Spiking neural networks (SNNs) are promoted as an energy-efficient substrate because sparse, event-driven activity replaces dense multiply-accumulates with cheap accumulates. We argue the energy dividend of sparsity is not a property of SNNs but of the task. Holding architecture fixed and swapping only the hidden unit (continuous vs. leaky-integrate-and-fire), plus a two-sided target-firing-rate probe, we measure how far activity can be pushed down before quality breaks. Low-load feed-forward perception sparsifies to 5% firing at no accuracy cost; a recurrent language model cannot go below ~50% -- the recurrent state must stay active to carry information. A spiking Transformer, by contrast, sparsifies freely to 2% (3 seeds) -- so the ceiling is a property of recurrent compression, not sequence modeling. Attention escapes the floor only by storing the full key-value cache, trading a firing floor for a memory wall: on neuromorphic hardware, recurrence and attention pay on different axes, neither escapes. We formalize the ceiling with an information-theoretic bound rho >= H_b^{-1}(log2 M / H) and confirm its predictions: the floor rises with memory load, falls with state width, and (refuting a naive memory-only reading) rises with task difficulty. A layer-wise input floor further caps op reduction under dense input, isolating event-driven perception as where neuromorphic hardware wins.
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 populations, value is frame-relative while price is frame-independent; a fleet that pools its resource and fuses its perception inherits the ceiling $G_{\rm fleet}\le I(X;Y_{1:m})\le H(X)$ (a corollary; an earlier sum-form claim was wrong and is corrected in v5). A dynamical layer yields an is/ought asymmetry from which alignment emerges as a control-stability condition. We test the single-frame laws on live language models, pre-registered: perception mutual information tracks realized capability (Spearman $ρ=0.977$ over 30 model$\times$domain points); out-of-sample $ΔG$ tracks $I(X;Y)$, shape-invariant across four task shapes ($n=42$, slope $0.953$); over-confidence is measurable dissipation. The stated continuation gate has since been run (pre-registered, frontier-model population): the coupled capacity-region prediction -- growth-gap law, coalition submodularity with an XOR synergy control, joint ceiling, Kelly selection -- is confirmed within its frozen bands on real agents; the mean-field residual law $\|Vg\|/γ$ found no domain (populations hold no goal dispersion) and is retired to its mathematical scope. The contribution is the unification and the governance mapping that follows.