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A题/数值分析检验/Prompt/2.md

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+TASK: Write a deterministic, language-agnostic specification for TTE computation.
+
+INPUT DATA:
+- MODEL_SPEC.events and MODEL_SPEC.tte_definition from Prompt 1
+- A simulated time grid t_k = t0 + k*dt, k=0..K
+- Arrays sampled at each grid point:
+  V_term[k], z[k], Δ[k]
+
+METHODOLOGY:
+1) Define event signals:
+   gV[k] = V_term[k] - V_cut
+   gz[k] = z[k] - 0
+   gΔ[k] = Δ[k] - 0
+2) Crossing rule:
+   A crossing occurs for event e when g_e[k-1] > 0 and g_e[k] ≤ 0.
+3) Interpolated crossing time for event e:
+   t_e* = t[k-1] + (0 - g_e[k-1])*(t[k]-t[k-1])/(g_e[k]-g_e[k-1])
+   (If denominator = 0, set t_e* = t[k].)
+4) Multi-event tie-breaking:
+   If multiple events cross in the same step, compute each t_e* and choose the smallest.
+   If equal within 1e-9, prioritize in this order:
+      DELTA_ZERO > V_CUTOFF > SOC_ZERO
+5) Output:
+   - TTE_seconds = t* - t0
+   - termination_reason
+   - termination_step_index k
+   - termination_values at t* using linear interpolation for (V_term, z, Δ)
+
+DELIVERABLES:
+A) “TTE_SPEC” section: the above as precise pseudocode with no ambiguity.
+B) A minimal test suite (exact numeric arrays) containing 3 tests:
+   Test 1: voltage cutoff triggers
+   Test 2: SOC hits zero first
+   Test 3: Δ hits zero first (power infeasible)
+For each test, provide expected outputs exactly (TTE_seconds, reason, t*).
+
+VALIDATION:
+- Must detect the correct earliest event (by construction of tests).
+- Must reproduce expected t* to within absolute error ≤ 1e-9 in the tests.
+- Must never take sqrt of negative Δ during event evaluation (use sampled Δ).
+
+OUTPUT FORMAT (strict):
+1) Header line: "TTE_SPEC_v1"
+2) Pseudocode block
+3) "TESTS_v1" as JSON with {tests:[...]} including expected outputs
+No additional text.