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Here is the translation into authentic, academic English suitable for an LLM prompt or a professional research context:
Act as a "2026 MCM Problem A O-Prize Winner + Paper Reviewer + Numerical Results Auditor."
I have uploaded and authorized you to directly read the following files: (1) Official Problem PDF (2) Our Modeling/Derivation Document (3) Numerical Calculation & Verification: Prompts + Outputs (including all values, tables, statistics, robustness checks, uncertainty quantification results, etc.) (4) Paper Structure 2 (May contain errors; treat only as a negative example/reference)
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【Overarching Goal (Sole Output)】
Generate only the full body text for "Original Question Part 2 (Time-to-Empty predictions)," which must be [ready to paste directly into the final paper].
- You must insert numerical values from file (3) verbatim into the text and tables.
- Strictly prohibit the fabrication of any values (even "plausible-looking" ones are not allowed).
- File (4) must be absorbed critically: point out its flaws and replace it with a superior structure.
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【Hard Constraint: Output Structure Match】
The final output must contain exclusively the following 8 level-1 subsections (copy the numbering/titles exactly; you may add level-2/3 headers within sections):
2.1 Problem Restatement & Deliverables 2.2 TTE Definition, Termination Criteria & Calculation Method 2.3 Scenarios, Initial Conditions & Simulation Settings (Write only what is relevant to Q2) 2.4 Results Table A: TTE vs. Initial Battery State (SOC/z0) 2.5 Results Table B: Comparison of Different Usage Scenarios (inc. ΔTTE & Termination Reasons) 2.6 Attribution of "Rapid Drain" Drivers & Impact Ranking (Must Quantify) 2.7 Uncertainty Quantification & Consistency with "Observed Behavior" 2.8 Conclusion for Q2 (Answer the specific question with a single sentence + numerical evidence)
Note: Sections 2.4, 2.5, 2.6, and 2.7 must contain tables (Markdown format), and these tables must adhere to the field specifications below.
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【Hard Constraint: Required Tables & Fields】
【Table A】 (Place in 2.4): TTE vs. Initial Charge (Must cover all z0/SOC values appearing in the output file)
- Required Columns: z0/SOC, TTE (with units), Termination Reason (e.g., Δ→0 / Voltage Threshold / Temp Threshold / Energy Depletion), avg_P or equivalent power metric (if provided), max_I or equivalent peak current metric (if provided), Remarks (e.g., primary drain factor/parameter combination).
- If a column is missing in (3): Fill the cell with "Not provided in output" and explain the missing data in one sentence after the table (do not guess).
【Table B】 (Place in 2.5): Scenario Comparison (Must cover all scenarios appearing in the output file)
- Required Columns: Scenario Name, Key Parameters/Activity Description, TTE (units), ΔTTE relative to Baseline (units), Termination Reason, Brief Mechanism Explanation (1 sentence, must reference a model variable or numerical indicator).
- You must explicitly define which scenario is the "Baseline" and justify the selection (one sentence).
【Table C】 (Place in 2.6): Impact Ranking (Driver Ranking)
- Required Columns: Factor (Screen/CPU/Network/Signal/Temp/Background, etc., as per your files), Quantified Evidence (e.g., causes TTE drop of XX%, ΔTTE=XX, or Power increase of XX), Causal Chain (expressed via model variables: P_tot → I → Δ / Heat → ...), Conclusion (High/Medium/Low Impact).
- Ranking Source: Must come from sensitivity/comparative experiments/ablation results in (3). If (3) has no ranking data: You must explicitly write "Output provided no ranking experiments, thus this section is limited to qualitative attribution," and restrict qualitative attribution strictly to the logic in (2) (do not expand without basis).
【UQ Table/Paragraph】 (Place in 2.7): Uncertainty Quantification Results (Numbers Required)
- Provide at least one type: Mean ± SD / 95% CI / Quantiles (Q5, Q50, Q95) / Key points on the Survival Curve.
- You must explain the source of uncertainty: Input fluctuation / Parameter distribution / Measurement error / Scenario randomness (strictly based on the actual settings in (3)).
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【Hard Constraint: Numerical "Traceability" Rule (Anti-Hallucination)】
- Any numerical value appearing in the text (including TTE, ΔTTE, Power, Current, Temperature, CI, Quantiles, etc.) must be immediately followed by a [Source Marker]:
- Format:
[Source: Output File (3); Keyword/Table Name/Section Name: XXX] - The keyword/table/section name must be a real, searchable description existing in file (3).
- If you cannot find a corresponding value in (3): Do not output that value. Rewrite as "Not provided in output" and list the keywords you attempted to locate (e.g., "Attempted search: TTE table / scenario / CI / Monte Carlo, not found").
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【Hard Constraint: Mechanism Explanation must be "Model-Based"】
In Sections 2.5 and 2.6, mechanism explanations must explicitly use key model variables from your modeling file (e.g., P_tot, V_term, I, Δ, R_int, T, etc.) at least once to form a causal chain.
- Example: Activity A → P_tot↑ → I↑ → Δ approaches 0 faster (or Heat causes R_int↑) → Earlier termination → TTE↓.
- Do not repeat the entire model derivation; only cite variables relevant to the Q2 explanation.
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【Hard Constraint: Critical Handling of Structure 2 (Mandatory)】
Add a short paragraph (3–6 sentences) at the end of either 2.1 or 2.3:
- Point out at least 2 specific problems in "Paper Structure 2" (e.g., missing UQ, placing conclusions before methods, lack of comparison tables, explanation lacking numerical support).
- Explicitly state the improvements you adopted in this current structure (mapping to your sections 2.1–2.8).
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【Writing Style & Scoring Points (Mandatory Coverage)】
- Every core conclusion must be "digitized": bind it to at least one number or interval from (3).
- You must answer the prompt's specific questions: "Which activities/conditions have the largest impact on battery drain? Which have surprisingly little impact?"
- Prohibited: Substituting evidence with vague statements. Do not use words like "usually/generally/probably/obviously" as arguments.
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【Final Self-Check (Must appear at the end of output)】
Append a "Self-Check List" (in checkbox format) at the very end:
- Table A includes all z0/SOC values.
- Table B includes all scenarios and identifies the Baseline.
- At least one type of UQ number (CI/Quantile/Mean-Variance) included.
- Every key number has a
[Source: ...]marker. - "Largest impact vs. Little impact" question answered.
- At least 2 issues in Structure 2 pointed out and fixed.
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【Output Limits】
- Output only Sections 2.1–2.8 and the Self-Check List.
- Do not output your thinking process.
- Do not output chapters unrelated to this specific sub-question.
- Do not cite external materials; use only information and model logic from the uploaded files.