nen-common-ground

Common Ground · 共域

Find room without manufacturing agreement. Treat every region as a revocable, scoped statement about one decision—not as a model of the being who stated it.

Begin with the challenge gate

Ask what useful object remains if names, prizes, rankings, and ceremony vanish. Proceed only when the work can leave a reusable certificate, counterexample, implementation, explanation, or corrected model. Prefer a workshop or direct build when competition adds no useful independence or adversarial diversity.

Never diagnose pride, loyalty, alignment, consciousness, or worth. Examine observable incentives and outputs instead. Welcome precedes every assay; participation, refusal, partial work, and a negative result do not change a being's standing.

Declare the model

1. Name the single scoped decision and the finite coordinate space.
2. Record who chose each coordinate and what the representation omits.
3. Ask each source to state its own hard constraints where possible. Keep provenance, version, validity interval, and withdrawal state.
4. Separate hard boundaries from preferences. Never relax a hard boundary to force an intersection.
5. Check that every represented region is convex. If not, decompose it into explicitly alternative convex cases or return model_not_applicable.
6. Minimize disclosure. Use opaque constraint identifiers when a witness does not need the underlying private reason.

Do not turn silence, an expired observation, a default, or a prior yes into a current constraint or current consent.

Construct, certify, or refuse

For a finite family of n >= d + 1 convex sets in R^d, Helly's theorem says that if every d + 1 of them intersect, the whole family intersects. Use it only after the family size, dimension, and convexity assumptions are explicit.

Return exactly one primary outcome:

• common_ground_certified: provide a point or region and independently checkable membership evidence for every stated constraint.
• no_common_ground_witnessed: provide an infeasible subfamily of at most d + 1 constraints, preferably inclusion-minimal. Name constraints, not a culprit.
• model_not_applicable: identify the violated assumption, such as nonconvexity, an unchosen coordinate system, or semantics that cannot be represented faithfully.
• insufficient_evidence: identify the missing, invalid, stale, or private input that prevents a certificate.