{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UN47HX3UMZLYGUH6YCZYAIT3SE","short_pith_number":"pith:UN47HX3U","canonical_record":{"source":{"id":"1808.03494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-08-10T11:45:22Z","cross_cats_sorted":["cs.CC","cs.DS","cs.GT"],"title_canon_sha256":"86d3d36a56b36ea61fec0994dadb0d56ec27904326c7aa411cf729973f3ebeb8","abstract_canon_sha256":"e333d4471735bf101a84f9f77e11401e8f37326e37f43420e5cecec6f6179356"},"schema_version":"1.0"},"canonical_sha256":"a379f3df7466578350fec0b380227b911c399f8f688748a3470893c6c36d1f2f","source":{"kind":"arxiv","id":"1808.03494","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03494","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03494v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03494","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"UN47HX3UMZLY","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UN47HX3UMZLYGUH6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UN47HX3U","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UN47HX3UMZLYGUH6YCZYAIT3SE","target":"record","payload":{"canonical_record":{"source":{"id":"1808.03494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-08-10T11:45:22Z","cross_cats_sorted":["cs.CC","cs.DS","cs.GT"],"title_canon_sha256":"86d3d36a56b36ea61fec0994dadb0d56ec27904326c7aa411cf729973f3ebeb8","abstract_canon_sha256":"e333d4471735bf101a84f9f77e11401e8f37326e37f43420e5cecec6f6179356"},"schema_version":"1.0"},"canonical_sha256":"a379f3df7466578350fec0b380227b911c399f8f688748a3470893c6c36d1f2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.870546Z","signature_b64":"VC/3YVXY7oHaT6OhD+UFWP5zn9874EVxJ0LUGDBTagnjGQWufZoTAPbQlYQAErm0vdyUmX4yYGHi7mdFm9jlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a379f3df7466578350fec0b380227b911c399f8f688748a3470893c6c36d1f2f","last_reissued_at":"2026-05-18T00:08:24.870013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.870013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.03494","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYtrJri2ggkHUNzdIUcR3SJA+AdA8Q1B36XxtHId96Y2BqJQQqR5YK9PWNXbwseILqMJ1X3BefXEuLFqjXZ7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:26:31.712947Z"},"content_sha256":"50904a61e90450fddb5dd6e3f4a73842e539d7c287787a3393219bdb567f2500","schema_version":"1.0","event_id":"sha256:50904a61e90450fddb5dd6e3f4a73842e539d7c287787a3393219bdb567f2500"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UN47HX3UMZLYGUH6YCZYAIT3SE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Solving Subtraction Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","cs.GT"],"primary_cat":"quant-ph","authors_text":"Dmitry Kravchenko, Kamil Khadiev","submitted_at":"2018-08-10T11:45:22Z","abstract_excerpt":"We study algorithms for solving Subtraction games, which sometimes are referred to as one-heap Nim games. We describe a quantum algorithm which is applicable to any game on DAG, and show that its query compexity for solving an arbitrary Subtraction game of $n$ stones is $O(n^{3/2}\\log n)$. The best known deterministic algorithms for solving such games are based on the dynamic programming approach. We show that this approach is asymptotically optimal and that classical query complexity for solving a Subtraction game is generally $\\Theta(n^2)$. This paper perhaps is the first explicit \"quantum\" "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03494","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":""},"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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pP/aDrqgaIj++0nkelD36hIfdTdo0CVDhphmRAKcSY8Is9hg3MknFGcMjPYscd3rs9TTJwRrxv3jWjL/Us4uBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:26:31.713658Z"},"content_sha256":"b6ba04bd8494a54c30478f6f0c292fb2e95ffcd6353ed3699889a63cd1d7a57c","schema_version":"1.0","event_id":"sha256:b6ba04bd8494a54c30478f6f0c292fb2e95ffcd6353ed3699889a63cd1d7a57c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UN47HX3UMZLYGUH6YCZYAIT3SE/bundle.json","state_url":"https://pith.science/pith/UN47HX3UMZLYGUH6YCZYAIT3SE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UN47HX3UMZLYGUH6YCZYAIT3SE/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":"2026-06-08T17:26:31Z","links":{"resolver":"https://pith.science/pith/UN47HX3UMZLYGUH6YCZYAIT3SE","bundle":"https://pith.science/pith/UN47HX3UMZLYGUH6YCZYAIT3SE/bundle.json","state":"https://pith.science/pith/UN47HX3UMZLYGUH6YCZYAIT3SE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UN47HX3UMZLYGUH6YCZYAIT3SE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UN47HX3UMZLYGUH6YCZYAIT3SE","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":"e333d4471735bf101a84f9f77e11401e8f37326e37f43420e5cecec6f6179356","cross_cats_sorted":["cs.CC","cs.DS","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-08-10T11:45:22Z","title_canon_sha256":"86d3d36a56b36ea61fec0994dadb0d56ec27904326c7aa411cf729973f3ebeb8"},"schema_version":"1.0","source":{"id":"1808.03494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03494","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03494v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03494","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"UN47HX3UMZLY","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UN47HX3UMZLYGUH6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UN47HX3U","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b6ba04bd8494a54c30478f6f0c292fb2e95ffcd6353ed3699889a63cd1d7a57c","target":"graph","created_at":"2026-05-18T00:08:24Z","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 study algorithms for solving Subtraction games, which sometimes are referred to as one-heap Nim games. We describe a quantum algorithm which is applicable to any game on DAG, and show that its query compexity for solving an arbitrary Subtraction game of $n$ stones is $O(n^{3/2}\\log n)$. The best known deterministic algorithms for solving such games are based on the dynamic programming approach. We show that this approach is asymptotically optimal and that classical query complexity for solving a Subtraction game is generally $\\Theta(n^2)$. This paper perhaps is the first explicit \"quantum\" ","authors_text":"Dmitry Kravchenko, Kamil Khadiev","cross_cats":["cs.CC","cs.DS","cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-08-10T11:45:22Z","title":"On the Complexity of Solving Subtraction Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03494","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":"sha256:50904a61e90450fddb5dd6e3f4a73842e539d7c287787a3393219bdb567f2500","target":"record","created_at":"2026-05-18T00:08:24Z","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":"e333d4471735bf101a84f9f77e11401e8f37326e37f43420e5cecec6f6179356","cross_cats_sorted":["cs.CC","cs.DS","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-08-10T11:45:22Z","title_canon_sha256":"86d3d36a56b36ea61fec0994dadb0d56ec27904326c7aa411cf729973f3ebeb8"},"schema_version":"1.0","source":{"id":"1808.03494","kind":"arxiv","version":1}},"canonical_sha256":"a379f3df7466578350fec0b380227b911c399f8f688748a3470893c6c36d1f2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a379f3df7466578350fec0b380227b911c399f8f688748a3470893c6c36d1f2f","first_computed_at":"2026-05-18T00:08:24.870013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.870013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VC/3YVXY7oHaT6OhD+UFWP5zn9874EVxJ0LUGDBTagnjGQWufZoTAPbQlYQAErm0vdyUmX4yYGHi7mdFm9jlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.870546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50904a61e90450fddb5dd6e3f4a73842e539d7c287787a3393219bdb567f2500","sha256:b6ba04bd8494a54c30478f6f0c292fb2e95ffcd6353ed3699889a63cd1d7a57c"],"state_sha256":"a3e60f08295d43e2e011b044beae4156badcb2aacfbfed6f5f0c53ea2f4d5115"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zm8diULSO1cMzUBGfKM4Z2O2t2+ylLXA/UolJDxoct1r3cAEJ42DJSh0gF2Qs9xyRhFdbCY68K1Kz74bgUJMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:26:31.718500Z","bundle_sha256":"059d04e28bbbd70c0c3b87db37d4c01e1ebd001cf7eba73b4a1d4edd0635160c"}}