# Math-CVD Candidate Report: [Concise Title of Mathematical Flaw]

**Candidate Tracking ID**: `[Submitter Reference, e.g. MATH-CAND-2026-0001 or SUBMISSION-42]`  
**Target Manuscript**: "[Full Paper Title]"  
**Authors**: [Author Names / Anonymous]  
**Year**: [YYYY] | **Paper Version**: `v1` (Affected: `['v1']`, Fixed In: `Unpatched` / `v2`)  
**arXiv ID**: `arXiv:[ID]v[N]` | **DOI**: `10.[XXXX]/[YYYY]`  
**Paper SHA-256**: `[64-character lowercase hex hash of evaluated file]`  
**Primary MSC2020**: `[XXYZZ]`  
**Weakness Archetype**: [Descriptive Archetype Name]  
**Governing Theorem**: [Foundational violated theorem, e.g. 1D Leibniz Integral Rule]  
**Epistemic Verdict**: `IMPOSSIBLE` | `CODE_FLAGGED` | `UNDECIDABLE` | `UNKNOWABLE`  
**Mathematical Coordinate**: `Section X.Y`, `Theorem/Lemma/Proposition N`, `Equation (M)`  

---

### 1. Affected Claim (Verbatim)
> "[Exact verbatim quotation of the erroneous claim or formula from the target manuscript]"

---

### 2. Technical Flaw Analysis
[Provide a step-by-step rigorous derivation showing where the deductive logic breaks down. Detail parameter aliasing, domain boundary omissions, or invalid operator commutations.]

---

### 3. Discrepancy Formula & Residual (\(\delta\))
- **Author's Step**:
  \[
  \text{[Author's Flawed Equation]}
  \]
- **True Mathematical Form**:
  \[
  \text{[Rigorous Equation under Governing Theorem]}
  \]
- **Dropped Residual (\(\delta\))**:
  \[
  \delta = \text{[True Form]} - \text{[Author's Form]} = \text{[Non-Zero Discrepancy]} \neq 0
  \]

---

### 4. Executable Reproducer & Counterexample (SymPy / Python)
```python
import sympy as sp

# Hermetic test script verifying non-zero residual delta
def verify_discrepancy():
    x = sp.Symbol('x')
    true_val = x**2 - 1
    claimed_val = x + 1
    residual = sp.simplify(true_val - claimed_val)
    assert residual != 0, "Residual must be non-zero"
    return True

if __name__ == "__main__":
    verify_discrepancy()
    print("Verification passed: Discrepancy confirmed.")
```

---

### 5. Remediation Patch
[Provide the mathematically sound formula restoring deductive validity.]

---

### 6. Machine-Readable Candidate Signature (YAML)
```yaml
candidate_id: 'CAND-[SLUG]'
title: '[Concise Vulnerability Title]'
category: '[ANALYSIS_CALCULUS | ALGEBRA_NUMBER_THEORY | STOCHASTIC_CONTROL | PDE_OPTIMIZATION | COMPUTER_ARITHMETIC]'
severity: '[CRITICAL | MAJOR | MODERATE]'
msc2020:
  - '[XXYZZ]'
matching_rules:
  ast_triggers:
    - pattern: '[LaTeX regex matching the flawed step]'
  negative_guards:
    - '[Regex matching sound repaired formulations]'
  llm_probe_prompt: |
    [Skeptical prompt checking if the flaw is present or repaired]
```