The bet. Value is a lawful, structural quantity — in the same category as information — currently left undefined only because, like information before 1948, it is confused with its semantic clothing. Strip the clothing and a structural quantity remains.
A theory of value is to agency what relativity is to motion. Value is frame-dependent on the agent's goal; the laws relating value across frames are universal. Relativity doesn't disqualify a quantity from being fundamental — it forces the theory to make the frame explicit.
The three load-bearing equations
The measure
The Logarithmic Value Law — forced by a single scale-invariance axiom, and
independently by multiplicative compounding. Optimal allocation puts resource where the goal-weight
is: eᵢ* ∝ kᵢ.
The capacity
A coding theorem for value: an agent's value-generation rate is bounded by the
mutual information between the world X and its perception Y. Value-throughput
is information-throughput.
The Second Law
Realized value = available value minus the value dissipated to miscalibration. Confident error drives growth negative — an exact, signed accounting in nats.
Shannon's quantities recur, load-bearing not decorative: entropy H as a
dissipation penalty, KL divergence D as available-minus-dissipated value, mutual information
I as the value ceiling, and the Fisher metric as the cross-frame invariant.
The method, copied from Shannon — deliberately
Shannon's 1948 paper worked because of one ruthless abstraction: he threw away meaning
and defined information as nothing but the reduction of uncertainty. From that came a measure
(−log p), a unit (the bit), and hard limits (channel capacity, the coding theorems).
The analogous move here: throw away morality, price, and human psychology. What remains is value as a frame-relative but lawful quantity — relative to an agent's goal the way information is relative to a prior, or energy to a reference frame. The frame is made explicit, not wished away.
Evidence — the theory predicts its own instantiation
closed-form predictions reproduced by a Monte-Carlo world — including value going negative under confident error, and a priced fleet that grows from agents that individually don't (Shannon's demon).
across 30 model×domain points (10-model ladder × 3 domains, pre-registered),
I(X;Y) tracks realized capability — not parameter count; out-of-sample
ΔG tracks I at slope 0.935.
the out-of-sample bridge ΔG ~ I(X;Y) generalizes across classification, reasoning,
sequential decision, and code — one relationship, slope ≈ 1, with one honestly-flagged
underpowered sub-check.
These are measured on real LLM outputs, with the same instrument you can run yourself → the Value-Meter.
Why this serves governing AI agents
- Per agent. Value-generation is capped by its perception's mutual information
I(X;Y). RaisingIper joule is the formal reason a cheap reflex can match expensive deliberation on a narrow task. - Across agents. Values are not cardinally comparable (Arrow). Coordinate them through an emergent price on shared resources — as economies coordinate incomparable utilities — never a god's-eye utility sum.
- Fleet design. Cultivate goal- and perception-diversity (positive-sum, covers more of
H(X)); suppress belief-divergence and goal-conflict. Headcount past perception-saturation buys nothing.
Honest status
Proven (within stated axioms)
the log law, the capacity theorem (achievability + converse), the Second-Law decomposition, the cross-frame exchange rate + Fisher invariant, and the fleet outer bounds.
Conjecture
the Second Law of Value as a global tendency; equilibrium-price existence beyond the convex regime.
Open
the exact multi-agent capacity region; cross-frame cardinal comparison (deliberately unsolved); the full dynamics of how goals, beliefs, and prices co-evolve.
What is and isn't new. None of the underlying mechanisms is individually new — the single-agent core is generalized Kelly (1956), the is/ought asymmetry is Hume / Armstrong & Mindermann (2018), and the alignment-stability algebra is elementary classical control. The contribution is the unification under one substrate-grounded quantity, the cross-frame/price layer, the fleet ceiling, and the governance mapping — reading goal-drift as a control problem yields the ordering incentive design beats oversight. The application is the contribution, not new theorems; claims are scoped to match.
Read the theory
The full development is public — the preprint is the polished read; the source repository has the derivations, the pre-registered experiments, and an explicit "where this breaks" section at the end of every doc.
New to it? Reading order: 00 framing → 01 the measure →
02 the limit → 03 many agents → 04 the fleet →
05 dynamics → 06 the real-agent test. Each is self-contained enough
to skim from its headline box.
Measure any agent's value profile
The most direct use of the theory: a tool that takes an agent's outputs vs ground truth and returns its value ceiling, realized rate, dissipation, and value-per-compute — in nats, with nulls and CIs, running entirely in your browser.
Open the Value-Meter →