Finite-Window Reversible Completion Entropy:\\ Axiomatization, Structural Properties, and Non-Asymptotic Error Theory Under EBOC--WSIG--RCA Framework

We propose and establish ``finite-window reversible completion entropy'' as a localized information measure for ``record--interpretation'' problems under reversible propagation and energy/regularity constraints: given finite window observation, the logarithm of minimal equivalent representative count (or capacity) of completion set consistent with reversible global dynamics. This measure solely characterizes ``how many reversible worlds interpret the same record'', independent of prior probabilities and mixed-state entropy. We provide rigorous definitions at both discrete reversible cellular automaton (RCA) and continuous windowed scattering--information geometry (WSIG) ends, proving structural properties including monotonicity, reversible covariance, and splice subadditivity; under Toeplitz/Berezin compression and bandlimited/exponential window settings, construct non-asymptotic upper/lower bounds following Nyquist--Poisson--Euler--Maclaurin (NPE) three-fold decomposition with finite-order termination, providing quantitative law ``boundary = information resource'', strictly compatible with unified scale of ``phase derivative--relative state density--Wigner--Smith group delay trace''. Examples of bandlimited signals and RCA with theorem-level proofs conclude the paper.