refactor(module-2): honest scientific reframing - Theorem→Proposition, validated claims only

CRITICAL HONESTY IMPROVEMENTS (academic integrity prioritized):

1. THEOREM 1 → PROPOSITION 1 (Section 2.4):
   - Downgraded "Theorem" to "Proposition" (weighted average is not a formal proof)
   - Removed misleading "proof" claiming FRI preserves worst-case guarantees
   - Honest framing: "FRI = sample-size weighted aggregation (heuristic, not formal guarantee)"
   - Added: "True worst-case threshold is min{E_k}, not FRI"
   - Remark 1: Comparison to conservative aggregation (FRI > min by construction)
   - Remark 2: Partial privacy (not "0% disclosure")
   - Remark 3: Novel contribution clarification (aggregating sensitivity metrics)

2. DECISION THRESHOLDS → EXPLORATORY FRAMEWORK (Section 2.5):
   - Removed misleading "optimal threshold" derivation with arbitrary parameters
   - Changed: "Practical Thresholds" → "Proposed FRI Thresholds (requiring validation)"
   - Added table with "Validation Status: ❌ Unvalidated" for all thresholds
   - Critical limitations: "No empirical validation", "Context-dependent", "Not rigid cutoffs"
   - Alternative conservative approach: Report both FRI and min{E_k}
   - Future validation priorities: RCT comparison, clinician surveys, FDA retrospective

3. AGGREGATION STRATEGY COMPARISON (Section 3.1):
   - Added Table 2 comparing Sample-size/Equal/Conservative/Optimistic strategies
   - Calculated actual weights: Site 1 (n=533, w=0.47), Site 2 (n=194, w=0.17), Site 3 (n=403, w=0.36)
   - Corrected FRI values with proper weighting (2.015 at 1k, not 1.961)
   - Showed 14.1% gap between FRI and min{E_k} at 1k scale
   - Demonstrated convergence: all strategies → same result at 100k/2.8m

4. STATISTICAL VALIDATION → HONEST ASSESSMENT (Section 3.2):
   - Removed misleading bootstrap test (K=3 sites insufficient for resampling)
   - Removed "ground truth E-value" claim (paradox: Synthea has no unmeasured confounding)
   - Changed to: "Observational convergence pattern" + "Limitations of synthetic data"
   - Honest: "Real validation requires RCT comparison (e.g., observational vs WHI RCT)"

5. PRIVACY CLAIMS DOWNGRADED (Section 3.6):
   - Changed: "0% covariate disclosure" → "Partial privacy, reduced disclosure"
   - Added: "Information leakage caveat" (E-values reveal effect size magnitudes)
   - Example: High E_k suggests strong confounders or large effects → partial inference possible
   - Formal DP: "Future work" (Laplace noise Δ/ε requires utility-privacy calibration)

6. THRESHOLD APPLICATION → UNVALIDATED ILLUSTRATION (Section 3.5):
   - Added "Unvalidated" labels to all threshold comparisons
   - Changed interpretation: "Under proposed (unvalidated) moderate threshold..."
   - Added 4 caveats: (1) No validation, (2) Context matters, (3) Conservative alternative, (4) Not RCT substitute

7. ABSTRACT REWRITTEN:
   - Removed: "Prove validity", "complete confounder privacy", "theoretically valid"
   - Changed to: "Propose and characterize", "partial privacy", "principled aggregation"
   - Added: "Thresholds require RCT validation", "Future work: real multi-site studies"

8. CONCLUSIONS COMPLETELY REWRITTEN (Section 6):
   - Removed: "Formal proof", "unique privacy advantage", "0% disclosure", "transforms methodology"
   - Honest assessment: "Proposes FRI", "characterizes properties", "demonstrates convergence"
   - Critical limitations upfront: (1) Synthetic data paradox, (2) 3-site only, (3) Threshold lack validation, (4) Binary outcomes
   - Final statement: "Contribution = extending E-values to federated settings, NOT fundamental breakthroughs"

9. REFERENCES ADDED:
   - Dwork et al. (2006) - Differential privacy foundations
   - Baicker et al., Chetty et al. - Real-world heterogeneity citations

Changes prioritize academic honesty over claims:
- No overstated "proofs" where heuristics exist
- No "0% privacy" where information leakage occurs
- No "validated thresholds" where validation is absent
- Honest about synthetic data limitations (cannot validate "unmeasured" confounding)
- Honest about contribution scope (characterization, not breakthroughs)

Author: watilde