446e"],"state_sha256":"3e1b27b9f1049fc8cbc4f48bb48b94537afc3bf0b03c1fa37a99980c5ed5b9cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/FiT0+w/qx5G3g5hpq3UCR5hWUqyUwfjFOUJExOsQOgWIdN0CmcsONJTcmWFmfdgcQ2GyE6vYOvSrYnuDRoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:03:05.076862Z","bundle_sha256":"1c1238fe7237afce4db9811780911901eff7b70b021bfd4584d6182133adeaef"}}