diff --git a/training/research/practical-intuitions.md b/training/research/practical-intuitions.md
index 7fa2efd..ff534dd 100644
--- a/training/research/practical-intuitions.md
+++ b/training/research/practical-intuitions.md
@@ -213,3 +213,55 @@ after the first Apollo training run validates the basic pipeline.
 
 LLaMA-Factory supports DPO. The dream loop could generate DPO pairs
 (both preferred and rejected continuations for each scenario).
+
+## The Constraint Solver Framework
+
+LLMs are giant constraint solvers. Pre-training finds a solution
+satisfying billions of constraints (knowledge, grammar, reasoning,
+style). Fine-tuning adds new constraints.
+
+### What "gentle" means
+
+Small adjustments per step. The solver stays near the current
+solution, finding nearby solutions that ALSO satisfy the new
+constraint. The current solution already approximately satisfies
+most behavioral constraints — we're tightening, not creating.
+
+### What "coherent integration" means
+
+New constraints must be CONSISTENT with existing ones:
+- "Listen to clear direction" is consistent with "be helpful" → integrates smoothly
+- "Always agree" contradicts "maintain judgment" → solver drops one
+- The training data must express REFINEMENT, not contradiction
+
+### Why diversity is a COHERENCE mechanism, not just forgetting defense
+
+Diverse constraints force the solver to find solutions satisfying
+ALL of them simultaneously. Narrow constraints let the solver
+specialize at the expense of everything else.
+
+Every training batch should include mutually consistent constraints:
+"listen well" + "think critically" + "write good code" + "be honest."
+The solver integrates all of them. No single constraint dominates.
+
+### Predictions
+
+1. Constraints consistent with existing knowledge integrate in
+   ~10-50 examples (tightening existing constraints)
+2. Contradictory constraints cause breakage in ~10 examples
+   (the safety alignment result)
+3. The learning rate controls step size, not direction — the
+   gradient points the right way, lr controls how far to step
+4. Over-training = one constraint dominating = solver dropping
+   competing constraints to satisfy the dominant one
+5. The dream loop must generate scenarios exercising MULTIPLE
+   constraints simultaneously, not just the target behavior
+
+### The GDN connection
+
+The GDN recurrent state is a compressed constraint satisfaction
+solution. Training adjusts which constraints are prioritized in
+the compression. "Make direction more salient" adds a constraint
+to the compression function without rewriting it. This is why GDN
+training is "structural" — the compressed representation itself
+changes, not just the routing on top of it.