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Scientific trace · 2025 → September 2026

Evidence forced the model to change.

Væringjar II did not begin with the current framework. The research moved from post-failure control of damaged hardware to a theory of controlled architectural evolution after three assumptions of the initial model became too weak.

The turning point →Open evidence library
Temporal diagram

One research line, two different formulations.

Problem formalisationSuper-critical operating modes: shutdown can be unacceptable; degraded operation must be reasoned about.PUB‑01 · PUB‑02
Damaged plantIrreversible damage is made explicit and resource state drives a degraded control regime.EXP‑01
Structural pathResidual resources are mapped to feasible states and graph-based post-failure reconfiguration.EXP‑02
Structural survivability worksEXP‑03 verifies an audited path \(c_0\to c_1\to c_3\) and preserves degraded mission functionality.EXP‑03 · TURNING POINT
Model revisionThe successful experiment exposes missing guarantees: epistemic failure, sequence stability and horizon-aware choice.DISSERTATION REVISION
Unified frameworkCapability + admissibility + timing over a graph of physical and epistemic configurations.PRE‑01 · PRE‑02 · PRE‑03
EXP‑03 answered its question — and made the next question unavoidable.Open section
Turning point

EXP‑03 answered its question — and made the next question unavoidable.

WHAT EXP‑03 ESTABLISHED

Structural reconfiguration can preserve a degraded mission.

  • irreversible resource loss is represented explicitly;
  • candidate configurations are constrained by a directed graph;
  • mission functionality and survivability can drive the choice;
  • the executed path is auditable and reproducible.
WHAT IT DID NOT ESTABLISH

The selected sequence is not yet a guaranteed trajectory.

  • \(\gamma(c)<1\) verifies each configuration, not arbitrary repeated switching;
  • \(\arg\max S\) chooses the best node now, not the best path over a dwell interval;
  • hardware operability alone cannot represent a model that is healthy in memory but wrong about the world;
  • reaction time says how fast to switch, not how frequently switching remains admissible.
Each missing guarantee produced a new research branch.Open section
Three falsification questions

Each missing guarantee produced a new research branch.

A / STABILITY

Can individually stable configurations form an unstable switching sequence?

Yes. The response was to import dwell-time analysis into architecture-level reconfiguration and derive a rate bound from the conditioning of the configuration certificates.

B / KNOWLEDGE

Can the system fail while all physical resources remain healthy?

Yes. A stale or invalid model can become the limiting resource. Model validity is therefore represented as an epistemic resource health coefficient.

C / DECISION

Is the best configuration now always the best next decision?

No. A candidate may lose admissibility during the interval in which the system is required to remain there. Selection becomes trajectory planning over the verified graph.

Initial formulation

Choose the best feasible degraded configuration.

\[ c^*(t)\in\operatorname*{arg\,max}_{c\in\mathcal C_{feas}(\rho(t))}S(c,\rho(t)). \] This formulation was sufficient for EXP‑03: two faults, a finite graph and a local stability gate.

It remains a valid special case. The revision does not discard it; it specifies the conditions under which it is safe to use.

Control the trajectory of an extended system state.Open section
Current formulation

Control the trajectory of an extended system state.

\[ Z(t)=\langle x,\rho,cfg,\alpha\rangle, \qquad \mathcal R=\mathcal R_{phys}\cup\mathcal R_{epist}, \qquad G_e=(\mathcal C,\mathcal T). \]
\[ \pi^*\in\operatorname*{arg\,max}_{\pi\subset G_e}\int_0^T S(Z(t))\,dt, \qquad t_{k+1}-t_k\ge\tau_d, \qquad \tau_d>\frac{\ln\mu}{2\gamma_{min}}. \] Capability gives the objective; the graph gives the guaranteed set; timing constrains when the architecture may change.
The revised model produced consequences that the initial formulation could not express.Open section
Results that changed the design

The revised model produced consequences that the initial formulation could not express.

Model deactivation thresholdFor low relative influence, critical validity approaches \(e^{-1}\approx0.368\): below it, removing a degraded model can increase capability.
Catalogue composition dominates tuningRemoving the worst-conditioned configuration reduced the required dwell time by 5×, versus at most 1.78× across decay-rate tuning.
Trajectory planning changes the safety outcomeIn the reference verification, unsafe operating time decreased from 3.55% to 1.90% with only a 0.12% loss in mean capability.
Validity management has mission valueValidity-aware resource allocation increased mean capability from 0.8918 to 0.9420 in the reference model.
Three papers document the revision from three angles.Open section
Preprint series · September 2026

Three papers document the revision from three angles.

PRE‑01Dwell-Time Conditions for Stable Runtime Reconfiguration of Self-Adaptive Control ArchitecturesWhy per-configuration stability is not enough; rate bounds, certificate conditioning and catalogue synthesis.
PRE‑02Model Validity as a System ResourceWhy hardware health is not the full resource state; critical validity, deactivation and restoration policy.
PRE‑03Capability, Admissibility and Timing: A Unified FrameworkThe current synthesis: architecture-derived capability, epistemic resources, admissible graph trajectories and real-time constraints.

Status: manuscript / preprint draft. Public bibliographic links should be added only after the preprints are deposited.

Scientific interpretation

This is not a replacement of the old results.

EXP‑01, EXP‑02 and EXP‑03 remain evidence for the claims they were designed to test. The model revision is a change in scope: the initial formulation becomes a restricted case of the current one.

That traceability is deliberate. The site shows where the theory came from, which assumption failed to scale, and which result justified each new term in the model.

Continue

Read the current formulation or inspect the experiments that led to it.

Current programme →Evidence library