Whether nearby values cooperate or compete.
Treats each window of your data as a miniature spin glass — a system where local constraints may be impossible to satisfy simultaneously. Fits the maximum-entropy pairwise interaction model and extracts three properties of the resulting energy landscape.
How strongly do positions in a window constrain each other? Monotonic signals have extreme coupling (each value predicts the next). Noise has near-zero coupling. Periodic orbits of the logistic map dominate the atlas: the period-3 window (r=3.83) scores 15.3, while white noise scores 0.01.
What fraction of local constraints are mutually contradictory? Three positions A, B, C are frustrated when A wants B up, B wants C up, but A wants C down — they can't all be satisfied. The Fibonacci word scores 1.0 (maximally frustrated): the golden ratio creates irreconcilable correlations at every scale. Pink noise scores 0.0 (all correlations agree). White noise scores ~0.5 (random constraints, half frustrated by chance). Quantum walk probability amplitudes also hit 1.0 — a different mechanism (interference) producing the same geometric signature.
How degenerate is the coupling spectrum? Near 0 means one dominant interaction mode (hierarchical structure). Near 1 means all modes are equally important. L-System (Dragon Curve) and Rule 110 score ~1.0; logistic period-4 scores 0.14.
How strongly does the nearest-neighbor coupling dominate over longer-range interactions? EEG Seizure (3.80), Ocean Swell (3.79), and Mackey-Glass (3.78) score highest — their smooth, locally correlated dynamics concentrate coupling at the nearest lag. Forest fire and constants score 0.0 (no dominant coupling distance). Evolved via ShinkaEvolve.
How much does the coupling matrix change between the first and second halves of the signal? Devil's Staircase (2.0) and Middle-Square (1.86) score highest — their dynamics shift character midstream, producing different interaction structures in each half. Sine wave scores near 0.0 (stable coupling throughout). This is a direct stationarity test on the Ising model's interaction structure. Evolved via ShinkaEvolve.
Lag (in bits) of the strongest autocorrelation in the binarized signal, gated by an IID significance floor (returns 0 when max|c(k)| < 5/√n_bits). Detects byte-alignment lattices in binary executables (Linux ELF=16, Windows PE=8, Mach-O=4) and period-locked sources (Chirikov=4, Rule 110=7, Quantum Walk=16). L-System Dragon and Collatz Flights peg the lag at 1024 (the full bit-window — their binary correlations decay slower than the window scale resolves); Fibonacci Word (987), Möbius Function (860), and Divisor Count (828) sit just below. Benford's Law, Bernoulli Shift, Wigner Semicircle, Entanglement Entropy, and Poisson Spacings all return 0 — no peak survives the IID gate. This is a categorical "what's the period?" detector rather than a graded score.
| Source | Domain | Value |
|---|---|---|
| Logistic r=3.83 (Period-3 Window) | chaos | 15.2634 |
| Logistic r=3.5 (Period-4) | chaos | 12.4844 |
| Sine Map (Feigenbaum) | chaos | 12.4844 |
| ··· | ||
| Forest Fire | exotic | 0.0000 |
| Liouville Function | number_theory | 0.0048 |
| √2 Digits | number_theory | 0.0050 |
| Source | Domain | Value |
|---|---|---|
| Mian-Chowla | number_theory | 2.0000 |
| Nikkei Returns | financial | 1.9823 |
| NASDAQ Returns | financial | 1.7509 |
| ··· | ||
| Forest Fire | exotic | 0.0000 |
| Quartic Map (Feigenbaum) | chaos | 0.0000 |
| Logistic Edge-of-Chaos | chaos | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| L-System (Dragon Curve) | exotic | 1024.0000 |
| Collatz Flights | number_theory | 1024.0000 |
| Critical Circle Map (Silver Mean) | chaos | 991.0000 |
| ··· | ||
| Logistic Chaos | chaos | 0.0000 |
| White Noise | noise | 0.0000 |
| AES Encrypted | binary | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Penrose Substitution | exotic | 1.0000 |
| Logistic r=3.74 (Period-5 Window) | chaos | 1.0000 |
| Fibonacci Word | exotic | 1.0000 |
| ··· | ||
| Critical Transition (Fold) | chaos | 0.0000 |
| Mian-Chowla | number_theory | 0.0000 |
| Riemann-Hardy-Littlewood | exotic | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| EEG Eyes Closed | medical | 3.7820 |
| EEG Seizure | medical | 3.7811 |
| Earthquake P-wave | geophysics | 3.7707 |
| ··· | ||
| Forest Fire | exotic | 0.0000 |
| L-System (Dragon Curve) | exotic | 0.0002 |
| Critical Circle Map (Bronze Mean) | chaos | 0.0012 |
| Source | Domain | Value |
|---|---|---|
| Forest Fire | exotic | 1.0000 |
| L-System (Dragon Curve) | exotic | 0.9998 |
| Partition Function | number_theory | 0.9962 |
| ··· | ||
| Mian-Chowla | number_theory | 0.1429 |
| Logistic r=3.2 (Period-2) | chaos | 0.1429 |
| Sine Map (Feigenbaum) | chaos | 0.1429 |
Boltzmann frustration is the framework's most specific quasicrystal detector. In the atlas, Fibonacci word is the only non-quantum source to achieve frustration = 1.0. The metric is encoding-invariant: it depends only on which positions are above or below the median, not on the byte values themselves. dominant_lag is the geometry's binary-period reporter; it's most useful as a categorical label (ELF=16, PE=8, Rule 110=7) rather than a continuous discriminator.