What happens
Two operators share one update rule and differ only in accuracy (p = 0.8
and 0.6) and in their starting endorsement. Each round one operator acts,
chosen with probability softmax(β·E). Endorsement moves toward observed
outcomes, E_i ← E_i + η(outcome − E_i), which is A5’s
Ė_ji = η_j[Q_ji − E_ji] in discrete time. η sets the memory kernel A6 §1B
named. Run with python3 scratch/formal/trust_loop.py: 200 seeds and
4,000 rounds per regime.
| Regime | Start (E0) | β | Result |
|---|---|---|---|
| scored every round | 0.5, 0.5 | 8 | better ends more endorsed 200/200; acts in 82% of late rounds |
| scored every round | 0.3, 0.9 | 8 | head start undone; better acts in 83% of late rounds |
| scored when acting | 0.3, 0.9 | 8 | better recovers in 200/200, median round 460 |
| scored when acting | 0.3, 0.9 | 30, 100 | worse operator never displaced, 200/200 |
| scored when acting | 0.5, 0.5 | 100 | worse operator holds most late rounds in 6/200 |
| scored every round (control) | 0.3, 0.9 | 100 | worse operator holds most late rounds in 0/200 |
Durability, under scoring every round with a fair start, is set by the memory kernel. With η = 0.01 the lead changes hands 0.0000 times per round in the second half. With η = 0.3 it changes 0.137 times per round.
What it shows
- Durable, differentiated authority with no authority primitive. Persistent precedence of the more accurate operator emerges from the endorsement rule alone. Its durability is a property of η, not of a second kind of authority. That is CLAIM-277’s first clause and A5’s “different dynamical regimes, not different ontological primitives”.
- The same loop entrenches. When influence is what buys the chance to be scored, as in A5’s chain of early advantage, then greater influence, then more visibility, an early leader keeps influence it would lose under scoring. The difference between the regimes is what is observed, not the rule.
What it cannot show
It is two operators with fixed accuracies. Niches, where competence shows only in rare contexts, and mutual regulation among many processes are not in it: QUESTION-083 keeps both. That real organizations score as the second regime does is A46’s niche-exclusion observation, not something this construction establishes.