# Unfolding definitions without hiding cycles

How can a vocabulary be unfolded through its own definitions without concealing circularity?

Expose definitions that reuse other defined objects, and compare compact names with recursively substituted forms.

Status: open problem. Formulation and comparisons: reconstruction. Development: historical branch.

## Alternative representations

### Named concepts

Affords: Keeps a large definition compact.

Limits or losses: Dependencies remain implicit.

### Substituted definitions

Affords: Makes reused definitions visible.

Limits or losses: Recursive substitution may never terminate or may erase useful distinctions.

## Tension

Unfolding can clarify a concept or merely move its circularity out of sight.

## Challenge

What marks an unresolved cycle, and when is a cycle a valid recursive definition?

This challenge is an editorial prompt, not a claim that the evidence already resolved it.

## Proposed next move

Unfold a small vocabulary with a depth bound and explicit cycle markers; compare readers’ interpretations.

Status: new model-proposed experiment or extension; not a reported result.

## Related problems

- [One structure, several renderings](structure-across-renderings.md) — opens a local operation (corpus_evidence). Changing the representation included substituting defined objects with their definitions.
- [The next description becomes another object](objectifying-the-meta-level.md) — exposes a recurrence (retrospective_connection). A definition can become an object for another definition; the analogy does not equate linguistic circularity with every formal limit.

## Evidence anchors

- basis-recursive-definitions: The material asks to identify defined objects that appear inside other definitions and replace their names with their definitions. A separate methodological question asks whether internal variants of an idea can help challenge it alongside opposing ideas. [Editorial paraphrase; presence of a proposal does not verify its truth.]

Root evidence and private recovery mappings are not part of this public release.

[Open in the reader](../index.html#node=recursive-definitions) · [All problems](../CATALOG.md)

## Research editions

- [Vertical Infinity and Reflexive Representation](../documents/vertical-infinity-and-reflexive-representation.md) (reconstruction).