embedded3 item 11: moving bodies (end-of-step mask, fresh-cell refill, space-time cut cell: step-averaged apertures, GCL wall flux, Reynolds-transport momentum), the 3D fresh-cell falsifier (plate / circle / stadium, wall + control-volume routes) and the Lipschitz sweep; ghost wall reproduces the 2D falsifier to the digit; cut wall 5–14× smoother on the circle, gates not met (fresh cell's first step); wall.rs split (impose.rs)

Co-Authored-By: Claude Fable 5.1 <[email protected]>

crates/specialized/rtx-cfd/tests/embedded3_falsifier.rs

@@ -0,0 +1,566 @@
+//! embedded3 item 11a: the fresh-cell falsifier of the 2D track
+//! (`embedded_fresh_cell_falsifier.rs`, omni-cortex
+//! `docs/fresh_cell_gcl_campaign.md`) on the 3D solver, per unit span —
+//! the rigid Turek–Hron flag (0.35 × 0.02 m) extruded across a periodic
+//! slab, oscillating transversely in still fluid at the flag's tip speed
+//! (1 m/s peak, 80 mm amplitude) on h = 1/152 at dt = 3.24e-4. Per step:
+//! the load per unit span (the ghost wall's traction route over the
+//! plate's samples; the cut wall's operator route), a far-field pressure
+//! probe, the fluid's kinetic energy, the fresh-cell count.
+//!
+//! Registered gates (`docs/embedded3_campaign.md` item 11):
+//! - GhostBinary reproduces the 2D wall's impulse: energy per flipped
+//!   column within 30 % of the 2D 0.048 J/m per flipped cell, spike RMS
+//!   exponent in dt ≈ −1 (published −0.8 for the raw volume source);
+//! - CutCell: energy per fresh column ≥ 20× lower, max force spike < 5 %
+//!   of ½ρU²L, exponent ∈ [−0.3, 0.3].
+//!
+//! Default run: dt only, both schemes (minutes on the host);
+//! `RTX_E3_FALSIFIER_LADDER=1` runs dt, dt/2, dt/4 and fits the exponent
+//! (the gated variant is `#[ignore]`); `RTX_E3_FALSIFIER_NZ` sets the
+//! span in cells (default 4); `RTX_E3_FALSIFIER_CSV=<dir>` dumps records.
+
+use rtx_cfd::solvers::incompressible::ConvectionScheme;
+use rtx_cfd::solvers::incompressible::embedded3::{
+    Body, Boundaries, Field, Fluid, Grid, Parameters, Side, Solver, WallScheme,
+};
+use std::io::Write as _;
+
+const RHO: f64 = 1000.0;
+const MU: f64 = 1.0;
+const N: usize = 152;
+const DT_FSI2: f64 = 3.24e-4;
+const HX: f64 = 0.175;
+const HY: f64 = 0.01;
+const AMP: f64 = 0.08;
+const U_PEAK: f64 = 1.0;
+const CX: f64 = 0.5;
+const CY0: f64 = 0.5;
+/// The 2D wall's measured energy per flipped cell (J/m at U = 1, h = 1/152).
+const ENERGY_2D: f64 = 0.048;
+
+fn span_cells() -> usize {
+    std::env::var("RTX_E3_FALSIFIER_NZ")
+        .ok()
+        .and_then(|v| v.parse().ok())
+        .unwrap_or(4)
+}
+
+fn center_y(t: f64) -> f64 {
+    CY0 + AMP * (U_PEAK / AMP * t).sin()
+}
+
+fn center_v(t: f64) -> f64 {
+    U_PEAK * (U_PEAK / AMP * t).cos()
+}
+
+fn plate_sdf(x: f64, y: f64, yc: f64) -> f64 {
+    let qx = (x - CX).abs() - HX;
+    let qy = (y - yc).abs() - HY;
+    let outside = (qx.max(0.0).powi(2) + qy.max(0.0).powi(2)).sqrt();
+    outside + qx.max(qy).min(0.0)
+}
+
+const R_CIRCLE: f64 = 0.05;
+
+/// `RTX_E3_FALSIFIER_BODY=circle`: the 2D falsifier's smooth body (a
+/// cylinder of radius 0.05 across the span) instead of the plate.
+fn circle_body() -> bool {
+    std::env::var("RTX_E3_FALSIFIER_BODY").is_ok_and(|v| v == "circle")
+}
+
+/// `RTX_E3_FALSIFIER_BODY=stadium`: the plate with semicircular ends
+/// (radius `HY`): the same length and thickness, a smooth interface for
+/// the cut geometry's linear interpolant.
+fn stadium_body() -> bool {
+    std::env::var("RTX_E3_FALSIFIER_BODY").is_ok_and(|v| v == "stadium")
+}
+
+fn stadium_sdf(x: f64, y: f64, yc: f64) -> f64 {
+    let half = HX - HY;
+    let qx = (x - CX).abs().max(half) - half;
+    (qx * qx + (y - yc).powi(2)).sqrt() - HY
+}
+
+fn plate(moving: bool) -> Body {
+    let yc = move |t: f64| if moving { center_y(t) } else { CY0 };
+    let vc = move |t: f64| if moving { center_v(t) } else { 0.0 };
+    if circle_body() {
+        return Body::from_sdf(move |x, y, _z, t| {
+            ((x - CX).powi(2) + (y - yc(t)).powi(2)).sqrt() - R_CIRCLE
+        })
+        .with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0));
+    }
+    if stadium_body() {
+        return Body::from_sdf(move |x, y, _z, t| stadium_sdf(x, y, yc(t)))
+            .with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0));
+    }
+    Body::from_sdf(move |x, y, _z, t| plate_sdf(x, y, yc(t)))
+        .with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0))
+}
+
+/// The load scale `½ρU²L` of the body (its length across the motion).
+fn load_scale() -> f64 {
+    let l = if circle_body() {
+        2.0 * R_CIRCLE
+    } else {
+        2.0 * HX
+    };
+    0.5 * RHO * U_PEAK * U_PEAK * l
+}
+
+/// Surface samples of the plate at `t`: `(x, y, z, nx, ny, area)` over the
+/// four edges at spacing `ds` and `nz` z levels.
+fn samples(
+    t: f64,
+    moving: bool,
+    ds: f64,
+    nz: usize,
+    dz: f64,
+) -> Vec<(f64, f64, f64, f64, f64, f64)> {
+    let yc = if moving { center_y(t) } else { CY0 };
+    let mut out = Vec::new();
+    if circle_body() {
+        let n = ((2.0 * std::f64::consts::PI * R_CIRCLE / ds).ceil() as usize).max(8);
+        let dth = 2.0 * std::f64::consts::PI / n as f64;
+        for k in 0..n {
+            let th = (k as f64 + 0.5) * dth;
+            let (sn, cs) = th.sin_cos();
+            for kz in 0..nz {
+                out.push((
+                    CX + R_CIRCLE * cs,
+                    yc + R_CIRCLE * sn,
+                    (kz as f64 + 0.5) * dz,
+                    cs,
+                    sn,
+                    R_CIRCLE * dth * dz,
+                ));
+            }
+        }
+        return out;
+    }
+    if stadium_body() {
+        let half = HX - HY;
+        let n_flat = ((2.0 * half / ds).ceil() as usize).max(1);
+        for k in 0..n_flat {
+            let x = CX - half + (k as f64 + 0.5) / n_flat as f64 * 2.0 * half;
+            for kz in 0..nz {
+                let z = (kz as f64 + 0.5) * dz;
+                let a = 2.0 * half / n_flat as f64 * dz;
+                out.push((x, yc + HY, z, 0.0, 1.0, a));
+                out.push((x, yc - HY, z, 0.0, -1.0, a));
+            }
+        }
+        let n_arc = ((std::f64::consts::PI * HY / ds).ceil() as usize).max(4);
+        for (cx, sign) in [(CX + half, 1.0), (CX - half, -1.0)] {
+            for k in 0..n_arc {
+                let th = -std::f64::consts::FRAC_PI_2
+                    + (k as f64 + 0.5) / n_arc as f64 * std::f64::consts::PI;
+                let (sn, cs) = th.sin_cos();
+                let (nx, ny) = (sign * cs, sn);
+                for kz in 0..nz {
+                    out.push((
+                        cx + HY * nx,
+                        yc + HY * ny,
+                        (kz as f64 + 0.5) * dz,
+                        nx,
+                        ny,
+                        std::f64::consts::PI * HY / n_arc as f64 * dz,
+                    ));
+                }
+            }
+        }
+        return out;
+    }
+    let (x0, x1, y0, y1) = (CX - HX, CX + HX, yc - HY, yc + HY);
+    let mut edge = |ax: f64, ay: f64, bx: f64, by: f64, nx: f64, ny: f64| {
+        let len = ((bx - ax).powi(2) + (by - ay).powi(2)).sqrt();
+        let n = ((len / ds).ceil() as usize).max(1);
+        for k in 0..n {
+            let s = (k as f64 + 0.5) / n as f64;
+            for kz in 0..nz {
+                out.push((
+                    ax + s * (bx - ax),
+                    ay + s * (by - ay),
+                    (kz as f64 + 0.5) * dz,
+                    nx,
+                    ny,
+                    len / n as f64 * dz,
+                ));
+            }
+        }
+    };
+    edge(x0, y0, x1, y0, 0.0, -1.0);
+    edge(x1, y0, x1, y1, 1.0, 0.0);
+    edge(x1, y1, x0, y1, 0.0, 1.0);
+    edge(x0, y1, x0, y0, -1.0, 0.0);
+    out
+}
+
+struct Record {
+    t: f64,
+    /// Load per unit span (the scheme's wall route).
+    fy: f64,
+    /// Load per unit span by the control-volume route (a box of whole
+    /// cells around the body, reading no near-wall value).
+    fy_cv: f64,
+    fresh: usize,
+    skipped: usize,
+    p_far: f64,
+    /// Kinetic energy per unit span over the fluid cells.
+    ke: f64,
+}
+
+struct Run {
+    records: Vec<Record>,
+    /// The largest kinetic-energy change per step at a step with fresh
+    /// cells (after the impulsive start) over that step's flipped columns
+    /// (J/m) — the 2D falsifier's 2.604 J/m over 54 cells = 0.048.
+    energy_per_flip: f64,
+    seconds: f64,
+}
+
+fn run(scheme: WallScheme, moving: bool, dt: f64, t_end: f64) -> Run {
+    let nz = span_cells();
+    let h = 1.0 / N as f64;
+    let lz = nz as f64 * h;
+    let mut solver = Solver::new(
+        Fluid {
+            density: RHO,
+            viscosity: MU,
+            reference_velocity: 1.0,
+            reference_length: 2.0 * HY,
+        },
+        Parameters {
+            corrector_steps: 2,
+            tolerance: 1e-8,
+            convection_scheme: ConvectionScheme::Upwind,
+            wall_scheme: scheme,
+            boundaries: Boundaries {
+                z0: Side::Periodic,
+                z1: Side::Periodic,
+                ..Boundaries::default()
+            },
+            ..Parameters::default()
+        },
+    );
+    solver.set_boundary_velocity(|_, _, _, _| (0.0, 0.0, 0.0));
+    if moving {
+        solver.set_moving_body(plate(true));
+    } else {
+        solver.set_body(plate(false));
+    }
+    let g = Grid::cubic(N, N, nz, h);
+    let mut field = Field::new(g);
+    solver.initialize(&mut field);
+    let steps = (t_end / dt).round() as usize;
+    let mut records = Vec::with_capacity(steps);
+    // The 2D definition: the largest |ΔKE| step's energy over that
+    // step's flipped columns.
+    let mut largest_jump = 0.0_f64;
+    let mut energy_per_flip = 0.0_f64;
+    let mut ke_prev: Option<f64> = None;
+    let start = std::time::Instant::now();
+    let (jp, ip, kp) = (
+        (0.92 * N as f64) as usize,
+        (0.5 * N as f64) as usize,
+        nz / 2,
+    );
+    for step in 0..steps {
+        let result = solver.advance(&mut field, dt);
+        let t = (step + 1) as f64 * dt;
+        let mask = solver.mask().expect("mask");
+        let body = solver.body().expect("body");
+        let (mut fy, mut skipped) = (0.0, 0usize);
+        match scheme {
+            WallScheme::GhostBinary => {
+                for (x, y, z, nx, ny, area) in samples(t, moving, 0.5 * h, nz, h) {
+                    match mask.traction_at(body, &field, MU, t, [x, y, z], [nx, ny, 0.0]) {
+                        Some(tr) => fy += tr[1] * area,
+                        None => skipped += 1,
+                    }
+                }
+            }
+            WallScheme::CutCell => {
+                fy = mask.cut_wall_force(body, &field, MU, t).expect("cut wall")[1];
+            }
+        }
+        fy /= lz;
+        let margin = 8;
+        let fy_cv = mask.control_volume_force(
+            &field,
+            dt,
+            RHO,
+            MU,
+            None,
+            (margin, N - margin, margin, N - margin, 0, nz),
+        )[1] / lz;
+        let p_far = field.p[g.cell(kp, jp, ip)];
+        let mut ke = 0.0;
+        for k in 0..nz {
+            for j in 0..N {
+                for i in 0..N {
+                    let idx = g.cell(k, j, i);
+                    if mask.is_fluid_cell(idx) {
+                        let uc = 0.5 * (field.u[g.uface(k, j, i)] + field.u[g.uface(k, j, i + 1)]);
+                        let vc = 0.5 * (field.v[g.vface(k, j, i)] + field.v[g.vface(k, j + 1, i)]);
+                        let wc = 0.5 * (field.w[g.wface(k, j, i)] + field.w[g.wface(k + 1, j, i)]);
+                        ke += 0.5 * RHO * (uc * uc + vc * vc + wc * wc) * h * h * h * mask.vol(idx);
+                    }
+                }
+            }
+        }
+        ke /= lz;
+        if let Some(prev) = ke_prev {
+            if step > 30 && result.fresh_cells > 0 && (ke - prev).abs() > largest_jump {
+                largest_jump = (ke - prev).abs();
+                // The plate's event is its row (the 2D divided by the row's
+                // 54 cells); the circle's is the step's fresh columns.
+                let columns = if circle_body() {
+                    result.fresh_cells as f64 / nz as f64
+                } else {
+                    (2.0 * HX / h).round()
+                };
+                energy_per_flip = largest_jump / columns;
+            }
+        }
+        ke_prev = Some(ke);
+        records.push(Record {
+            t,
+            fy,
+            fy_cv,
+            fresh: result.fresh_cells,
+            skipped,
+            p_far,
+            ke,
+        });
+    }
+    Run {
+        records,
+        energy_per_flip,
+        seconds: start.elapsed().as_secs_f64(),
+    }
+}
+
+/// Spike series: the load minus its 21-step running median.
+fn spikes(f: &[f64]) -> Vec<f64> {
+    let w = 10usize;
+    (0..f.len())
+        .map(|k| {
+            let lo = k.saturating_sub(w);
+            let hi = (k + w + 1).min(f.len());
+            let mut win: Vec<f64> = f[lo..hi].to_vec();
+            win.sort_by(|a, b| a.partial_cmp(b).unwrap());
+            f[k] - win[win.len() / 2]
+        })
+        .collect()
+}
+
+struct Stats {
+    rms_force: f64,
+    rms_spike: f64,
+    max_spike: f64,
+    rms_spike_cv: f64,
+    max_spike_cv: f64,
+    rms_pfar_spike: f64,
+    max_pfar_spike: f64,
+    max_ke_jump: f64,
+    fresh_total: usize,
+    skipped_max: usize,
+}
+
+fn stats(records: &[Record], t_lo: f64, t_hi: f64) -> Stats {
+    let fy: Vec<f64> = records.iter().map(|r| r.fy).collect();
+    let sp = spikes(&fy);
+    let fcv: Vec<f64> = records.iter().map(|r| r.fy_cv).collect();
+    let spc = spikes(&fcv);
+    let pf: Vec<f64> = records.iter().map(|r| r.p_far).collect();
+    let spf = spikes(&pf);
+    let idx: Vec<usize> = (0..records.len())
+        .filter(|&k| records[k].t >= t_lo && records[k].t <= t_hi)
+        .collect();
+    let rms = |v: &dyn Fn(usize) -> f64| {
+        (idx.iter().map(|&k| v(k) * v(k)).sum::<f64>() / idx.len().max(1) as f64).sqrt()
+    };
+    Stats {
+        rms_force: rms(&|k| fy[k]),
+        rms_spike: rms(&|k| sp[k]),
+        max_spike: idx.iter().map(|&k| sp[k].abs()).fold(0.0, f64::max),
+        rms_spike_cv: rms(&|k| spc[k]),
+        max_spike_cv: idx.iter().map(|&k| spc[k].abs()).fold(0.0, f64::max),
+        rms_pfar_spike: rms(&|k| spf[k]),
+        max_pfar_spike: idx.iter().map(|&k| spf[k].abs()).fold(0.0, f64::max),
+        max_ke_jump: idx
+            .iter()
+            .filter(|&&k| k > 0)
+            .map(|&k| (records[k].ke - records[k - 1].ke).abs())
+            .fold(0.0, f64::max),
+        fresh_total: idx.iter().map(|&k| records[k].fresh).sum(),
+        skipped_max: idx.iter().map(|&k| records[k].skipped).max().unwrap_or(0),
+    }
+}
+
+fn dump(dir: &str, name: &str, records: &[Record]) {
+    let path = std::path::Path::new(dir).join(format!("{name}.csv"));
+    let mut f = std::fs::File::create(path).expect("csv");
+    writeln!(f, "t,fy,fy_cv,fresh,skipped,p_far,ke").unwrap();
+    for r in records {
+        writeln!(
+            f,
+            "{:.6},{:.6e},{:.6e},{},{},{:.6e},{:.6e}",
+            r.t, r.fy, r.fy_cv, r.fresh, r.skipped, r.p_far, r.ke
+        )
+        .unwrap();
+    }
+}
+
+struct Verdict {
+    energy_per_flip: f64,
+    max_spike: f64,
+    exponent: Option<f64>,
+}
+
+fn falsify(scheme: WallScheme, ladder: bool) -> Verdict {
+    let csv_dir = std::env::var("RTX_E3_FALSIFIER_CSV").ok();
+    let period = 2.0 * std::f64::consts::PI * AMP / U_PEAK;
+    let t_end = 0.3 * period;
+    let (t_lo, t_hi) = (0.02 * period, 0.28 * period);
+    let rest = run(scheme, false, DT_FSI2, t_end);
+    let s0 = stats(&rest.records, t_lo, t_hi);
+    println!(
+        "  {scheme:?} plate AT REST, dt {DT_FSI2:.2e} ({:.0} s): rms force {:.3e}, rms spike {:.3e}, max spike {:.3e}, fresh {}, skipped max {}",
+        rest.seconds, s0.rms_force, s0.rms_spike, s0.max_spike, s0.fresh_total, s0.skipped_max
+    );
+    if let Some(d) = &csv_dir {
+        dump(d, &format!("{scheme:?}_rest"), &rest.records);
+    }
+    let dts: Vec<f64> = if ladder {
+        vec![DT_FSI2, DT_FSI2 / 2.0, DT_FSI2 / 4.0]
+    } else {
+        vec![DT_FSI2]
+    };
+    let mut points = Vec::new();
+    let mut energy = 0.0_f64;
+    let mut max_spike = 0.0_f64;
+    for &dt in &dts {
+        let r = run(scheme, true, dt, t_end);
+        let s = stats(&r.records, t_lo, t_hi);
+        println!(
+            "  {scheme:?} plate MOVING, dt {dt:.3e} ({} steps, {:.0} s): rms force {:.3e}, rms spike {:.3e} ({:.1}x rest), max spike {:.3e} N/m ({:.2e} of ½ρU²L), fresh cells {} ({:.2}/step), skipped max {}",
+            r.records.len(),
+            r.seconds,
+            s.rms_force,
+            s.rms_spike,
+            s.rms_spike / s0.rms_spike.max(1e-300),
+            s.max_spike,
+            s.max_spike / load_scale(),
+            s.fresh_total,
+            s.fresh_total as f64 / r.records.len() as f64,
+            s.skipped_max
+        );
+        println!(
+            "    control-volume route: rms spike {:.3e}, max spike {:.3e} N/m ({:.2e} of ½ρU²L)",
+            s.rms_spike_cv,
+            s.max_spike_cv,
+            s.max_spike_cv / load_scale()
+        );
+        println!(
+            "    far probe p(0.5, 0.92): rms spike {:.3e}, max spike {:.3e}; max |ΔKE| per step {:.3e} J/m; energy per flipped column {:.3e} J/m ({:.2} of the 2D wall's {ENERGY_2D})",
+            s.rms_pfar_spike,
+            s.max_pfar_spike,
+            s.max_ke_jump,
+            r.energy_per_flip,
+            r.energy_per_flip / ENERGY_2D
+        );
+        if let Some(d) = &csv_dir {
+            dump(d, &format!("{scheme:?}_moving_dt{dt:.3e}"), &r.records);
+        }
+        assert!(s.rms_force.is_finite() && s.rms_spike.is_finite());
+        if dt == DT_FSI2 {
+            energy = r.energy_per_flip;
+            max_spike = s.max_spike;
+        }
+        points.push((dt, s.rms_spike));
+    }
+    let exponent = (points.len() >= 2).then(|| {
+        let xs: Vec<f64> = points.iter().map(|p| p.0.ln()).collect();
+        let ys: Vec<f64> = points.iter().map(|p| p.1.ln()).collect();
+        let mx = xs.iter().sum::<f64>() / xs.len() as f64;
+        let my = ys.iter().sum::<f64>() / ys.len() as f64;
+        let num: f64 = xs.iter().zip(&ys).map(|(x, y)| (x - mx) * (y - my)).sum();
+        let den: f64 = xs.iter().map(|x| (x - mx).powi(2)).sum();
+        let e = num / den;
+        println!(
+            "  {scheme:?}: spike RMS ~ (dt)^{e:.2} across {} time steps",
+            points.len()
+        );
+        e
+    });
+    Verdict {
+        energy_per_flip: energy,
+        max_spike,
+        exponent,
+    }
+}
+
+#[test]
+fn oscillating_plate_both_walls() {
+    let ladder = std::env::var("RTX_E3_FALSIFIER_LADDER").is_ok();
+    println!(
+        "  body: {}",
+        if circle_body() {
+            "circle R 0.05"
+        } else if stadium_body() {
+            "stadium 0.35 x 0.02 (semicircular ends)"
+        } else {
+            "plate 0.35 x 0.02"
+        }
+    );
+    let ghost = falsify(WallScheme::GhostBinary, ladder);
+    let cut = falsify(WallScheme::CutCell, ladder);
+    println!(
+        "  energy per flipped column: ghost {:.3e}, cut {:.3e} (ratio {:.1}x); max spike: ghost {:.3e}, cut {:.3e} N/m",
+        ghost.energy_per_flip,
+        cut.energy_per_flip,
+        ghost.energy_per_flip / cut.energy_per_flip.max(1e-300),
+        ghost.max_spike,
+        cut.max_spike
+    );
+    assert!(
+        ghost.energy_per_flip > 0.0,
+        "the binary wall must flip cells"
+    );
+}
+
+/// The registered gates on the dt ladder.
+#[test]
+#[ignore = "item 11's gated ladder (dt, dt/2, dt/4 on both walls; tens of minutes on the host)"]
+fn oscillating_plate_gates() {
+    let ghost = falsify(WallScheme::GhostBinary, true);
+    let cut = falsify(WallScheme::CutCell, true);
+    let ratio = ghost.energy_per_flip / cut.energy_per_flip.max(1e-300);
+    println!(
+        "  GATES: ghost energy per flipped column {:.3e} ({:.2} of 2D), exponent {:.2}; cut energy {:.3e} ({:.1}x lower), max spike {:.3e} N/m ({:.2e} of ½ρU²L), exponent {:.2}",
+        ghost.energy_per_flip,
+        ghost.energy_per_flip / ENERGY_2D,
+        ghost.exponent.unwrap(),
+        cut.energy_per_flip,
+        ratio,
+        cut.max_spike,
+        cut.max_spike / load_scale(),
+        cut.exponent.unwrap()
+    );
+    let g2d = ghost.energy_per_flip / ENERGY_2D;
+    assert!(
+        (0.7..=1.3).contains(&g2d),
+        "ghost energy per flip {g2d:.2} of 2D"
+    );
+    assert!(ratio >= 20.0, "cut energy only {ratio:.1}x lower");
+    assert!(
+        cut.max_spike < 0.05 * load_scale(),
+        "cut max spike {:.3e}",
+        cut.max_spike
+    );
+    let e = cut.exponent.unwrap();
+    assert!((-0.3..=0.3).contains(&e), "cut exponent {e:.2}");
+}