Referee review of the four Lab programs — October 2026

Referee review of the four Lab programs — October 2026

Question. Read as a journal referee would, do the four programs (39 posts and appendices plus the magnetic-flux-lifts article) contain typos, logical or mathematical errors, numbers that disagree with their own artifacts, or figures below standard?

Method. One referee pass per program (Forbidden Directions split into theory and real-data halves), each reading every file in full and checking numbers against research/<program>/ docs and artifacts; errors were fixed only when the correct statement could be verified (derivation, artifact, or primary source). A separate figure audit viewed every referenced image. Verdict for all four programs: minor revision — no headline result changed.

Errors corrected

Program Correction Verified against
Geometry of Seeing Non-inflectional elastica curvature rescaled: $(2/\sqrt m)\,\mathrm{dn}(s/\sqrt m \mid m)$, not $2\,\mathrm{dn}(s\mid m)$ pendulum ODE; Appendix A3
  Mirror coincidence condition $\theta_A\in{0,\pi}$ (was $\equiv 0 \bmod 2\pi$) symmetry $(x,y,\theta)\to(x,-y,-\theta)$
  Conjugate/cut-time theorems attributed to Sachkov 2010 (were “2011, Thm 2.1”) arXiv:0903.0727
  A5 no longer boxes $t_\text{cut}=t_\text{Maxwell}$ as general; cut/conjugate definitions fixed Part 4
  A4: AGM convergence caption, “quartic in sn”; A5 sample-code error bound ($2.4\times10^{-2}$, not $10^{-6}$) run of the code
  Agrachev–Sachkov chapter pointers (PMP Ch. 12, Lie groups Ch. 18, Jacobi equation Ch. 21) book contents
Cosmic Web Planck bridge significance 2.2σ (was 2.4σ in B3/B5) e3e_results.json
  Early flawed win +0.07; oracle gap closed “85–90% (86% on matched seeds)” 50-seed report; E5 artifacts
  “Hessian wins 50/50 seeds” false in one cell (lift wins 3/50) e0_results_straight.json
  Palatini action coefficient $1/(32\pi G)$ (was $1/(16\pi G)$) $\epsilon_{abcd}e^a e^b R^{cd}=2R\,\mathrm{vol}$
  Caustic taxonomy: $A_3$ walls, $A_4/D_4$ filaments, $A_5/D_5$ nodes Feldbrugge et al. 2018
  Tidal-ellipsoid labels (two positive in-plane eigenvalues = filament) Appendix B2, src/fields.py
Caustics to Groups Two-trailer car is Goursat (2,3,4,5), not Cartan (2,3,5) src/liegroup.py
  SE(2) invariants $\kappa=\chi>0$ (was $\kappa<0$); G₂ is the smallest exceptional group structure constants
  SE(3) is six-dimensional; bracket figure now a true four-move commutator code; rendered
  Measured slopes, “perfect diagonal” (Cartan 24/25), abnormal-existence claim scoped e0_results.json, E1
Forbidden Directions D3: a rank-2 fold keeps $k=1$, $Q=6$ (was $k=2$ “at the fold”) article Cor. 5.1
  Tolerances: closed form $4\times10^{-9}$ (was $10^{-10}$); Conjecture A $\lesssim10^{-7}$ (was $10^{-8}$) p5_series.json
  Growth vector is a local confirmation, not an independent detector run_p2_nulls.py
  Fan-plane types: radial = node, spiral = focus (was “X / O”) null topology
  Jupiter longitudes are east System III; sphere-degree values re-ordered j2b_sensitivity.json
  T96 audit covers the 70 core-box nulls, not all 149; dates, units, Dungey estimate S4/S5 docs

Also: 2 KaTeX parse errors, undefined labels (G1, R3, F2, O6, Conjecture A) defined at first use, and ~40 spelling/grammar/notation fixes.

Figures

22 figures regenerated from their artifacts (presentation only): in-figure titles and prose blocks removed, axes labelled with units and scale, colourbars added, legends moved off the data, an eight-panel strip re-laid as 2×4, and a real plotting bug fixed (a stray chord across the Jupiter spine). Captions and alt text now carry everything removed from the images.

Open items for the author (not changed — unverifiable or author’s call)

  1. Caustics artifacts on disk are reduced runs (e1: n_eval = 10; e0: 6 trials) while posts quote the full runs (25 seeds, K = 30). Re-run or re-point.
  2. Caustics: “it is a theorem” that local caustics are group-blind — ADE universality covers generic Lagrangian maps; no Engel/Cartan computation shown.
  3. Cosmic Web Part 1 “Deviations” list omits the dataset swaps (Quijote/TNG → in-house PM + CAMELS; SDSS DR17 → BOSS DR12 CMASS).
  4. Cosmic Web read-only docs (SYNTHESIS, MODEL-CARD, PAPER-DRAFT) still say 89%.
  5. Cosmic Web Part 2 per-bin figure mixes seed sets (5-seed ZA/oracle vs seeds 4–6).
  6. Grochowski reference (Part 3): probably Bull. Polish Acad. Sci. Math. 50 (2002).
  7. Forbidden Directions: no physical scale (Mm/px) for null heights; J∥ has no units; “peak 4777 G” and the T96 audit counts are in no artifact; j2_census.json (33/40) and j2b_sensitivity.json (32/40) disagree slightly.
  8. Forbidden Directions Part 4 title calls the analytic ABC-like field “a real dynamo field”.
  9. Geometry of Seeing Part 4 title “The Open Problem: Exact Cut Time on SE(2)” contradicts its body (SE(2) is solved; the open problem is beyond it).
  10. Geometry of Seeing: “Sachkov 2011, eqs. 24–28” and the reflection-group generators not checked against the journal versions; schematic plane panels have no axis labels.

Glossary