| # Unfolding definitions without hiding cycles |
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| How can a vocabulary be unfolded through its own definitions without concealing circularity? |
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| Expose definitions that reuse other defined objects, and compare compact names with recursively substituted forms. |
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| Status: open problem. Formulation and comparisons: reconstruction. Development: historical branch. |
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| ## Alternative representations |
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| ### Named concepts |
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| Affords: Keeps a large definition compact. |
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| Limits or losses: Dependencies remain implicit. |
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| ### Substituted definitions |
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| Affords: Makes reused definitions visible. |
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| Limits or losses: Recursive substitution may never terminate or may erase useful distinctions. |
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| ## Tension |
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| Unfolding can clarify a concept or merely move its circularity out of sight. |
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| ## Challenge |
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| What marks an unresolved cycle, and when is a cycle a valid recursive definition? |
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| This challenge is an editorial prompt, not a claim that the evidence already resolved it. |
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| ## Proposed next move |
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| Unfold a small vocabulary with a depth bound and explicit cycle markers; compare readers’ interpretations. |
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| Status: new model-proposed experiment or extension; not a reported result. |
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| ## Related problems |
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| - [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. |
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| ## Evidence anchors |
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| - 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.] |
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| Root evidence and private recovery mappings are not part of this public release. |
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| [Open in the reader](../index.html#node=recursive-definitions) · [All problems](../CATALOG.md) |
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| ## Research editions |
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| - [Vertical Infinity and Reflexive Representation](../documents/vertical-infinity-and-reflexive-representation.md) (reconstruction). |
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