idkmesh

Coordination Criticality and Finite-Difference Response

Status: synthetic mechanism experiment implemented as E021

Issue: #49

Research question

Can a small controlled load perturbation reveal a fragile verification queue before an absolute utilization or backlog threshold does?

Statistical physics motivates the question through susceptibility,

chi_X = d E[X] / d h

and, for particular equilibrium systems, fluctuation-response relationships. IDKMesh is not assumed to be an equilibrium system. E021 uses only the empirical finite difference

chi_(y,u) ~= (E[y | u + delta_u] - E[y | u]) / delta_u

as an engineering measurement. A steep queue response is not evidence of a thermodynamic phase transition.

Model

../../experiments/criticality_susceptibility.py is a discrete two-stage queue:

20 generator slots
 -> worker queue (capacity 12/tick)
 -> verifier queue (capacity 8/tick)
 -> verified outcome

Each operating point is evaluated with three variants:

  1. control: constant base load;
  2. probe: +5% load for 40 ticks, followed by recovery;
  3. stress: the same +5% increase remains active through the horizon.

For a seed, all variants share the exact arrival, defect, and detection draws. This common-random-number design makes the paired difference attributable to the load schedule. It does not make the synthetic workload representative of a real community or production verifier.

The experiment records queue mean, peak and variance; latency; verified throughput; escaped synthetic failures; and recovery time. Responses are reported with two-sided normal-approximation 95% intervals across seeds. Raw trial records and per-tick queue histories remain in the compressed result.

Ordinary baselines

E021 compares its predeclared superlinear-response alert against:

The future-stress label is the first load cell where at least half of matched sustained-stress runs end with a verifier-capacity-sized backlog and positive post-probe growth. This is a benchmark definition, not a universal overload criterion.

Result and use

The 40-seed result is documented in ../../experiments/E021-coordination-criticality.md. Susceptibility warned earlier in this grid, but at the cost of false alarms; it did not dominate the utilization baseline. The useful control-plane conclusion is therefore conditional:

A bounded probe may expose fragility, but it should remain one signal beside queueing baselines, with its alert cost calibrated on representative work.

The signal can inform issue #14 verification-scaling experiments. It cannot grant acceptance, deployment, or merge authority.

Follow-up boundary

The next experiment should add worker churn and heterogeneous cells only as a new, separately reviewed cohort. E021 intentionally keeps the first result small enough to reproduce and falsify.