What a finite learning device has recorded and what will hold value for it on future tasks are not the same quantity. We develop a typed accounting for finite-state learning devices that separates four components: a training-side fit functional
Φfit, the record-correlation stock
JD=I(M;D), an update-side search ledger
σM, and an operational capital value
V(M;T,b). This value is the work gap between an informed protocol class and a blind class obtained by deleting the memory-read port and re-optimizing from scratch. (I) Separation: for every
n, there is a device family on which record correlation and world correlation grow by
nln2 while the capital gain is exactly zero. In the
flat∗ regime, data-free updates never increase
V. (II) Capitalization ledger: an exact
flat∗ extraction identity and a universal ledger identity give, for (F5
′)-stable
M-local updates under a no-discarded-record-correlation condition (f), the bound
ηcap≤1 for the capitalization efficiency
ηcap=ΔV/(kTσM), together with necessary and sufficient conditions for equality. (III) Value retention: for the retention gap
Lgen and retention ratio
ρgen (the former carries no sign constraint; the latter is defined for positive training-side value and is not confined to
[0,1]) we give a two-layer alignment domain: an exact exchange rate between value and the side-information-adjusted record fit
I(M′;D∣Y) without any record-side-information independence assumption, and a raw record-stock exchange rate under a joint side-information neutrality condition
(M,D)⊥Y, whose boundary is marked by an explicit one-time-pad witness. These are statements about finite-device value retention under task-distribution shift, not a theory of statistical generalization.