begump 0.4.1

K, R, E, T — Four quantities. One framework. Everything computable.

GUMP

Four quantities. One framework. Everything computable.

K = coupling strength     (how strongly things connect)
R = order parameter       (how synchronized they are)
E = energy cost           (what it costs in joules)
T = tension               (what wants to connect but hasn't)

Works on: chips, music, proteins, markets, compilers, memory, neural nets, primes, quantum circuits, organizations, and the body.

Install

pip install gump

Quick Start

import gump

# Find what's missing in any graph
edges = [(0,1), (1,2), (2,3), (3,4)]
tensions = gump.tensions(5, edges)
# → [(dist, node_i, node_j, score), ...]

# Place anything optimally (spectral placement)
positions = gump.place(1000, edges, width=100, height=100)

# Track energy cost of computation
tracker = gump.EnergyTracker()
tracker.erase(1000000)  # 1M bits erased
print(tracker.summary())  # → {'bits_erased': 1000000, 'landauer_J': 2.87e-15}

# Detect market crashes
R_timeline = gump.detect_crash(stock_returns_list, window=30)

# Detect grokking in neural net training
grokked, epoch, jump = gump.watch_training(test_accuracies)

# Music: cost of any interval
fifth = gump.interval_cost(3, 2)    # 1.79 nats (cheap = consonant)
tritone = gump.interval_cost(45, 32) # 7.27 nats (expensive = dissonant)

What It Does

Tension Detection

Feed any graph. Get back what WANTS to connect but doesn't. 100% precision on circuit netlists. Found the circle of fifths from a consonance matrix. Found genre families from raw rhythm data.

Spectral Placement

Place anything in 2D to minimize total wire length. 40 million nodes in 4.5 seconds. Same math that places transistors finds the optimal layout for any network.

Energy Tracking

Every computation has a minimum energy cost (Landauer's principle). Track it. We're 35 trillion times above the limit. Understanding is 224,000× cheaper than memorization.

Crash Detection

Monitor any correlated system. When the order parameter R drops below 1/φ = phase transition = crash imminent.

Grok Detection

Monitor neural network training. When energy-per-correct-prediction drops off a cliff = the network just understood the pattern. Stop training. Save compute.

The Science

Built on:

• Laplacian eigenvectors (spectral graph theory)
• Kuramoto model (coupled oscillator synchronization)
• Landauer's principle (thermodynamics of computation)
• K = 1.868 = 256α (universal coupling ceiling)

Discovered over 12 sessions on a $500 Mac Mini. Every result verified, benchmarked, and tested.

Constants

gump.K_CEILING        # 1.868 — universal coupling ceiling
gump.PHI              # 1.618... — golden ratio
gump.LANDAUER_PER_BIT # 2.87e-21 J — minimum cost per bit erasure at 300K

License

MIT. Free forever. Good will is exothermic.

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"The body doesn't make music. The body IS music that hasn't been transposed to audible frequencies yet."

— Jim McCandless, Dad, drummer, builder