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A题/数值分析检验/Prompt/1.md

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+TASK: Produce MODEL_SPEC v1.0 (canonical, frozen). Output JSON only.
+
+INPUT DATA (read from the uploaded markdown files):
+- State vector and inputs:
+  x(t) = [z(t), v_p(t), T_b(t), S(t), w(t)]
+  u(t) = [L(t), C(t), N(t), Ψ(t), T_a(t)]
+- Equations to include exactly:
+  (A) Power mapping P_tot(t) = P_bg + P_scr(L) + P_cpu(C) + P_net(N,Ψ,w)
+  (B) Terminal voltage V_term = V_oc(z) - v_p - I*R0(T_b,S)
+  (C) SOC ODE: dz/dt = - I / (3600 * Q_eff(T_b,S))
+  (D) Polarization ODE: dv_p/dt = I/C1 - v_p/(R1*C1)
+  (E) Thermal ODE: dT_b/dt = ( I^2*R0 + I*v_p - hA*(T_b - T_a) ) / C_th
+  (F) Tail ODE: dw/dt = (σ(N)-w)/τ(N) with τ_up, τ_down switching rule
+  (G) CPL closure:
+      R0*I^2 - (V_oc(z)-v_p)*I + P_tot = 0
+      I = (V_oc(z)-v_p - sqrt(Δ)) / (2*R0)
+      Δ = (V_oc(z)-v_p)^2 - 4*R0*P_tot
+  (H) V_oc(z) (modified Shepherd): V_oc(z)=E0 - K(1/z - 1) + A*exp(-B(1-z))
+  (I) R0(T_b,S) Arrhenius + SOH factor
+  (J) Q_eff(T_b,S) temperature + aging factor with max-floor
+
+METHODLOGY (must define explicitly in JSON):
+1) Domain constraints and guards:
+   - z ∈ [0,1], S ∈ (0,1], w ∈ [0,1]
+   - define z_eff = max(z, z_min) for V_oc to avoid 1/z singularity
+   - define Q_eff_floor to avoid negative capacity
+2) Event functions and termination logic:
+   Define three event functions:
+   gV(t)=V_term(t)-V_cut
+   gz(t)=z(t)   (threshold 0)
+   gΔ(t)=Δ(t)   (threshold 0)
+   Terminate at first crossing where any event function becomes ≤ 0.
+   Record termination_reason ∈ {"V_CUTOFF","SOC_ZERO","DELTA_ZERO"}.
+3) Define TTE precisely:
+   TTE = t* - t0 where t* is the earliest event time.
+   Use linear interpolation between the last two time samples for the event that triggers termination.
+
+DELIVERABLE (JSON ONLY):
+Return a JSON object with keys:
+- "states" (list of {name, unit, bounds})
+- "inputs" (list of {name, unit, bounds})
+- "parameters" (list of {name, unit, description})
+- "equations" (each equation as a string; use the exact variable names)
+- "guards" (z_min, Q_eff_floor, clamp rules)
+- "events" (definition of gV, gz, gΔ; termination logic)
+- "tte_definition" (interpolation formula and tie-breaking rule if multiple cross in same step)
+- "numerics" (method="RK4_nested_CPL", dt_symbol="dt", stage_recompute_current=true)
+
+VALIDATION (must be encoded as JSON fields too):
+- "dimension_check": list required units consistency checks
+- "monotonicity_check": SOC must be non-increasing while I>=0
+- "feasibility_check": Δ must be >=0 before sqrt; if Δ<0 at any evaluation, event triggers
+
+OUTPUT FORMAT:
+JSON only, no markdown, no prose.