{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ERXSIERGBWKVVQH4RD66GCBEXG","short_pith_number":"pith:ERXSIERG","canonical_record":{"source":{"id":"1701.05584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-01-19T20:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"76c89593e5bc4559dfe004b5326e68bccae6f0b672c1d83f7e28ab426df70828","abstract_canon_sha256":"091e860beaffb574e40404827a7757ccebafbf38d4ab689bd497302211e3a927"},"schema_version":"1.0"},"canonical_sha256":"246f2412260d955ac0fc88fde30824b9a77f53f7c0f4be2ada307c42840dc1c7","source":{"kind":"arxiv","id":"1701.05584","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05584","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05584v1","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05584","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"ERXSIERGBWKV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERXSIERGBWKVVQH4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERXSIERG","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ERXSIERGBWKVVQH4RD66GCBEXG","target":"record","payload":{"canonical_record":{"source":{"id":"1701.05584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-01-19T20:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"76c89593e5bc4559dfe004b5326e68bccae6f0b672c1d83f7e28ab426df70828","abstract_canon_sha256":"091e860beaffb574e40404827a7757ccebafbf38d4ab689bd497302211e3a927"},"schema_version":"1.0"},"canonical_sha256":"246f2412260d955ac0fc88fde30824b9a77f53f7c0f4be2ada307c42840dc1c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:29.079794Z","signature_b64":"twcK7BSzgmMIHLiuv5EFK/ubgDOerQJ7tedM+WrL/UKMMPxU2w+HqHPOeuTTP2SNDdfw1eMC5g7/1CF5RG6aAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"246f2412260d955ac0fc88fde30824b9a77f53f7c0f4be2ada307c42840dc1c7","last_reissued_at":"2026-05-18T00:52:29.079394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:29.079394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.05584","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":"2026-05-18T00:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7EyNkdzV+MvXrPFlcnVxZ0PsU8DLM3qLQRVxVC00gnWZfdGnS8qwvhn+FwR27AfEtHxUttLwUqIjYXLzngKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T14:22:39.363268Z"},"content_sha256":"eceedd14c672201366bcdfc47afe498cc6769eaed7d2802eab5a6e0028850a42","schema_version":"1.0","event_id":"sha256:eceedd14c672201366bcdfc47afe498cc6769eaed7d2802eab5a6e0028850a42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ERXSIERGBWKVVQH4RD66GCBEXG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adiabatic quantum computing solution of the knapsack problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Mark W. Coffey","submitted_at":"2017-01-19T20:06:46Z","abstract_excerpt":"We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class problem Hamiltonian requiring $n+c$ qubits and a much more efficient one using $n+[\\log_2 c]+1$ qubits. The discussion includes a brief mention of classical algorithms for knapsack, applications of this commonly occurring problem, and the relevance of further studies both theoretically and numerically of the behavior of the energy gap. Included too is a demonst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05584","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":"2026-05-18T00:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ZDah7Fc4isoGOS+uFbBS652LyMXKrwg45PFXwsUO+urwR6G/DXnc4FnzMKnhKx1coLfdm+ffYD4/RhPopbYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T14:22:39.363723Z"},"content_sha256":"c1734a2562d2b86e6089716e8b9ec21e5661f4a9decc031a51f7eeff0e7eb459","schema_version":"1.0","event_id":"sha256:c1734a2562d2b86e6089716e8b9ec21e5661f4a9decc031a51f7eeff0e7eb459"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERXSIERGBWKVVQH4RD66GCBEXG/bundle.json","state_url":"https://pith.science/pith/ERXSIERGBWKVVQH4RD66GCBEXG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERXSIERGBWKVVQH4RD66GCBEXG/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":"2026-08-20T14:22:39Z","links":{"resolver":"https://pith.science/pith/ERXSIERGBWKVVQH4RD66GCBEXG","bundle":"https://pith.science/pith/ERXSIERGBWKVVQH4RD66GCBEXG/bundle.json","state":"https://pith.science/pith/ERXSIERGBWKVVQH4RD66GCBEXG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERXSIERGBWKVVQH4RD66GCBEXG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ERXSIERGBWKVVQH4RD66GCBEXG","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":"091e860beaffb574e40404827a7757ccebafbf38d4ab689bd497302211e3a927","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-01-19T20:06:46Z","title_canon_sha256":"76c89593e5bc4559dfe004b5326e68bccae6f0b672c1d83f7e28ab426df70828"},"schema_version":"1.0","source":{"id":"1701.05584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05584","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05584v1","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05584","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"ERXSIERGBWKV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERXSIERGBWKVVQH4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERXSIERG","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:c1734a2562d2b86e6089716e8b9ec21e5661f4a9decc031a51f7eeff0e7eb459","target":"graph","created_at":"2026-05-18T00:52:29Z","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 illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class problem Hamiltonian requiring $n+c$ qubits and a much more efficient one using $n+[\\log_2 c]+1$ qubits. The discussion includes a brief mention of classical algorithms for knapsack, applications of this commonly occurring problem, and the relevance of further studies both theoretically and numerically of the behavior of the energy gap. Included too is a demonst","authors_text":"Mark W. Coffey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-01-19T20:06:46Z","title":"Adiabatic quantum computing solution of the knapsack problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05584","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:eceedd14c672201366bcdfc47afe498cc6769eaed7d2802eab5a6e0028850a42","target":"record","created_at":"2026-05-18T00:52:29Z","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":"091e860beaffb574e40404827a7757ccebafbf38d4ab689bd497302211e3a927","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-01-19T20:06:46Z","title_canon_sha256":"76c89593e5bc4559dfe004b5326e68bccae6f0b672c1d83f7e28ab426df70828"},"schema_version":"1.0","source":{"id":"1701.05584","kind":"arxiv","version":1}},"canonical_sha256":"246f2412260d955ac0fc88fde30824b9a77f53f7c0f4be2ada307c42840dc1c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"246f2412260d955ac0fc88fde30824b9a77f53f7c0f4be2ada307c42840dc1c7","first_computed_at":"2026-05-18T00:52:29.079394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:29.079394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"twcK7BSzgmMIHLiuv5EFK/ubgDOerQJ7tedM+WrL/UKMMPxU2w+HqHPOeuTTP2SNDdfw1eMC5g7/1CF5RG6aAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:29.079794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eceedd14c672201366bcdfc47afe498cc6769eaed7d2802eab5a6e0028850a42","sha256:c1734a2562d2b86e6089716e8b9ec21e5661f4a9decc031a51f7eeff0e7eb459"],"state_sha256":"249b8c897b7c1a54c9a4ccc3bd6a9597debaeb7568b4db0ffa280e9ac9f8f83a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T9d6oBtH+TzG2ELKSp0FF86aT+g3MwnluHDOPgLdjcSwaCRyX23Gy5aHots8fRHTF8PlfwKLnwCxKTdQqbcUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T14:22:39.368316Z","bundle_sha256":"5c2e0c020ad8c6070fd61beda45d28895f1efae0892ed8e2a844fc61605ebd4e"}}