Nested Forcing Chain
A Nested Forcing Chain runs an inner deduction on the candidate state created by an outer assumption. The inner result can extend the outer chain, but it remains conditional on that outer assumption until the outer proof is complete.
What is a Nested Forcing Chain?
Nesting changes the depth of the proof, not its truth rules. An inner AIC, fish, subset, or forcing deduction uses the temporary state inherited from the outer branch. Its conclusion is therefore not independent of that branch.
How to spot it
A Nested Forcing Chain adds an inner chain search to an already assumed temporary state. It may be difficult to follow by hand, but difficulty and product ranking are separate from its validity. A complete explanation must show the outer assumption, the state inherited by the inner chain, the inner conclusion, and how the outer proof is finally discharged.
The logic
If outer assumption A enables an inner proof of P, the valid statement is A implies P. P becomes unconditional only if A is later proved true, or if every exhaustive outer alternative also proves P. Calling the inner result independent would discard a necessary premise.