η̂ₜ
Estimated adaptive evidence-integration rate.
Published September 6, 2026 · v0.2
Homo sapiens
How can we test whether an adaptive system can still use valid corrective evidence to update its internal model and adjust its response?
01 / Published Research
The research question — without diagnostic shorthand
BenchEWS Individual investigates the conditions under which an observing adaptive system loses the capacity to use valid corrective evidence to update its internal model and adapt its response — and whether changes in this process can be measured over time.
Status boundary: BenchEWS Individual is a published theoretical research line within the BenchEWS Research Programme. It provides a falsifiable hypothesis and methods framework for studying time-resolved changes in adaptive evidence integration, prediction-error persistence, and candidate behavioral lock-in dynamics.
02 / Mathematics
An exact decomposition, not a universal shortcut
The earlier shorthand AC1(PE) ≈ 1 − η is not a general identity. The published v0.2 uses the exact decomposition:
PEₜ₊₁ = (Oₜ₊₁ − Oₜ) + (1 − ηₜ)PEₜPEₜ₊₁ = (1 − ηₜ)PEₜ + (εₜ₊₁ − εₜ)Under a locally near-stationary environment, the second form follows. The composite noise term is generally not independent of the current prediction error. Persistence must therefore be tested as model-, regime-, and condition-dependent. ρ₁(PE) = −η/2 applies only to the fully specified minimal model.
Open the mathematical boundary →03 / Measurement Architecture
Minimal measurement vector
Four measurement slots structure a possible time-resolved test. The vector is published but has not been empirically validated.
BI(t) = [ η̂ₜ, Persistence(PE)ₜ, I(S;R)ₜ, Trecovery ]Persistence(PE)ₜ
Abstract slot for prediction-error persistence; AC1 is a primary candidate, not a universally fixed metric.
I(S;R)ₜ
Rolling environment–response mutual information; a normalized robustness measure such as NMI may supplement it.
T_recovery
Time or number of trials required to return to a defined baseline after perturbation.
04 / Falsifiability & Estimator Latency
Ten hard falsification criteria
The framework specifies ten explicit conditions under which its central temporal-lead hypothesis should be considered unsupported or falsified. These include null and competing models, parameter recovery, robustness to window selection, and correction for estimator-specific delays.
Observed lead is not necessarily genuine lead
Measures use different window lengths and detection delays. An apparently earlier warning may therefore be created or shifted by the estimator itself. Observed lead and estimator-latency-corrected lead must be reported separately.
05 / Studio 3.0 Research Horizon
From the published framework to planned Studio 3.0 infrastructure
- 01Published: theoretical framework, mathematical derivations, measurement candidates, falsification criteria, and proposed experimental architecture.
- 02Planned: methodological operationalization, experimental design, parameter recovery, estimator-latency tests, and competing-model analysis.
- 03Still open: reproducible Studio 3.0 implementation, real data collection, independent replication, and empirical validation.
Binding separation: BenchEWS Individual v0.2 = published theoretical framework. BenchEWS Studio 3.0 = PLANNED · NOT IMPLEMENTED · NOT VERIFIED.
06 / Ethical Boundaries
Binding ethical boundary
BenchEWS Individual studies time-resolved processes within defined observational and experimental regimes. The framework does not support moral, diagnostic, or global judgments about a person.
- no psychiatric or medical diagnosis
- no automated personality, ideology, or employee assessment
- no credit, insurance, law-enforcement, or government profiling decisions
- no covert surveillance or moral ranking
07 / Cross-scale Research
Two scales of the same overarching question
Quality-Driven Propagation & Adaptive Reopening addresses networked information systems; BenchEWS Individual addresses individual adaptive systems. Both ask when adaptive systems lose correction pathways and how that loss might become measurable. They do not constitute an empirically confirmed unified theory.