feat(api): add short_id column for consistent LLM UUID handling

Resolves validation failures where LLM fabricated full UUIDs from 8-char
prefixes shown in context, causing 'unknown product_id' errors.

Root Cause Analysis:
- Context showed 8-char short IDs: '77cbf37c' (Phase 2 optimization)
- Function tool returned full UUIDs: '77cbf37c-3830-4927-...'
- LLM saw BOTH formats, got confused, invented UUIDs for final response
- Validators rejected fabricated UUIDs as unknown products

Solution: Consistent 8-char short_id across LLM boundary:
1. Database: New short_id column (8 chars, unique, indexed)
2. Context: Shows short_id (was: str(id)[:8])
3. Function tools: Return short_id (was: full UUID)
4. Translation layer: Expands short_id → UUID before validation
5. Database: Stores full UUIDs (no schema change for existing data)

Changes:
- Added products.short_id column with unique constraint + index
- Migration populates from UUID prefix, handles collisions via regeneration
- Product model auto-generates short_id for new products
- LLM contexts use product.short_id consistently
- Function tools return product.short_id
- Added _expand_product_id() translation layer in routines.py
- Integrated expansion in suggest_routine() and suggest_batch()
- Validators work with full UUIDs (no changes needed)

Benefits:
✅ LLM never sees full UUIDs, no format confusion
✅ Maintains Phase 2 token optimization (~85% reduction)
✅ O(1) indexed short_id lookups vs O(n) pattern matching
✅ Unique constraint prevents collisions at DB level
✅ Clean separation: 8-char for LLM, 36-char for application

From production error:
  Step 1: unknown product_id 77cbf37c-3830-4927-9669-07447206689d
  (LLM invented the last 28 characters)

Now resolved: LLM uses '77cbf37c' consistently, translation layer
expands to real UUID before validation.

backend/innercontext/api/llm_context.py

@@ -117,7 +117,7 @@ def build_product_context_summary(product: Product, has_inventory: bool = False)
     safety_str = f" safety={{{','.join(safety_flags)}}}" if safety_flags else ""
 
     return (
-        f"{status} {str(product.id)[:8]} | {product.brand} {product.name} "
+        f"{status} {product.short_id} | {product.brand} {product.name} "
         f"({product.category}){effects_str}{safety_str}"
     )
 

backend/innercontext/api/product_llm_tools.py

@@ -96,9 +96,12 @@ def _map_product_details(
     The 128-ingredient INCI list was consuming ~15KB per product.
     For safety/clinical decisions, actives + effect_profile are sufficient.
 
+    Uses short_id (8 chars) for LLM consistency - translation layer expands
+    to full UUID before validation/database storage.
+
     Args:
         product: Product to map
-        pid: Product ID string
+        pid: Product short_id (8 characters, e.g., "77cbf37c")
         last_used_on: Last usage date
         include_inci: Whether to include full INCI list (default: False)
 
@@ -193,7 +196,7 @@ def build_product_details_tool_handler(
             products_payload.append(
                 _map_product_details(
                     product,
-                    full_id,  # Always use full ID in response
+                    product.short_id,  # Return short_id for LLM consistency
                     last_used_on=last_used_on_by_product.get(full_id),
                 )
             )

backend/innercontext/api/routines.py

@@ -400,6 +400,42 @@ def _get_products_with_inventory(
     return set(inventory_rows)
 
 
+def _expand_product_id(session: Session, short_or_full_id: str) -> UUID | None:
+    """
+    Expand 8-char short_id to full UUID, or validate full UUID.
+
+    Translation layer between LLM world (8-char short_ids) and application world
+    (36-char UUIDs). LLM sees/uses short_ids for token optimization, but
+    validators and database use full UUIDs.
+
+    Args:
+        session: Database session
+        short_or_full_id: Either short_id ("77cbf37c") or full UUID
+
+    Returns:
+        Full UUID if product exists, None otherwise
+    """
+    # Already a full UUID?
+    if len(short_or_full_id) == 36:
+        try:
+            uuid_obj = UUID(short_or_full_id)
+            # Verify it exists
+            product = session.get(Product, uuid_obj)
+            return uuid_obj if product else None
+        except (ValueError, TypeError):
+            return None
+
+    # Short ID (8 chars) - indexed lookup
+    if len(short_or_full_id) == 8:
+        product = session.exec(
+            select(Product).where(Product.short_id == short_or_full_id)
+        ).first()
+        return product.id if product else None
+
+    # Invalid length
+    return None
+
+
 def _build_objectives_context(include_minoxidil_beard: bool) -> str:
     if include_minoxidil_beard:
         return (
@@ -686,17 +722,26 @@ def suggest_routine(
     except json.JSONDecodeError as e:
         raise HTTPException(status_code=502, detail=f"LLM returned invalid JSON: {e}")
 
-    steps = [
-        SuggestedStep(
-            product_id=UUID(s["product_id"]) if s.get("product_id") else None,
-            action_type=s.get("action_type") or None,
-            action_notes=s.get("action_notes"),
-            region=s.get("region"),
-            why_this_step=s.get("why_this_step"),
-            optional=s.get("optional"),
+    # Translation layer: Expand short_ids (8 chars) to full UUIDs (36 chars)
+    steps = []
+    for s in parsed.get("steps", []):
+        product_id_str = s.get("product_id")
+        product_id_uuid = None
+
+        if product_id_str:
+            # Expand short_id or validate full UUID
+            product_id_uuid = _expand_product_id(session, product_id_str)
+
+        steps.append(
+            SuggestedStep(
+                product_id=product_id_uuid,
+                action_type=s.get("action_type") or None,
+                action_notes=s.get("action_notes"),
+                region=s.get("region"),
+                why_this_step=s.get("why_this_step"),
+                optional=s.get("optional"),
+            )
         )
-        for s in parsed.get("steps", [])
-    ]
 
     summary_raw = parsed.get("summary") or {}
     confidence_raw = summary_raw.get("confidence", 0)
@@ -854,11 +899,19 @@ def suggest_batch(
         raise HTTPException(status_code=502, detail=f"LLM returned invalid JSON: {e}")
 
     def _parse_steps(raw_steps: list) -> list[SuggestedStep]:
+        """Parse steps and expand short_ids to full UUIDs."""
         result = []
         for s in raw_steps:
+            product_id_str = s.get("product_id")
+            product_id_uuid = None
+
+            if product_id_str:
+                # Translation layer: expand short_id to full UUID
+                product_id_uuid = _expand_product_id(session, product_id_str)
+
             result.append(
                 SuggestedStep(
-                    product_id=UUID(s["product_id"]) if s.get("product_id") else None,
+                    product_id=product_id_uuid,
                     action_type=s.get("action_type") or None,
                     action_notes=s.get("action_notes"),
                     region=s.get("region"),

backend/innercontext/models/product.py

@@ -142,6 +142,12 @@ class Product(ProductBase, table=True):
     __domains__: ClassVar[frozenset[Domain]] = frozenset({Domain.SKINCARE})
 
     id: UUID = Field(default_factory=uuid4, primary_key=True)
+    short_id: str = Field(
+        max_length=8,
+        unique=True,
+        index=True,
+        description="8-character short ID for LLM contexts (first 8 chars of UUID)",
+    )
 
     # Override 9 JSON fields with sa_column (only in table model)
     inci: list[str] = Field(
@@ -214,6 +220,11 @@ class Product(ProductBase, table=True):
         if self.price_currency is not None:
             self.price_currency = self.price_currency.upper()
 
+        # Auto-generate short_id from UUID if not set
+        # Migration handles existing products; this is for new products
+        if not hasattr(self, "short_id") or not self.short_id:
+            self.short_id = str(self.id)[:8]
+
         return self
 
     def to_llm_context(