Persistence or Turnover? A galaxy–galaxy lensing programme for the excess-acceleration fork in KiDS-1000. II. Certified spectroscopic isolation, a four-fold reproduced deep-tail slope, and a frozen decision protocol for DESI DR2

Abstract

Paper I validated the lensing instrument; this second paper supplies the missing ingredient — certifiable isolation — and takes the campaign to the edge of decision. A six-entry isolation-criterion ledger documents four instructive failures: photometric-redshift isolation fails three ways (including a general pathology in which near-empty photo-z neighbourhoods preferentially select catalogue label errors — objects that do not lens because they are not what their labels claim), and the classic 0.1 M* spectroscopic criterion is shown by an in-data completeness audit to be uncertifiable at joint GAMA×KiDS-Bright depth. Two certifiable criteria survive — GAMA G3C group-catalogue non-membership (mock-calibrated) and a per-lens strictest-certifiable-threshold "peer-or-better" cut — and their registered union across GAMA DR4 and DESI DR1 BGS spectroscopy (1,051 deg² of the KiDS-North strip) yields 39,015 certified-isolated lenses, with the environment purge verified in the data (outer stack amplitude 2.07 → 0.45–1.11 M⊙ pc⁻²; isolated-RAR offset +0.48 → +0.23 dex). Against this sample the pre-registered acceptance bar — eight points spanning ≥ 1.25 decades at ≤ 0.10 dex — misses by one point at five thousandths of a dex (seven qualify; the eighth carries 0.105), precisely as the campaign's pre-data power forecast (N_req ≈ 4.5×10⁴), now confirmed by four independent samples, said it would. The evidence meanwhile cuts cleanly both ways: a pre-registered supplementary likelihood leg measures the deep-tail slope at 0.660 ± 0.071 — excluding the halo point-mass turnover at 4.8σ and sitting marginally steep of the metric 1/2 at +2.3σ, the fourth independent reproduction of a ≃ 0.6 slope — while at union precision the metric branch's zero-freedom inner profile is disfavoured in full-profile goodness-of-fit (Δχ² = −38.6 in the halo branch's favour). The decision protocol is frozen verbatim, its mechanical execution on DESI DR2 pre-announced as a catalogue-swap in a committed pipeline, and the series' verdict section left deliberately vacant. All three possible outcomes are argued to be individually interesting — the third, a persistent slope near 0.6 that is neither 1/2 nor 1, perhaps most of all.

Keywords

How to cite

Elliman, D. (2026). Persistence or Turnover? A galaxy–galaxy lensing programme for the excess-acceleration fork in KiDS-1000. II. Certified spectroscopic isolation, a four-fold reproduced deep-tail slope, and a frozen decision protocol for DESI DR2. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21215879

@techreport{elliman2026r8lensingforkpaper2,
  author      = {Elliman, David},
  title       = {Persistence or Turnover? A galaxy–galaxy lensing programme for the excess-acceleration fork in KiDS-1000. II. Certified spectroscopic isolation, a four-fold reproduced deep-tail slope, and a frozen decision protocol for DESI DR2},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21215879},
  url         = {https://neusym.ai/papers/r8_lensing_fork_paper2}
}