diff --git a/.changelog/add-subtraction-flooring-pattern.yaml b/.changelog/add-subtraction-flooring-pattern.yaml
new file mode 100644
index 0000000..dda4f7a
--- /dev/null
+++ b/.changelog/add-subtraction-flooring-pattern.yaml
@@ -0,0 +1,6 @@
+- bump: patch
+  changes:
+    added:
+      - Add Pattern 5 to policyengine-vectorization-skill documenting correct use of max_() when subtracting values and flooring at zero
+      - Add floor subtraction pattern to Quick Reference Card
+      - Document the "phantom income" bug pattern found in MT income tax implementation
diff --git a/.changelog/state-income-tax-conformity.yaml b/.changelog/state-income-tax-conformity.yaml
new file mode 100644
index 0000000..8af9d30
--- /dev/null
+++ b/.changelog/state-income-tax-conformity.yaml
@@ -0,0 +1,4 @@
+- bump: patch
+  changes:
+    added:
+      - Add guidance on state income tax conformity to federal rules in policyengine-implementation-patterns-skill
diff --git a/agents/country-models/document-collector.md b/agents/country-models/document-collector.md
index 048b020..7e37d75 100644
--- a/agents/country-models/document-collector.md
+++ b/agents/country-models/document-collector.md
@@ -252,6 +252,31 @@ reference = "https://www.law.cornell.edu/..."  # Full clickable URL
 - "[Program] categorical eligibility"
 - "[Program] benefit formula"
 
+**CRITICAL: Pay Special Attention to Income Definitions**
+
+When collecting documentation for tax credits or income-based programs, carefully note the **exact income definition** used in the statute. Many programs use modified versions of standard measures:
+
+- Look for phrases like "AGI **plus**..." or "AGI **minus**..."
+- Common patterns:
+  - "adjusted gross income plus exemptions"
+  - "modified adjusted gross income"
+  - "income as defined in section [X]"
+  - "gross income less certain deductions"
+
+**Example:** Arizona Family Tax Credit (ARS 43-1073) specifies:
+> "Arizona adjusted gross income, plus the amount subtracted for exemptions under section 43-1023"
+
+This means the eligibility threshold uses `az_agi + az_exemptions`, NOT just `az_agi`.
+
+**Documentation template for modified income:**
+```markdown
+### Income Definition
+**Statute Citation**: [Exact citation]
+**Income Measure**: [Standard measure] PLUS/MINUS [adjustments]
+**Exact Statutory Language**: "[Quote the statute]"
+**Implementation**: variable_name + adjustment_variable_name
+```
+
 ### 3. Verify Currency
 - Check "effective date" on all documents
 - Search for "final rule" to find recent changes
diff --git a/agents/country-models/edge-case-generator.md b/agents/country-models/edge-case-generator.md
index 671795d..86878a2 100644
--- a/agents/country-models/edge-case-generator.md
+++ b/agents/country-models/edge-case-generator.md
@@ -176,6 +176,7 @@ For each detected pattern:
 ### Income-Based Programs
 - Zero income
 - Negative income (self-employment losses)
+- **CRITICAL**: Negative income combined with zero expenses/deductions (catches incorrect eligibility/benefit bugs)
 - Income exactly at each threshold
 - Maximum possible income
 
@@ -197,10 +198,17 @@ For each detected pattern:
 
 ### Benefit Calculations
 - Minimum benefit scenarios
-- Maximum benefit scenarios  
+- Maximum benefit scenarios
 - Zero benefit (just above cutoff)
 - Rounding edge cases
 
+### Tax Credit Programs
+- Negative income with zero deductible expenses (property tax, rent, etc.)
+- Negative income with positive deductible expenses
+- Zero income scenarios
+- Income exactly at phase-out thresholds
+- Maximum credit scenarios with minimum qualifying expenses
+
 ## Output Format
 
 Generate test files with clear documentation:
diff --git a/agents/country-models/implementation-validator.md b/agents/country-models/implementation-validator.md
index 4df521b..619851d 100644
--- a/agents/country-models/implementation-validator.md
+++ b/agents/country-models/implementation-validator.md
@@ -304,6 +304,30 @@ Implementation passes when:
 - Proper federal/state separation
 - Include effective dates
 
+**CRITICAL: Watch for Modified Income Definitions**
+
+Many state tax credits and benefits use **modified versions** of standard income measures. The statute will specify:
+- "AGI **plus** [certain additions]" (e.g., "AGI plus exemptions")
+- "AGI **minus** [certain subtractions]" (e.g., "AGI less student loan interest")
+- "Income as defined in [other statute section]"
+
+**Example from Arizona Family Tax Credit (ARS 43-1073):**
+```python
+# ❌ WRONG - Uses only AGI
+income = tax_unit("az_agi", period)
+eligible = income <= threshold
+
+# ✅ CORRECT - Uses AGI plus exemptions per statute
+income = tax_unit("az_agi", period) + tax_unit("az_exemptions", period)
+eligible = income <= threshold
+```
+
+**Validation checklist:**
+- [ ] Read the statute's exact income definition language
+- [ ] Check if it references AGI "plus" or "minus" any adjustments
+- [ ] Verify the variable uses the correct modified income measure
+- [ ] Document the specific statute citation that defines the income measure
+
 ### Benefit Calculations
 - All rates from parameters
 - Min/max thresholds parameterized
diff --git a/changelog_entry.yaml b/changelog_entry.yaml
index ebe6f77..bb8dd0c 100644
--- a/changelog_entry.yaml
+++ b/changelog_entry.yaml
@@ -1,4 +1,6 @@
 - bump: patch
   changes:
+    added:
+      - Document bracket parameter pattern for handling negative values (-.inf vs 0 thresholds) in parameter patterns skill
     changed:
       - Add critical warning against mixing adds/subtracts with custom formulas in implementation patterns skill
diff --git a/skills/technical-patterns/policyengine-implementation-patterns-skill/SKILL.md b/skills/technical-patterns/policyengine-implementation-patterns-skill/SKILL.md
index c9855a8..ee05dd9 100644
--- a/skills/technical-patterns/policyengine-implementation-patterns-skill/SKILL.md
+++ b/skills/technical-patterns/policyengine-implementation-patterns-skill/SKILL.md
@@ -352,6 +352,83 @@ first_person: 14_580
 fpg_multiplier: 2.0  # 200% of FPG
 ```
 
+### State Income Tax Conformity to Federal Rules
+
+**CRITICAL: State income taxes should reference federal income sources and limits, not redefine them**
+
+Most state income taxes start with federal definitions and then make specific adjustments. When implementing state income tax:
+
+**✅ CORRECT - Reference federal income sources:**
+```python
+class ms_agi(Variable):
+    """Mississippi adjusted gross income"""
+    value_type = float
+    entity = TaxUnit
+    definition_period = YEAR
+    label = "Mississippi adjusted gross income"
+    unit = USD
+
+    def formula(tax_unit, period, parameters):
+        # Start with federal AGI, which already includes
+        # federal capital loss limits and other federal rules
+        federal_agi = tax_unit("adjusted_gross_income", period)
+
+        # Apply Mississippi-specific additions/subtractions
+        ms_additions = tax_unit("ms_additions_to_agi", period)
+        ms_subtractions = tax_unit("ms_subtractions_from_agi", period)
+
+        return federal_agi + ms_additions - ms_subtractions
+```
+
+**❌ WRONG - Redefining income sources:**
+```python
+# DON'T create state-specific parameters like:
+# parameters/gov/states/ms/tax/income/income_sources.yaml
+# containing:
+#   - capital_gains
+#   - long_term_capital_gains
+#   - short_term_capital_gains
+
+# This bypasses federal limits like the $3,000 capital loss deduction limit
+```
+
+**Why this matters:**
+- Federal income tax applies capital loss limits before reporting AGI
+- State income taxes that start from federal AGI automatically inherit these limits
+- Creating separate state income source parameters bypasses federal rules
+- Results in incorrect calculations (e.g., unlimited capital loss deductions)
+
+**Common state conformity patterns:**
+1. **Full conformity** - State AGI = Federal AGI (rare)
+2. **Rolling conformity** - State follows current federal rules
+3. **Static conformity** - State follows federal rules as of a specific date
+4. **Selective conformity** - State follows federal but with specific modifications
+
+**Implementation approach:**
+- Always start with federal income sources/AGI/taxable income as the base
+- Use state parameters only for state-specific additions, subtractions, or modifications
+- Reference federal variables: `adjusted_gross_income`, `taxable_income`, etc.
+- Don't recreate federal income aggregation logic at the state level
+
+**Example - Mississippi specifics:**
+```python
+class ms_additions_to_agi(Variable):
+    """Mississippi additions to federal AGI"""
+    # Add state-specific income items not in federal AGI
+    adds = [
+        "ms_state_bond_interest",
+        "ms_other_additions"
+    ]
+
+class ms_subtractions_from_agi(Variable):
+    """Mississippi subtractions from federal AGI"""
+    # Subtract state-specific deductions
+    adds = [
+        "ms_retirement_income_exclusion",
+        "ms_other_subtractions"
+    ]
+```
+
 ---
 
 ## Code Reuse Patterns
diff --git a/skills/technical-patterns/policyengine-parameter-patterns-skill/SKILL.md b/skills/technical-patterns/policyengine-parameter-patterns-skill/SKILL.md
index 709eb7d..128a06f 100644
--- a/skills/technical-patterns/policyengine-parameter-patterns-skill/SKILL.md
+++ b/skills/technical-patterns/policyengine-parameter-patterns-skill/SKILL.md
@@ -314,6 +314,52 @@ metadata:
   label: State PROGRAM earned income disregard percentage
 ```
 
+### Bracket-Based Parameters
+
+**CRITICAL: Handling Negative Values**
+
+When creating bracket-based parameters (e.g., tax credits based on AGI), the first bracket threshold MUST be `-.inf` if negative values are possible, NOT `0`.
+
+**❌ WRONG - Excludes negative AGI:**
+```yaml
+# threshold.yaml (for single filers)
+brackets:
+  - threshold:
+      2023-01-01: 0      # ❌ Bug: negative AGI excluded!
+    amount:
+      2023-01-01: 300
+  - threshold:
+      2023-01-01: 30_000
+    amount:
+      2023-01-01: 110
+```
+
+**✅ CORRECT - Includes all possible values:**
+```yaml
+# threshold.yaml (for single filers)
+brackets:
+  - threshold:
+      2023-01-01: -.inf  # ✅ Covers negative AGI
+    amount:
+      2023-01-01: 300
+  - threshold:
+      2023-01-01: 30_000
+    amount:
+      2023-01-01: 110
+```
+
+**When to use `-.inf`:**
+- Income-based calculations (AGI can be negative)
+- Any parameter where negative input values are valid
+- Tax credits, deductions, or benefits based on earnings
+
+**When `0` is appropriate:**
+- Age thresholds (always non-negative)
+- Count-based parameters (household size, number of dependents)
+- Resource limits (assets can't be negative)
+
+**Real-world example:** Hawaii Food/Excise Tax Credit uses AGI brackets. The first threshold must be `-.inf` to correctly handle taxpayers with negative AGI (e.g., business losses).
+
 ---
 
 ## 7. Validation Checklist
diff --git a/skills/technical-patterns/policyengine-vectorization-skill/SKILL.md b/skills/technical-patterns/policyengine-vectorization-skill/SKILL.md
index ee9243f..74df12e 100644
--- a/skills/technical-patterns/policyengine-vectorization-skill/SKILL.md
+++ b/skills/technical-patterns/policyengine-vectorization-skill/SKILL.md
@@ -92,6 +92,46 @@ elif amount > maximum:
 # Or: amount = max_(0, min_(amount, maximum))
 ```
 
+### Pattern 5: Flooring Subtraction Results (CRITICAL)
+
+When subtracting values and wanting to floor at zero, you must wrap the **entire subtraction** in `max_()`:
+
+```python
+# Common scenario: income after deductions/losses
+❌ WRONG - Creates phantom negative values:
+income = max_(income, 0) - capital_loss  # If capital_loss > income, result is negative!
+
+✅ CORRECT - Properly floors at zero:
+income = max_(income - capital_loss, 0)  # Entire subtraction floored
+
+# Real example from MT income tax bug:
+❌ WRONG - Tax on phantom negative income:
+def formula(tax_unit, period, parameters):
+    income = tax_unit("adjusted_gross_income", period)
+    capital_gains = tax_unit("capital_gains", period)
+
+    # BUG: If capital_gains is negative (loss), this creates negative income
+    # But max_() only floors income, not the result
+    regular_income = max_(income, 0) - capital_gains
+    return calculate_tax(regular_income)  # Tax on negative number!
+
+✅ CORRECT - No phantom income:
+def formula(tax_unit, period, parameters):
+    income = tax_unit("adjusted_gross_income", period)
+    capital_gains = tax_unit("capital_gains", period)
+
+    # Properly floors the entire result
+    regular_income = max_(income - capital_gains, 0)
+    return calculate_tax(regular_income)  # Never negative
+```
+
+**Why this matters:**
+- If `capital_gains = -3000` (loss), then `income - capital_gains = income + 3000`
+- The wrong pattern `max_(income, 0) - capital_gains` allows the subtraction to make the result negative
+- This creates "phantom income" where none exists, leading to incorrect tax calculations
+
+**Rule:** When the formula is `A - B` and you want the result floored at zero, use `max_(A - B, 0)`, NOT `max_(A, 0) - B`.
+
 ---
 
 ## 3. When if-else IS Acceptable
@@ -287,10 +327,92 @@ def test_vectorization():
 | Boolean OR | `or` | `\|` |
 | Boolean NOT | `not` | `~` |
 | Bounds checking | `if x < 0: x = 0` | `max_(0, x)` |
+| Floor subtraction | `max_(x, 0) - y` ❌ | `max_(x - y, 0)` ✅ |
 | Complex logic | Nested if | Nested where/select |
 
 ---
 
+## 8. Debugging Phantom Values in Tax Calculations
+
+### Problem: Non-Zero Tax Despite Zero Taxable Income
+
+When state tax calculations produce small non-zero values (e.g., $277) even though taxable income is zero, check for:
+
+#### Root Cause 1: Implicit Type Conversion in min/max Operations
+
+```python
+# Example from Montana income tax bug
+❌ WRONG - Creates phantom values:
+def formula(tax_unit, period, parameters):
+    regular_tax_before_credits = tax_unit("mt_income_tax_before_credits", period)
+    credits = tax_unit("mt_income_tax_refundable_credits", period)
+
+    # BUG: min() with int 0 converts float array to int, losing precision
+    # When regular_tax_before_credits = 0.0, this can produce non-zero results
+    return max_(regular_tax_before_credits - credits, 0)
+
+✅ CORRECT - Preserves array types:
+def formula(tax_unit, period, parameters):
+    regular_tax_before_credits = tax_unit("mt_income_tax_before_credits", period)
+    credits = tax_unit("mt_income_tax_refundable_credits", period)
+
+    # Use max_() which handles arrays correctly
+    return max_(regular_tax_before_credits - credits, 0)
+```
+
+#### Root Cause 2: Phantom Intermediate Values in Calculation Chains
+
+When taxable income is zero but tax is non-zero, trace the calculation chain:
+
+```python
+# Tax calculation chain (Montana example)
+taxable_income: 0          # ✓ Correct
+rate: 0.0475              # Used despite zero income
+brackets: [15_600]        # Used despite zero income
+tax_before_credits: 277.41 # ❌ PHANTOM VALUE
+
+# The bug: Brackets calculated regular tax even when taxable income was zero
+# due to missing zero-check in bracket calculation
+```
+
+#### Debugging Pattern
+
+When you see phantom tax values:
+
+1. **Check the calculation chain** - Run test with verbose output to see intermediate values:
+   ```bash
+   pytest tests/file.py -vv
+   ```
+
+2. **Verify zero-income handling** - Look for formulas that don't short-circuit on zero income:
+   ```python
+   ✅ GOOD:
+   def formula(entity, period, parameters):
+       taxable_income = entity("taxable_income", period)
+       # Short-circuit when income is zero
+       return where(taxable_income == 0, 0, calculate_tax(...))
+
+   ❌ BAD:
+   def formula(entity, period, parameters):
+       # Always calculates, even when income is zero
+       return calculate_brackets(taxable_income, rates, brackets)
+   ```
+
+3. **Check type consistency** - Ensure operations preserve NumPy array dtypes:
+   ```python
+   ✅ Use: max_(value, 0) or clip(value, 0, None)
+   ❌ Avoid: max(value, 0) - Python's max can cause type issues
+   ```
+
+#### Common Symptoms
+
+- Tax calculated despite zero taxable income
+- Small non-zero values when expecting exactly zero
+- Tax values that don't match manual calculations
+- Capital gains deductions not properly reducing taxable income
+
+---
+
 ## For Agents
 
 When implementing formulas:
@@ -300,4 +422,5 @@ When implementing formulas:
 4. **Use NumPy operators** (&, |, ~) not Python (and, or, not)
 5. **Test with arrays** to ensure vectorization
 6. **Parameter conditions** can use if-else (scalars)
-7. **Entity data** must use vectorized operations
\ No newline at end of file
+7. **Entity data** must use vectorized operations
+8. **Debug phantom values** by tracing calculation chains and checking type preservation
\ No newline at end of file