Soil Anderson Deep Dive — Track 4 Domain Exemplar
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Soil Anderson Deep Dive — Track 4 Domain Exemplar
Anderson localization — originally a condensed matter physics concept (waves in disordered media) — applied to soil microbial ecology. The key insight: quorum sensing (QS) in soil pore networks is structurally isomorphic to electron transport in disordered lattices.
This notebook loads 9 Track 4 soil experiments, each validated against a published field study, and visualizes the Anderson-QS connection.
Data sources: experiments/results/170_* through 178_*
For other springs: this is what a domain deep-dive looks like. Pick your most compelling cross-domain connection and build a notebook around it.
import json
from pathlib import Path
import matplotlib
# matplotlib backend set by environment
import matplotlib.pyplot as plt
import numpy as np
RESULTS = Path('..') / 'experiments' / 'results'
def load_soil(dirname):
d = RESULTS / dirname
if d.exists():
jsons = list(d.glob('*.json'))
if jsons:
with open(jsons[0]) as f:
return json.load(f)
return None
soil_170 = load_soil('170_soil_qs_pore_geometry')
soil_171 = load_soil('171_soil_pore_diversity')
soil_172 = load_soil('172_soil_distance_colonization')
soil_173 = load_soil('173_notill_brandt_farm')
soil_174 = load_soil('174_notill_meta_analysis')
soil_175 = load_soil('175_notill_longterm_tillage')
soil_176 = load_soil('176_soil_biofilm_aggregate')
soil_177 = load_soil('177_soil_structure_function')
soil_178 = load_soil('178_tillage_microbiome')
loaded = sum(1 for d in [soil_170, soil_171, soil_172, soil_173, soil_174,
soil_175, soil_176, soil_177, soil_178] if d is not None)
print(f'Loaded {loaded}/9 soil experiment baselines')Experiment 170: QS Probability vs Pore Geometry
The Anderson connection: soil pore size controls effective disorder W. Small pores (clay) → high W → localized (no QS). Large pores (sand) → low W → extended (QS active).
Martinez et al. 2023 provided the pore geometry framework.
if soil_170 and 'pore_mapping' in soil_170:
pores = soil_170['pore_mapping']
pore_sizes = [p['pore_um'] for p in pores]
qs_probs = [p['qs_probability'] for p in pores]
w_values = [p['effective_w'] for p in pores]
connectivity = [p['connectivity'] for p in pores]
fig, axes = plt.subplots(1, 3, figsize=(15, 5))
# QS probability vs pore size
ax = axes[0]
ax.plot(pore_sizes, qs_probs, 'o-', color='#2ecc71', linewidth=2, markersize=8)
ax.set_xlabel('Pore size (\u00b5m)')
ax.set_ylabel('QS probability')
ax.set_title('Quorum Sensing vs Pore Size')
ax.axhline(y=0.5, color='red', linestyle='--', alpha=0.5, label='Critical threshold')
ax.legend()
ax.grid(True, alpha=0.3)
# Effective disorder W vs pore size
ax = axes[1]
ax.plot(pore_sizes, w_values, 's-', color='#e74c3c', linewidth=2, markersize=8)
ax.set_xlabel('Pore size (\u00b5m)')
ax.set_ylabel('Effective disorder W')
ax.set_title('Anderson Disorder Parameter')
ax.axhline(y=16.5, color='blue', linestyle='--', alpha=0.5, label='W_c (critical)')
ax.legend()
ax.grid(True, alpha=0.3)
# Connectivity vs pore size
ax = axes[2]
ax.plot(pore_sizes, connectivity, 'D-', color='#3498db', linewidth=2, markersize=8)
ax.set_xlabel('Pore size (\u00b5m)')
ax.set_ylabel('Connectivity')
ax.set_title('Network Connectivity')
ax.grid(True, alpha=0.3)
plt.suptitle('Exp 170: Pore Geometry \u2192 Anderson Disorder \u2192 QS Probability',
fontsize=14, fontweight='bold')
plt.tight_layout()
plt.savefig('/tmp/wetspring_05_pore_qs.png', dpi=150, bbox_inches='tight')
plt.show()
else:
print('Exp 170 data not available')Chemotaxis as Disorder Reduction
Bacterial chemotaxis reduces the effective disorder by 15%, shifting the Anderson transition. The benefit is maximal near the critical disorder W_c = 16.5.
if soil_170 and 'chemotaxis' in soil_170:
chem = soil_170['chemotaxis']
sweep = chem['disorder_sweep']
w_vals = [s['w'] for s in sweep]
p_no = [s['p_no_chemotaxis'] for s in sweep]
p_with = [s['p_with_chemotaxis'] for s in sweep]
benefit = [s['benefit'] for s in sweep]
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
ax = axes[0]
ax.plot(w_vals, p_no, 'o-', color='#e74c3c', label='Without chemotaxis', linewidth=2)
ax.plot(w_vals, p_with, 's-', color='#2ecc71', label='With chemotaxis', linewidth=2)
ax.set_xlabel('Disorder W')
ax.set_ylabel('QS probability')
ax.set_title('Chemotaxis Shifts the Anderson Transition')
ax.axvline(x=16.5, color='blue', linestyle='--', alpha=0.5, label='W_c')
ax.legend()
ax.grid(True, alpha=0.3)
ax = axes[1]
ax.bar(w_vals, benefit, width=2, color='#9b59b6', alpha=0.8)
ax.set_xlabel('Disorder W')
ax.set_ylabel('Benefit (\u0394 QS probability)')
ax.set_title('Chemotaxis Benefit — Maximal Near W_c')
ax.grid(True, alpha=0.3)
plt.suptitle(f'Chemotaxis Reduces Effective Disorder by {chem["reduction_pct"]}%',
fontsize=14, fontweight='bold')
plt.tight_layout()
plt.savefig('/tmp/wetspring_05_chemotaxis.png', dpi=150, bbox_inches='tight')
plt.show()
else:
print('Chemotaxis data not available')Integrated Soil Types
The model applied to real soil types: sandy loam, clay, no-till aggregates, and tilled soil. Anderson localization predicts QS activity directly from pore geometry.
if soil_170 and 'integrated' in soil_170:
soils = soil_170['integrated']
fig, ax = plt.subplots(figsize=(10, 6))
names = [s['name'] for s in soils]
qs_probs = [s['qs_probability'] for s in soils]
coop = [s['coop_survival'] for s in soils]
colors = ['#2ecc71' if s['qs_active'] else '#e74c3c' for s in soils]
x = np.arange(len(names))
width = 0.35
bars1 = ax.bar(x - width/2, qs_probs, width, label='QS probability', color=colors, alpha=0.8)
bars2 = ax.bar(x + width/2, coop, width, label='Cooperative survival', color='#3498db', alpha=0.6)
ax.set_ylabel('Probability')
ax.set_title('Soil Type \u2192 QS Activity \u2192 Cooperative Survival')
ax.set_xticks(x)
ax.set_xticklabels(names, rotation=15, ha='right', fontsize=9)
ax.legend()
ax.axhline(y=0.5, color='gray', linestyle=':', alpha=0.5)
ax.grid(True, alpha=0.2, axis='y')
plt.tight_layout()
plt.savefig('/tmp/wetspring_05_soil_types.png', dpi=150, bbox_inches='tight')
plt.show()
print('Soil type predictions:')
for s in soils:
status = 'QS ACTIVE' if s['qs_active'] else 'QS SUPPRESSED'
print(f' {s["name"]:<40s} W={s["effective_w"]:<6.1f} '
f'P(QS)={s["qs_probability"]:.4f} {status}')
else:
print('Integrated soil data not available')Track 4 Experiment Overview
9 experiments, each validated against a specific published paper.
experiments = [
('170', 'Soil QS Pore Geometry', 'Martinez 2023', soil_170),
('171', 'Soil Pore Diversity', 'Feng 2024', soil_171),
('172', 'Distance Colonization', 'Mukherjee 2024', soil_172),
('173', 'No-Till Brandt Farm', 'Islam 2014', soil_173),
('174', 'No-Till Meta-Analysis', 'Zuber 2016', soil_174),
('175', 'Long-Term Tillage', 'Liang 2015', soil_175),
('176', 'Biofilm Aggregate', 'Tecon 2017', soil_176),
('177', 'Structure-Function', 'Rabot 2018', soil_177),
('178', 'Tillage Microbiome', 'Wang 2025', soil_178),
]
print(f'{"Exp":>4s} {"Title":<30s} {"Paper":<18s} {"Data Keys"}')
print('=' * 80)
for exp_id, title, paper, data in experiments:
if data:
keys = [k for k in data.keys() if k != 'math_verification']
print(f'{exp_id:>4s} {title:<30s} {paper:<18s} {len(keys)} sections')
else:
print(f'{exp_id:>4s} {title:<30s} {paper:<18s} NOT LOADED')
print(f'\nAll {loaded} experiments have frozen Python baselines.')
print('Each has a corresponding Rust validator in barracuda/src/bin/.')The Anderson Isomorphism
Physics (hotSpring) Biology (wetSpring)
────────────────── ──────────────────────
Electron in lattice ↔ Bacterium in soil pore
Disorder W ↔ Pore geometry variation
Critical W_c = 16.5 ↔ Pore size ~50\u00b5m threshold
Extended state (conducts) ↔ QS active (cooperates)
Localized state (insulates)↔ QS suppressed (isolated)
Anderson transition ↔ Tillage disruption
Chemotaxis ↔ Disorder reduction (\u039412-15%)This is the key scientific insight: the same mathematics that describes electron transport in disordered solids predicts microbial cooperation in soil pore networks. The Rust implementation validates both domains using shared barraCuda primitives (erf_f64, eigenvalue solvers, spectral methods).
hotSpring validates the physics. wetSpring validates the biology. groundSpring provides the uncertainty budget. The composition proves they’re the same math.
baseCamp Paper 06: No-till Anderson
Source: syntheticChemistry/wetSpring | Hub: primals.eco/lab/springs/wetspring