scripts/governing_equations.py

#!/usr/bin/env python3
"""
Governing physical, chemical, and mathematical relations for all 75 Earth-system
sub-disciplines (SUBTOPIC_PROFILES), plus mid-sentence case and punctuation normalizers
for UnsolvedEarth v1.3.0.
"""

import re

GOVERNING_RELATIONS_BY_SUB_ID = {
    # Category 1: Deep Earth, Tectonics, Geodynamics, and Geomagnetism
    "core_dynamo_inner_core": [
        "magnetic induction $\\partial_t \\mathbf{B} = \\nabla \\times (\\mathbf{u} \\times \\mathbf{B}) + \\eta_m \\nabla^2 \\mathbf{B}$ at $\\mathrm{Ek} \\sim 10^{-15}$ and $\\mathrm{Pm} \\sim 10^{-6}$",
        "Elsasser number $\\Lambda = \\sigma B^2 / (\\rho \\Omega) \\sim O(1)$ and thermochemical buoyancy flux $F_B = F_T + F_\\xi$",
    ],
    "lower_mantle_plumes_transition_zone": [
        "Clapeyron slope $dP/dT = \\Delta S / \\Delta V$ across the $410\\,\\mathrm{km}$ ($\\gamma > 0$) and $660\\,\\mathrm{km}$ ($\\gamma \\le 0$) phase boundaries",
        "thermochemical buoyancy ratio $B = \\Delta \\rho_{\\mathrm{chem}} / (\\rho_0 \\alpha \\Delta T)$ and Rayleigh number $\\mathrm{Ra} = \\rho g \\alpha \\Delta T D^3 / (\\eta \\kappa)$",
    ],
    "subduction_slab_mantle_wedge": [
        "composite dislocation-diffusion creep $\\dot{\\varepsilon}_{ij} = (A_{\\mathrm{dis}} \\tau_E^{n-1} + A_{\\mathrm{diff}} d^{-p}) C_{\\mathrm{OH}}^r \\exp[-(E^* + P V^*)/RT] \\tau_{ij}$",
        "slab thermal parameter $\\Phi_{\\mathrm{slab}} = t_{\\mathrm{age}} v_{\\mathrm{conv}} \\sin\\theta$ governing dehydration reactions",
    ],
    "continental_rifting_breakup_margins": [
        "Buck dike-assisted versus tectonic stretching yield $\\Delta \\sigma_{\\mathrm{magma}} = \\rho_c g z - \\rho_m g z + P_{\\mathrm{ex}} \\le \\sigma_Y(\\varepsilon, \\dot{\\varepsilon})$",
        "McKenzie lithospheric thinning factor $\\beta = L / L_0$ and syn-rift isostatic subsidence $S_i(\\beta)$",
    ],
    "craton_orogen_continental_crust": [
        "viscous thin-sheet Argand number $\\mathrm{Ar} = g \\rho_c (1 - \\rho_c/\\rho_m) H_c^2 / (\\eta_{\\mathrm{eff}} U_0)$",
        "isopycnic cratonic root stability $\\Delta \\rho(T, X_{\\mathrm{Mg\\#}}) = \\rho_0 [ -\\alpha (T - T_0) + \\beta_{\\mathrm{chem}} \\Delta X_{\\mathrm{Mg\\#}} ] \\approx 0$",
    ],
    # Category 2: Earthquakes, Volcanoes, Tsunamis, and Geohazards
    "earthquake_rupture_fault_mechanics": [
        "rate-and-state friction $\\tau = \\sigma_n' [\\mu_0 + a \\ln(V/V_0) + b \\ln(V_0 \\theta / D_c)]$ with thermal pressurization $\\partial_t P_f = \\Lambda_{\\mathrm{TP}} \\tau V / w + D_{\\mathrm{hyd}} \\partial_{yy} P_f$",
        "elastodynamic fracture energy balance $G_c = \\int_0^{D_c} (\\tau(u) - \\tau_r) du$ and critical nucleation size $L_c = \\mu D_c / [(b - a) \\sigma_n']$",
    ],
    "slow_slip_tremor_megathrust": [
        "effective normal stress $\\sigma_n' = \\sigma_n - \\alpha_B P_f$ under near-lithostatic pore-fluid factor $\\lambda_f = P_f / \\sigma_v \\to 1$",
        "slow-slip moment-duration scaling $M_0 = \\mu \\bar{D} A \\propto T^\\alpha$ across velocity-transition regimes",
    ],
    "volcanic_plumbing_eruption_degassing": [
        "multiphase magma viscosity $\\eta(\\phi_c, C_{\\mathrm{H2O}}, T) = \\eta_{\\mathrm{melt}}(C_{\\mathrm{H2O}}, T) (1 - \\phi_c / \\phi_m)^{-B \\phi_m}$ and Deborah fragmentation criterion $\\mathrm{De} = \\eta \\dot{\\gamma} / G_\\infty \\ge 10^{-2}$",
        "conduit momentum-continuity balance $\\rho_m u \\partial_z u = -\\partial_z P - \\rho_m g - F_{\\mathrm{wall}}(u, \\eta)$ with volatile exsolution $X_g(P)$",
    ],
    "tsunami_seafloor_displacement": [
        "dispersive Boussinesq shallow-water wave propagation $\\partial_t \\eta + \\nabla \\cdot [(h + \\eta)\\mathbf{u}] = \\partial_t \\zeta_{\\mathrm{seafloor}}$ with phase speed $c = \\sqrt{g h (1 - k^2 h^2 / 3)}$",
        "Okada elastic/inelastic coseismic vertical seafloor uplift $u_z(x,y)$ amplifying shallow trench slip $D_{\\mathrm{trench}}$",
    ],
    "landslide_debris_flow_mass_wasting": [
        "Iverson undrained pore-pressure diffusion $\\partial_t p^* - D_{\\mathrm{hyd}} \\partial_{zz} p^* = -\\rho_s g \\dot{\\gamma} \\tan\\psi_{\\mathrm{dil}}$ and basal resistance $\\tau_b = (\\sigma_n - p_b) \\tan\\phi + \\tau_{\\mathrm{visc}}$",
        "apparent Heim runout friction $\\mu_{\\mathrm{app}} = H_{\\mathrm{drop}} / L_{\\mathrm{runout}}$ vs. Coulomb friction $\\tan\\phi'$",
    ],
    # Category 3: Geochemistry, Mineralogy, Petrology, and Earth Materials
    "low_temp_aqueous_clay_sorption_interface": [
        "Transition State Theory dissolution rate $r = k_+ A_{\\mathrm{reactive}} \\prod a_i^{n_i} [1 - \\exp(\\Delta G_r / (\\sigma R T))]$",
        "surface complexation triple-layer electrostatic equilibrium $K_{\\mathrm{int}} = K_{\\mathrm{app}} \\exp(F \\Delta Z \\Psi_0 / R T)$",
    ],
    "igneous_petrology_magmatic_differentiation": [
        "open-system assimilation-fractional crystallization (AFC) $dC_m/dF = [r/(r-1)] C_a / F - D_{\\mathrm{bulk}} C_m / F$ and oxygen fugacity $\\Delta \\mathrm{FMQ}$",
        "McKenzie compaction length $\\delta_c = \\sqrt{k_\\phi (\\zeta + 4\\eta/3) / \\mu_f}$ governing melt extraction from crystal mush",
    ],
    "hydrothermal_ore_deposits_metallogeny": [
        "fluid-melt metal partitioning $D_M^{\\mathrm{fluid/melt}}(P, T, X_{\\mathrm{Cl}}, X_{\\mathrm{S}}, f\\mathrm{O}_2)$ and Helgeson-Kirkham-Flowers log $K(T, \\rho_w)$",
        "chalcophile sulfide-silicate partitioning $D_{\\mathrm{Cu,Au}}^{\\mathrm{sulf/sil}} \\sim 10^3\\text{--}10^5$ vs. volatile saturation timing",
    ],
    "isotope_geochemistry_geochronology": [
        "Urey-Bigeleisen-Mayer equilibrium fractionation $10^3 \\ln \\alpha_{A-B} \\approx A \\Delta \\langle F \\rangle / T^2$ vs. kinetic/diffusive fractionation $(m_1/m_2)^\\beta$",
        "Dodson diffusive closure temperature $T_c = E_a / [R \\ln(A \\tau D_0 / a^2)]$ modified by alpha-recoil damage fraction $f_a$",
    ],
    "high_pressure_mineral_physics_metamorphism": [
        "Birch-Murnaghan 3rd-order equation of state $P(V) = \\frac{3}{2} K_0 [(V_0/V)^{7/3} - (V_0/V)^{5/3}] \\{1 + \\frac{3}{4}(K_0' - 4)[(V_0/V)^{2/3} - 1]\\}$",
        "tectonic overpressure deviation $\\Delta P_{\\mathrm{tect}} = P_{\\mathrm{mean}} - \\rho g z$ bounded by deviatoric shear strength $\\tau_{\\mathrm{yield}}$",
    ],
    # Category 4: Geologic Time, Paleoclimate, Stratigraphy, and Earth History
    "quaternary_orbital_ice_core_paleoclimate": [
        "Milankovitch insolation-forced ice volume $dV_{\\mathrm{ice}}/dt = I(65^\\circ\\mathrm{N}, e, \\varepsilon, \\varpi) - V_{\\mathrm{ice}}/\\tau_{\\mathrm{ablation}}(p\\mathrm{CO}_2)$",
        "bipolar seesaw heat balance $C_S dT_S/dt = -\\Delta Q_{\\mathrm{AMOC}}(t) - \\lambda_S T_S$",
    ],
    "greenhouse_hyperthermals_cenozoic_mesozoic": [
        "carbon-cycle isotope mass balance $\\Delta \\delta^{13}\\mathrm{C}_{\\mathrm{ex}} = M_{\\mathrm{emit}} (\\delta^{13}\\mathrm{C}_{\\mathrm{src}} - \\delta^{13}\\mathrm{C}_0) / (M_0 + M_{\\mathrm{emit}})$ and Walker silicate weathering $F_{\\mathrm{sil}} \\propto p\\mathrm{CO}_2^\\beta \\exp(\\Delta T / T_e)$",
        "Earth System Sensitivity $\\mathrm{ESS} = \\Delta T_s / \\log_2(p\\mathrm{CO}_2 / p\\mathrm{CO}_{2,0})$ incorporating slow cryosphere-albedo feedbacks",
    ],
    "precambrian_oxygenation_early_earth": [
        "global redox-carbon burial balance $F_{\\mathrm{O2,source}} = F_{\\mathrm{total\\,C}} \\cdot f_{\\mathrm{org}}(\\delta^{13}\\mathrm{C}) + F_{\\mathrm{pyr}} - F_{\\mathrm{volc\\,red}} - F_{\\mathrm{ox\\,weath}}(p\\mathrm{O}_2)$",
        "planetary radiative balance $(S_\\odot(t)/4)(1 - A_p) = \\mathrm{OLR}(T_s, p\\mathrm{CO}_2, p\\mathrm{CH}_4, P_{\\mathrm{N2}})$",
    ],
    "mass_extinction_paleoecology_turnover": [
        "ecophysiological Metabolic Index $\\Phi = A_0 (p\\mathrm{O}_2 / p\\mathrm{O}_{2,\\mathrm{crit}}) \\exp[-(E_0 / k_B)(1/T - 1/T_{\\mathrm{ref}})] \\ge \\Phi_{\\mathrm{crit}}$",
        "birth-death diversification rate $dN_{\\mathrm{taxa}}/dt = (\\lambda_{\\mathrm{spec}} - \\mu_{\\mathrm{ext}}(\\Delta T, \\Omega_{\\mathrm{arag}}, [\\mathrm{H_2S}])) N_{\\mathrm{taxa}}$",
    ],
    "basin_stratigraphy_provenance_diagenesis": [
        "Sadler stratigraphic completeness power law $R(\\Delta t) = R_0 (\\Delta t)^{-\\beta_S}$ and diffusive basin subsidence $\\partial_t z_s = S_{\\mathrm{tect}} + \\nabla \\cdot (\\kappa_s \\nabla z_s)$",
        "early diagenetic advection-diffusion-reaction $\\phi \\partial_t C_i + \\partial_z (\\phi w C_i - \\phi D_s \\partial_z C_i) = \\sum R_i$",
    ],
    # Category 5: Geomorphology, Sediments, and Surface Processes
    "fluvial_channel_sediment_transport": [
        "Shields dimensionless bed shear stress $\\tau^* = \\tau_b / [(\\rho_s - \\rho_w) g D_{50}] \\ge \\tau^*_c$ and Exner conservation $(1 - \\lambda_p) \\partial_t \\eta = -\\nabla \\cdot \\mathbf{q}_b$",
        "Rouse suspended sediment concentration profile $C(z)/C_a = [(h-z)/z \\cdot a/(h-a)]^{\\mathrm{Ro}}$ where $\\mathrm{Ro} = w_s / (\\kappa u_*)$",
    ],
    "tectonic_geomorphology_orogenic_erosion": [
        "stream-power incision and hillslope diffusion $\\partial_t z = U(x,y) - K A^m |\\nabla z|^n + D \\nabla^2 z$ and integral $\\chi = \\int_{x_b}^x (A_0/A(x'))^{m/n} dx'$",
        "cosmogenic $^{10}\\mathrm{Be}$ steady-state denudation $N_{10} = P_0 / (\\lambda_{10} + \\rho_r \\varepsilon / \\Lambda_{\\mathrm{atten}})$",
    ],
    "aeolian_dunes_dust_loess_geomorphology": [
        "Bagnold-Shao saltation threshold $u_{*t} = A_N \\sqrt{(\\rho_p - \\rho_a) g d / \\rho_a + \\gamma_{\\mathrm{cohes}} / (\\rho_a d)}$ and horizontal flux $Q_{\\mathrm{salt}} \\propto (\\rho_a / g) u_* (u_*^2 - u_{*t}^2)$",
        "dune dispersion relation $\\sigma(k) + i \\omega(k) = Q_0 k^2 (A_{\\mathrm{hydro}} + i B_{\\mathrm{hydro}}) / (1 + i k L_{\\mathrm{sat}})$",
    ],
    "karst_cave_glacial_periglacial_geomorphology": [
        "Hallet-Walder frost-cracking intensity $\\mathrm{FCI} \\propto \\int |\\nabla T| k_h(T) d z$ in the $-3\\text{ to }-8\\,^\\circ\\mathrm{C}$ window and glacial abrasion $\\dot{E}_g = K_g u_b^l N_{\\mathrm{eff}}^m$",
        "karst conduit dissolution kinetics $r_{\\mathrm{CaCO3}} = k_n (1 - C / C_{\\mathrm{eq}})^n$ across the laminar-turbulent breakthrough switch",
    ],
    "hillslope_soil_erosion_gully_badlands": [
        "nonlinear Roering hillslope sediment flux $\\mathbf{q}_s = -D \\nabla z / [1 - (|\\nabla z| / S_c)^2]$ coupled with soil production $P_{\\mathrm{soil}}(h) = P_0 \\exp(-\\alpha h)$",
        "gully headcut detachment rate $E_d = k_d (\\tau_{\\mathrm{flow}} - \\tau_c(c_{\\mathrm{root}}))$",
    ],
    # Category 6: Atmosphere, Weather, and Atmospheric Chemistry
    "cloud_microphysics_aerosol_ccn_in": [
        "Köhler droplet activation supersaturation $S(r) = 1 + A/r - \\kappa_{\\mathrm{hyg}} r_{\\mathrm{dry}}^3 / r^3$ and Wegener-Bergeron-Findeisen relaxation $\\tau_{\\mathrm{phase}}^{-1} = 4\\pi D_v (N_w r_w + N_i C_i)$",
        "autoconversion-accretion warm-rain balance $\\partial_t q_r = k_{\\mathrm{auto}} q_c^{\\alpha_1} N_d^{-\\alpha_2} + k_{\\mathrm{accr}} q_c q_r$",
    ],
    "tropospheric_chemistry_soa_ozone_radicals": [
        "tropospheric $\\mathrm{HO}_x\\text{--}\\mathrm{NO}_x\\text{--}\\mathrm{VOC}$ ozone production $P(\\mathrm{O}_3) = k_{\\mathrm{HO2+NO}}[\\mathrm{HO}_2][\\mathrm{NO}] + \\sum_i k_{\\mathrm{RO2+NO}}[\\mathrm{RO}_{2,i}][\\mathrm{NO}]$",
        "volatility basis set (VBS) gas-particle partitioning $\\xi_i = (1 + C_i^*(T) / C_{\\mathrm{OA}})^{-1}$ with reactive uptake $\\gamma_{\\mathrm{het}}$",
    ],
    "convective_storms_tropical_cyclones_monsoon": [
        "convective available potential energy $\\mathrm{CAPE} = \\int_{\\mathrm{LFC}}^{\\mathrm{EL}} g (\\theta_{v,\\mathrm{parcel}} - \\theta_{v,\\mathrm{env}})/\\theta_{v,\\mathrm{env}} dz$ and entraining plume mass flux $\\partial_z \\ln M = \\varepsilon - \\delta$",
        "column moist static energy budget $\\langle \\partial_t h \\rangle = -\\langle \\nabla \\cdot (\\mathbf{u} h) \\rangle + \\langle Q_R \\rangle + \\mathrm{LHF} + \\mathrm{SHF}$",
    ],
    "stratosphere_mesosphere_gravity_waves_ozone": [
        "transformed Eulerian mean (TEM) wave-driven circulation $\\partial_t \\bar{u} - f_0 \\bar{v}^* = (\\rho_0 a \\cos\\phi)^{-1} \\nabla \\cdot \\mathbf{F}_{\\mathrm{EP}} + X_{\\mathrm{GW}}$",
        "Chapman-halogen catalytic ozone loss $d[\\mathrm{O}_3]/dt = 2 J_{\\mathrm{O2}}[\\mathrm{O}_2] - 2 k_{\\mathrm{O+O3}}[\\mathrm{O}][\\mathrm{O}_3] - \\sum_{\\mathrm{X=Cl,Br,NO,HO}} R_{\\mathrm{cat,X}}$",
    ],
    "boundary_layer_turbulence_air_surface_exchange": [
        "Monin-Obukhov similarity dimensionless shear $\\phi_m(z/L_{\\mathrm{MO}}) = (\\kappa z / u_*) \\partial_z \\bar{u}$ where $L_{\\mathrm{MO}} = -u_*^3 \\bar{\\theta}_v / (\\kappa g \\overline{w'\\theta_v'})$",
        "turbulent kinetic energy (TKE) balance $\\partial_t \\bar{e} = -\\overline{u'w'} \\partial_z \\bar{u} + (g/\\bar{\\theta}_v)\\overline{w'\\theta_v'} - \\partial_z \\overline{w'e} - \\varepsilon$",
    ],
    # Category 7: Climate Dynamics, Feedbacks, Predictability, and Extremes
    "climate_sensitivity_cloud_radiative_feedbacks": [
        "radiative feedback decomposition $N(t) = \\Delta F(t) + (\\lambda_P + \\lambda_{\\mathrm{WV+LR}} + \\lambda_{\\mathrm{alb}} + \\lambda_{\\mathrm{cld}} + \\Delta \\lambda_{\\mathrm{pattern}}(t)) \\Delta T_s(t)$",
        "Equilibrium Climate Sensitivity $\\mathrm{ECS} = -F_{2\\times\\mathrm{CO2}} / \\lambda_{\\mathrm{net}}$",
    ],
    "enso_pdo_amo_modes_teleconnections": [
        "recharge-oscillator ENSO dynamics $dT_E/dt = R_{\\mathrm{Bjerknes}} T_E + \\gamma h_W - \\epsilon T_E^3, \\quad dh_W/dt = -r h_W - \\alpha T_E$",
        "Rossby wave stationary wavenumber $K_s = a \\cos\\phi \\sqrt{(\\beta_M / \\bar{u})}$ governing teleconnection waveguides",
    ],
    "extreme_events_heatwaves_blocking_compound": [
        "Ertel potential vorticity budget $D_t Q = \\rho^{-1} (\\boldsymbol{\\omega}_a \\cdot \\nabla \\dot{\\theta}) + \\rho^{-1} \\nabla \\theta \\cdot (\\nabla \\times \\mathbf{F})$ in blocking anticyclones",
        "thermodynamic vs. dynamic extreme precipitation scaling $\\delta P_{\\mathrm{ext}} \\approx -\\langle \\omega' \\delta q_{\\mathrm{sat}}(T) \\rangle - \\langle \\delta \\omega' q_{\\mathrm{sat}}(T) \\rangle$",
    ],
    "global_carbon_climate_tipping_feedbacks": [
        "Arora carbon-climate feedback framework $\\Delta C_L + \\Delta C_O = (\\beta_L + \\beta_O) \\Delta C_A + (\\gamma_L + \\gamma_O) \\Delta T_s$",
        "early-warning critical slowing down autocorrelation $\\mathrm{AR}(1) = \\exp(-\\lambda_{\\mathrm{rest}} \\Delta t) \\to 1$ and variance $\\sigma_x^2 = \\sigma_\\eta^2 / (2 \\lambda_{\\mathrm{rest}})$",
    ],
    "monsoon_hydroclimate_itcz_shifts": [
        "energetic ITCZ latitude scaling $\\phi_{\\mathrm{ITCZ}} \\approx -\\frac{1}{a} \\frac{\\mathrm{AHT}_{\\mathrm{eq}}}{\\mathrm{NEI}_{\\mathrm{eq}}}$ where $\\mathrm{NEI} = R_{\\mathrm{TOA}} - \\nabla \\cdot \\mathbf{F}_{\\mathrm{ocean}}$",
        "moisture budget decomposition $P' - E' = -g^{-1} \\nabla \\cdot \\int_0^{p_s} (\\bar{\\mathbf{u}} q' + \\mathbf{u}' \\bar{q} + \\mathbf{u}' q') dp$",
    ],
    # Category 8: Cryosphere, Permafrost, and Sea Level
    "ice_sheet_grounding_line_marine_instability": [
        "Schoof grounding-line flux $q_g = [A (\\rho_i g)^3 (1 - \\rho_i/\\rho_w)^3 / (4^3 C_b)]^{1/(m+1)} h_g^{(m+n+3)/(m+1)}$ with Coulomb-regularized basal sliding $\\tau_b = C u_b^m N (u_b^m / (C_0 N)^m + 1)^{-1/m}$",
        "three-equation sub-ice-shelf melt balance $\\rho_i L_f \\dot{m} = \\rho_w c_w u_* \\Gamma_T (T_w - T_b(S_b, P_b))$",
    ],
    "mountain_glaciers_mass_balance_debris": [
        "glacier climatic mass and surface energy balance $Q_{\\mathrm{melt}} = Q_{\\mathrm{SW}}(1 - \\alpha) + Q_{\\mathrm{LW}}^\\downarrow - \\varepsilon \\sigma T_s^4 + Q_H + Q_E + Q_G(h_{\\mathrm{debris}})$",
        "shallow-ice / higher-order Glen's flow law $\\dot{\\varepsilon}_{ij} = A(T') \\tau_E^{n-1} \\tau_{ij}$ ($n \\in [3, 4]$)",
    ],
    "sea_ice_dynamics_thermodynamics_leads": [
        "Hibler-Mellor sea-ice momentum and thickness distribution $\\rho_i h D_t \\mathbf{u}_i = \\boldsymbol{\\tau}_a + \\boldsymbol{\\tau}_w - \\rho_i h f \\hat{\\mathbf{k}} \\times \\mathbf{u}_i - \\rho_i h g \\nabla \\eta + \\nabla \\cdot \\boldsymbol{\\sigma}_{\\mathrm{rheol}}$",
        "Stefan basal ice growth-melt balance $\\rho_i L_f dh_i/dt = k_i (T_f - T_s)/h_i - F_w$",
    ],
    "permafrost_thermokarst_active_layer_carbon": [
        "Stefan phase-change heat conduction $C_{\\mathrm{eff}}(T) \\partial_t T = \\partial_z (k(T) \\partial_z T)$ where $C_{\\mathrm{eff}}(T) = C_v + L_f \\rho_w (\\partial \\theta_u / \\partial T)$",
        "anoxic vs. oxic permafrost carbon mineralization $F_C = k_{\\mathrm{ox}}(T) C_{\\mathrm{thaw}}(z \\le z_{\\mathrm{wt}}) + k_{\\mathrm{CH4}}(T) C_{\\mathrm{thaw}}(z \\ge z_{\\mathrm{wt}})$",
    ],
    "snowpack_hydrology_sea_level_gia": [
        "gravitationally self-consistent sea-level equation $S(\\theta,\\phi,t) = \\rho_w^{-1} G(\\theta,\\phi,t) - U_{\\mathrm{GIA}}(\\theta,\\phi,t) + c(t)$",
        "snowpack mass and cold-content energy balance $d(\\mathrm{SWE})/dt = P_{\\mathrm{snow}} + P_{\\mathrm{rain}} - E_{\\mathrm{sub}} - M_{\\mathrm{outflow}}$",
    ],
    # Category 9: Physical Oceanography and Ocean Circulation
    "amoc_overturning_deep_water_formation": [
        "residual overturning streamfunction $\\Psi_{\\mathrm{res}} = \\bar{\\Psi}_{\\mathrm{Euler}} + \\Psi^*$ where $\\Psi^* = (\\overline{v'b'}) / \\bar{b}_z$ and Stommel salt-advection feedback $F_{\\mathrm{ovS}} = -\\frac{1}{S_0} \\int \\bar{v}(z) \\bar{S}^*(z) dz dx$",
        "thermal wind overturning scaling $\\partial_{zz} \\Psi \\propto (g / f_0 \\rho_0) \\Delta_x \\rho$",
    ],
    "mesoscale_submesoscale_eddies_fronts": [
        "quasi-geostrophic potential vorticity conservation $D_g q_{\\mathrm{QG}}/Dt = 0$ where $q_{\\mathrm{QG}} = \\nabla_h^2 \\psi + f + \\partial_z [(f_0^2 / N^2) \\partial_z \\psi]$",
        "submesoscale Ertel potential vorticity $q = (f \\hat{\\mathbf{z}} + \\nabla \\times \\mathbf{u}) \\cdot \\nabla b \\le 0$ criterion for symmetric instability",
    ],
    "internal_waves_tides_diapycnal_mixing": [
        "Osborn turbulent diapycnal diffusivity $\\kappa_\\rho = \\Gamma \\varepsilon / N^2$ with mixing efficiency $\\Gamma = R_f / (1 - R_f) \\approx 0.2$",
        "advective-diffusive abyssal buoyancy balance $\\mathbf{u} \\cdot \\nabla b + w N^2 = \\partial_z (\\kappa_\\rho(z) N^2)$",
    ],
    "upper_ocean_mixed_layer_marine_heatwaves": [
        "mixed-layer temperature budget $\\partial_t T_m = Q_{\\mathrm{net}}/(\\rho_0 c_p h_m) - \\mathbf{u}_m \\cdot \\nabla_h T_m - w_e H(w_e) (T_m - T_{-h_m})/h_m + \\kappa_h \\nabla_h^2 T_m$",
        "turbulent Langmuir number $\\mathrm{La}_t = \\sqrt{u_* / U_{\\mathrm{Stokes}}}$ governing Stokes-vortex mixed-layer entrainment",
    ],
    "coastal_shelf_marginal_sea_circulation": [
        "along-shelf geostrophic and Ekman cross-shelf transport $U_E = \\tau_{\\mathrm{wind}}^y / (\\rho_0 f)$ with topographic Taylor-Proudman constraint $\\mathbf{u} \\cdot \\nabla (f/H) = 0$",
        "Simpson-Hunter tidal mixing parameter $\\log_{10}(H / U_{\\mathrm{tide}}^3)$ governing shelf-sea front locations",
    ],
    # Category 10: Marine Biogeochemistry, Seafloor, and Ocean-Ecosystem Coupling
    "biological_carbon_pump_export_phytoplankton": [
        "Martin power-law POC flux attenuation $F_{\\mathrm{POC}}(z) = F_{\\mathrm{POC}}(z_0) (z / z_0)^{-b(T, [\\mathrm{O}_2])}$ where $b = k_{\\mathrm{remin}}(T) / w_{\\mathrm{sink}}$",
        "Sverdrup-Behrenfeld phytoplankton net growth $dP/dt = [\\mu(I, T, \\mathrm{N, Fe}) - m_{\\mathrm{graz}}(Z) - w_s/h_m] P$",
    ],
    "ocean_deoxygenation_omz_nitrogen_cycle": [
        "interior oxygen balance $\\partial_t [\\mathrm{O}_2] + \\mathbf{u} \\cdot \\nabla [\\mathrm{O}_2] - \\nabla \\cdot (\\mathbf{K} \\nabla [\\mathrm{O}_2]) = -r_{\\mathrm{O2:C}} R_{\\mathrm{org}}(z, T)$ with apparent oxygen utilization $\\mathrm{AOU} = [\\mathrm{O}_2]_{\\mathrm{sat}}(T, S) - [\\mathrm{O}_2]$",
        "suboxic fixed-nitrogen deficit $\\mathrm{N}^* = [\\mathrm{NO}_3^-] - 16 [\\mathrm{PO}_4^{3-}] + 2.9\\,\\mu\\mathrm{mol\\,kg^{-1}}$",
    ],
    "ocean_acidification_carbonate_alkalinity": [
        "carbonate saturation state $\\Omega = [\\mathrm{Ca}^{2+}][\\mathrm{CO}_3^{2-}] / K_{sp}^*(T, S, P)$ and Revelle buffer factor $\\gamma_{\\mathrm{DIC}} = (\\partial \\ln p\\mathrm{CO}_2 / \\partial \\ln \\mathrm{DIC})_{\\mathrm{TA}} \\approx 8\\text{--}15$",
        "air-sea $\\mathrm{CO}_2$ gas flux $F_{\\mathrm{CO2}} = k_w K_0(T, S) (p\\mathrm{CO}_2^{\\mathrm{sea}} - p\\mathrm{CO}_2^{\\mathrm{air}})$",
    ],
    "geotraces_trace_metals_hydrothermal_vents": [
        "organic-ligand iron complexation $\\mathrm{Fe}' + L_i \\rightleftharpoons \\mathrm{Fe}L_i$ with conditional stability constant $K_{\\mathrm{Fe}L_i, \\mathrm{Fe}'}^{\\mathrm{cond}} = [\\mathrm{Fe}L_i] / ([\\mathrm{Fe}'][L_i']) \\sim 10^{11}\\text{--}10^{13}\\,\\mathrm{M}^{-1}$",
        "reversible particle scavenging balance $\\partial_t C_d = J_{\\mathrm{source}} - k_1 C_p C_d + k_{-1} C_{\\mathrm{part}}$",
    ],
    "marine_sediment_early_diagenesis_benthic_flux": [
        "Berner 1D early diagenetic reaction-transport $\\phi \\partial_t C_i = \\partial_z (\\phi D_{\\mathrm{bio+mol}} \\partial_z C_i - \\phi \\omega_{\\mathrm{sed}} C_i) + \\phi \\alpha_{\\mathrm{irr}}(C_0 - C_i) + \\sum R_i$",
        "Redox terminal electron-acceptor sequence ($\\mathrm{O}_2 \\to \\mathrm{NO}_3^- \\to \\mathrm{Mn(IV)} \\to \\mathrm{Fe(III)} \\to \\mathrm{SO}_4^{2-} \\to \\mathrm{CH}_4$) across the sulfate-methane transition",
    ],
    # Category 11: Hydrology, Groundwater, and the Water Cycle
    "catchment_runoff_transit_time_uph": [
        "Kirchner dynamical catchment storage-discharge sensitivity $g(Q) = dQ/dS = (-dQ/dt) / (Q - P + E)$ and power-law recession $-dQ/dt = a Q^b$",
        "master transit-time StorAge Selection (SAS) transport $\\partial_t S_T(T, t) + \\partial_T S_T(T, t) = J(t) - Q(t) \\Omega_Q(S_T, t) - E(t) \\Omega_E(S_T, t)$",
    ],
    "groundwater_aquifer_karst_fractured_flow": [
        "3D transient groundwater flow $S_s \\partial_t h = \\nabla \\cdot (\\mathbf{K} \\nabla h) + W$ and Cubic Law fracture transmissivity $T_f = (\\rho g b^3) / (12 \\mu)$",
        "dual-domain mobile-immobile solute transport $\\theta_m \\partial_t C_m + \\theta_{im} \\partial_t C_{im} = \\nabla \\cdot (\\theta_m \\mathbf{D} \\nabla C_m) - \\mathbf{q} \\cdot \\nabla C_m$",
    ],
    "vadose_zone_evapotranspiration_ecohydrology": [
        "Richards unsaturated flow $\\partial_t \\theta(\\psi) = \\nabla \\cdot [K(\\psi) \\nabla (\\psi + z)] - S_{\\mathrm{root}}(\\psi)$ coupled with Penman-Monteith evapotranspiration $\\lambda E = [\\Delta (R_n - G) + \\rho_a c_p \\mathrm{VPD} / r_a] / [\\Delta + \\gamma (1 + r_s / r_a)]$",
        "Budyko hydroclimatic partitioning $E/P = [1 + (E_0 / P)^{-\\omega}]^{-1/\\omega}$",
    ],
    "hyporheic_river_groundwater_lake_wetland": [
        "hyporheic Damköhler number $\\mathrm{Da} = \\tau_{\\mathrm{res}} k_{\\mathrm{rxn}}$ governing aerobic-to-denitrifying redox transition along bedform streamlines",
        "1D Saint-Venant transient channel-storage routing $\\partial_t A + \\partial_x Q = q_{\\mathrm{lat}} - q_{\\mathrm{hyp}}(A_s / A) \\partial_t (C_s - C)$",
    ],
    "hydroclimatic_extremes_floods_drought_propagation": [
        "Generalized Extreme Value (GEV) non-stationary return level $G(x; \\mu(t), \\sigma(t), \\xi) = \\exp\\{-[1 + \\xi ((x - \\mu(t))/\\sigma(t))]^{-1/\\xi}\\}$",
        "runoff-precipitation elasticity $\\varepsilon_Q = (\\bar{P}/\\bar{Q}) (dQ/dP)$ shifting across multi-year drought states",
    ],
    # Category 12: Soils, Critical Zone, and Terrestrial Biogeochemistry
    "soil_organic_carbon_mineral_stabilization_priming": [
        "microbial-mineral soil carbon dynamics $dC_{\\mathrm{MAOM}}/dt = f_{\\mathrm{MAOM}} \\cdot \\mathrm{CUE}(T) V_{\\max}(T) \\frac{C_{\\mathrm{DOC}} B_{\\mathrm{mic}}}{K_m + C_{\\mathrm{DOC}}} (1 - \\frac{C_{\\mathrm{MAOM}}}{C_{\\max}}) - k_{\\mathrm{des}}(T, [\\mathrm{oxalate}]) C_{\\mathrm{MAOM}}$",
        "temperature sensitivity $Q_{10} = \\exp[10 E_a / (R T (T + 10))]$ modified by organo-mineral sorption",
    ],
    "critical_zone_weathering_regolith_architecture": [
        "1D reactive transport weathering front propagation $w_{\\mathrm{front}} = q_{\\mathrm{infil}} (C_{\\mathrm{eq}} - C_0) / (\\rho_b m_{\\mathrm{min}})$ and Maher Damköhler number $\\mathrm{Da}_{\\mathrm{weath}} = k_{\\mathrm{eff}} A_s L / q_{\\mathrm{infil}}$",
        "chemical depletion fraction $\\mathrm{CDF} = 1 - [\\mathrm{Zr}]_{\\mathrm{parent}} / [\\mathrm{Zr}]_{\\mathrm{weathered}}$",
    ],
    "rhizosphere_mycorrhiza_nutrient_stoichiometry": [
        "stoichiometric microbial carbon-nitrogen mineralization $F_{\\mathrm{N,min}} = R_{\\mathrm{decomp}} [ (\\mathrm{C:N})_{\\mathrm{sub}}^{-1} - \\mathrm{CUE} \\cdot (\\mathrm{C:N})_{\\mathrm{mic}}^{-1} ]$",
        "rhizosphere radial reaction-diffusion $\\theta \\partial_t C_i = r^{-1} \\partial_r [r (\\theta D_e \\partial_r C_i + v_0 r_0 C_i)] - R_{\\mathrm{sorp+bio}}$",
    ],
    "peatland_wetland_redox_methane_biogeochemistry": [
        "net wetland methane flux $F_{\\mathrm{CH4}} = (1 - f_{\\mathrm{ox}}(z_{\\mathrm{wt}}, T)) \\int_{z_{\\mathrm{wt}}}^Z R_{\\mathrm{CH4}}(z, T) dz + F_{\\mathrm{ebull}} + F_{\\mathrm{aerenchyma}}$",
        "Nernst redox potential $E_h = E_h^0 - \\frac{R T}{n F} \\ln([\\mathrm{Red}]/[\\mathrm{Ox}]) - 0.059 \\frac{m}{n} \\mathrm{pH}$",
    ],
    "dryland_biocrust_inorganic_carbon_caliche": [
        "pedogenic carbonate equilibrium $\\mathrm{Ca}^{2+} + 2\\,\\mathrm{HCO}_3^- \\rightleftharpoons \\mathrm{CaCO}_3(s) + \\mathrm{CO}_2(g) + \\mathrm{H}_2\\mathrm{O}$ driven by soil $p\\mathrm{CO}_2(z)$ and evaporation",
        "pulse-reserve dryland carbon balance $\\mathrm{NEE}(t) = R_{\\mathrm{Birch}}(\\Delta \\theta_w) - \\mathrm{GPP}(\\theta_w - \\theta_{\\mathrm{wilt}}, \\mathrm{VPD})$",
    ],
    # Category 13: Ecosystem-Earth Interactions, Land Change, and Environmental Response
    "forest_mortality_drought_carbon_sink": [
        "Sperry-Tyree xylem hydraulic conductance $K(\\psi) = K_{\\max} \\exp[-(-\\psi / b)^c]$ with critical cavitation threshold $\\psi_{50} / \\psi_{88}$",
        "Farquhar-Medlyn coupled photosynthesis-conductance $A_n = \\min(A_c(V_{c\\max}, C_i), A_j(J_{\\max}, C_i)) - R_d$ with $g_s = g_0 + 1.6(1 + g_1/\\sqrt{\\mathrm{VPD}}) A_n / C_a$",
    ],
    "wildfire_regimes_pyrogenic_carbon_recovery": [
        "Rothermel-Byram fireline intensity $I_B = H_c w_{\\mathrm{fuel}} R_{\\mathrm{spread}}(U, \\theta_{\\mathrm{slope}}, m_f(\\mathrm{VPD}))$",
        "net post-fire radiative forcing $\\Delta F_{\\mathrm{net}}(t) = \\Delta F_{\\mathrm{GHG}}(E_{\\mathrm{CO2,CH4,N2O}}) + \\Delta F_{\\mathrm{aer}} + \\Delta R_{\\mathrm{SW}}(\\Delta \\alpha_{\\mathrm{surf}}(t))$",
    ],
    "land_use_change_albedo_biophysical_feedbacks": [
        "surface temperature decomposition $\\Delta T_s \\approx \\frac{\\lambda_0}{1 + f_{\\mathrm{eb}}} [ -S_{\\mathrm{SW}}^\\downarrow \\Delta \\alpha + \\Delta Q_{\\mathrm{LW}}^\\downarrow - \\lambda E \\frac{\\Delta r_s}{r_a + r_s} + \\frac{H + \\lambda E}{r_a (1 + \\beta^{-1})} \\Delta r_a ]$",
        "moisture-recycling precipitation fraction $\\rho_{\\mathrm{recyc}} = P_{\\mathrm{evap\\text{-}upwind}} / P_{\\mathrm{total}} = 1 - \\exp(-\\int (E / F_{\\mathrm{vapor}}) ds)$",
    ],
    "phenology_treeline_permafrost_ecosystem_shifts": [
        "chilling-photoperiod-forcing thermal time $\\sum_{t=t_0}^{t_{\\mathrm{bud}}} \\max(0, T(t) - T_{\\mathrm{base}}) \\ge F^*(C_{\\mathrm{chill}}, L_{\\mathrm{day}})$",
        "seasonal net ecosystem carbon balance $\\mathrm{NECB} = \\int (\\mathrm{GPP}(t) - R_{\\mathrm{auto}}(t) - R_{\\mathrm{het}}(T, \\theta)) dt - F_{\\mathrm{disturb}} - F_{\\mathrm{DOC}}$",
    ],
    "agricultural_agroecosystem_ghg_nitrogen": [
        "hole-in-the-pipe soil $\\mathrm{NO}$ and $\\mathrm{N_2O}$ flux $F_{\\mathrm{N2O}} = (k_{\\mathrm{nit}} [\\mathrm{NH}_4^+] + k_{\\mathrm{denit}} [\\mathrm{NO}_3^-]) \\cdot f_{\\mathrm{N2O/(N2O+N2)}}(\\mathrm{WFPS}, \\mathrm{pH}, C_{\\mathrm{labile}})$",
        "watershed anthropogenic Nitrogen Input (NANI) retention $F_{\\mathrm{river\\,N}} = (1 - f_{\\mathrm{denit}} - f_{\\mathrm{storage}}) \\cdot \\mathrm{NANI}$",
    ],
    # Category 14: Pollution, Contaminant Fate, and Environmental Quality
    "pfas_forever_chemicals_transport_fate": [
        "air-water interfacial vadose retardation $R_f = 1 + (\\rho_b K_d(\\mathrm{f_{oc}}))/\\theta_w + (K_{ai}(C, I) A_{ai}(\\theta_w))/\\theta_w$ where $K_{ai} = -(R T)^{-1} (\\partial \\gamma_{\\mathrm{aw}} / \\partial C)$",
        "sequential precursor biotransformation $\\partial_t C_k + R_{f,k}^{-1} \\mathbf{v} \\cdot \\nabla C_k = y_{k-1\\to k} \\lambda_{k-1} C_{k-1} - \\lambda_k C_k$",
    ],
    "microplastics_nanoplastics_weathering_vectors": [
        "DLVO colloidal attachment-detachment transport $\\partial_t C + v \\partial_x C - D \\partial_{xx} C = -k_{\\mathrm{att}}(\\Phi_{\\mathrm{DLVO}}, I) \\psi_{\\mathrm{block}} C + k_{\\mathrm{det}} \\rho_b S / \\theta$",
        "shape-dependent Dietrich settling velocity $w_s^* = f(D^*, \\mathrm{CSF}, P_{\\mathrm{roundness}}, \\rho_p(\\text{biofilm}) - \\rho_w)$",
    ],
    "heavy_metals_mercury_arsenic_methylation_redox": [
        "reductive dissolution and arsenic/mercury speciation $\\partial_t [\\mathrm{MeHg}] = k_{\\mathrm{meth}}(\\mathrm{hgcAB}, [\\mathrm{HS}^-], \\mathrm{DOM}) [\\mathrm{Hg(II)}_{\\mathrm{bioavail}}] - (k_{\\mathrm{demeth}} + J_{\\mathrm{photored}}) [\\mathrm{MeHg}]$",
        "Rayleigh compound-specific / mass-independent isotope fractionation $\\delta(f) = \\delta_0 + \\varepsilon \\ln f$",
    ],
    "emerging_organic_contaminants_ppcp_arg_pesticides": [
        "direct + sensitized photolysis and biodegradation rate $k_{\\mathrm{tot}} = J_{\\mathrm{direct}}(\\Phi_\\lambda) + k_{\\cdot\\mathrm{OH}}[\\cdot\\mathrm{OH}] + k_{^3\\mathrm{CDOM}}[\\mathrm{^3CDOM^*}] + k_{\\mathrm{bio}} X_{\\mathrm{mic}}$",
        "Freundlich nonlinear sorption isotherm $q_e = K_F C_w^n$ producing concentration-dependent retardation $R(C_w) = 1 + (\\rho_b / \\theta) n K_F C_w^{n-1}$",
    ],
    "radionuclides_nutrient_eutrophication_harmful_blooms": [
        "phosphorus-nitrogen-temperature harmful algal bloom growth $\\mu_{\\mathrm{HAB}} = \\mu_{\\max}(T) \\min\\left(\\frac{[\\mathrm{SRP}]}{K_P + [\\mathrm{SRP}]}, \\frac{[\\mathrm{DIN}]}{K_N + [\\mathrm{DIN}]}\\right) f(I) - m_{\\mathrm{flush}}(Q/V)$",
        "benthic internal phosphorus loading $J_{P,\\mathrm{sed}} = J_{\\mathrm{oxic}} + J_{\\mathrm{anox}} / (1 + ([\\mathrm{O}_2]_{\\mathrm{bot}} / K_{\\mathrm{O2}})^p)$",
    ],
    # Category 15: Coasts, Deltas, Drylands, Urban Environments, and Coupled Human-Earth Systems
    "coastal_morphodynamics_shoreline_barrier_marshes": [
        "salt-marsh ecogeomorphic elevation balance $dz_m/dt = Q_{\\mathrm{min}}(h_d, C_{\\mathrm{SSC}}) + Q_{\\mathrm{org}}(B_{\\mathrm{veg}}(h_d)) - S_{\\mathrm{comp}} - \\mathrm{RSLR}$",
        "alongshore CERC wave sediment transport $Q_l = K_{\\mathrm{CERC}} (\\rho_w g^{3/2} / [16 \\sqrt{\\gamma_b} (\\rho_s - \\rho_w)(1 - \\lambda_p)]) H_b^{5/2} \\sin(2\\alpha_b)$",
    ],
    "river_deltas_avulsion_subsidence_salinity": [
        "relative sea-level rise and delta subsidence $\\mathrm{RSLR}_{\\mathrm{net}} = \\dot{\\eta}_{\\mathrm{eustatic}} + S_{\\mathrm{GIA}} + \\int_0^Z m_v(z) \\partial_t P_{\\mathrm{pore}}(z) dz + S_{\\mathrm{creep}} - \\dot{\\eta}_{\\mathrm{aggrad}}$",
        "estuarine MacCready salt-intrusion length $L_s \\propto H^3 N_0^2 / (K_v Q_{\\mathrm{river}})$ and backwater length $L_{\\mathrm{bw}} = H_{\\mathrm{bf}} / S_0$",
    ],
    "urban_heat_island_canyon_hydrology_emissions": [
        "urban canopy energy balance $Q^* + Q_F = Q_H + Q_E + \\Delta Q_S + \\Delta Q_A$ with sky-view factor $\\psi_{\\mathrm{svf}}(H/W)$ radiative trapping",
        "urban storm-runoff Flashiness Index and Green-Ampt impervious-connected infiltration $f_p(t) = K_{\\mathrm{eff}} (1 + \\psi_f \\Delta \\theta / F(t))$",
    ],
    "dryland_desertification_oasis_dust_coupled": [
        "Rietkerk ecohydrological Turing-cusp vegetation-water coupling $\\partial_t B = c g_{\\max} \\frac{W}{W + k_1} B - d B + D_B \\nabla^2 B, \\quad \\partial_t W = \\alpha R \\frac{B + k_2 w_0}{B + k_2} - g_{\\max} \\frac{W}{W + k_1} B - r_w W + D_W \\nabla^2 W$",
        "closed endorheic terminal-lake area balance $A_L dh_L/dt = Q_{\\mathrm{in}} - Q_{\\mathrm{divert}} + A_L (P_L - E_L(S_L, T))$",
    ],
    "coupled_human_natural_coastal_infra_risk": [
        "compound coastal-fluvial-pluvial surge momentum $\\partial_t \\eta_{\\mathrm{tot}} = \\eta_{\\mathrm{tide}} + \\eta_{\\mathrm{surge}}(\\tau_{\\mathrm{wind}}, \\Delta P_a) + \\eta_{\\mathrm{wave}} + \\eta_{\\mathrm{river}}(Q_f) + \\Delta \\eta_{\\mathrm{nonlin}}(Q_f, \\eta_{\\mathrm{surge}})$",
        "coupled socio-hydrological flood-memory levee dynamics $dM_{\\mathrm{risk}}/dt = \\alpha_{\\mathrm{shock}} D_{\\mathrm{flood}} - \\mu_{\\mathrm{forget}} M_{\\mathrm{risk}}$",
    ],
}

PROPER_NOUN_KEEP_SET = {
    "Earth", "Earth's", "Antarctic", "Antarctica", "Arctic", "Subarctic",
    "Atlantic", "Pacific", "Indian", "Southern", "Mediterranean", "Caribbean",
    "Baltic", "Adriatic", "Aegean", "Bering", "Beaufort", "Chukchi", "Laptev",
    "Barents", "Kara", "Weddell", "Ross", "Amundsen", "Bellingshausen", "Scotia",
    "Tasman", "Coral", "Red", "Black", "Caspian", "Aral", "Dead", "Yellow",
    "Bohai", "Okhotsk", "Japan", "Java", "Banda", "Sulu", "Celebes", "Timor",
    "Arafura", "Andaman", "Arabian", "Bengal", "Persian", "Oman", "Aden",
    "Mexico", "California", "Alaska", "Hudson", "Baffin", "Labrador", "Irminger",
    "Norwegian", "Greenland", "Iceland", "Icelandic", "Svalbard", "Fennoscandia",
    "Fennoscandian", "Scandinavia", "Scandinavian", "Alps", "Alpine", "Pyrenees",
    "Apennine", "Apennines", "Carpathian", "Carpathians", "Dinarides", "Hellenic",
    "Anatolia", "Anatolian", "Caucasus", "Zagros", "Makran", "Sulaiman",
    "Himalaya", "Himalayan", "Himalayas", "Karakoram", "Pamir", "Hindu", "Kush",
    "Tibet", "Tibetan", "Kunlun", "Qilian", "Qinling", "Dabie", "Sulu", "Tianshan",
    "Tian", "Shan", "Altai", "Sayan", "Baikal", "Tarim", "Qaidam", "Junggar",
    "Ordos", "Sichuan", "Songliao", "Bohaiwan", "Yangtze", "Cathaysia", "Loess",
    "Hengduan", "Yunnan", "Guizhou", "Sunda", "Banda", "Sumatra", "Java",
    "Borneo", "Sulawesi", "Mindanao", "Luzon", "Taiwan", "Ryukyu", "Nankai",
    "Izu", "Bonin", "Mariana", "Kuril", "Kamchatka", "Aleutian", "Cascadia",
    "Cordillera", "Cordilleran", "Sierra", "Nevada", "Rocky", "Laramide",
    "Colorado", "Yellowstone", "Snake", "Columbia", "Basin", "Appalachian",
    "Appalachians", "Ouachita", "Newark", "Michigan", "Superior", "Erie",
    "Ontario", "Huron", "Chesapeake", "Mississippi", "Missouri", "Ohio",
    "Rio", "Grande", "Baja", "Yucatan", "Chicxulub", "Mesoamerica", "Andes",
    "Andean", "Altiplano", "Puna", "Atacama", "Patagonia", "Patagonian",
    "Nazca", "Cocos", "Juan", "Fuca", "Rivera", "Scotia", "Amazon", "Amazonia",
    "Amazonian", "Orinoco", "Parana", "Pantanal", "Cerrado", "Guiana", "Brazilian",
    "Brazil", "Peru", "Chile", "Chilean", "Peruvian", "Ecuador", "Colombia",
    "Venezuela", "Argentina", "Bolivia", "Africa", "African", "Sahara", "Saharan",
    "Sahel", "Sahelian", "Congo", "Zaire", "Niger", "Nile", "Zambezi", "Limpopo",
    "Okavango", "Kalahari", "Namib", "Benguela", "Agulhas", "Somali", "Afar",
    "Ethiopian", "Ethiopia", "Turkana", "Tanganyika", "Malawi", "Victoria",
    "Kilimanjaro", "Rukwa", "Albert", "Kivu", "Kaapvaal", "Zimbabwe", "Bushveld",
    "Karoo", "Etendeka", "Parana", "Deccan", "Rajmahal", "Siberian", "Siberia",
    "Emeishan", "Tarim", "Ontong", "Kerguelen", "Broken", "Ninetyeast", "Hawaiian",
    "Hawaii", "Emperor", "Galapagos", "Azores", "Canary", "Cape", "Verde",
    "Reunion", "Tristan", "Gough", "Bouvet", "Marion", "Crozet", "Macquarie",
    "Hikurangi", "Taupo", "Kermadec", "Tonga", "Lau", "Fiji", "Vanuatu",
    "Solomon", "Papua", "New", "Zealand", "Australia", "Australian", "Pilbara",
    "Yilgarn", "Gawler", "Murray", "Darling", "Eyre", "Great", "Barrier",
    "Europe", "European", "Asia", "Asian", "North", "South", "East", "West",
    "Central", "Western", "Eastern", "Northern", "Southern", "Equatorial",
    "Indo", "Eurasia", "Eurasian", "Gondwana", "Laurasia", "Pangaea", "Pangea",
    "Rodinia", "Columbia", "Nuna", "Kenorland", "Vaalbara", "Ur", "Tethys",
    "Tethyan", "Paleo", "Neo", "Panthalassa", "Iapetus", "Rheic", "Variscan",
    "Caledonian", "Grenville", "Trans", "Hudson", "Superior", "Slave", "Wyoming",
    "Fennoscandian", "Sarmatia", "Volgo", "Uralia", "Dharwar", "Bastar",
    "Singhbhum", "Bundelkhand", "Aravalli", "Madagascar", "Sri", "Lanka",
    "India", "China", "Chinese", "Indian", "Russian", "Russia", "Canada",
    "Canadian", "United", "States", "British", "Britain", "UK", "France",
    "French", "Germany", "German", "Italy", "Italian", "Spain", "Spanish",
    "Iberia", "Iberian", "Norway", "Sweden", "Finland", "Poland", "Greece",
    "Turkey", "Iran", "Iranian", "Iraqi", "Saudi", "Arabia", "Egypt", "Morocco",
    "Atlas", "Rif", "Betic", "Gibraltar", "Messinian", "Zanclean",
    "Hadean", "Archean", "Archaean", "Eoarchean", "Paleoarchean", "Mesoarchean",
    "Neoarchean", "Proterozoic", "Paleoproterozoic", "Mesoproterozoic",
    "Neoproterozoic", "Siderian", "Rhyacian", "Orosirian", "Statherian",
    "Calymmian", "Ectasian", "Stenian", "Tonian", "Cryogenian", "Ediacaran",
    "Sturtian", "Marinoan", "Gaskiers", "Lomagundi", "Jatuli", "Shunga",
    "Phanerozoic", "Paleozoic", "Cambrian", "Ordovician", "Hirnantian",
    "Silurian", "Devonian", "Frasnian", "Famennian", "Carboniferous",
    "Mississippian", "Pennsylvanian", "Permian", "Guadalupian", "Lopingian",
    "Changhsingian", "Induan", "Mesozoic", "Triassic", "Carnian", "Rhaetian",
    "Jurassic", "Toarcian", "Cretaceous", "Aptian", "Albian", "Cenomanian",
    "Turonian", "Santonian", "Campanian", "Maastrichtian", "Cenozoic",
    "Paleogene", "Paleocene", "Danian", "Thanetian", "Eocene", "Ypresian",
    "Lutetian", "Bartonian", "Priabonian", "Oligocene", "Rupelian", "Chattian",
    "Neogene", "Miocene", "Aquitanian", "Burdigalian", "Langhian", "Serravallian",
    "Tortonian", "Messinian", "Pliocene", "Zanclean", "Piacenzian", "Quaternary",
    "Pleistocene", "Gelasian", "Calabrian", "Chibanian", "Tarantian", "Holocene",
    "Greenlandian", "Northgrippian", "Meghalayan", "Anthropocene", "Precambrian",
    "Bølling", "Allerød", "Younger", "Dryas", "Heinrich", "Dansgaard", "Oeschger",
    "Bond", "Eemian", "Sangamonian", "Weichselian", "Wisconsinan", "Laurentide",
    "Cordilleran", "Fennoscandian", "Barents", "Kara",
    "El", "Niño", "Nino", "La", "Niña", "Nina", "Walker", "Hadley", "Ferrel",
    "Rossby", "Kelvin", "Helmholtz", "Rayleigh", "Taylor", "Bjerknes", "Madden",
    "Julian", "Coriolis", "Ekman", "Sverdrup", "Stommel", "Munk", "Kuroshio",
    "Oyashio", "Gulf", "Loop", "Florida", "California", "Humboldt", "Benguela",
    "Canary", "Leeuwin", "Mindanao", "Indonesian", "Throughflow", "Beaufort",
    "Weddell", "Ross", "Zapiola", "Mann", "Azores", "Irminger", "Labrador",
    "Mekong", "Ganges", "Brahmaputra", "Irrawaddy", "Salween", "Red", "Pearl",
    "Zhujiang", "Liao", "Hai", "Huai", "Amur", "Lena", "Yenisei", "Ob", "Kolyma",
    "Indigirka", "Mackenzie", "Yukon", "Fraser", "Rhine", "Danube", "Rhone",
    "Po", "Ebro", "Tagus", "Thames", "Seine", "Elbe", "Oder", "Vistula",
    "Volga", "Don", "Dnieper", "Tigris", "Euphrates", "Syr", "Amu", "Darya",
    "Darcy", "Richards", "Stokes", "Navier", "Coulomb", "Mohr", "Byerlee",
    "Weertman", "Glen", "Clausius", "Clapeyron", "Monin", "Obukhov", "Budyko",
    "Penman", "Monteith", "Shields", "Exner", "Rouse", "Froude", "Reynolds",
    "Peclet", "Péclet", "Damkohler", "Damköhler", "Prandtl", "Nusselt",
    "Sherwood", "Biot", "Terzaghi", "Angstrom", "Ångström", "Mie", "Raman",
    "Brillouin", "Mössbauer", "Mossbauer", "Arrhenius", "Michaelis", "Menten",
    "Monod", "Redfield", "Martin", "Hallett", "Mossop", "Wegener", "Bergeron",
    "Findeisen", "Twomey", "Albrecht", "Ertel", "Eliassen", "Palm", "Sawyer",
    "Charney", "Lorenz", "Boussinesq", "Alfvén", "Alfven", "Fokker", "Planck",
    "Vlasov", "Maxwell", "Ohm", "Savart", "Poynting", "Cassak", "Swisdak",
    "Dungey", "Van", "Allen", "Milankovitch", "Sadler", "Berner", "Kirchner",
    "Horton", "Strahler", "Manning", "Chezy", "Saint", "Venant", "Green", "Ampt",
    "Thiem", "Theis", "Dupuit", "Forchheimer", "Ghyben", "Herzberg", "Bagnold",
    "Rothermel", "Byram", "Farquhar", "Medlyn", "Ball", "Berry", "Sperry",
    "Tyree", "Köhler", "Kohler", "Urey", "Bigeleisen", "Mayer", "Dodson",
    "Birch", "Murnaghan", "Rankine", "Hugoniot", "Clapeyron", "Goldich",
    "Bowen", "Wilson", "Wadati", "Benioff", "Gutenberg", "Richter", "Omori",
    "Utsu", "Kostrov", "Eshelby", "Okada", "Savage", "Hutter", "Iverson",
    "Mogi", "McTigue", "Hashin", "Shtrikman", "Archie", "Kozeny", "Carman",
    "Gassmann", "leverett", "Brooks", "Corey", "Genuchten", "Freundlich",
    "Langmuir", "Temkin", "Dubinin", "BET", "DLVO", "Smoluchowski", "Ostwald",
    "Gibbs", "Thomson", "Kelvin", "Stefan", "Fourier", "Fick", "Nernst",
    "Einstein", "Debye", "Hückel", "Huckel", "Davies", "Pitzer", "Setchenow",
    "Henry", "Raoult", "Dalton", "Beer", "Lambert", "Schwarzschild", "Planck",
    "Stefan", "Boltzmann", "Wien", "Kirchhoff", "Eddington", "Chandrasekhar",
    "America", "American", "Americas", "San", "Andreas", "Santa", "St.", "Helens",
    "Mg", "Sr", "Nd", "Pb", "Hf", "Os", "Re", "Lu", "Sm", "Rb", "Ar", "He", "Ne",
    "Xe", "Kr", "Be", "Al", "Ca", "Fe", "Mn", "Ni", "Cu", "Zn", "Mo", "Cr", "Hg",
    "Se", "Sb", "Cd", "Tl", "Ba", "Li", "Cl", "Br", "Si", "Ti", "Zr", "Nb", "Ta",
    "Ce", "La", "Eu", "Gd", "Yb", "Th", "Ra", "Rn", "Bi", "Ag", "Au", "Pt", "Pd",
    "Ir", "Ru", "Rh", "Co", "Sc", "Ga", "Ge", "Sn", "Cs", "Na", "Te",
}


def normalize_mid_sentence_case(phrase: str) -> str:
    """
    Normalize a nominalized paper title phrase for mid-sentence insertion:
    1. Replace any internal colons ':' or semicolons ';' with smooth connectors so zero colons leak.
    2. Normalize Unicode hyphens and lowercase Title-Case common words and hyphenated parts
       (e.g., 'Upper-Ocean Eddy' -> 'upper-ocean eddy', 'Ice‐Cored' -> 'ice-cored'),
       while preserving proper geographic/geologic/eponymous nouns, chemical symbols, and acronyms.
    """
    if not phrase:
        return ""
    s = phrase.strip()
    # Normalize Unicode hyphens (\u2010, \u2011, \u2012) to ASCII hyphen '-'
    s = re.sub(r"[\u2010\u2011\u2012]", "-", s)
    # Replace colons/semicolons so zero colons ever appear inside synthesized questions
    s = re.sub(r"\s*:\s*(?:the\s+)?role\s+of\s+", " and the role of ", s, flags=re.I)
    s = re.sub(r"\s*:\s*(?:from\s+)", " from ", s, flags=re.I)
    s = re.sub(r"\s*:\s*(?:in\s+)", " in ", s, flags=re.I)
    s = re.sub(r"\s*[:;]\s*", " regarding ", s)

    def _norm_subtoken(tok: str) -> str:
        if not tok:
            return tok
        # Preserve tokens containing accented Latin characters (e.g., Tröllaskagi, Kīlauea, Mössbauer, Alfvén)
        if re.search(r"[À-ÖØ-öø-ÿĀ-ž]", tok):
            return tok
        # Strip punctuation around token to inspect core
        m = re.match(r"^([^A-Za-z0-9δΔεμλ]*)([A-Za-z0-9δΔεμλ'’\.\(\)\/\+\-]+?)([^A-Za-z0-9δΔεμλ]*)$", tok)
        if not m:
            return tok
        pre, core, post = m.group(1), m.group(2), m.group(3)
        # Keep tokens with digits, chemical formulas, Roman numerals, or >=2 uppercase letters
        if any(ch.isdigit() for ch in core):
            return tok
        upper_count = sum(1 for ch in core if ch.isupper())
        if upper_count >= 2:
            return tok
        # Single-letter chemical/wave symbols (e.g., P-wave, S-wave, C-cycle, N-addition, K-feldspar, X-ray, L-band)
        if len(core) == 1 and core in ("P", "S", "C", "N", "K", "O", "H", "F", "B", "U", "V", "W", "I", "X", "L", "Q", "E", "D"):
            return tok
        if core in PROPER_NOUN_KEEP_SET or core.rstrip("'s") in PROPER_NOUN_KEEP_SET:
            return tok
        # If it is a normal Title-Case word (First letter uppercase, rest lowercase, length >= 2), lowercase it
        if len(core) >= 2 and core[0].isupper() and core[1:].islower():
            return f"{pre}{core.lower()}{post}"
        return tok

    out_words = []
    for word in s.split():
        if "-" in word:
            parts = word.split("-")
            if len(parts[0]) == 1 and parts[0].isupper():
                norm_parts = [parts[0]] + [_norm_subtoken(p) for p in parts[1:]]
            else:
                norm_parts = [_norm_subtoken(p) for p in parts]
            out_words.append("-".join(norm_parts))
        else:
            out_words.append(_norm_subtoken(word))

    res = " ".join(out_words)
    res = re.sub(r"\s+", " ", res).strip()
    return res