8. Measuring What Is Real

Recoveries treated the order as configuration. It also moves—and central features appear only dynamically.

κ is measurable

For any law: what fraction of violations meet the force, how reliably, how fast? Orders obsess over validity and nearly ignore κ—though κ is what makes law real. High validity + near-zero κ = functional dead letter. κ varying by party = selective enforcement = determinacy failure measured. An order that audits κ like a budget can see force draining from commitments or pooling outside checks. Unmonitored coupling is where capture first takes hold below validity-tracking’s sightline.

Update law: least motion made exact

When a case forces µ to move, the form is the minimum-relative-entropy step—the unique update that incorporates the case and imports nothing else:

µ′ ∝ µ e^{V/τ}

(Same family as intelligent economics’ choice tilt, read as legal reference update.)
DKL term prices motion; value term pulls with the case. Ratio honours the constraint; obiter is surplus the minimisation discards.

Limits: τ → ∞ sticky, cannot learn; τ → 0 perfect snap to maximisers, nothing in reserve—the boundary “improvement is capture” will name. Same divergence is the cost members pay for departing the internal standard.

Precedent: two engines, two timescales

• Within a case: freeze µ long enough to decide—or no determinate answer.
• Across cases: update µ—or the order cannot learn.

Finality / res judicata: freeze made permanent for a dispute. Overruling needs warrant that exceeds instability cost—same threshold family as departing a frozen reference.

Evolution of law: punctuated kinetics

Legal history is not smooth creep. Long stasis, then abrupt reorganisation. Gradualist stories treat abruptness as contingency. The object treats it as generic kinetics of a reference with multiple stable settlements.

Selection on usefulness: doctrines that let people predict and coordinate gain missionary share (judges, scholars, public internalisers); incoherent ones lose. Barriers between settlements make crossing times steep in barrier height over temperature—long apparent permanence, then fast transition. Lock-in: barrier dwarfs temperature. Revolution: barrier crossing.

Consequences legal historians see but rarely derive:

1. Critical slowing — doctrines wobble (splits, inconsistency) before they fall.
2. Hysteresis — law does not jump back when pressure recedes (recognised rights don’t auto-unrecognise).
3. Polarisation threshold — below a critical temperature, shared legal µ can split into two self-maintaining incompatible readings of one constitution without anyone’s values changing—only the cost of maintaining divergent legal reality fell. Repair is rebuilding common reference or raising the cost of separate ones—not only “winning the argument.”

Evolution of law is doxic dynamics with the monopoly as stakes. Next: what happens when maintainers are no longer the same kind as the community.