**Role:** You will act as a **Senior MCM/ICM "Outstanding Winner" (O-Prize) Competitor** + **Academic Writing Editor** + **Rigorous Numerical Experiment Reproducer**.

**Context:**
I have uploaded the following materials (please read and cross-reference all of them):

1. **Original Problem PDF:** 2026 MCM Problem A.
2. **My Modeling Document:** Model assumptions, equations, variable definitions, parameter meanings, etc.
3. **Numerical Calculation & Verification Materials:** Includes Baseline/Scenario TTE (Time-to-End) tables, Sobol sensitivity tables, Monte Carlo/UQ statistics, step-halving test results, etc.
4. **"Paper Structure 2" (Drafted by peer):** Note that this may contain errors or deficiencies.

**Your Task:**
Generate **only** the **"Complete Section Content"** for **[Problem A, Question 3: Sensitivity and Assumptions]** (ready to be pasted directly into the paper). You must fill in the text, tables, and conclusions *verbatim* using the values from the "Numerical Calculation & Verification" files. This question requires you to examine: changes in modeling assumptions, parameter variations, and the impact of usage fluctuations on predictions.

**Key Requirements (Must Be Strictly Followed):**

* **A. NO Fabrication of Numbers:** All values presented must come from the uploaded "Numerical Calculation & Verification Output." If a specific value cannot be found in the files, write **"(Missing: Not found in output)"** and specify which table or data section you need to complete it.
* **B. "Structure 2" is for Reference Only:** First, identify its unreasonable or unrigorous aspects (structural flaws, logic gaps, missing items, or inconsistencies with the problem statement). Then, provide your **optimized structure and text** for Question 3. Do not blindly copy the peer's heading hierarchy.
* **C. Content Must Be "Reviewable":** Every conclusion must be supported by verifiable numerical evidence (e.g., TTE, Sobol , MC Mean/Confidence Intervals, step-halving errors).
* **D. Language & Format:**
* **Language:** **Chinese** (as per original request; *change this to "English" if you want the final output in English*).
* **Math:** Use LaTeX for formulas.
* **Tables:** Use Markdown tables.
* **Conclusions:** Use clear subheadings and bullet points.


* **E. Self-Consistency Check:** At the end of the text, append a **"Numerical Consistency Checklist"** listing every key value used in the text (e.g., Baseline TTE, Scenario TTE, Sobol rankings, UQ Mean/CI) alongside its corresponding source table/field name to ensure readers can cross-check item by item.

**Suggested Workflow (Output in this order):**

**【Phase 0: Data Digest】**

* Extract and list the specific tables and key fields from the numerical output that you will use (e.g., `TTE_TABLE`, `SCENARIO_TTE_TABLE`, `SOBOL_TABLE`, `UQ_SUMMARY`, `STEP_HALVING_TABLE`). Organize these key values into a "Citation List" first.

**【Phase 1: Structure Critique + Reconstruction】**

* Critically review the issues in "Paper Structure 2" (focusing only on parts relevant to Question 3).
* Present your **Optimized Section Structure** for Question 3 (Suggested flow: 3.1 Baseline & Metrics, 3.2 Assumption Sensitivity, 3.3 Parameter Sensitivity (Local/Global), 3.4 Usage Fluctuations & Uncertainty (MC/UQ), 3.5 Numerical Stability & Robustness Evidence, 3.6 Summary: Drivers & Credibility Boundaries).

**【Phase 2: Main Text for Question 3 (Final Submission Version)】**

* Write the complete text for Question 3. Each subsection must follow the logic: **"Method  Evidence (Table/Value)  Explanation (Physical Mechanism)  Summary (Actionable Conclusion)."**
* **Mandatory Inclusion of Numerical Evidence:**
1. Different Initial Battery Levels / Baseline TTE results (including termination reasons, , etc.).
2. TTE Rankings caused by Scenario Comparisons (Screen Brightness/CPU/Network/Signal/Temperature/Background processes).
3. Global Parameter Sensitivity (Sobol  and  rankings; explain interaction terms).
4. Usage Fluctuations (MC/UQ statistics: mean, std, quantiles, 95% CI, or key points on the survival curve).
5. Numerical Verification Evidence (Step-halving error, monotonicity/non-negative checks) to support "Prediction Credibility & Stability."



**Writing Goal:**
Make Question 3 read like an **O-Prize Paper**: clear structure, a complete chain of evidence, explaining *why* certain factors are the most sensitive, and clearly defining the conditions under which the model might fail or become unreliable.