Persistence or Turnover? A galaxy–galaxy lensing programme for the excess-acceleration fork in KiDS-1000. I. Pipeline, frame forensics, and instrument validation

Abstract

The opening paper of an observational programme aimed at deciding, with public lensing data, one of the dark sector's sharpest forks. Around an isolated galaxy the excess radial acceleration g_ex = g_obs − g_bar discriminates two pictures that agree where data has historically been plentiful and separate in the deep, low-acceleration tail: in the metric-reading picture the excess continues as a square root, g_ex = √(a₀ g_bar), at all radii — no scale, no edge — while in the standard halo picture the excess tracks a finite reservoir, saturating beyond the truncated halo's edge and falling away toward GM_tot/R², leaving only the two-halo term. Stacked weak lensing measures g_ex directly, and mock-catalogue closure shows the deep window is a persistence-versus-vanishing discrimination worth tens of standard deviations at modern survey power. Phase A, reported here on public KiDS-1000 data: a production ΔΣ pipeline (tomographic Σ_crit from the released n(z) with the foreground dead fraction included, boost and random-point corrections, 131-region jackknife covariance); release-verified survey parameters; a complete instrument-forensics account in which four null science runs were traced — via the frame-invariance of cosmic shear versus the frame-dependence of galaxy–galaxy lensing, and an eight-variant frame adjudication on a cluster-scale control resolving at 16.6σ/18.0σ — to a single parity convention (e₂ → −e₂) in the tangent frame; three failed isolation criteria, rejected and documented, including a general pathology of photometric-redshift isolation cuts; a validated instrument — the pre-registered 5σ detection bar, never adjusted, cleared at 14.6σ on a declared 50,000-lens subsample; and a first, deliberately modest structure test in which the square-root continuation fits the measured profile well (χ² = 15.3/9) and the halo alternative, fitted with a Phase-A two-halo surrogate, achieves statistical parity (Δχ² = +1.2, ΔAIC = −0.8) only by pinning at its mass-grid edge — a flagged, unresolved configuration. The registered acceptance protocol for the decision — eight points spanning ≥ 1.25 decades at ≤ 0.10 dex at 5σ, with a persistence statistic, fixed before the data and never adjusted — is restated and remains untouched. The fork is not decided here; the instrument that can decide it now exists and is validated.

Keywords

How to cite

Elliman, D. (2026). Persistence or Turnover? A galaxy–galaxy lensing programme for the excess-acceleration fork in KiDS-1000. I. Pipeline, frame forensics, and instrument validation. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21211019

@techreport{elliman2026r8lensingforkphasea,
  author      = {Elliman, David},
  title       = {Persistence or Turnover? A galaxy–galaxy lensing programme for the excess-acceleration fork in KiDS-1000. I. Pipeline, frame forensics, and instrument validation},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21211019},
  url         = {https://neusym.ai/papers/r8_lensing_fork_phase_a}
}