A Mathematical Theory of Value: a synthesis on goal-directed agency under resource constraints
We propose that value -- the quantity goal-directed agents create, destroy, and exchange -- is a lawful structural quantity in the same category as information. Following Shannon's method, we make one ruthless abstraction: value is the rate at which an agent converts a resource into goal-progress, relative to a frame fixed by its goal. A scale-invariance axiom forces a logarithmic measure, $V=\sum_i k_i\ln e_i$; compounding of a reinvested resource forces the same form via the ergodicity argument of Peters (2019) -- kin routes, a consistency check, not an over-determination. We derive a coding theorem of value, $ΔG \le I(X;Y)$; realized value decomposes as $G=D(q\|r)-D(q\|p)$. For populat...
| Authors | Cheng Qian |
|---|---|
| Primary category | physics.soc-ph |
| Published | 10 June 2026 |
| Last updated at source | 3 July 2026 |
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