{"query": "The check digit that catches a mistyped number", "count": 20, "results": [{"id": "card_works_luhn", "title": "The check digit that catches a mistyped number", "shelf": "the-works", "surface": "secular", "snippet": "The Luhn and ISBN algorithms embed a check digit so a single wrong digit is caught before it becomes a wrong order or a wrong book. Two standards, both verified.  Worked & sealed by the engine — Luhn(", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_dimensional_analysis", "title": "Dimensional analysis & similarity (Buckingham Π)", "shelf": "theories", "surface": "secular", "snippet": "Dimensional analysis & similarity (Buckingham Π) — an engine domain that can touch it: physics. Calibration: seals — dimensional consistency and Π-group counts check exactly. Any true physical equatio", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_real_estate_valuation", "title": "Real-estate valuation (cap rate, DCF)", "shelf": "theories", "surface": "secular", "snippet": "Real-estate valuation (cap rate, DCF) — an engine domain that can touch it: real_estate. Calibration: seals — cap rate, NOI and discounted cash flows compute. CAP RATE = net operating income ÷ price. ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_src_openstax_anatomy_and_physiology_2e_chapter_review_6112a6f1", "title": "Chapter Review — Anatomy and Physiology 2e", "shelf": "medicine", "surface": "secular", "snippet": "Chapter Review\n\n2.1\n\nElements and Atoms: The Building Blocks of Matter\n\nThe human body is composed of elements, the most abundant of which are oxygen (O), carbon (C), hydrogen (H) and nitrogen (N). Yo", "authority_tier": "reference", "source": "OpenStax: Anatomy and Physiology 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_anatomy_and_physiology_chapter_review_3e151ada", "title": "Chapter Review — Anatomy and Physiology", "shelf": "medicine", "surface": "secular", "snippet": "Chapter Review\n\n2.1\n\nElements and Atoms: The Building Blocks of Matter\n\nThe human body is composed of elements, the most abundant of which are oxygen (O), carbon (C), hydrogen (H) and nitrogen (N). Yo", "authority_tier": "reference", "source": "OpenStax: Anatomy and Physiology (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_theory_stellar_nucleosynthesis_the_hr_diagram", "title": "Stellar nucleosynthesis & the HR diagram", "shelf": "theories", "surface": "secular", "snippet": "Stellar nucleosynthesis & the HR diagram — an engine domain that can touch it: astronomy. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. Where t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_src_openstax_anatomy_and_physiology_2e_review_questions_95f64ff2", "title": "Review Questions — Anatomy and Physiology 2e", "shelf": "medicine", "surface": "secular", "snippet": "Review Questions\n\n4.\n\nTogether, just four elements make up more than 95 percent of the body’s mass. These include ________.\n\ncalcium, magnesium, iron, and carbon\n\noxygen, calcium, iron, and nitrogen\n\n", "authority_tier": "reference", "source": "OpenStax: Anatomy and Physiology 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_anatomy_and_physiology_review_questions_b373a7e0", "title": "Review Questions — Anatomy and Physiology", "shelf": "medicine", "surface": "secular", "snippet": "Review Questions\n\n4.\n\nTogether, just four elements make up more than 95 percent of the body’s mass. These include ________.\n\ncalcium, magnesium, iron, and carbon\n\noxygen, calcium, iron, and nitrogen\n\n", "authority_tier": "reference", "source": "OpenStax: Anatomy and Physiology (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_theory_br_nsted_lowry_acid_base_theory_ph", "title": "Brønsted–Lowry acid–base theory & pH", "shelf": "theories", "surface": "secular", "snippet": "Brønsted–Lowry acid–base theory & pH — an engine domain that can touch it: chemistry. Calibration: seals — pH, pKa and buffer calculations compute exactly. An acid DONATES a proton, a base ACCEPTS one", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_calc_checksum_mod", "title": "Checksums (mod arithmetic)", "shelf": "calculations", "surface": "secular", "snippet": "Checksums (mod arithmetic) — cybersecurity. Formula: sum * w mod m. Canonical FORM: check_digit (weighted sum mod n = 0) — ISBN, Luhn and CRC all catch errors by a modulus. Same form, different domain", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_doc_validation_luhn", "title": "Luhn", "shelf": "calculations", "surface": "secular", "snippet": "Luhn — document_validation. Formula: Luhn checksum mod 10 = 0. Canonical FORM: check_digit (weighted sum mod n = 0) — engine verifier doc_validation.luhn — the deterministic check the concordance runs", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_spine_domain_atomic", "title": "Atomic — what this engine can check", "shelf": "atomic", "surface": "secular", "snippet": "The atomic shelf of the keeping. This engine holds a deterministic verifier for atomic: hand it a claim in the ATOM_VERIFY shape and it returns a verdict, the worked trail, and a re-checkable seal. It", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_src_book_48406", "title": "The Atomic Fingerprint: Neutron Activation Analysis — Bernard Keisch", "shelf": "gutenberg", "surface": "secular", "snippet": "The Atomic Fingerprint: Neutron Activation Analysis, by Bernard Keisch. Subjects: Nuclear activation analysis. Read the full text (public domain): https://www.gutenberg.org/ebooks/48406", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_theory_big_bang_cosmology_expansion", "title": "Big Bang cosmology & expansion (Hubble's law)", "shelf": "theories", "surface": "secular", "snippet": "Big Bang cosmology & expansion (Hubble's law) — an engine domain that can touch it: astronomy. Calibration: partial — the Hubble relation verifies; the origin claim is map-only (RESONANCE). v = H₀d: r", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_second_law_of_thermodynamics", "title": "Second law of thermodynamics (entropy)", "shelf": "theories", "surface": "secular", "snippet": "Second law of thermodynamics (entropy) — an engine domain that can touch it: thermodynamics. Calibration: partial — efficiency and entropy changes compute; the arrow of time is map-only. The entropy o", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_law_of_large_numbers", "title": "Law of large numbers", "shelf": "theories", "surface": "secular", "snippet": "Law of large numbers — an engine domain that can touch it: statistics. Calibration: partial — convergence checks verify; the limit statement is map-only. As a sample grows, its mean converges to the t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_src_book_6682", "title": "Nets to Catch the Wind — Elinor Wylie", "shelf": "gutenberg", "surface": "secular", "snippet": "Nets to Catch the Wind, by Elinor Wylie. Subjects: Poetry. Read the full text (public domain): https://www.gutenberg.org/ebooks/6682", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_word_neutron", "title": "neutron", "shelf": "dictionary", "surface": "secular", "snippet": "neutron: (noun) an elementary particle with 0 charge and mass about equal to a proton; enters into the structure of the atomic nucleus", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_calc_v_doc_validation_isbn10", "title": "Isbn10", "shelf": "calculations", "surface": "secular", "snippet": "Isbn10 — document_validation. Formula: sum(i*d_i) mod 11 = 0. Canonical FORM: check_digit (weighted sum mod n = 0) — engine verifier doc_validation.isbn10 — the deterministic check the concordance run", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_doc_validation_isbn13", "title": "Isbn13", "shelf": "calculations", "surface": "secular", "snippet": "Isbn13 — document_validation. Formula: weighted sum mod 10 = 0. Canonical FORM: check_digit (weighted sum mod n = 0) — engine verifier doc_validation.isbn13 — the deterministic check the concordance r", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "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_works_luhn"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}