Non-Formal Explanation¶

This document describes the formal contract of Structural Explainability without reference to implementation or theorem-proving details.

It explains what the contract requires, why it exists, and what it constrains.

Purpose¶

The formal contract defines the minimal structural conditions under which:

identity can be evaluated
persistence can be tracked over time
systems can be compared
disagreement can persist without breaking structure

These conditions are independent of interpretation.

Core idea¶

A system is admissible if identity and persistence can be evaluated without relying on meaning, role, or interpretation.

This requires:

fixed identity conditions
explicit structural relationships
separation between structure and interpretation

Identity and persistence¶

Structural Explainability does not assume a single notion of identity.

Instead, identity is evaluated under distinct regime profiles.

Each profile defines:

what counts as “the same”
what counts as “different”
how transformations affect identity

Regime profiles¶

The contract requires nine identity-and-persistence regime profiles:

Unsplit profiles¶

OBL — obligation-bearing entity
OCC — time-indexed occurrence
REC — descriptive record

These do not require refinement under admissible transformations.

ENR-L — locus-bound referent
ENR-I — instrument-bound referent

Two representations can refer to the same locus even when artifacts differ, but cannot remain the same artifact once branching produces distinct objects.

CTX-E — extension-based context
CTX-S — structure-based context

Two representations can apply to the same cases even when internally structured differently, but cannot be the same structure once decomposition changes that organization.

NOR refinement (structural vs content)¶

NOR-C — content-sensitive normative structure
NOR-S — structure-sensitive normative structure

Two representations can encode the same normative content while differing in structure, but cannot remain the same structure once that organization changes.

A single regime is insufficient when a transformation must be:

identity-preserving under one basis, and
identity-breaking under another

This creates split pressure.

The ENR, CTX, and NOR refinements are forced by this condition.

The result is a lower bound of nine regime profiles.

Relations¶

Relations connect entities but do not determine identity.

They describe structure, not meaning.

Allowed relation primitives include:

equivalent
narrower
broader
overlaps
none

These relations do not alter identity conditions.

Neutrality¶

The contract requires structural neutrality.

This means:

identity is not derived from interpretation
causal or normative meaning is not embedded in structure
multiple incompatible interpretations may exist over the same structure

Interpretation is external to the substrate.

Consequences¶

Comparison¶

Two systems are comparable if their structures can be aligned under the same regime profiles and relations.

Interpretation differences do not affect comparability.

Persistence of disagreement¶

Disagreement does not break structure.

Different interpretations can coexist over the same structural representation.

Transformation¶

Changes to a system are evaluated structurally:

whether identity is preserved
whether admissibility is maintained
how regime classifications are affected

Boundary¶

The formal contract defines:

what is structurally admissible

It does not define:

what things mean
what is true or false
what should be done

Those belong to interpretive or domain-specific layers.