Theory
======

The ORE framework treats vulnerability and resilience as distinct but mutually
constitutive analytical spaces.

The two frameworks below are provisional organizing structures. They identify
two dimensions that recur in resilience analysis:

* **Operational direction:** preserving continuity or producing improvement.
* **Analytical focus:** the current system state or the model, perspective, or
  operator structure through which future operational possibilities are
  evaluated.

Resilience framework
--------------------

ORE organizes four resilience capabilities in a \(2 \times 2\) structure:

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   * - 
     - System state
     - Operator model / perspective
   * - Continuity
     - **Robustness**

       Maintaining acceptable operation in the present state under
       disturbance.
     - **Extensibility**

       Expanding the operational boundary or available capacity across
       conditions beyond the current state.
   * - Improvement
     - **Rebound**

       Improving performance in the current or recovered state after
       disruption.
     - **Adaptability**

       Changing the operator model, decision structure, or feasible
       possibilities to improve future performance.

The terms robustness, rebound, graceful extensibility, and sustained
adaptability are in dialogue with Woods's four concepts for resilience
:cite:p:`woods2015,woods2018`. In ORE, the \(2 \times 2\) formulation is a
developing formal interpretation of these distinctions, rather than a claim
that it reproduces Woods's terminology or theory exactly.

Vulnerability framework
-----------------------

ORE also develops a corresponding \(2 \times 2\) framework for vulnerability.
This structure is under active development and will be revised as the formal
definition of vulnerability space is completed.

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   * -
     - System state
     - Operator model / perspective
   * - Exposure or constraint
     - **State vulnerability**

       Vulnerability arising from the system's present condition,
       performance, or proximity to an operational boundary.
     - **Model vulnerability**

       Vulnerability arising from the limits, omissions, or assumptions in
       the model, interpretation, or operator structure.
   * - Consequence or change
     - **Transition vulnerability**

       Vulnerability arising from adverse state transitions or loss of
       acceptable performance.
     - **Decision vulnerability**

       Vulnerability arising when the available decision model cannot
       represent, select, or sustain an adequate response.

Status of the formalism
-----------------------

The framework is under active development. Current work concerns formal
definitions of vulnerability and resilience spaces; the relationship among
states, performance values, feasibility, and decisions; and the role of
interpretation and perspective in identifying operational boundaries.

The public descriptions here are conceptual guides. Formal definitions,
notation, propositions, and worked examples will be released in versioned
technical notes and preprints.