Probability as Residual Structure Under Partial Executability An Implicit Derivation within the Binary-Constructivist Constraint Framework (BCCF)

This paper derives probability as a necessary structural feature within the Binary-Constructivist Constraint Framework (BCCF). Rather than treating probability as epistemic uncertainty, observer-dependent choice, or a consequence of measurement, the paper shows that probabilistic structure arises inevitably when attempted persistence encounters incompatibility under partial executability. The argument proceeds by implicit derivation, constraining where probability cannot reside until its placement becomes unavoidable. Probability is shown to precede stable persistence, observers, and energetic wash-out, emerging as the residual geometry of unresolved continuation prior to elimination. No new axioms are introduced, no empirical claims are made, and existing physical theories remain unmodified. The paper closes the probability loop within BCCF by situating probability as an early, universal consequence of constrained emergence rather than a late interpretive artifact.