operatorO_R — Gaussian coarse-graining
carrier candidatesaxis · frame · topology · skeleton
scalesR = [5,10,20,40,80,160] Mpc
grid96³
thresholdtop 10% density voxels
connectivity26-neighbor
correctionsselection-fn + ZoA
controlsshuffle · survey_radial · field_shuffle · poisson
INPUT DATA
N galaxies—
volume (Mpc³)—
dataset—
PARAMETERS
GRID RESOLUTION
THRESHOLD PERCENTILE
SCALE LADDER (MPC)
51020
4080160
R = 20 Mpc
STRUCTURAL VERDICT
AWAITING
COMPUTATION
COLLAPSE
CTRL
GEO
BOUNDARY
DEEP
LAYER 1 — GEOMETRY
LAYER 2 — STABILITY
axis_total_path—
axis_max_step—
frame_total_path—
J_max (LCF)—
first_unstable_R—
control_beat—
FALSIFIER STATUS → STRUCTURE COLLAPSE if any fails
J_max ≤ J_crit (0.30)
S_topo ≥ T_crit (0.30)
axis_max ≤ A_crit (30°)
ctrl: S_topo · J_max · S_axis · LCF_std (≥3/4 pooled)
LARGEST COMPONENT FRACTION