We introduce behavior-bound signatures (BBS), a signature framework in which each signature attests not only to signer authenticity but also to the satisfaction of a prescribed behavioral policy. Unlike traditional digital signatures—whose acceptance is determined by identity validity alone—BBS enforces compliance at the level of the verification predicate: a signature is accepted if and only if a zero-knowledge proof establishes that a residual function value δ(x)=∣ϕ(x)−τ∣\delta(x)=|\phi(x)-\tau|δ(x)=∣ϕ(x)−τ∣ lies below a threshold ε\varepsilonε. Thus, compliance safety is reduced to zero-knowledge soundness rather than to external monitoring or honest-majority assumptions. We formalize policy-soundness under chosen-message attacks (PS-CMA), extending EUF-CMA by requiring that no adversary can produce a valid signature for any message whose induced action violates the policy predicate. We prove that BBS achieves PS-CMA security under standard assumptions: binding of Pedersen commitments, collision resistance of Poseidon, and soundness of the underlying zero-knowledge proof system (e.g., Bulletproofs or PLONK). Our construction instantiates the policy predicate via a private structure function ϕ(x)\phi(x)ϕ(x) and enforces δ(x)<ε\delta(x)<\varepsilonδ(x)<ε through a zero-knowledge range constraint, while revealing no information about the private parameters. Sequential signatures compose into a hash-linked trajectory, enabling verifiable ordering and completeness of action sequences. We additionally define the Function Approximation Inversion Problem (FAIP) as a conjectured hardness property of the structure function, and emphasize that the security of BBS does not rely on this conjecture.