Open research direction
Paper: Paper 1 (v11.3) § 3 and § 5; downgraded to structural analogy at Paper 3 (v9.1) § 7
Authoritative claim file: validation/claims/g-r-c-practice-domains.md
What is a precise definition of "generative sufficiency" (the G in G∧R∧C) for domains whose constructs are not recursively enumerable — architecture, cinema, painting?
And: does the G∧R∧C-derived five-position topology hold for such domains as theorem, as structural observation, or as analogy?
Possible approaches
- Type-theoretic refinement (dependent types per domain).
- Enriched category theory (enrichment over a base encoding material / cognitive constraints).
- Grothendieck fibration (fibred category over kinds of constraints).
- Rigorous negative result — no non-trivial extension of G∧R∧C to practice domains is faithful to the informal intuition.
See CONTRIBUTING.md § 4 for acceptance criteria.
Domain(s)
- Category theory (primary)
- Formal logic
- Philosophy of mathematics
Status
Open research direction; unbounded time horizon.
Why it matters
This is the structural hinge of the paper series. Paper 1 claims the five positions follow from G∧R∧C. Paper 3 § 7 downgrades the G∧R∧C ↔ D1–D3 mapping to structural analogy. The inconsistency is visible and load-bearing; a clean resolution would allow the papers to be uniformly framed.
Open research direction
Paper: Paper 1 (v11.3) § 3 and § 5; downgraded to structural analogy at Paper 3 (v9.1) § 7
Authoritative claim file:
validation/claims/g-r-c-practice-domains.mdWhat is a precise definition of "generative sufficiency" (the G in G∧R∧C) for domains whose constructs are not recursively enumerable — architecture, cinema, painting?
And: does the G∧R∧C-derived five-position topology hold for such domains as theorem, as structural observation, or as analogy?
Possible approaches
See
CONTRIBUTING.md§ 4 for acceptance criteria.Domain(s)
Status
Open research direction; unbounded time horizon.
Why it matters
This is the structural hinge of the paper series. Paper 1 claims the five positions follow from G∧R∧C. Paper 3 § 7 downgrades the G∧R∧C ↔ D1–D3 mapping to structural analogy. The inconsistency is visible and load-bearing; a clean resolution would allow the papers to be uniformly framed.