Saturation dynamics · random 3-SAT at the threshold

Two Attractors

Bounded-width resolution doesn't degrade gradually, it flips. The closure ends up either an avalanche of twenty thousand clauses or starves at five hundred — with almost nothing in between. These four panels show why: it is a bistable system, and the observed two-humped distribution is its basins of attraction.

Addendum, September 3, 2026. SAT Without AND and OR adds two things to this report from the block formulation. First, the same seed — clause pairs sharing two places — is readable before any saturation runs, in O(m²), and it separates igniting from starving instances with AUC 0.91. Second, widening the layer does not help at all: the ignition density is identical for width 3 and width 4 and gets worse from width 5, because every possible merge lands on level 4 anyway. The state-dependent branching factor R used here remains the sharper formulation — a round-wise λ separates worse.

Saturation runs in rounds: the clauses of round t generate those of round t+1. A resolvent of width ≤ 3 arises only when two clauses share a literal besides the pivot literal — the fuller the closure, the more partners each new clause finds. The reproduction number R is therefore not a constant, but depends on what has already accumulated. That makes the system autocatalytic.

Panel 1The feedback loop

R gegen den angesammelten Abschluss, 5 842 Runden aus 400 unerfüllbaren instances (n = 45…80, α = 4.27, width 3). The curve rises from 0.38, crosses 1 at |A| ≈ 670, reaches 1.38 and falls back below it at |A| ≈ 10,500, because space runs out. The flow line below reads this as a one-dimensional system: filled dot = stable, open = unstable. Two attractors, one separatrix. Split by outcome (dashed), it becomes clear that it is one dynamic and not two kinds of instances: the starving ones stay below 1 in every range and never cross.

Panel 2The trajectories

Forty trajectories at n = 53, the half-height point. All start identically and decay indistinguishably for the first eight rounds. Then they split: the blue ones die, the brass-colored ones turn around. One of them falls to as low as two new clauses per round and then recovers to the hundreds — that is a trajectory that grazes the separatrix and lands on the right side.

Panel 3The crossing

The heart of the matter, and it is not in Panel 1: the required supply grows, the own supply does not. For a trajectory to sustain itself, it must have accumulated |A|* clauses — and this threshold grows linearly, |A|*(n) = 23.3·n − 649 (r = 0.9510, measured at n = 45…65, extrapolated above that). What an instance can muster on its own strength, by contrast, stays unchanged at around 500 clauses, across n = 40 to 90. Where the two cross, the system flips: at n = 49.2. That is the third independent measurement pointing to the same spot — after the ignition share (52.9) and the zero-crossing of R at |A| = 500 (49.6).

That explains why n tips the balance. What remains is whether the ignited state disappears at all — and the answer to that was not the expected one.

Panel 4The bifurcation diagram

Control parameter is n, 60 instances each. One would expect the ignited state to vanish at n ≈ 53. It does not: the maximum of R stays above 1 up to n ≈ 87, the system stays bistable. What drops below 1 at n ≈ 50 is R at the start of the trajectory, where |A| is still at 500. After that the front decays faster than it accumulates supply, and it never reaches the separatrix. In the shaded band the attractor thus still exists — it is just that no path leads there anymore.

Panel 5The consequence

The share of instances that ignite — the order parameter. Points measured, curves fitted logistically. The zero-crossing from Panel 3 (n = 49.6) matches the half-height point measured independently here, n₅₀(3) = 52.9, to within three variables, from two completely different measurements. And the width-4 transition is sharper, not wider: 12.3 variables against 18.4. At width 3 it first takes an ignition spark at all, whose expected count is 20.5/n — the spread of this Poisson count blurs the transition. At width 4 ignition always happens, and what is left is the pure threshold.

Quantity	Width 3	Width 4
Half-height point n₅₀	52.9	108.2
Transition 90 % → 10 %	18.4	12.3
Closure at ignition	≈ 20,000	0.6–4.0 M
Closure at starvation	≈ 500	10,000–33,000

From the two half-height points follows the inverse function of resolution width: w*(n) ≈ 3 + (n − 53)/55 ≈ 0.018·n. Ben-Sasson and Wigderson proved that w* must grow linearly in n; in their result the constant sits inside the Ω-sign. Here it is measured.

And from this falls a sharper version of the old finding. "The space does not contain the proof" is not quite right — it contains it up to n ≈ 87. At n = 80 an instance is short by about 700 clauses to sustain itself: 1,215 needed against 530 of its own. That is a linear shortfall. What is notable about this is that a completely different measurement in this project arrived at the same shape — 0.8 binary clauses per variable make the hardness collapse. Two routes, different objects, both times a linear top-up suffices. The question thus shifts from "does the proof exist?" to "is there a cheap way to generate linearly many valid clauses of width ≤ 3?" — which is narrower and measurable.

View code & data — R as a function of the accumulated closure

solver/src/bin/rueckkopplung.rs

//! # `rueckkopplung` — R as a function of the accumulated closure
//!
//! The front sequences (`bahnen.rs`) show that saturation is not a simple
//! branching process with fixed R. Both outcomes decay identically at
//! first; then one dies and the other TURNS AROUND — one trajectory falls
//! to as low as two clauses per round and then recovers to the hundreds.
//!
//! The explanation is a feedback loop. A resolvent of width <= 3
//! arises only when two clauses share a literal besides the pivot
//! literal. The more clauses lie in the closure, the more such partners
//! there are for each new clause — hence
//!
//!     R = R(|A|),  increasing in |A|.
//!
//! That makes the system autocatalytic, and the dynamics have two
//! basins of attraction: if the front dies before enough has accumulated,
//! the closure starves; if it survives to |A| > |A|*, where R = 1, it ignites.
//! |A|* is the **separatrix**, and crossing it is the bifurcation.
//!
//! What is measured is exactly that: across all instances and all rounds,
//! the pair (accumulated |A|, ratio of the next front to the current one).
use ordnungssolver::cdcl;
use ordnungssolver::erzeuger::{self, Zufall};
use ordnungssolver::formel::Urteil;
use ordnungssolver::saettigung::Saettiger;

fn main() {
    let a: Vec<String> = std::env::args().collect();
    let je: usize = a.get(1).and_then(|s| s.parse().ok()).unwrap_or(60);
    let ns: Vec<usize> = a.get(2).map(|s| s.split(',').map(|x| x.parse().unwrap()).collect())
        .unwrap_or_else(|| vec![45, 50, 53, 56, 60, 65]);

    // Pairs (accumulated |A| before the round, R of this round), split by
    // outcome — so it becomes visible whether the curve is the same for both.
    let mut paare: Vec<(f64, f64, bool)> = Vec::new();
    for &n in &ns {
        let mut saat = 7_000_000u64 + n as u64 * 1000;
        let mut gef = 0;
        while gef < je {
            let mut r = Zufall::neu(saat);
            saat += 1;
            let f = erzeuger::dichte3sat(n, 4.27, &mut r);
            if cdcl::stufe3(&f, 5_000_000).0 != Urteil::Unerfuellbar {
                continue;
            }
            gef += 1;
            let mut s = Saettiger::neu(f.n, 3);
            let ab = s.saettige(&f, 3_000_000);
            let ff = &ab.frontgroessen;
            let mut kum = 0usize;
            for t in 0..ff.len().saturating_sub(1) {
                kum += ff[t];
                if ff[t] >= 3 {
                    paare.push((kum as f64, ff[t + 1] as f64 / ff[t] as f64, ab.widerlegt));
                }
            }
        }
    }

    println!("================================================================================");
    println!("R AS A FUNCTION OF THE ACCUMULATED CLOSURE");
    println!("================================================================================");
    println!("{} rounds from {} instances (n = {:?}, alpha = 4.27, width 3)",
             paare.len(), je * ns.len(), ns);
    println!();
    println!("If the feedback loop holds, R grows with |A| and crosses 1.");
    println!("And the curve must be the same for BOTH outcomes — otherwise it");
    println!("would not be one shared dynamic but two different kinds of instance.");
    println!();
    println!("{:>14} {:>8} {:>10} {:>10} {:>10} {:>10}",
             "|A| range", "rounds", "R all", "R starve", "R avalanche", "share>1");
    let mut kante = 150.0f64;
    while kante < 60000.0 {
        let hi = kante * 1.6;
        let g: Vec<&(f64, f64, bool)> = paare.iter().filter(|p| p.0 >= kante && p.0 < hi).collect();
        if g.len() >= 12 {
            let m = |v: Vec<f64>| if v.is_empty() { f64::NAN } else { v.iter().sum::<f64>() / v.len() as f64 };
            let alle = m(g.iter().map(|p| p.1).collect());
            let hu = m(g.iter().filter(|p| !p.2).map(|p| p.1).collect());
            let la = m(g.iter().filter(|p| p.2).map(|p| p.1).collect());
            let ueber = g.iter().filter(|p| p.1 > 1.0).count() as f64 / g.len() as f64;
            println!("{:>6.0}..{:<7.0} {:>8} {:>10.3} {:>10.3} {:>10.3} {:>9.0}%",
                     kante, hi, g.len(), alle, hu, la, 100.0 * ueber);
        }
        kante = hi;
    }

    // --- The bifurcation diagram: how n shifts the curve --------------------
    println!();
    println!("================================================================================");
    println!("THE BIFURCATION DIAGRAM — how n lowers the curve");
    println!("================================================================================");
    println!("The same measurement separately for each n. The control parameter is n,");
    println!("the order parameter is the MAXIMUM of R over |A|. If it drops below 1,");
    println!("no trajectory can ignite anymore — that is the bifurcation point.");
    println!();
    println!("{:>5} {:>10} {:>10} {:>10} {:>12} {:>10}",
             "n", "R at 500", "R at 1500", "R at 5000", "R maximum", "p3");
    for &n in &ns {
        let mut saat = 8_000_000u64 + n as u64 * 1000;
        let mut gef = 0;
        let mut pn: Vec<(f64, f64)> = Vec::new();
        let mut poly = 0usize;
        while gef < je {
            let mut r = Zufall::neu(saat);
            saat += 1;
            let f = erzeuger::dichte3sat(n, 4.27, &mut r);
            if cdcl::stufe3(&f, 5_000_000).0 != Urteil::Unerfuellbar {
                continue;
            }
            gef += 1;
            let mut s = Saettiger::neu(f.n, 3);
            let ab = s.saettige(&f, 3_000_000);
            if ab.widerlegt { poly += 1; }
            let ff = &ab.frontgroessen;
            let mut kum = 0usize;
            for t in 0..ff.len().saturating_sub(1) {
                kum += ff[t];
                if ff[t] >= 3 {
                    pn.push((kum as f64, ff[t + 1] as f64 / ff[t] as f64));
                }
            }
        }
        let bei = |z: f64| {
            let g: Vec<f64> = pn.iter().filter(|p| p.0 >= z / 1.6 && p.0 < z * 1.6).map(|p| p.1).collect();
            if g.is_empty() { f64::NAN } else { g.iter().sum::<f64>() / g.len() as f64 }
        };
        // Maximum over logarithmic bins with enough occupancy
        let mut rmax = f64::NAN;
        let mut k = 150.0f64;
        while k < 40000.0 {
            let hi = k * 1.6;
            let g: Vec<f64> = pn.iter().filter(|p| p.0 >= k && p.0 < hi).map(|p| p.1).collect();
            if g.len() >= 10 {
                let m = g.iter().sum::<f64>() / g.len() as f64;
                if !(rmax > m) { rmax = m; }
            }
            k = hi;
        }
        println!("{:>5} {:>10.3} {:>10.3} {:>10.3} {:>12.3} {:>9.0}%",
                 n, bei(500.0), bei(1500.0), bei(5000.0), rmax,
                 100.0 * poly as f64 / gef as f64);
    }

    println!();
    println!("Reading. If R rises with |A| and crosses 1, then |A|* at the crossing is the");
    println!("separatrix: below it the process dies, above it it ignites. The");
    println!("starved runs must then all end BELOW |A|*, and the avalanches");
    println!("come out above it.");
}

daten/rueckkopplung.csv, grouped by outcome

Outcome	Rows	R min	R median	R max
hunger	2428	0.0000	0.5746	6.0000
lawine	3414	0.0213	1.1424	7.3333

5842 rows total, n ∈ {45,50,53,56,60,65} — one pair per round (accumulated |A|, R = ratio of next to current front), grouped by outcome.

View raw data — daten/rueckkopplung.csv

daten/rueckkopplung.csv

n,kumuliert,R,ausgang
45,192,0.41146,lawine
45,271,1.05063,lawine
45,354,0.97590,lawine
45,435,1.17284,lawine
45,530,0.77895,lawine
45,604,1.25676,lawine
45,697,1.72043,lawine
45,857,1.16250,lawine
45,1043,1.59677,lawine
45,1340,1.94276,lawine
45,1917,1.92201,lawine
45,3026,0.97746,lawine
45,4110,1.48708,lawine
45,5722,1.51923,lawine
45,8171,1.20621,lawine
45,11125,1.10596,lawine
45,14392,0.51515,lawine
45,16075,0.05407,lawine
45,192,0.44792,lawine
45,278,0.93023,lawine
45,358,1.31250,lawine
45,463,0.88571,lawine
45,556,0.75269,lawine
45,626,1.08571,lawine
45,702,0.64474,lawine
45,751,1.40816,lawine
45,820,1.36232,lawine
45,914,1.53191,lawine
45,1058,1.11111,lawine
45,1218,1.18750,lawine
45,1408,1.16842,lawine
45,1630,1.58559,lawine
45,1982,1.22443,lawine
45,2413,1.35963,lawine
45,2999,1.55119,lawine
45,3908,1.28933,lawine
45,5080,1.27560,lawine
45,6575,1.15050,lawine
45,8295,1.25116,lawine
45,10447,0.78717,lawine
45,12141,0.11098,lawine
45,192,0.40625,lawine
45,270,0.85897,lawine
45,337,1.55224,lawine
45,441,1.08654,lawine
45,554,1.22124,lawine
45,692,0.96377,lawine
45,825,1.06767,lawine
45,967,1.09859,lawine
45,1123,1.12821,lawine
45,1299,0.82386,lawine
45,1444,1.67586,lawine
45,1687,0.83951,lawine
45,1891,1.62255,lawine
45,2222,1.13897,lawine
45,2599,1.79310,lawine
45,3275,1.40237,lawine
45,4223,1.33861,lawine
45,5492,1.32467,lawine
45,7173,1.29804,lawine
45,9355,0.94867,lawine
45,11425,0.38744,lawine
45,12227,0.13342,lawine
45,192,0.31771,lawine
45,253,0.88525,lawine
45,307,1.27778,lawine
45,376,1.37681,lawine
45,471,0.73684,lawine
45,541,1.71429,lawine
45,661,1.59167,lawine
45,852,1.92670,lawine
45,1220,1.40489,lawine
45,1737,1.59574,lawine
45,2562,1.89455,lawine
45,4125,0.88740,lawine
45,5512,1.41456,lawine
45,7474,1.22630,lawine
45,9880,0.68828,lawine
45,11536,0.74034,lawine
45,12762,0.64763,lawine
45,192,0.33333,lawine
45,256,1.01562,lawine
45,321,1.23077,lawine
45,401,1.41250,lawine
45,514,1.23009,lawine
45,653,1.71223,lawine
45,891,1.49580,lawine
45,1247,1.28371,lawine
45,1704,1.30416,lawine
45,2300,1.50671,lawine
45,3198,1.84744,lawine
45,4857,1.62809,lawine
45,7558,1.24176,lawine
45,10912,1.08676,lawine
45,14557,0.21674,lawine
45,192,0.45833,lawine
45,280,1.25000,lawine
45,390,1.00909,lawine
45,501,1.52252,lawine
45,670,1.45562,lawine
45,916,1.34553,lawine
45,1247,1.52568,lawine
45,1752,1.69901,lawine
45,2610,1.73543,lawine
45,4099,1.66958,lawine
45,6585,1.15487,lawine
45,9456,0.97806,lawine
45,12264,0.27137,lawine
45,191,0.37696,lawine
45,263,0.73611,lawine
45,316,0.94340,lawine
45,366,0.74000,lawine
45,403,0.91892,lawine
45,437,1.02941,lawine
45,472,0.77143,lawine
45,499,0.70370,lawine
45,518,1.31579,lawine
45,543,0.80000,lawine
45,563,0.95000,lawine
45,582,2.47368,lawine
45,629,1.14894,lawine
45,683,1.44444,lawine
45,761,0.79487,lawine
45,823,1.11290,lawine
45,892,0.79710,lawine
45,947,1.45455,lawine
45,1027,1.66250,lawine
45,1160,1.33835,lawine
45,1338,0.66854,lawine
45,1457,0.36975,lawine
45,1501,1.15909,lawine
45,1552,1.60784,lawine
45,1634,1.39024,lawine
45,1748,1.56140,lawine
45,1926,1.55618,lawine
45,2203,1.29964,lawine
45,2563,1.40833,lawine
45,3070,1.38067,lawine
45,3770,1.26714,lawine
45,4657,1.22210,lawine
45,5741,1.07565,lawine
45,6907,1.34734,lawine
45,8478,1.20496,lawine
45,10371,1.32805,lawine
45,12885,0.80111,lawine
45,14899,0.33118,lawine
45,15566,0.07046,lawine
45,192,0.40104,lawine
45,269,1.28571,lawine
45,368,1.24242,lawine
45,491,1.16260,lawine
45,634,1.79021,lawine
45,890,1.44531,lawine
45,1260,1.54054,lawine
45,1830,1.52456,lawine
45,2699,1.34868,lawine
45,3871,1.53669,lawine
45,5672,1.30761,lawine
45,8027,0.96858,lawine
45,10308,0.34108,lawine
45,11086,0.29434,lawine
45,192,0.38021,lawine
45,265,0.71233,lawine
45,317,1.40385,lawine
45,390,1.15068,lawine
45,474,1.39286,lawine
45,591,1.14530,lawine
45,725,1.73134,lawine
45,957,1.69828,lawine
45,1351,1.04822,lawine
45,1764,0.73366,lawine
45,2067,1.37294,lawine
45,2483,1.47356,lawine
45,3096,1.56281,lawine
45,4054,1.42171,lawine
45,5416,1.35095,lawine
45,7256,0.76250,lawine
45,8659,0.68710,lawine
45,9623,0.82988,lawine
45,10423,0.36250,lawine
45,192,0.39583,lawine
45,268,0.97368,lawine
45,342,1.18919,lawine
45,430,1.72727,lawine
45,582,1.39474,lawine
45,794,1.06132,lawine
45,1019,1.15556,lawine
45,1279,1.27692,lawine
45,1611,1.96386,lawine
45,2263,2.04601,lawine
45,3597,1.60120,lawine
45,5733,0.70646,lawine
45,7242,0.39563,lawine
45,192,0.39062,hunger
45,267,0.89333,hunger
45,334,0.71642,hunger
45,382,0.37500,hunger
45,400,0.61111,hunger
45,411,0.72727,hunger
45,419,0.25000,hunger
45,192,0.48958,lawine
45,286,0.92553,lawine
45,373,1.37931,lawine
45,493,1.50000,lawine
45,673,1.07778,lawine
45,867,0.78866,lawine
45,1020,1.48366,lawine
45,1247,1.22467,lawine
45,1525,1.33094,lawine
45,1895,1.56757,lawine
45,2475,1.25000,lawine
45,3200,1.30207,lawine
45,4144,1.34004,lawine
45,5409,1.27826,lawine
45,7026,1.16203,lawine
45,8905,1.03406,lawine
45,10848,0.81215,lawine
45,12426,0.62611,lawine
45,13414,0.05364,lawine
45,192,0.41146,lawine
45,271,0.70886,lawine
45,327,1.21429,lawine
45,395,0.48529,lawine
45,428,0.48485,lawine
45,444,1.18750,lawine
45,463,2.00000,lawine
45,501,0.60526,lawine
45,524,1.52174,lawine
45,559,0.57143,lawine
45,579,0.95000,lawine
45,598,1.42105,lawine
45,625,0.77778,lawine
45,646,0.61905,lawine
45,659,0.23077,lawine
45,662,2.33333,lawine
45,669,1.42857,lawine
45,679,2.40000,lawine
45,703,1.00000,lawine
45,727,1.91667,lawine
45,773,1.52174,lawine
45,843,0.97143,lawine
45,911,1.67647,lawine
45,1025,0.88596,lawine
45,1126,1.53465,lawine
45,1281,1.57419,lawine
45,1525,1.20492,lawine
45,1819,1.29592,lawine
45,2200,1.75328,lawine
45,2868,1.24401,lawine
45,3699,0.98315,lawine
45,4516,1.24480,lawine
45,5533,1.24582,lawine
45,6800,1.24152,lawine
45,8373,1.13287,lawine
45,10155,0.98709,lawine
45,11914,0.60148,lawine
45,12972,0.05293,lawine
45,192,0.46354,lawine
45,281,0.92135,lawine
45,363,1.14634,lawine
45,457,1.02128,lawine
45,553,1.63542,lawine
45,710,1.91720,lawine
45,1011,1.42857,lawine
45,1441,1.89070,lawine
45,2254,1.68266,lawine
45,3622,1.60965,lawine
45,5824,1.74614,lawine
45,9669,0.90637,lawine
45,13154,0.51019,lawine
45,14932,0.24016,lawine
45,192,0.46354,hunger
45,281,0.70787,hunger
45,344,0.79365,hunger
45,394,0.70000,hunger
45,429,0.60000,hunger
45,450,0.52381,hunger
45,461,0.54545,hunger
45,467,2.16667,hunger
45,480,0.38462,hunger
45,485,1.80000,hunger
45,494,0.77778,hunger
45,501,0.71429,hunger
45,506,0.80000,hunger
45,510,0.00000,hunger
45,192,0.42188,lawine
45,273,0.83951,lawine
45,341,0.77941,lawine
45,394,0.52830,lawine
45,422,0.64286,lawine
45,440,0.50000,lawine
45,449,2.44444,lawine
45,471,1.13636,lawine
45,496,0.76000,lawine
45,515,2.00000,lawine
45,553,0.78947,lawine
45,583,1.36667,lawine
45,624,1.17073,lawine
45,672,1.20833,lawine
45,730,1.70690,lawine
45,829,1.45455,lawine
45,973,1.56250,lawine
45,1198,0.80000,lawine
45,1378,0.88889,lawine
45,1538,0.97500,lawine
45,1694,1.10256,lawine
45,1866,1.43023,lawine
45,2112,1.52439,lawine
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45,192,0.39062,hunger
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45,192,0.51042,lawine
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45,9044,0.82450,lawine
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45,192,0.43229,hunger
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45,417,0.70732,hunger
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45,502,0.50000,hunger
45,505,0.66667,hunger
45,192,0.48958,lawine
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45,192,0.39062,hunger
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45,317,0.90000,hunger
45,362,0.64444,hunger
45,391,0.41379,hunger
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45,412,0.55556,hunger
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45,426,0.66667,hunger
45,192,0.48958,lawine
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45,192,0.45312,lawine
45,279,0.77011,lawine
45,346,0.76119,lawine
45,397,0.94118,lawine
45,445,1.20833,lawine
45,503,0.94828,lawine
45,558,1.12727,lawine
45,620,1.25806,lawine
45,698,1.19231,lawine
45,791,1.13978,lawine
45,897,1.66981,lawine
45,1074,1.69492,lawine
45,1374,1.25000,lawine
45,1749,0.97600,lawine
45,2115,0.92077,lawine
45,2452,0.97626,lawine
45,2781,1.26748,lawine
45,3198,1.29976,lawine
45,3740,1.36716,lawine
45,4481,1.50607,lawine
45,5597,1.43638,lawine
45,7200,1.25452,lawine
45,9211,1.01939,lawine
45,11261,1.11707,lawine
45,13551,0.56594,lawine
45,14847,0.11034,lawine
50,213,0.35211,lawine
50,288,1.05333,lawine
50,367,0.73418,lawine
50,425,0.86207,lawine
50,475,0.90000,lawine
50,520,0.71111,lawine
50,552,0.31250,lawine
50,562,0.20000,lawine
50,582,1.72222,lawine
50,613,0.96774,lawine
50,643,1.53333,lawine
50,689,0.43478,lawine
50,709,1.20000,lawine
50,733,0.87500,lawine
50,754,1.09524,lawine
50,777,1.43478,lawine
50,810,1.84848,lawine
50,871,1.59016,lawine
50,968,1.44330,lawine
50,1108,0.88571,lawine
50,1232,1.06452,lawine
50,1364,1.33333,lawine
50,1540,0.96591,lawine
50,1710,1.51765,lawine
50,1968,1.44186,lawine
50,2340,1.45161,lawine
50,2880,1.65741,lawine
50,3775,1.54302,lawine
50,5156,1.39247,lawine
50,7079,1.49142,lawine
50,9947,1.19247,lawine
50,13367,1.30526,lawine
50,17831,0.80108,lawine
50,21407,0.13423,lawine
50,213,0.32394,hunger
50,282,0.98551,hunger
50,350,0.80882,hunger
50,405,0.83636,hunger
50,451,0.69565,hunger
50,483,0.75000,hunger
50,507,0.87500,hunger
50,528,1.00000,hunger
50,549,0.80952,hunger
50,566,0.82353,hunger
50,580,0.78571,hunger
50,591,1.09091,hunger
50,603,1.08333,hunger
50,616,0.84615,hunger
50,627,1.09091,hunger
50,639,0.33333,hunger
50,643,2.75000,hunger
50,654,0.18182,hunger
50,213,0.34742,hunger
50,287,0.54054,hunger
50,327,0.77500,hunger
50,358,0.83871,hunger
50,384,0.73077,hunger
50,403,1.00000,hunger
50,422,0.57895,hunger
50,433,1.00000,hunger
50,444,1.09091,hunger
50,456,1.16667,hunger
50,470,1.14286,hunger
50,486,0.81250,hunger
50,499,0.53846,hunger
50,506,0.71429,hunger
50,511,0.00000,hunger
50,213,0.50704,lawine
50,321,1.16667,lawine
50,447,1.07937,lawine
50,583,1.27206,lawine
50,756,1.15029,lawine
50,955,1.51759,lawine
50,1257,1.69536,lawine
50,1769,1.33008,lawine
50,2450,2.23495,lawine
50,3972,1.64192,lawine
50,6471,1.13045,lawine
50,9296,0.91327,lawine
50,11876,0.49264,lawine
50,13147,0.68371,lawine
50,14016,0.42002,lawine
50,14381,0.45753,lawine
50,213,0.41315,lawine
50,301,1.04545,lawine
50,393,1.09783,lawine
50,494,0.75248,lawine
50,570,1.32895,lawine
50,671,0.88119,lawine
50,760,1.40449,lawine
50,885,1.60800,lawine
50,1086,1.16915,lawine
50,1321,1.21277,lawine
50,1606,0.83860,lawine
50,1845,0.74895,lawine
50,2024,0.76536,lawine
50,2161,0.64234,lawine
50,2249,1.32955,lawine
50,2366,1.27350,lawine
50,2515,1.81208,lawine
50,2785,1.57407,lawine
50,3210,1.65412,lawine
50,3913,1.55192,lawine
50,5004,1.37122,lawine
50,6500,1.12968,lawine
50,8190,1.31065,lawine
50,10405,1.01038,lawine
50,12643,0.76273,lawine
50,14350,0.26186,lawine
50,213,0.38498,hunger
50,295,0.91463,hunger
50,370,0.66667,hunger
50,420,0.96000,hunger
50,468,0.41667,hunger
50,488,0.45000,hunger
50,497,0.33333,hunger
50,500,1.33333,hunger
50,504,0.00000,hunger
50,213,0.38967,hunger
50,296,0.51807,hunger
50,339,1.48837,hunger
50,403,0.70312,hunger
50,448,0.64444,hunger
50,477,0.82759,hunger
50,501,0.79167,hunger
50,520,0.52632,hunger
50,530,0.30000,hunger
50,533,0.00000,hunger
50,213,0.43192,lawine
50,305,0.77174,lawine
50,376,0.56338,lawine
50,416,0.92500,lawine
50,453,0.70270,lawine
50,479,2.57692,lawine
50,546,1.32836,lawine
50,635,1.32584,lawine
50,753,0.92373,lawine
50,862,1.28440,lawine
50,1002,1.10000,lawine
50,1156,1.25325,lawine
50,1349,0.95855,lawine
50,1534,1.19459,lawine
50,1755,1.33937,lawine
50,2051,1.17230,lawine
50,2398,1.59654,lawine
50,2952,1.16065,lawine
50,3595,1.55054,lawine
50,4592,1.34002,lawine
50,5928,1.16093,lawine
50,7479,1.09413,lawine
50,9176,1.36594,lawine
50,11494,1.33779,lawine
50,14595,0.57207,lawine
50,16369,0.29989,lawine
50,213,0.38028,hunger
50,294,0.66667,hunger
50,348,0.77778,hunger
50,390,0.97619,hunger
50,431,0.70732,hunger
50,460,0.58621,hunger
50,477,1.35294,hunger
50,500,0.95652,hunger
50,522,0.54545,hunger
50,534,0.91667,hunger
50,545,0.81818,hunger
50,554,0.55556,hunger
50,559,0.40000,hunger
50,213,0.35681,hunger
50,289,0.68421,hunger
50,341,0.86538,hunger
50,386,0.84444,hunger
50,424,0.55263,hunger
50,445,0.47619,hunger
50,455,1.40000,hunger
50,469,1.07143,hunger
50,484,0.66667,hunger
50,494,1.10000,hunger
50,505,0.27273,hunger
50,508,0.00000,hunger
50,213,0.45070,lawine
50,309,0.84375,lawine
50,390,0.75309,lawine
50,451,0.93443,lawine
50,508,0.56140,lawine
50,540,0.53125,lawine
50,557,0.76471,lawine
50,570,1.23077,lawine
50,586,1.25000,lawine
50,606,1.50000,lawine
50,636,0.90000,lawine
50,663,1.07407,lawine
50,692,1.34483,lawine
50,731,0.87179,lawine
50,765,1.02941,lawine
50,800,2.68571,lawine
50,894,1.27660,lawine
50,1014,0.88333,lawine
50,1120,1.34906,lawine
50,1263,1.74126,lawine
50,1512,0.29317,lawine
50,1585,0.49315,lawine
50,1621,1.52778,lawine
50,1676,0.38182,lawine
50,1697,0.85714,lawine
50,1715,0.83333,lawine
50,1730,0.80000,lawine
50,1742,1.66667,lawine
50,1762,1.55000,lawine
50,1793,1.19355,lawine
50,1830,1.10811,lawine
50,1871,0.65854,lawine
50,1898,2.81481,lawine
50,1974,1.19737,lawine
50,2065,0.89011,lawine
50,2146,1.46914,lawine
50,2265,0.99160,lawine
50,2383,1.94068,lawine
50,2612,1.25764,lawine
50,2900,0.82292,lawine
50,3137,0.91561,lawine
50,3354,1.43318,lawine
50,3665,1.21865,lawine
50,4044,1.39050,lawine
50,4571,1.08729,lawine
50,5144,1.50262,lawine
50,6005,1.23229,lawine
50,7066,1.51555,lawine
50,8674,1.25062,lawine
50,10685,0.93287,lawine
50,12561,0.74414,lawine
50,13957,0.56232,lawine
50,14742,0.50191,lawine
50,15136,0.31980,lawine
50,213,0.39906,lawine
50,298,0.64706,lawine
50,353,1.76364,lawine
50,450,1.26804,lawine
50,573,1.34959,lawine
50,739,1.65663,lawine
50,1014,1.27273,lawine
50,1364,1.47714,lawine
50,1881,2.43714,lawine
50,3141,1.39921,lawine
50,4904,1.50766,lawine
50,7562,1.39278,lawine
50,11264,1.11372,lawine
50,15387,0.91754,lawine
50,19170,0.34840,lawine
50,212,0.36792,lawine
50,290,1.03846,lawine
50,371,1.11111,lawine
50,461,1.88889,lawine
50,631,1.94118,lawine
50,961,1.13030,lawine
50,1334,1.61394,lawine
50,1936,1.75581,lawine
50,2993,1.97446,lawine
50,5080,1.53426,lawine
50,8282,0.93567,lawine
50,11278,0.67190,lawine
50,13291,0.97864,lawine
50,15261,0.60609,lawine
50,16455,0.30570,lawine
50,16820,0.10411,lawine
50,213,0.42723,lawine
50,304,1.09890,lawine
50,404,0.76000,lawine
50,480,1.07895,lawine
50,562,1.01220,lawine
50,645,1.18072,lawine
50,743,1.11224,lawine
50,852,1.40367,lawine
50,1005,1.11765,lawine
50,1176,1.38012,lawine
50,1412,1.69915,lawine
50,1813,1.28928,lawine
50,2330,1.59574,lawine
50,3155,1.65333,lawine
50,4519,1.15689,lawine
50,6097,1.32066,lawine
50,8181,1.20058,lawine
50,10683,1.12990,lawine
50,13510,0.66855,lawine
50,213,0.41315,hunger
50,301,0.68182,hunger
50,361,0.81667,hunger
50,410,0.91837,hunger
50,455,1.00000,hunger
50,500,0.51111,hunger
50,523,0.69565,hunger
50,539,0.68750,hunger
50,550,0.54545,hunger
50,556,0.33333,hunger
50,564,1.00000,hunger
50,567,1.66667,hunger
50,572,0.40000,hunger
50,213,0.35681,hunger
50,289,0.89474,hunger
50,357,0.85294,hunger
50,415,1.17241,hunger
50,483,0.97059,hunger
50,549,1.42424,hunger
50,643,2.25532,hunger
50,855,0.56604,hunger
50,975,0.58333,hunger
50,1045,0.37143,hunger
50,1071,0.80769,hunger
50,1092,0.85714,hunger
50,1110,1.44444,hunger
50,1136,0.42308,hunger
50,1147,0.36364,hunger
50,1151,0.50000,hunger
50,213,0.35681,hunger
50,289,0.68421,hunger
50,341,0.61538,hunger
50,373,0.65625,hunger
50,394,0.90476,hunger
50,413,0.36842,hunger
50,420,0.57143,hunger
50,424,1.00000,hunger
50,428,1.00000,hunger
50,432,0.75000,hunger
50,435,0.33333,hunger
50,213,0.34742,lawine
50,287,0.95946,lawine
50,358,1.01408,lawine
50,430,1.04167,lawine
50,505,0.94667,lawine
50,576,1.11268,lawine
50,655,0.81013,lawine
50,719,1.18750,lawine
50,795,1.00000,lawine
50,871,0.61842,lawine
50,918,1.38298,lawine
50,983,1.81538,lawine
50,1101,0.97458,lawine
50,1216,2.03478,lawine
50,1450,1.15812,lawine
50,1721,1.37638,lawine
50,2094,0.91153,lawine
50,2434,1.17941,lawine
50,2835,0.87032,lawine
50,3184,1.53295,lawine
50,3719,1.25234,lawine
50,4389,1.51045,lawine
50,5401,1.14130,lawine
50,6556,1.10736,lawine
50,7835,1.27912,lawine
50,9471,1.53484,lawine
50,11982,1.19235,lawine
50,14976,0.46460,lawine
50,16367,0.23221,lawine
50,212,0.37736,lawine
50,292,0.81250,lawine
50,357,1.09231,lawine
50,428,1.45070,lawine
50,531,0.64078,lawine
50,597,1.00000,lawine
50,663,0.84848,lawine
50,719,0.87500,lawine
50,768,1.34694,lawine
50,834,0.96970,lawine
50,898,0.96875,lawine
50,960,1.70968,lawine
50,1066,1.08491,lawine
50,1181,1.08696,lawine
50,1306,1.48000,lawine
50,1491,0.87027,lawine
50,1652,1.39752,lawine
50,1877,1.22667,lawine
50,2153,0.87319,lawine
50,2394,0.72199,lawine
50,2568,1.21839,lawine
50,2780,1.48113,lawine
50,3094,1.36624,lawine
50,3523,1.30769,lawine
50,4084,1.82709,lawine
50,5109,1.84585,lawine
50,7001,1.39323,lawine
50,9637,1.43816,lawine
50,13428,0.78001,lawine
50,16385,0.53568,lawine
50,213,0.40376,lawine
50,299,0.79070,lawine
50,367,1.30882,lawine
50,456,0.88764,lawine
50,535,1.11392,lawine
50,623,1.14773,lawine
50,724,0.78218,lawine
50,803,1.62025,lawine
50,931,1.27344,lawine
50,1094,1.55215,lawine
50,1347,1.15810,lawine
50,1640,1.31741,lawine
50,2026,1.48964,lawine
50,2601,0.93739,lawine
50,3140,1.66048,lawine
50,4035,1.37542,lawine
50,5266,1.64094,lawine
50,7286,1.24356,lawine
50,9798,0.85350,lawine
50,11942,0.89272,lawine
50,13856,0.39133,lawine
50,213,0.33333,hunger
50,284,0.67606,hunger
50,332,0.91667,hunger
50,376,0.86364,hunger
50,414,0.81579,hunger
50,445,1.25806,hunger
50,484,0.61538,hunger
50,508,0.87500,hunger
50,529,1.04762,hunger
50,551,0.86364,hunger
50,570,0.47368,hunger
50,579,2.11111,hunger
50,598,0.73684,hunger
50,612,1.28571,hunger
50,630,0.50000,hunger
50,639,0.22222,hunger
50,213,0.36620,lawine
50,291,0.88462,lawine
50,360,0.69565,lawine
50,408,0.95833,lawine
50,454,0.54348,lawine
50,479,1.40000,lawine
50,514,1.05714,lawine
50,551,0.56757,lawine
50,572,0.76190,lawine
50,588,0.87500,lawine
50,602,1.28571,lawine
50,620,0.33333,lawine
50,626,4.83333,lawine
50,655,1.48276,lawine
50,698,0.51163,lawine
50,720,1.45455,lawine
50,752,2.34375,lawine
50,827,1.18667,lawine
50,916,0.74157,lawine
50,982,1.12121,lawine
50,1056,0.82432,lawine
50,1117,1.72131,lawine
50,1222,1.29524,lawine
50,1358,0.58088,lawine
50,1437,0.58228,lawine
50,1483,0.86957,lawine
50,1523,0.80000,lawine
50,1555,0.81250,lawine
50,1581,1.03846,lawine
50,1608,2.14815,lawine
50,1666,0.98276,lawine
50,1723,1.05263,lawine
50,1783,1.10000,lawine
50,1849,0.72727,lawine
50,1897,1.08333,lawine
50,1949,1.28846,lawine
50,2016,0.95522,lawine
50,2080,2.00000,lawine
50,2208,1.17969,lawine
50,2359,1.05298,lawine
50,2518,1.56604,lawine
50,2767,1.12048,lawine
50,3046,1.39427,lawine
50,3435,1.52956,lawine
50,4030,1.30252,lawine
50,4805,1.33161,lawine
50,5837,1.39341,lawine
50,7275,1.56885,lawine
50,9531,1.31605,lawine
50,12500,0.79151,lawine
50,14850,0.74723,lawine
50,16606,0.50740,lawine
50,17497,0.07071,lawine
50,213,0.43192,lawine
50,305,0.97826,lawine
50,395,1.00000,lawine
50,485,0.81111,lawine
50,558,1.01370,lawine
50,632,0.89189,lawine
50,698,1.03030,lawine
50,766,1.00000,lawine
50,834,0.60294,lawine
50,875,0.95122,lawine
50,914,1.10256,lawine
50,957,1.34884,lawine
50,1015,1.60345,lawine
50,1108,0.91398,lawine
50,1193,2.68235,lawine
50,1421,1.46930,lawine
50,1756,1.40597,lawine
50,2227,1.08493,lawine
50,2738,1.13112,lawine
50,3316,1.44983,lawine
50,4154,1.12411,lawine
50,5096,1.34501,lawine
50,6363,1.47751,lawine
50,8235,1.09295,lawine
50,10281,1.02346,lawine
50,12375,0.62989,lawine
50,13694,0.12130,lawine
50,213,0.32394,hunger
50,282,0.52174,hunger
50,318,0.88889,hunger
50,350,0.65625,hunger
50,371,0.66667,hunger
50,385,0.28571,hunger
50,389,1.50000,hunger
50,395,2.00000,hunger
50,407,0.33333,hunger
50,411,0.75000,hunger
50,414,0.33333,hunger
50,213,0.44131,lawine
50,307,1.06383,lawine
50,407,2.27000,lawine
50,634,1.75330,lawine
50,1032,0.85930,lawine
50,1374,3.25731,lawine
50,2488,2.01436,lawine
50,4732,1.74421,lawine
50,8646,0.26137,lawine
50,213,0.37089,lawine
50,292,1.03797,lawine
50,374,1.06098,lawine
50,461,1.25287,lawine
50,570,1.12844,lawine
50,693,1.39024,lawine
50,864,1.03509,lawine
50,1041,1.17514,lawine
50,1249,1.60577,lawine
50,1583,1.53293,lawine
50,2095,1.52930,lawine
50,2878,1.42273,lawine
50,3992,1.40305,lawine
50,5555,1.65003,lawine
50,8134,1.12253,lawine
50,11029,0.72159,lawine
50,13118,0.56056,lawine
50,14289,0.09564,lawine
50,212,0.36792,lawine
50,290,0.93590,lawine
50,363,1.19178,lawine
50,450,0.87356,lawine
50,526,1.09211,lawine
50,609,0.93976,lawine
50,687,0.66667,lawine
50,739,0.86538,lawine
50,784,0.88889,lawine
50,824,0.72500,lawine
50,853,1.37931,lawine
50,893,1.25000,lawine
50,943,0.84000,lawine
50,985,1.14286,lawine
50,1033,1.56250,lawine
50,1108,1.40000,lawine
50,1213,1.52381,lawine
50,1373,1.07500,lawine
50,1545,1.70930,lawine
50,1839,1.17347,lawine
50,2184,1.31594,lawine
50,2638,1.15859,lawine
50,3164,1.01901,lawine
50,3700,1.31716,lawine
50,4406,1.38810,lawine
50,5386,1.92449,lawine
50,7272,1.34252,lawine
50,9804,1.54028,lawine
50,13704,1.03641,lawine
50,17746,0.08709,lawine
50,213,0.34742,hunger
50,287,0.60811,hunger
50,332,0.53333,hunger
50,356,0.54167,hunger
50,369,1.15385,hunger
50,384,0.20000,hunger
50,387,0.66667,hunger
50,212,0.39623,lawine
50,296,1.09524,lawine
50,388,1.14130,lawine
50,493,0.76190,lawine
50,573,1.15000,lawine
50,665,1.80435,lawine
50,831,1.29518,lawine
50,1046,1.52558,lawine
50,1374,0.95732,lawine
50,1688,1.49363,lawine
50,2157,1.58849,lawine
50,2902,1.24966,lawine
50,3833,1.41676,lawine
50,5152,1.38211,lawine
50,6975,1.48821,lawine
50,9688,1.41098,lawine
50,13516,0.52717,lawine
50,15534,0.48662,lawine
50,16516,0.21385,lawine
50,212,0.43396,lawine
50,304,1.01087,lawine
50,397,0.95699,lawine
50,486,0.95506,lawine
50,571,0.82353,lawine
50,641,1.30000,lawine
50,732,1.39560,lawine
50,859,1.22047,lawine
50,1014,1.27742,lawine
50,1212,1.65152,lawine
50,1539,1.44037,lawine
50,2010,1.44161,lawine
50,2689,1.34610,lawine
50,3603,1.20897,lawine
50,4708,0.85973,lawine
50,5658,0.84316,lawine
50,6459,1.27466,lawine
50,7480,1.57101,lawine
50,9084,1.41272,lawine
50,11350,0.92189,lawine
50,13439,1.14074,lawine
50,15822,0.52581,lawine
50,17075,0.07023,lawine
50,213,0.41315,hunger
50,301,0.84091,hunger
50,375,0.82432,hunger
50,436,0.60656,hunger
50,473,1.00000,hunger
50,510,0.64865,hunger
50,534,0.66667,hunger
50,550,0.75000,hunger
50,562,0.75000,hunger
50,571,0.22222,hunger
50,211,0.34123,lawine
50,283,0.86111,lawine
50,345,0.80645,lawine
50,395,0.80000,lawine
50,435,0.97500,lawine
50,474,1.25641,lawine
50,523,1.40816,lawine
50,592,0.42029,lawine
50,621,2.10345,lawine
50,682,0.31148,lawine
50,701,3.63158,lawine
50,770,1.13043,lawine
50,848,0.58974,lawine
50,894,1.65217,lawine
50,970,1.31579,lawine
50,1070,1.16000,lawine
50,1186,1.25000,lawine
50,1331,0.84138,lawine
50,1453,1.14754,lawine
50,1593,1.50714,lawine
50,1804,1.37915,lawine
50,2095,1.38144,lawine
50,2497,1.53234,lawine
50,3113,1.46104,lawine
50,4013,1.45222,lawine
50,5320,1.57001,lawine
50,7372,1.72953,lawine
50,10921,1.13018,lawine
50,14932,0.37921,lawine
50,213,0.36620,lawine
50,291,1.05128,lawine
50,373,1.06098,lawine
50,460,1.11494,lawine
50,557,1.41237,lawine
50,694,1.35766,lawine
50,880,1.76882,lawine
50,1209,1.39514,lawine
50,1668,1.61656,lawine
50,2410,1.28167,lawine
50,3361,1.09569,lawine
50,4403,1.12572,lawine
50,5576,1.29923,lawine
50,7100,1.15092,lawine
50,8854,1.24686,lawine
50,11041,1.18976,lawine
50,13643,0.64950,lawine
50,15333,0.04852,lawine
50,213,0.40845,lawine
50,300,1.00000,lawine
50,387,0.74713,lawine
50,452,0.90769,lawine
50,511,1.77966,lawine
50,616,2.16190,lawine
50,843,1.03524,lawine
50,1078,1.79149,lawine
50,1499,1.25178,lawine
50,2026,1.81214,lawine
50,2981,1.56230,lawine
50,4473,1.62198,lawine
50,6893,1.39215,lawine
50,10262,1.08549,lawine
50,13919,0.31009,lawine
50,213,0.35211,lawine
50,288,0.73333,lawine
50,343,0.94545,lawine
50,395,0.67308,lawine
50,430,0.82857,lawine
50,459,0.72414,lawine
50,480,0.90476,lawine
50,499,0.68421,lawine
50,512,4.15385,lawine
50,566,1.11111,lawine
50,626,1.21667,lawine
50,699,1.21918,lawine
50,788,1.33708,lawine
50,907,1.55462,lawine
50,1092,1.01081,lawine
50,1279,1.49198,lawine
50,1558,1.61649,lawine
50,2009,1.05100,lawine
50,2483,1.26371,lawine
50,3082,1.50584,lawine
50,3984,1.18736,lawine
50,5055,1.43044,lawine
50,6587,1.43473,lawine
50,8785,0.94177,lawine
50,10855,0.92222,lawine
50,12764,0.97695,lawine
50,14629,0.64772,lawine
50,15837,0.06126,lawine
50,213,0.39906,lawine
50,298,1.38824,lawine
50,416,1.25424,lawine
50,564,1.36486,lawine
50,766,1.39109,lawine
50,1047,1.39146,lawine
50,1438,1.74425,lawine
50,2120,1.55718,lawine
50,3182,1.51883,lawine
50,4795,1.16243,lawine
50,6670,1.05600,lawine
50,8650,1.13232,lawine
50,10892,1.14987,lawine
50,13470,0.70132,lawine
50,15278,0.05476,lawine
50,213,0.38967,lawine
50,296,0.69880,lawine
50,354,1.06897,lawine
50,416,1.01613,lawine
50,479,0.84127,lawine
50,532,1.22642,lawine
50,597,1.01538,lawine
50,663,1.04545,lawine
50,732,1.15942,lawine
50,812,0.90000,lawine
50,884,1.00000,lawine
50,956,0.61111,lawine
50,1000,0.86364,lawine
50,1038,0.78947,lawine
50,1068,1.00000,lawine
50,1098,2.50000,lawine
50,1173,1.09333,lawine
50,1255,1.41463,lawine
50,1371,1.46552,lawine
50,1541,1.28824,lawine
50,1760,1.17808,lawine
50,2018,1.32946,lawine
50,2361,0.91545,lawine
50,2675,1.08280,lawine
50,3015,1.50882,lawine
50,3528,1.32164,lawine
50,4206,1.69764,lawine
50,5357,1.52129,lawine
50,7108,1.32267,lawine
50,9424,0.99223,lawine
50,11722,1.41993,lawine
50,14985,0.54919,lawine
50,16777,0.03237,lawine
50,213,0.37089,hunger
50,292,0.83544,hunger
50,358,0.69697,hunger
50,404,0.71739,hunger
50,437,0.57576,hunger
50,456,1.57895,hunger
50,486,0.56667,hunger
50,503,0.29412,hunger
50,508,0.40000,hunger
50,213,0.38967,lawine
50,296,0.78313,lawine
50,361,1.16923,lawine
50,437,1.30263,lawine
50,536,1.21212,lawine
50,656,1.40833,lawine
50,825,1.30178,lawine
50,1045,1.32273,lawine
50,1336,1.14433,lawine
50,1669,1.17417,lawine
50,2060,1.27110,lawine
50,2557,1.52918,lawine
50,3317,1.05921,lawine
50,4122,1.50559,lawine
50,5334,1.27145,lawine
50,6875,1.25698,lawine
50,8812,1.59164,lawine
50,11895,1.11807,lawine
50,15342,0.87757,lawine
50,18367,0.13785,lawine
50,213,0.32394,hunger
50,282,0.78261,hunger
50,336,0.81481,hunger
50,380,0.68182,hunger
50,410,0.63333,hunger
50,429,0.42105,hunger
50,437,0.62500,hunger
50,442,0.60000,hunger
50,445,0.33333,hunger
50,213,0.38967,hunger
50,296,0.69880,hunger
50,354,0.53448,hunger
50,385,0.58065,hunger
50,403,0.55556,hunger
50,413,1.10000,hunger
50,424,1.27273,hunger
50,438,0.50000,hunger
50,445,0.85714,hunger
50,451,0.33333,hunger
50,466,0.69231,hunger
50,475,0.44444,hunger
50,479,0.50000,hunger
50,213,0.36620,hunger
50,291,0.76923,hunger
50,351,0.83333,hunger
50,401,0.96000,hunger
50,449,0.66667,hunger
50,481,0.87500,hunger
50,509,0.53571,hunger
50,524,1.26667,hunger
50,543,1.52632,hunger
50,572,0.86207,hunger
50,597,0.40000,hunger
50,607,0.20000,hunger
50,213,0.37559,hunger
50,293,0.67500,hunger
50,347,0.83333,hunger
50,392,0.91111,hunger
50,433,0.73171,hunger
50,463,0.60000,hunger
50,481,0.55556,hunger
50,491,0.80000,hunger
50,499,1.12500,hunger
50,508,1.22222,hunger
50,519,1.72727,hunger
50,538,1.57895,hunger
50,568,0.83333,hunger
50,593,0.48000,hunger
50,605,0.66667,hunger
50,613,2.37500,hunger
50,632,0.57895,hunger
50,643,0.27273,hunger
50,646,0.33333,hunger
50,650,2.00000,hunger
50,656,2.50000,hunger
50,671,1.06667,hunger
50,687,0.62500,hunger
50,697,0.80000,hunger
50,705,1.00000,hunger
50,713,0.25000,hunger
50,213,0.34742,lawine
50,287,0.68919,lawine
50,338,0.76471,lawine
50,377,0.61538,lawine
50,401,0.83333,lawine
50,421,1.20000,lawine
50,445,1.75000,lawine
50,487,0.71429,lawine
50,517,0.70000,lawine
50,538,1.61905,lawine
50,572,0.91176,lawine
50,603,0.93548,lawine
50,632,0.93103,lawine
50,659,1.96296,lawine
50,712,1.41509,lawine
50,787,0.70667,lawine
50,840,2.11321,lawine
50,952,1.54464,lawine
50,1125,1.20809,lawine
50,1334,1.54067,lawine
50,1656,1.09627,lawine
50,2009,1.09915,lawine
50,2397,1.21907,lawine
50,2870,1.35095,lawine
50,3509,1.17684,lawine
50,4261,1.25931,lawine
50,5208,1.83316,lawine
50,6944,1.35196,lawine
50,9291,1.26331,lawine
50,12256,0.86476,lawine
50,14820,0.97309,lawine
50,17315,0.25772,lawine
50,212,0.41981,lawine
50,301,0.94382,lawine
50,385,0.76190,lawine
50,449,1.07812,lawine
50,518,1.50725,lawine
50,622,1.10577,lawine
50,737,1.76522,lawine
50,940,1.27094,lawine
50,1198,1.31008,lawine
50,1536,1.22189,lawine
50,1949,1.20823,lawine
50,2448,1.07014,lawine
50,2982,1.38577,lawine
50,3722,1.19595,lawine
50,4607,1.28362,lawine
50,5743,1.40405,lawine
50,7338,1.66959,lawine
50,10001,1.27075,lawine
50,13385,0.96277,lawine
50,16643,0.07980,lawine
50,213,0.34272,hunger
50,286,0.87671,hunger
50,350,0.82812,hunger
50,403,0.62264,hunger
50,436,0.75758,hunger
50,461,0.48000,hunger
50,473,0.41667,hunger
50,478,0.80000,hunger
50,482,0.25000,hunger
50,213,0.41315,lawine
50,301,0.80682,lawine
50,372,0.84507,lawine
50,432,1.41667,lawine
50,517,1.28235,lawine
50,626,1.07339,lawine
50,743,1.15385,lawine
50,878,1.50370,lawine
50,1081,1.79310,lawine
50,1445,1.34615,lawine
50,1935,1.38776,lawine
50,2615,1.52059,lawine
50,3649,1.47969,lawine
50,5179,1.21961,lawine
50,7045,1.67256,lawine
50,10166,0.93944,lawine
50,13098,0.71010,lawine
50,15180,0.16715,lawine
50,213,0.34742,lawine
50,287,0.89189,lawine
50,353,0.63636,lawine
50,395,0.97619,lawine
50,436,0.70732,lawine
50,465,0.75862,lawine
50,487,0.72727,lawine
50,503,0.87500,lawine
50,517,0.71429,lawine
50,527,1.90000,lawine
50,546,1.05263,lawine
50,566,0.95000,lawine
50,585,1.05263,lawine
50,605,0.80000,lawine
50,621,0.87500,lawine
50,635,1.14286,lawine
50,651,2.31250,lawine
50,688,1.75676,lawine
50,753,1.26154,lawine
50,835,1.15854,lawine
50,930,1.45263,lawine
50,1068,1.05072,lawine
50,1213,1.62759,lawine
50,1449,1.12288,lawine
50,1714,0.97358,lawine
50,1972,1.17442,lawine
50,2275,1.41584,lawine
50,2704,1.48951,lawine
50,3343,0.90297,lawine
50,3920,1.09012,lawine
50,4549,1.38633,lawine
50,5421,1.36927,lawine
50,6615,1.36516,lawine
50,8245,1.30429,lawine
50,10371,1.27563,lawine
50,13083,0.67367,lawine
50,14910,0.62781,lawine
50,16057,0.37140,lawine
50,212,0.38679,lawine
50,294,0.81707,lawine
50,361,0.70149,lawine
50,408,0.80851,lawine
50,446,0.86842,lawine
50,479,1.09091,lawine
50,515,0.80556,lawine
50,544,0.55172,lawine
50,560,4.81250,lawine
50,637,0.81818,lawine
50,700,1.20635,lawine
50,776,1.27632,lawine
50,873,0.75258,lawine
50,946,1.16438,lawine
50,1031,2.35294,lawine
50,1231,1.07000,lawine
50,1445,1.22430,lawine
50,1707,1.20992,lawine
50,2024,0.95899,lawine
50,2328,0.93092,lawine
50,2611,1.64311,lawine
50,3076,1.56559,lawine
50,3804,1.04533,lawine
50,4565,1.53219,lawine
50,5731,1.46055,lawine
50,7434,1.49794,lawine
50,9985,1.20698,lawine
50,13064,0.76551,lawine
50,15421,0.26305,lawine
50,213,0.42723,hunger
50,304,0.74725,hunger
50,372,0.79412,hunger
50,426,1.01852,hunger
50,481,0.89091,hunger
50,530,1.73469,hunger
50,615,0.69412,hunger
50,674,0.86441,hunger
50,725,0.72549,hunger
50,762,0.54054,hunger
50,782,1.65000,hunger
50,815,0.42424,hunger
50,829,0.64286,hunger
50,838,0.88889,hunger
50,846,1.12500,hunger
50,855,0.88889,hunger
50,863,0.25000,hunger
50,869,0.25000,hunger
53,226,0.35398,hunger
53,306,0.63750,hunger
53,357,0.72549,hunger
53,394,0.81081,hunger
53,424,0.43333,hunger
53,437,0.61538,hunger
53,445,0.12500,hunger
53,226,0.36726,hunger
53,309,0.73494,hunger
53,370,0.57377,hunger
53,405,0.54286,hunger
53,424,1.10526,hunger
53,445,0.90476,hunger
53,464,2.26316,hunger
53,507,0.95349,hunger
53,548,0.95122,hunger
53,587,0.92308,hunger
53,623,0.50000,hunger
53,641,0.88889,hunger
53,657,0.25000,hunger
53,661,0.00000,hunger
53,225,0.39111,lawine
53,313,0.65909,lawine
53,371,0.81034,lawine
53,418,0.65957,lawine
53,449,0.54839,lawine
53,466,1.88235,lawine
53,498,1.56250,lawine
53,548,1.30000,lawine
53,613,1.36923,lawine
53,702,1.06742,lawine
53,797,0.77895,lawine
53,871,1.12162,lawine
53,954,1.20482,lawine
53,1054,1.53000,lawine
53,1207,0.92157,lawine
53,1348,1.01418,lawine
53,1491,1.16783,lawine
53,1658,0.92814,lawine
53,1813,0.64516,lawine
53,1913,1.47000,lawine
53,2060,0.85034,lawine
53,2185,1.98400,lawine
53,2433,1.79435,lawine
53,2878,1.40225,lawine
53,3502,0.95513,lawine
53,4098,1.35067,lawine
53,4903,1.21366,lawine
53,5880,1.39099,lawine
53,7239,1.32965,lawine
53,9046,1.20255,lawine
53,11219,1.59641,lawine
53,14688,1.26607,lawine
53,19080,0.61134,lawine
53,21765,0.09199,lawine
53,226,0.38496,hunger
53,313,0.71264,hunger
53,375,0.62903,hunger
53,414,1.05128,hunger
53,455,1.19512,hunger
53,504,0.89796,hunger
53,548,1.15909,hunger
53,599,0.90196,hunger
53,645,0.82609,hunger
53,683,1.05263,hunger
53,723,1.12500,hunger
53,768,0.40000,hunger
53,786,1.11111,hunger
53,806,0.65000,hunger
53,819,0.23077,hunger
53,822,0.33333,hunger
53,226,0.35398,hunger
53,306,0.97500,hunger
53,384,0.82051,hunger
53,448,0.40625,hunger
53,474,0.84615,hunger
53,496,1.09091,hunger
53,520,0.95833,hunger
53,543,1.21739,hunger
53,571,0.71429,hunger
53,591,0.85000,hunger
53,608,0.58824,hunger
53,618,1.70000,hunger
53,635,0.58824,hunger
53,645,0.60000,hunger
53,651,1.16667,hunger
53,658,1.85714,hunger
53,671,0.61538,hunger
53,679,0.87500,hunger
53,686,0.42857,hunger
53,689,0.00000,hunger
53,226,0.33186,lawine
53,301,0.70667,lawine
53,354,0.84906,lawine
53,399,1.04444,lawine
53,446,1.44681,lawine
53,514,0.91176,lawine
53,576,0.77419,lawine
53,624,1.18750,lawine
53,681,1.21053,lawine
53,750,1.00000,lawine
53,819,0.85507,lawine
53,878,1.15254,lawine
53,946,1.27941,lawine
53,1033,1.58621,lawine
53,1171,0.85507,lawine
53,1289,1.50847,lawine
53,1467,1.83708,lawine
53,1794,0.91437,lawine
53,2093,1.15050,lawine
53,2437,1.00000,lawine
53,2781,1.03198,lawine
53,3136,1.30141,lawine
53,3598,1.56494,lawine
53,4321,1.90318,lawine
53,5697,1.47892,lawine
53,7732,1.38133,lawine
53,10543,1.28922,lawine
53,14167,0.98675,lawine
53,17743,0.86158,lawine
53,20824,0.66926,lawine
53,22886,0.15713,lawine
53,225,0.34667,hunger
53,303,0.55128,hunger
53,346,1.39535,hunger
53,406,0.60000,hunger
53,442,0.44444,hunger
53,458,1.31250,hunger
53,479,0.71429,hunger
53,494,1.00000,hunger
53,509,2.80000,hunger
53,551,0.42857,hunger
53,569,0.88889,hunger
53,585,0.12500,hunger
53,226,0.39823,lawine
53,316,0.75556,lawine
53,384,0.82353,lawine
53,440,0.96429,lawine
53,494,0.57407,lawine
53,525,1.51613,lawine
53,572,0.78723,lawine
53,609,1.70270,lawine
53,672,1.49206,lawine
53,766,0.94681,lawine
53,855,0.77528,lawine
53,924,1.79710,lawine
53,1048,0.79839,lawine
53,1147,1.38384,lawine
53,1284,1.01460,lawine
53,1423,3.06475,lawine
53,1849,1.10798,lawine
53,2321,1.06356,lawine
53,2823,1.71116,lawine
53,3682,1.16414,lawine
53,4682,1.61100,lawine
53,6293,1.56673,lawine
53,8817,1.26268,lawine
53,12004,1.11045,lawine
53,15543,0.77593,lawine
53,18289,0.31974,lawine
53,226,0.35841,hunger
53,307,0.75309,hunger
53,368,0.68852,hunger
53,410,0.52381,hunger
53,432,0.95455,hunger
53,453,0.76190,hunger
53,469,0.75000,hunger
53,481,0.25000,hunger
53,484,0.00000,hunger
53,226,0.43363,lawine
53,324,0.69388,lawine
53,392,0.73529,lawine
53,442,1.04000,lawine
53,494,1.28846,lawine
53,561,0.89552,lawine
53,621,1.30000,lawine
53,699,0.94872,lawine
53,773,1.01351,lawine
53,848,0.78667,lawine
53,907,2.42373,lawine
53,1050,1.30769,lawine
53,1237,1.18182,lawine
53,1458,1.65158,lawine
53,1823,1.17808,lawine
53,2253,1.41628,lawine
53,2862,1.86207,lawine
53,3996,1.57848,lawine
53,5786,1.51006,lawine
53,8489,0.96818,lawine
53,11106,1.07872,lawine
53,13929,0.83918,lawine
53,16298,0.62896,lawine
53,17788,0.07718,lawine
53,226,0.37611,lawine
53,311,0.62353,lawine
53,364,0.39623,lawine
53,385,0.85714,lawine
53,403,0.94444,lawine
53,420,0.52941,lawine
53,429,1.00000,lawine
53,438,0.33333,lawine
53,441,1.33333,lawine
53,445,1.75000,lawine
53,452,1.14286,lawine
53,460,0.50000,lawine
53,464,0.50000,lawine
53,469,7.33333,lawine
53,491,1.31818,lawine
53,520,1.13793,lawine
53,553,0.75758,lawine
53,578,0.68000,lawine
53,595,0.76471,lawine
53,608,1.84615,lawine
53,632,1.75000,lawine
53,674,1.42857,lawine
53,734,1.75000,lawine
53,839,0.92381,lawine
53,936,0.98969,lawine
53,1032,0.88542,lawine
53,1117,0.95294,lawine
53,1198,1.07407,lawine
53,1285,1.09195,lawine
53,1380,0.83158,lawine
53,1459,0.84810,lawine
53,1526,1.01493,lawine
53,1594,0.85294,lawine
53,1652,1.34483,lawine
53,1730,1.60256,lawine
53,1855,1.64000,lawine
53,2060,1.22439,lawine
53,2311,0.43825,lawine
53,2421,1.02727,lawine
53,2534,0.82301,lawine
53,2627,1.58065,lawine
53,2774,1.12245,lawine
53,2939,1.20000,lawine
53,3137,1.60606,lawine
53,3455,0.74843,lawine
53,3693,1.47059,lawine
53,4043,1.38286,lawine
53,4527,0.72521,lawine
53,4878,1.09687,lawine
53,5263,1.37403,lawine
53,5792,1.01701,lawine
53,6330,1.47770,lawine
53,7125,1.25912,lawine
53,8126,1.55944,lawine
53,9687,1.21268,lawine
53,11580,1.16323,lawine
53,13782,1.07902,lawine
53,16158,0.90572,lawine
53,18310,0.61571,lawine
53,226,0.38496,lawine
53,313,0.64368,lawine
53,369,0.92857,lawine
53,421,0.84615,lawine
53,465,1.00000,lawine
53,509,0.72727,lawine
53,541,1.18750,lawine
53,579,0.55263,lawine
53,600,2.42857,lawine
53,651,1.41176,lawine
53,723,1.45833,lawine
53,828,1.10476,lawine
53,944,1.71552,lawine
53,1143,1.66834,lawine
53,1475,1.09639,lawine
53,1839,1.45055,lawine
53,2367,1.76894,lawine
53,3301,1.49893,lawine
53,4701,1.60357,lawine
53,6946,1.38976,lawine
53,10066,1.26122,lawine
53,14001,0.68996,lawine
53,16716,0.15396,lawine
53,225,0.30667,hunger
53,294,0.55072,hunger
53,332,0.92105,hunger
53,367,0.54286,hunger
53,386,2.00000,hunger
53,424,0.63158,hunger
53,448,0.54167,hunger
53,461,0.61538,hunger
53,469,0.62500,hunger
53,474,1.60000,hunger
53,482,0.25000,hunger
53,226,0.45133,lawine
53,328,0.75490,lawine
53,405,0.83117,lawine
53,469,1.03125,lawine
53,535,1.09091,lawine
53,607,1.58333,lawine
53,721,1.20175,lawine
53,858,1.32117,lawine
53,1039,1.18232,lawine
53,1253,1.50467,lawine
53,1575,0.86025,lawine
53,1852,1.11552,lawine
53,2161,0.93528,lawine
53,2450,1.31834,lawine
53,2831,1.17848,lawine
53,3280,1.48775,lawine
53,3948,1.58084,lawine
53,5004,1.54735,lawine
53,6638,1.04896,lawine
53,8352,1.23046,lawine
53,10461,1.10242,lawine
53,12786,1.28387,lawine
53,15771,0.37621,lawine
53,226,0.38938,hunger
53,314,0.64773,hunger
53,371,1.21053,hunger
53,440,1.00000,hunger
53,509,0.98551,hunger
53,577,0.72059,hunger
53,626,0.73469,hunger
53,662,0.88889,hunger
53,694,0.25000,hunger
53,702,1.37500,hunger
53,713,1.27273,hunger
53,727,0.78571,hunger
53,738,0.81818,hunger
53,747,0.88889,hunger
53,755,0.87500,hunger
53,762,1.57143,hunger
53,773,0.63636,hunger
53,780,0.42857,hunger
53,783,0.33333,hunger
53,226,0.37611,hunger
53,311,0.71765,hunger
53,372,0.63934,hunger
53,411,1.20513,hunger
53,458,0.95745,hunger
53,503,0.88889,hunger
53,543,0.65000,hunger
53,569,0.53846,hunger
53,583,0.42857,hunger
53,589,0.00000,hunger
53,226,0.34956,lawine
53,305,0.70886,lawine
53,361,0.96429,lawine
53,415,0.75926,lawine
53,456,0.85366,lawine
53,491,0.94286,lawine
53,524,0.90909,lawine
53,554,1.26667,lawine
53,592,1.73684,lawine
53,658,1.69697,lawine
53,770,1.66071,lawine
53,956,1.11828,lawine
53,1164,0.86538,lawine
53,1344,1.51111,lawine
53,1616,0.93015,lawine
53,1869,1.18182,lawine
53,2168,0.92642,lawine
53,2445,0.91336,lawine
53,2698,1.58893,lawine
53,3100,0.92040,lawine
53,3470,1.90270,lawine
53,4174,0.83239,lawine
53,4760,0.94881,lawine
53,5316,1.17446,lawine
53,5969,1.45942,lawine
53,6922,2.12067,lawine
53,8943,1.58387,lawine
53,12144,1.23586,lawine
53,16100,0.85920,lawine
53,19499,0.33039,lawine
53,226,0.39823,lawine
53,316,0.95556,lawine
53,402,0.70930,lawine
53,463,0.73770,lawine
53,508,0.88889,lawine
53,548,0.82500,lawine
53,581,1.30303,lawine
53,624,1.13953,lawine
53,673,0.87755,lawine
53,716,1.51163,lawine
53,781,1.52308,lawine
53,880,1.23232,lawine
53,1002,0.91803,lawine
53,1114,1.11607,lawine
53,1239,1.92800,lawine
53,1480,1.21577,lawine
53,1773,1.23549,lawine
53,2135,1.14088,lawine
53,2548,1.12349,lawine
53,3012,1.17672,lawine
53,3558,1.26374,lawine
53,4248,1.63333,lawine
53,5375,1.33185,lawine
53,6876,1.38974,lawine
53,8962,1.20470,lawine
53,11475,1.24672,lawine
53,14608,0.95340,lawine
53,17595,0.57951,lawine
53,19326,0.08319,lawine
53,226,0.38938,lawine
53,314,0.60227,lawine
53,367,1.18868,lawine
53,430,0.79365,lawine
53,480,0.94000,lawine
53,527,0.76596,lawine
53,563,1.25000,lawine
53,608,0.73333,lawine
53,641,1.00000,lawine
53,674,0.69697,lawine
53,697,1.00000,lawine
53,720,1.26087,lawine
53,749,1.00000,lawine
53,778,1.55172,lawine
53,823,1.42222,lawine
53,887,0.92188,lawine
53,946,1.28814,lawine
53,1022,0.60526,lawine
53,1068,1.73913,lawine
53,1148,1.37500,lawine
53,1258,0.76364,lawine
53,1342,1.42857,lawine
53,1462,1.48333,lawine
53,1640,1.55618,lawine
53,1917,1.34296,lawine
53,2289,1.23656,lawine
53,2749,0.61522,lawine
53,3032,0.78445,lawine
53,3254,0.87838,lawine
53,3449,1.28718,lawine
53,3700,1.29880,lawine
53,4026,1.32515,lawine
53,4458,1.31250,lawine
53,5025,1.64198,lawine
53,5956,1.51450,lawine
53,7366,1.10000,lawine
53,8917,1.08317,lawine
53,10597,1.20774,lawine
53,12626,1.61262,lawine
53,15898,1.08649,lawine
53,19453,0.39803,lawine
53,20868,0.04382,lawine
53,226,0.31416,hunger
53,297,0.64789,hunger
53,343,0.76087,hunger
53,378,0.45714,hunger
53,394,1.18750,hunger
53,413,0.73684,hunger
53,427,0.64286,hunger
53,436,0.55556,hunger
53,441,0.40000,hunger
53,446,0.33333,hunger
53,225,0.35111,hunger
53,304,0.63291,hunger
53,354,0.80000,hunger
53,394,0.42500,hunger
53,411,0.29412,hunger
53,416,0.40000,hunger
53,226,0.27434,lawine
53,288,1.20968,lawine
53,363,0.77333,lawine
53,421,1.22414,lawine
53,492,1.43662,lawine
53,594,1.11765,lawine
53,708,1.12281,lawine
53,836,2.17969,lawine
53,1115,1.13262,lawine
53,1431,1.21519,lawine
53,1815,1.11719,lawine
53,2244,1.34499,lawine
53,2821,0.91161,lawine
53,3347,1.41065,lawine
53,4089,1.22237,lawine
53,4996,1.47630,lawine
53,6335,1.22778,lawine
53,7979,1.47993,lawine
53,10412,1.50555,lawine
53,14075,0.99563,lawine
53,17722,0.22402,lawine
53,226,0.30973,hunger
53,296,0.68571,hunger
53,344,0.68750,hunger
53,377,0.45455,hunger
53,392,0.60000,hunger
53,401,0.22222,hunger
53,226,0.37611,lawine
53,311,1.04706,lawine
53,400,0.70787,lawine
53,463,0.82540,lawine
53,515,1.21154,lawine
53,578,1.12698,lawine
53,649,0.85915,lawine
53,710,0.70492,lawine
53,753,0.97674,lawine
53,795,1.42857,lawine
53,855,1.35000,lawine
53,936,0.79012,lawine
53,1000,1.68750,lawine
53,1108,1.39815,lawine
53,1259,1.21192,lawine
53,1442,0.87432,lawine
53,1602,2.14375,lawine
53,1945,1.14577,lawine
53,2338,0.85242,lawine
53,2673,1.45075,lawine
53,3159,1.64609,lawine
53,3959,1.59500,lawine
53,5235,1.24373,lawine
53,6822,1.84814,lawine
53,9755,1.24105,lawine
53,13395,1.01676,lawine
53,17096,0.35531,lawine
53,226,0.33186,lawine
53,301,0.93333,lawine
53,371,0.98571,lawine
53,440,0.84058,lawine
53,498,0.84483,lawine
53,547,1.16327,lawine
53,604,1.05263,lawine
53,664,1.31667,lawine
53,743,1.34177,lawine
53,849,0.85849,lawine
53,940,1.23077,lawine
53,1052,0.68750,lawine
53,1129,1.58442,lawine
53,1251,0.81148,lawine
53,1350,1.36364,lawine
53,1485,0.75556,lawine
53,1587,0.86275,lawine
53,1675,1.67045,lawine
53,1822,1.55782,lawine
53,2051,1.24454,lawine
53,2336,1.92982,lawine
53,2886,1.48000,lawine
53,3700,1.27150,lawine
53,4735,1.42222,lawine
53,6207,1.49253,lawine
53,8404,1.30178,lawine
53,11264,1.30385,lawine
53,14993,0.58300,lawine
53,17167,0.57314,lawine
53,18413,0.08106,lawine
53,226,0.35398,hunger
53,306,0.96250,hunger
53,383,0.51948,hunger
53,423,0.60000,hunger
53,447,0.29167,hunger
53,454,0.00000,hunger
53,226,0.37168,lawine
53,310,0.71429,lawine
53,370,0.86667,lawine
53,422,0.84615,lawine
53,466,0.56818,lawine
53,491,0.84000,lawine
53,512,1.28571,lawine
53,539,0.66667,lawine
53,557,1.16667,lawine
53,578,0.52381,lawine
53,589,1.09091,lawine
53,601,1.25000,lawine
53,616,0.80000,lawine
53,628,0.91667,lawine
53,639,0.54545,lawine
53,645,1.16667,lawine
53,652,1.85714,lawine
53,665,1.30769,lawine
53,682,0.88235,lawine
53,697,2.00000,lawine
53,727,1.50000,lawine
53,772,0.77778,lawine
53,807,0.82857,lawine
53,836,0.62069,lawine
53,854,0.94444,lawine
53,871,0.76471,lawine
53,884,1.30769,lawine
53,901,1.23529,lawine
53,922,0.71429,lawine
53,937,1.20000,lawine
53,955,0.88889,lawine
53,971,0.81250,lawine
53,984,2.23077,lawine
53,1013,2.86207,lawine
53,1096,1.03614,lawine
53,1182,2.18605,lawine
53,1370,1.04255,lawine
53,1566,1.19388,lawine
53,1800,1.22650,lawine
53,2087,1.10453,lawine
53,2404,0.94637,lawine
53,2704,1.74333,lawine
53,3227,0.99618,lawine
53,3748,1.65067,lawine
53,4608,0.95698,lawine
53,5431,1.12151,lawine
53,6354,1.76490,lawine
53,7983,1.31369,lawine
53,10123,1.13879,lawine
53,12560,1.18876,lawine
53,15457,1.30652,lawine
53,19242,0.44756,lawine
53,226,0.42920,lawine
53,323,0.89691,lawine
53,410,1.13793,lawine
53,509,0.98990,lawine
53,607,1.31633,lawine
53,736,0.94574,lawine
53,858,1.18852,lawine
53,1003,1.23448,lawine
53,1182,1.10056,lawine
53,1379,1.57868,lawine
53,1690,1.95177,lawine
53,2297,1.50906,lawine
53,3213,1.45087,lawine
53,4542,1.37998,lawine
53,6376,1.46892,lawine
53,9070,1.23682,lawine
53,12402,1.18067,lawine
53,16336,0.82562,lawine
53,19584,0.06065,lawine
53,226,0.34513,hunger
53,304,0.89744,hunger
53,374,0.67143,hunger
53,421,0.59574,hunger
53,449,2.07143,hunger
53,507,0.89655,hunger
53,559,0.65385,hunger
53,593,0.64706,hunger
53,615,0.59091,hunger
53,628,2.30769,hunger
53,658,0.96667,hunger
53,687,1.06897,hunger
53,718,0.87097,hunger
53,745,0.55556,hunger
53,760,0.13333,hunger
53,765,0.33333,hunger
53,769,1.00000,hunger
53,772,2.00000,hunger
53,778,1.00000,hunger
53,784,0.50000,hunger
53,787,2.00000,hunger
53,793,0.16667,hunger
53,226,0.37168,lawine
53,310,1.08333,lawine
53,401,0.89011,lawine
53,482,2.18519,lawine
53,659,1.46893,lawine
53,919,0.81923,lawine
53,1132,0.99061,lawine
53,1343,1.91943,lawine
53,1748,1.60988,lawine
53,2400,1.43558,lawine
53,3336,1.48718,lawine
53,4728,1.79741,lawine
53,7230,1.37170,lawine
53,10662,1.23106,lawine
53,14887,0.02130,lawine
53,226,0.34956,lawine
53,305,0.77215,lawine
53,366,1.01639,lawine
53,428,1.30645,lawine
53,509,1.03704,lawine
53,593,1.97619,lawine
53,759,1.00000,lawine
53,925,1.12048,lawine
53,1111,1.33333,lawine
53,1359,0.87097,lawine
53,1575,1.00000,lawine
53,1791,1.30556,lawine
53,2073,1.60993,lawine
53,2527,1.32599,lawine
53,3129,1.51495,lawine
53,4041,1.43421,lawine
53,5349,1.31804,lawine
53,7073,1.40023,lawine
53,9487,1.12552,lawine
53,12204,0.88185,lawine
53,14600,0.92070,lawine
53,16806,0.09021,lawine
53,225,0.42667,lawine
53,321,0.98958,lawine
53,416,0.64211,lawine
53,477,0.75410,lawine
53,523,1.45652,lawine
53,590,1.04478,lawine
53,660,0.78571,lawine
53,715,1.70909,lawine
53,809,1.07447,lawine
53,910,1.77228,lawine
53,1089,1.57542,lawine
53,1371,1.63830,lawine
53,1833,1.33766,lawine
53,2451,1.46926,lawine
53,3359,1.49670,lawine
53,4718,1.48492,lawine
53,6736,1.00793,lawine
53,8770,1.27827,lawine
53,11370,1.28500,lawine
53,14711,0.71057,lawine
53,17085,0.36731,lawine
53,17957,0.10092,lawine
53,226,0.35398,lawine
53,306,1.07500,lawine
53,392,0.86047,lawine
53,466,1.87838,lawine
53,605,0.95683,lawine
53,738,1.00000,lawine
53,871,1.22556,lawine
53,1034,1.30061,lawine
53,1246,1.24528,lawine
53,1510,1.13636,lawine
53,1810,0.95333,lawine
53,2096,1.39510,lawine
53,2495,1.15038,lawine
53,2954,1.59041,lawine
53,3684,1.66575,lawine
53,4900,1.54688,lawine
53,6781,1.45720,lawine
53,9522,1.42904,lawine
53,13439,0.84759,lawine
53,16759,0.15392,lawine
53,226,0.36283,hunger
53,308,0.82927,hunger
53,376,0.83824,hunger
53,433,0.98246,hunger
53,489,0.73214,hunger
53,530,0.82927,hunger
53,564,0.70588,hunger
53,588,0.66667,hunger
53,604,0.43750,hunger
53,611,1.28571,hunger
53,620,0.44444,hunger
53,624,1.50000,hunger
53,630,1.50000,hunger
53,639,0.77778,hunger
53,646,1.42857,hunger
53,656,0.70000,hunger
53,663,0.42857,hunger
53,666,0.66667,hunger
53,226,0.39381,hunger
53,315,0.86517,hunger
53,392,0.76623,hunger
53,451,0.83051,hunger
53,500,0.53061,hunger
53,526,0.61538,hunger
53,542,0.81250,hunger
53,555,0.92308,hunger
53,567,0.91667,hunger
53,578,1.18182,hunger
53,591,0.53846,hunger
53,598,0.42857,hunger
53,601,0.33333,hunger
53,226,0.41593,lawine
53,320,0.70213,lawine
53,386,0.93939,lawine
53,448,1.29032,lawine
53,528,0.86250,lawine
53,597,2.04348,lawine
53,738,0.97872,lawine
53,876,0.87681,lawine
53,997,1.85950,lawine
53,1222,2.04444,lawine
53,1682,0.85870,lawine
53,2077,1.08608,lawine
53,2506,1.39394,lawine
53,3104,1.93144,lawine
53,4259,1.74978,lawine
53,6280,1.36616,lawine
53,9041,1.11373,lawine
53,12116,0.84715,lawine
53,14721,0.58042,lawine
53,16233,0.19709,lawine
53,226,0.34513,lawine
53,304,0.67949,lawine
53,357,0.73585,lawine
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53,225,0.39111,hunger
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56,15589,1.30015,lawine
56,20865,0.87528,lawine
56,25483,0.25401,lawine
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56,1320,2.00000,lawine
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56,3049,0.72402,lawine
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56,5548,1.17589,lawine
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56,8916,1.67235,lawine
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56,16744,0.45407,lawine
56,239,0.34728,hunger
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56,480,0.61702,lawine
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56,692,2.06977,lawine
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56,1096,1.39565,lawine
56,1417,1.05919,lawine
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56,2024,1.15730,lawine
56,2333,1.62460,lawine
56,2835,1.29084,lawine
56,3483,1.08333,lawine
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56,4998,1.04551,lawine
56,5848,1.29882,lawine
56,6952,1.42120,lawine
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56,10702,1.41495,lawine
56,13788,1.09106,lawine
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56,238,0.39916,hunger
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56,1037,1.20330,lawine
56,1256,0.73059,lawine
56,1416,1.10000,lawine
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56,2271,1.65260,lawine
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56,5370,0.95174,lawine
56,6435,1.29953,lawine
56,7819,1.12283,lawine
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56,11841,1.31199,lawine
56,15079,0.83076,lawine
56,17769,0.51078,lawine
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56,356,0.65000,hunger
56,382,0.73077,hunger
56,401,1.94737,hunger
56,438,0.56757,hunger
56,459,1.04762,hunger
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56,575,2.00000,hunger
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56,622,1.00000,hunger
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56,644,0.43636,hunger
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56,721,0.41379,hunger
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80,488,0.00000,hunger
80,342,0.22807,hunger
80,420,0.65385,hunger
80,471,0.25490,hunger
80,484,0.38462,hunger
80,489,0.60000,hunger
80,492,1.33333,hunger
80,496,0.25000,hunger
80,342,0.23099,hunger
80,421,0.45570,hunger
80,457,0.36111,hunger
80,470,0.46154,hunger
80,476,0.66667,hunger
80,480,0.75000,hunger
80,483,0.66667,hunger
80,342,0.24269,hunger
80,425,0.61446,hunger
80,476,0.56863,hunger
80,505,0.44828,hunger
80,518,0.23077,hunger
80,521,0.00000,hunger
80,342,0.21345,hunger
80,415,0.42466,hunger
80,446,0.25806,hunger
80,454,0.25000,hunger
80,342,0.29240,hunger
80,442,0.68000,hunger
80,510,0.60294,hunger
80,551,0.95122,hunger
80,590,0.48718,hunger
80,609,0.31579,hunger
80,615,0.16667,hunger
80,342,0.28070,hunger
80,438,0.58333,hunger
80,494,0.67857,hunger
80,532,0.23684,hunger
80,541,0.44444,hunger
80,545,0.75000,hunger
80,548,1.66667,hunger
80,553,0.20000,hunger
80,342,0.20760,hunger
80,413,0.56338,hunger
80,453,0.60000,hunger
80,477,0.41667,hunger
80,487,0.40000,hunger
80,491,0.50000,hunger
80,342,0.22807,hunger
80,420,0.38462,hunger
80,450,0.23333,hunger
80,457,0.57143,hunger
80,461,0.50000,hunger
80,342,0.19883,hunger
80,410,0.41176,hunger
80,438,0.39286,hunger
80,449,0.18182,hunger

Measured on 17 and 18 August 2026, α = 4.27, only confirmed unsatisfiable instances. Panel 1 from 5,842 rounds, Panel 2 from 40 trajectories, Panel 3 from the same rounds as Panel 1, Panel 4 from 60 instances each, Panel 5 from 480 (width 3) and 330 (width 4) instances. Tools rueckkopplung, bahnen, schnellp4; raw data daten/*.csv. A first attempt that estimated the reproduction number as a constant predicted the wrong thing and is recorded in BIFURKATION.md §2.