Dark Matter vs. MOND vs. Category τ

Anchor paper: Gallardo et al., 2026 pairwise-kSZ constraint on the large-scale gravitational force law.

Review status: Program pre-registration; external review not yet completed.

Abstract

The note places the Panta Rhei force-law stance on the Gallardo et al. 2026 pairwise-kSZ constraint: Category τ rejects both a new dark-matter particle and a fundamental MOND transition at the tested scale, while committing to a Newtonian inverse-square force-law exponent in the cluster-pair regime. The note defines falsification surfaces and reporting targets rather than claiming external acceptance.

Pairwise-kSZ force-law constraint

The anchor result estimates a generalized gravitational force-law exponent on cluster-pair separations and reports tension with MOND-like behavior.

Relation to this note: Used as an observational target for a categorical pre-registration outside the dark-matter-versus-MOND two-way framing.

Core Claim

At the cluster-pair scales probed by the anchor result, the categorical framework predicts the inverse-square force-law exponent while still rejecting a particle dark-matter sector.

What This Note Does Not Claim

• It does not claim that the full pairwise-kSZ amplitude has already been derived in closed form.
• It does not claim that standard dark matter has been empirically ruled out.
• It does not claim that MOND-like galaxy-scale behavior is globally absent.

Falsification and Challenge Surface

• A future high-precision pairwise-kSZ force-law exponent inconsistent with the inverse-square value at the stated scale.
• Failure to produce the promised amplitude-level categorical account.
• Breakdown of the framework's sector-exhaustion or capacity-gradient claims.

Reading Note

The PDF contains the full argument. This web page records the public metadata, claim boundary, verification posture, and related site surfaces for the citable Research Note artifact.