{"query": "Hydrology — the water cycle and the flow of rivers", "count": 20, "results": [{"id": "card_floor_hydrology", "title": "Hydrology — the water cycle and the flow of rivers", "shelf": "codex", "surface": "secular", "snippet": "River discharge is velocity times cross-section (Q = v A); only 2.5 percent of Earth water is fresh. Pillars rest on earth science (basins and the cycle), chemistry (water the solvent) and meteorology", "authority_tier": "engine_derived", "source": "Narrow Highway — hydrology", "readable": false, "generated": false}, {"id": "card_theory_fluid_mechanics", "title": "Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes)", "shelf": "theories", "surface": "secular", "snippet": "Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes) — an engine domain that can touch it: hydrology. Calibration: seals — continuity, Bernoulli and Reynolds number compute directly. CONTINUITY first:", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_hydrologic_cycle_open_channel_flow", "title": "Hydrologic cycle & open-channel flow (Manning, Darcy)", "shelf": "theories", "surface": "secular", "snippet": "Hydrologic cycle & open-channel flow (Manning, Darcy) — an engine domain that can touch it: hydrology. Calibration: seals — Manning velocity, Darcy flow and catchment volumes compute. Water circulates", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_domchk_hydrology_claimed_total_head_m", "title": "Hydrology: total head m", "shelf": "hydrology", "surface": "secular", "snippet": "A worked check in hydrology: total head m.\n\nGIVEN\n  velocity_m_s = 2\n\nCLAIMED\n  claimed_total_head_m = 20.534\n\nTHE ENGINE'S VERDICT\n  hydrology.bernoulli_head: CONFIRMED — head = 20.5362 m (matches cl", "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_works_manning", "title": "How fast water runs in an open channel", "shelf": "the-works", "surface": "secular", "snippet": "Manning's equation gives the velocity of water in a channel from its roughness, depth and slope — here 3.33 m/s. It sizes culverts, canals and storm drains.  Worked & sealed by the engine — V = (1/0.0", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_domchk_hydrology_claimed_velocity_m_s", "title": "Hydrology: velocity m s", "shelf": "hydrology", "surface": "secular", "snippet": "A worked check in hydrology: velocity m s.\n\nGIVEN\n  velocity_m_s = 2\n\nCLAIMED\n  claimed_velocity_m_s = 2.43\n\nTHE ENGINE'S VERDICT\n  hydrology.manning_velocity: CONFIRMED — V = 2.4325 m/s (matches clai", "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_domchk_hydrology_claimed_runoff", "title": "Hydrology: runoff", "shelf": "hydrology", "surface": "secular", "snippet": "A worked check in hydrology: runoff.\n\nGIVEN\n  rainfall_intensity = 50\n\nCLAIMED\n  claimed_runoff = 3500\n\nTHE ENGINE'S VERDICT\n  hydrology.rational_runoff: CONFIRMED — Q = 3500.0000 (matches claim)\n\nAND", "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_domchk_hydrology_claimed_darcy_velocity_m_s", "title": "Hydrology: darcy velocity m s", "shelf": "hydrology", "surface": "secular", "snippet": "A worked check in hydrology: darcy velocity m s.\n\nGIVEN\n  hydraulic_radius_m = 1\n\nCLAIMED\n  claimed_darcy_velocity_m_s = 1e-06\n\nTHE ENGINE'S VERDICT\n  hydrology.darcy_velocity: CONFIRMED — q = 1.00000", "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_spine_domain_hydrology", "title": "Hydrology — what this engine can check", "shelf": "hydrology", "surface": "secular", "snippet": "The hydrology shelf of the keeping. This engine holds a deterministic verifier for hydrology: hand it a claim in the HYD_VERIFY shape and it returns a verdict, the worked trail, and a re-checkable sea", "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_hydrology_flow", "title": "Flow - discharge and the continuity equation", "shelf": "codex", "surface": "secular", "snippet": "Q = v A governs every river and flood (sealed); conservation of mass is the continuity equation. Rests on earth science.", "authority_tier": "engine_derived", "source": "Narrow Highway — hydrology", "readable": false, "generated": false}, {"id": "card_src_word_hydrology", "title": "hydrology", "shelf": "dictionary", "surface": "secular", "snippet": "hydrology: (noun) the branch of geology that studies water on the earth and in the atmosphere: its distribution and uses and conservation", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_etym_hydrology", "title": "hydrology", "shelf": "etymology", "surface": "secular", "snippet": "hydrology: etymology (Webster 1913) — n.: [Hydro-, 1 + -logy: cf. F. hydrologie.]. 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_calc_v_hydrology_manning_velocity", "title": "Manning velocity", "shelf": "calculations", "surface": "secular", "snippet": "Manning velocity — hydrology. Formula: v = (1/n) R^(2/3) S^(1/2). Canonical FORM: power_law (y = a * x^k) — engine verifier hydrology.manning_velocity — the deterministic check the concordance runs. S", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_hydrology_rational_runoff", "title": "Rational runoff", "shelf": "calculations", "surface": "secular", "snippet": "Rational runoff — hydrology. Formula: Q = C i A. Canonical FORM: product_law (q = f1 * f2 * ...) — engine verifier hydrology.rational_runoff — the deterministic check the concordance runs. Same form, ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_hydrology_bernoulli_head", "title": "Bernoulli head", "shelf": "calculations", "surface": "secular", "snippet": "Bernoulli head — hydrology. Formula: h = z + p/(rho g) + v^2/(2g). Canonical FORM: conservation (in = out + change_in_store) — engine verifier hydrology.bernoulli_head — the deterministic check the co", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_hydrology_darcy_velocity", "title": "Darcy velocity", "shelf": "calculations", "surface": "secular", "snippet": "Darcy velocity — hydrology. Formula: q = -K dh/dl. Canonical FORM: linear_flux (flux = conductance * gradient) — engine verifier hydrology.darcy_velocity — the deterministic check the concordance runs", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_master_flux_gradient", "title": "Master equation: J = -k * grad(phi)", "shelf": "bridges", "surface": "secular", "snippet": "a flow driven linearly by a difference — the same law wherever something runs down a gradient. ONE equation, 7 domains, connected by a change of variable: electrical [J = current density, k = conducti", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_hydrology_the_cycle", "title": "The cycle - precipitation and runoff", "shelf": "codex", "surface": "secular", "snippet": "Evaporation, precipitation and runoff keep the 2.5 percent fresh water moving (sealed). Rests on meteorology.", "authority_tier": "engine_derived", "source": "Narrow Highway — hydrology", "readable": false, "generated": false}, {"id": "card_calc_darcy_flow", "title": "Darcy's law", "shelf": "calculations", "surface": "secular", "snippet": "Darcy's law — hydrology. Formula: Q = -K dh/dl. Canonical FORM: linear_flux (flux = conductance * gradient) — groundwater flux driven by a head gradient. Same form, different domain: this is the linea", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_spine_hydrology", "title": "Hydrology — a spine", "shelf": "spine", "surface": "secular", "snippet": "The pillars.", "authority_tier": "engine_derived", "source": "Narrow Highway — hydrology", "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_floor_hydrology"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}