{"query": "0-1 knapsack (cap 5) → optimal value 7", "count": 20, "results": [{"id": "card_v_03794e9aea45", "title": "0-1 knapsack (cap 5) → optimal value 7", "shelf": "operations_research", "surface": "secular", "snippet": "Verdict: HOLDS.\n• operations_research.knapsack_01: optimal_value=7.0 (matches claim)\nSealed and independently re-checkable: https://narrowhighway.com/s/146ec914dad0d44e177cd894b09742163848ac2508926d7b", "authority_tier": "engine", "source": "Verified by the engine — operations_research", "readable": false, "generated": false}, {"id": "card_calc_v_operations_research_knapsack_01", "title": "Knapsack 01", "shelf": "calculations", "surface": "secular", "snippet": "Knapsack 01 — operations_research. Formula: 0-1 knapsack (DP). Canonical FORM: optimization (d/dx f = 0) — engine verifier operations_research.knapsack_01 — the deterministic check the concordance run", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_works_knapsack", "title": "The best a knapsack can carry", "shelf": "the-works", "surface": "secular", "snippet": "Given items of weight and value and a fixed capacity, the 0-1 knapsack picks the most valuable subset that fits — here a total value of 7 within a weight of 5. The core of scheduling, budgeting and ca", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_span_5b1cc65fa68c", "title": "Illustrations", "shelf": "practical", "surface": "secular", "snippet": "_Page_\r\n  \"Nessmuk\"                         _Frontispiece_\r\n  Knapsack and Ditty-Bag                         7\r\n  Hatchet and Knives                             8\r\n  Indian Camp                       ", "authority_tier": "primary_pd", "source": "Woodcraft and Camping", "readable": true, "generated": false}, {"id": "card_src_word_knapsack", "title": "knapsack", "shelf": "dictionary", "surface": "secular", "snippet": "knapsack: (noun) a bag carried by a strap on your back or shoulder — syn: backpack, back pack, packsack, rucksack, haversack", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_book_17532", "title": "Two Knapsacks: A Novel of Canadian Summer Life — John Campbell", "shelf": "gutenberg", "surface": "secular", "snippet": "Two Knapsacks: A Novel of Canadian Summer Life, by John Campbell. Subjects: Canada -- Fiction. Read the full text (public domain): https://www.gutenberg.org/ebooks/17532", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_pron_knapsack", "title": "knapsack", "shelf": "pronunciation", "surface": "secular", "snippet": "knapsack: pronounced (ARPABET) N AE1 P S AE2 K. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_book_78129", "title": "The nature lover's knapsack — Edwin Osgood, 1870-1965 [Editor] Grover", "shelf": "gutenberg", "surface": "secular", "snippet": "The nature lover's knapsack, by Edwin Osgood, 1870-1965 [Editor] Grover. Subjects: English poetry; American poetry; Nature -- Poetry. Read the full text (public domain): https://www.gutenberg.org/eboo", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_etym_knapsack", "title": "knapsack", "shelf": "etymology", "surface": "secular", "snippet": "knapsack: etymology (Webster 1913) — n.: [D. knapzak; knappen to eat + zak a bag. See Knap, v. t., and Sack.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_book_11535", "title": "Views A-foot; Or, Europe Seen with Knapsack and Staff — Bayard Taylor", "shelf": "gutenberg", "surface": "secular", "snippet": "Views A-foot; Or, Europe Seen with Knapsack and Staff, by Bayard Taylor. Subjects: Europe -- Description and travel. Read the full text (public domain): https://www.gutenberg.org/ebooks/11535", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_seal_8f4c8f834bf693596262243547fdfef631df65028484c9b0b223ecb321e98f65", "title": "Receipt 8f4c8f834bf6… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"operations_research\",\n  \"dimensions\": [\n   \"conservation_balance\",\n   \"reasoning\",\n   \"time_sequence\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    ", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_principle_napoleon_bonaparte_1d5dc8028c", "title": "Napoleon Bonaparte: There are five things the soldier should never be without--his musket, his ammunition, his knapsack, his provi", "shelf": "strategy", "surface": "secular", "snippet": "There are five things the soldier should never be without--his musket, his ammunition, his knapsack, his provisions (for at least four days), and his entrenching-tool.", "authority_tier": "primary", "source": "Napoleon Bonaparte, The Officer's Manual: Napoleon's Maxims of War (tr. D'Aguilar) (1831) — Project Gutenberg #50750, public domain", "readable": true, "generated": false}, {"id": "card_src_etym_valise", "title": "valise", "shelf": "etymology", "surface": "secular", "snippet": "valise: etymology (Webster 1913) — n.: [F. valise; cf. It. valigia, Sp. balija, LL. valisia, valesia; of uncertain origin, perhaps through (assumed) LL. vidulitia, from L. vidulus a leathern trunk; a ", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_etym_budge", "title": "budge", "shelf": "etymology", "surface": "secular", "snippet": "budge: etymology (Webster 1913) — v. i.: [F. bouger to stir, move (akin to Pr. bojar, bolegar, to stir, move, It. bulicare to boil, bubble), fr. L. bullire. See Boil, v. i.]; a.: [See Budge, v.]; n.: ", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_comm_john_gill_pro_10_20", "title": "John Gill on Proverbs 10:20", "shelf": "commentary", "surface": "witness", "snippet": "The tongue of the just is as choice silver,.... Which utters things precious, pure, pleasant, and profitable; things for worth and value as choice silver; the doctrines of the Gospel, the power of whi", "authority_tier": "reference", "source": "John Gill's Exposition of the Old and New Testaments — Public Domain", "readable": false, "generated": false}, {"id": "card_n_05f7744be9ca", "title": "Martyrdom of Polycarp XV", "shelf": "patristics", "surface": "witness", "snippet": "When he had pronounced this _amen_, and so finished his prayer, those who were appointed for the purpose kindled the fire. And as the flame blazed forth in great fury, we, to whom it was given to witn", "authority_tier": "father", "source": "Martyrdom of Polycarp (trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_c0950f401038", "title": "Barnabas VI", "shelf": "patristics", "surface": "witness", "snippet": "announced by the prophets._ When, therefore, He has fulfilled the commandment, what saith He? “Who is he that will contend with me? let him oppose me: or who is he that will enter into judgment with m", "authority_tier": "father", "source": "Epistle of Barnabas (trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_e90bcaad8cd2", "title": "Amazing Grace", "shelf": "hymns", "surface": "witness", "snippet": "Amazing grace! How sweet the sound\nThat saved a wretch like me!\nI once was lost, but now am found,\nWas blind, but now I see.\n\n'Twas grace that taught my heart to fear,\nAnd grace my fears relieved;\nHow", "authority_tier": "external_aligned", "source": "John Newton (1779)", "readable": false, "generated": false}, {"id": "card_n_a81af80cfb59", "title": "Ignatius to the Ephesians XIII", "shelf": "patristics", "surface": "witness", "snippet": "Take heed, then, often to come together to give thanks to God, and show forth His praise. For when ye assemble frequently in the same place, the powers of Satan are destroyed, and the destruction at w", "authority_tier": "father", "source": "Ignatius to the Ephesians (shorter recension; trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_9fab9883e012", "title": "Martyrdom of Polycarp XVIII", "shelf": "patristics", "surface": "witness", "snippet": "The centurion then, seeing the strife excited by the Jews, placed the body in the midst of the fire, and consumed it. Accordingly, we afterwards took up his bones, as being more precious than the most", "authority_tier": "father", "source": "Martyrdom of Polycarp (trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_v_03794e9aea45"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}