Why it is a question
THEORY-191 (four natural odour sources and one perceptual data set, LIT-872) and THEORY-192 (twelve CA1 sessions, LIT-876) report that rank orders of correlations have the Betti-curve signature of a 3D hyperbolic ball and not of a uniform Euclidean cube. On 2026-10-19 both were narrowed to the data measured and promoted, at the owner’s direction, carrying out the promotion audit’s batch 018 (record/promotion-audit/decisions/THEORY-191.yaml and THEORY-192.yaml, ADR-047 v3). Their promote_when clauses moved here unchanged.
It is open for two reasons.
- The nulls. The only flat null in each paper is a uniform cube. For the odour data, the fitted model is a thin shell, and there hyperbolic distance rises strictly with angle, so a sphere or near-sphere in Euclidean space would give nearly the same rank order (NOTE-672: a Spearman correlation of about 0.91 in a simulation of the fitted shell). For CA1, uniform sampling in a hyperbolic ball is close to an exponential distribution of a scale coordinate in flat space, which is the paper’s own half-space picture (NOTE-668, NOTE-670).
- Replication. Each result is one study by one group.
What would answer it
From THEORY-191’s former promote_when: an independent analysis of natural odour co-occurrence data, from other odour sources or by another group, that finds the same Betti-curve match to a hyperbolic geometry AND rejects flat models that share the shell’s low-dimensional, near-spherical arrangement: points on or near a 2-sphere in Euclidean space, or a flat space with an exponentially distributed scale coordinate. A replication that again compares the hyperbolic shell only against uniform Euclidean cubes does not count, because on a thin shell that comparison cannot separate a hyperbolic metric from a sphere.
From THEORY-192’s former promote_when: an independent analysis, on CA1 recordings other than the CRCNS hc-3 and 48-m-track sessions, or by another group on the same data, that finds the same Betti-curve match to a 3D hyperbolic ball AND rejects Euclidean models with an exponentially distributed size coordinate (multiscale fields in a flat space). A replication that again compares hyperbolic against uniform Euclidean sampling alone does not count, because that comparison cannot separate a hyperbolic metric from an exponential distribution of field scales.
A positive answer bears on THEORY-618, the general hyperbolic-geometry hypothesis that extends both. QUESTION-025 notes the same limit for co-occurrence geometries.