Nothing new — this is the field-standard time-series feature set, embedded inside the atlas as our reference baseline.
Catch24 is not a geometry. It is the canonical catch22 feature set (Lubba et al. 2019) plus two location/scale features (mean and spread, making catch24), exposed as named atlas columns. We keep it as a lens so the standard comparator every time-series practitioner already knows sits inside the atlas's own redundancy structure — equivalence classes, PCA, dedup, uniqueness. It is the converse of the external capability assessment: rather than asking "what does the framework add over catch24?", it asks "where does catch24 land among the framework's own lenses?" Every novel metric is vetted against it — the rule-1 doppelgänger test requires a new axis to add over catch24, plain spectral, and AR, not merely beat its own baseline. Input is min-max normalized like every other lens, so only DN_Mean and DN_Spread_Std are affected by that normalization; the 22 catch22 features are mean/variance-independent by construction. Requires the optional pycatch22 dependency; undefined features (e.g. on a constant) report NaN row-preserving so the atlas still builds.
Mode of the value distribution (5-bin histogram).
Mode of the value distribution (10-bin histogram).
Mean of the normalized signal (the first catch24 location feature).
Standard deviation of the normalized signal (the second catch24 scale feature).
How the median shifts as positive outliers are progressively included (upper-tail timing).
Same, for negative outliers (lower-tail timing).
Fraction of successive differences exceeding 40 — a heart-rate-variability measure of step-to-step jumpiness. Autocorrelation & predictability
First lag where the autocorrelation decays below 1/e (correlation length).
First lag at which the autocorrelation reaches a local minimum.
Automutual information at lag 2 (5 bins) — nonlinear lag-2 dependence.
Time-reversal-asymmetry statistic (mean cubed lag-1 difference).
Exponential-fit residual of the distance distribution in a 2-D delay embedding.
First minimum of the Gaussian automutual information (decorrelation lag).
Change in correlation timescale after one-step mean forecasting.
Error of a 3-step local-mean forecast (short-range predictability). Scaling & fluctuation
Detrended-fluctuation-analysis scaling proportion (long-range correlation).
Rescaled-range (Hurst) scaling proportion. Spectral & periodicity
Centroid (center of mass) of the Welch power spectrum.
Power in the lowest fifth of the spectrum.
Wang periodicity measure (strongest period at threshold 0.01). Symbolic & motif
Longest run of consecutive values above the mean.
Longest run of consecutive decreasing steps.
Covariance of the 3-symbol transition-matrix diagonal (coarse-grained predictability).
Entropy of length-3 motifs over three quantile bins.
| Source | Origin | Value |
|---|---|---|
| Takagi Function | special-functions | 98.7170 |
| Magnetic Pendulum (3-Magnet) | continuous-flows | 56.9308 |
| fBm (Persistent) | stochastic-process | 37.4338 |
| ··· | ||
| Sine Wave | signal-synthesis | 0.0000 |
| Logistic r=3.2 (Period-2) | iterated-maps | 0.0000 |
| Rudin-Shapiro | symbolic-dynamics | 0.0000 |
| Source | Origin | Value |
|---|---|---|
| OTOC Growth | random-matrix-quantum | 13359.0000 |
| Levy Flight | stochastic-process | 6815.5000 |
| Rudin-Shapiro | symbolic-dynamics | 6455.5333 |
| ··· | ||
| Henon Map | iterated-maps | 1.0000 |
| Fibonacci Word | symbolic-dynamics | 1.0000 |
| Collatz Cycle Word | number-theory | 1.0000 |
| Source | Origin | Value |
|---|---|---|
| Riemann-Hardy-Littlewood | number-theory | 1.5593 |
| Sawtooth Wave | signal-synthesis | 1.5092 |
| Chua's Circuit | continuous-flows | 1.4760 |
| ··· | ||
| Penrose Substitution | symbolic-dynamics | 0.0000 |
| Fibonacci Word | symbolic-dynamics | 0.0000 |
| Rule 30 | symbolic-dynamics | 0.0000 |
| Source | Origin | Value |
|---|---|---|
| Levy Flight | stochastic-process | 2722.4283 |
| ETH/BTC Ratio | financial | 2380.4553 |
| Spectral Form Factor | random-matrix-quantum | 2362.3976 |
| ··· | ||
| Logistic r=3.2 (Period-2) | iterated-maps | 0.3161 |
| Logistic r=3.5 (Period-4) | iterated-maps | 0.3236 |
| Sine Map (Feigenbaum) | iterated-maps | 0.3307 |
| Source | Origin | Value |
|---|---|---|
| Rainfall (ORD Hourly) | atmospheric | 2.4267 |
| Critical Circle Map | iterated-maps | 2.3464 |
| Circle Map Quasiperiodic | iterated-maps | 2.3164 |
| ··· | ||
| Logistic r=3.83 (Period-3 Window) | iterated-maps | -3.5814 |
| Critical Circle Map (Bronze Mean) | iterated-maps | -3.1434 |
| Henon Map | iterated-maps | -2.9043 |
| Source | Origin | Value |
|---|---|---|
| Aubry-André Critical | random-matrix-quantum | 3.6296 |
| Fibonacci Tight-Binding | random-matrix-quantum | 2.5806 |
| Rainfall (ORD Hourly) | atmospheric | 2.5671 |
| ··· | ||
| Shuffled Blocks | stochastic-process | -1.4390 |
| Network Packet Sizes | algorithmic-bytes | -1.2776 |
| Copeland-Erdős | number-theory | -1.1043 |
| Source | Origin | Value |
|---|---|---|
| Aubry-André Critical | random-matrix-quantum | 7.3919 |
| Fibonacci Tight-Binding | random-matrix-quantum | 5.3090 |
| Rainfall (ORD Hourly) | atmospheric | 5.2444 |
| ··· | ||
| MFPT Inner Unloaded | machine-vibration | -1.9998 |
| Nikkei Returns | financial | -1.2091 |
| Network Packet Sizes | algorithmic-bytes | -1.1063 |
| Source | Origin | Value |
|---|---|---|
| Forest Fire | self-organized-criticality | 0.9799 |
| ECG Beat Conformity | physiological | 0.9361 |
| Henon Near-Crisis (a=1.43) | iterated-maps | 0.8984 |
| ··· | ||
| Aubry-André Critical | random-matrix-quantum | 0.0018 |
| Rainfall (ORD Hourly) | atmospheric | 0.0021 |
| Fibonacci Tight-Binding | random-matrix-quantum | 0.0027 |
| Source | Origin | Value |
|---|---|---|
| Nikkei Returns | financial | 0.3841 |
| GOES X-Ray Flux | astrophysical | 0.3833 |
| Potomac River Flow | geophysical | 0.3344 |
| ··· | ||
| SIR Epidemic | continuous-flows | -0.8051 |
| Critical Transition (Fold) | iterated-maps | -0.5100 |
| BTC Close Price | financial | -0.4519 |
| Source | Origin | Value |
|---|---|---|
| Critical Transition (Fold) | iterated-maps | 0.9291 |
| Goldbach r(2n) | number-theory | 0.5231 |
| Ambient Microseism | geophysical | 0.3714 |
| ··· | ||
| SIR Epidemic | continuous-flows | -0.9744 |
| OTOC Growth | random-matrix-quantum | -0.8563 |
| Spectral Form Factor | random-matrix-quantum | -0.7830 |
| Source | Origin | Value |
|---|---|---|
| Logistic r=3.2 (Period-2) | iterated-maps | 0.5000 |
| Thue-Morse | symbolic-dynamics | 0.5000 |
| L-System (Dragon Curve) | symbolic-dynamics | 0.5000 |
| ··· | ||
| Aubry-André Critical | random-matrix-quantum | 0.0133 |
| Stable Noise | stochastic-process | 0.0174 |
| Fibonacci Tight-Binding | random-matrix-quantum | 0.0183 |
| Source | Origin | Value |
|---|---|---|
| Van der Pol Oscillator | continuous-flows | 1.0084 |
| Sine Wave | signal-synthesis | 1.0003 |
| Blue Noise | stochastic-process | 1.0000 |
| ··· | ||
| Critical Transition (Fold) | iterated-maps | 0.0002 |
| Spectral Form Factor | random-matrix-quantum | 0.0003 |
| fBm (Antipersistent) | stochastic-process | 0.0003 |
| Source | Origin | Value |
|---|---|---|
| Logistic r=3.5 (Period-4) | iterated-maps | 1.3333 |
| Logistic r=3.2 (Period-2) | iterated-maps | 1.3333 |
| Sine Map (Feigenbaum) | iterated-maps | 1.3316 |
| ··· | ||
| Takagi Function | special-functions | 0.0047 |
| OTOC Growth | random-matrix-quantum | 0.0075 |
| Riemann-Hardy-Littlewood | number-theory | 0.0089 |
| Source | Origin | Value |
|---|---|---|
| Brownian Walk | stochastic-process | 40.0000 |
| Takagi Function | special-functions | 40.0000 |
| fBm (Antipersistent) | stochastic-process | 40.0000 |
| ··· | ||
| Henon Map | iterated-maps | 1.0000 |
| Collatz Cycle Word | number-theory | 1.0000 |
| DNA SARS-CoV-2 | genomic | 1.0000 |
| Source | Origin | Value |
|---|---|---|
| Stern-Brocot Walk | number-theory | 1.0000 |
| Logistic r=3.74 (Period-5 Window) | iterated-maps | 1.0000 |
| Phyllotaxis | number-theory | 1.0000 |
| ··· | ||
| fBm (Persistent) | stochastic-process | 0.0000 |
| Sine Wave | signal-synthesis | 0.0000 |
| Period-Doubled Wave | signal-synthesis | 0.0000 |
| Source | Origin | Value |
|---|---|---|
| Potomac River Flow | geophysical | 3990.0000 |
| Rudin-Shapiro | symbolic-dynamics | 3529.8000 |
| PID Controller | control-systems | 3512.5333 |
| ··· | ||
| OTOC Growth | random-matrix-quantum | 0.0000 |
| Critical Transition (Fold) | iterated-maps | 0.0000 |
| Critical Circle Map (Bronze Mean) | iterated-maps | 2.0000 |
| Source | Origin | Value |
|---|---|---|
| Spectral Form Factor | random-matrix-quantum | 4014.5000 |
| OTOC Growth | random-matrix-quantum | 3549.0000 |
| Exponential Chirp | signal-synthesis | 1993.0000 |
| ··· | ||
| Logistic Chaos | iterated-maps | 2.0000 |
| Kolakoski Sequence | symbolic-dynamics | 2.0000 |
| Logistic r=3.83 (Period-3 Window) | iterated-maps | 2.0000 |
| Source | Origin | Value |
|---|---|---|
| Levy Flight | stochastic-process | 6449.7000 |
| fBm (Persistent) | stochastic-process | 6235.3000 |
| Hilbert Walk | symbolic-dynamics | 5470.9000 |
| ··· | ||
| Logistic r=3.2 (Period-2) | iterated-maps | 2.0000 |
| Golden-Mean β-Shift | symbolic-dynamics | 2.0000 |
| Periodic Word | symbolic-dynamics | 2.0000 |
| Source | Origin | Value |
|---|---|---|
| Ramanujan Tau | number-theory | 2.1972 |
| BSL Residues | number-theory | 2.1972 |
| Benford's Law | stochastic-process | 2.1971 |
| ··· | ||
| Forest Fire | self-organized-criticality | 0.0000 |
| Mian-Chowla | number-theory | 0.0600 |
| Devil's Staircase | special-functions | 0.2422 |
| Source | Origin | Value |
|---|---|---|
| Forest Fire | self-organized-criticality | 0.3333 |
| Mian-Chowla | number-theory | 0.3240 |
| Devil's Staircase | special-functions | 0.2749 |
| ··· | ||
| Ramanujan Tau | number-theory | 0.0000 |
| White Noise | stochastic-process | 0.0000 |
| ChaCha20 | algorithmic-bytes | 0.0000 |
| Source | Origin | Value |
|---|---|---|
| Riemann-Hardy-Littlewood | number-theory | 0.8720 |
| Pulse-Width Modulation | signal-synthesis | 0.8340 |
| Takagi Function | special-functions | 0.8200 |
| ··· | ||
| Tribonacci Word | symbolic-dynamics | 0.1200 |
| Periodic Word | symbolic-dynamics | 0.1200 |
| Ocean Swell | geophysical | 0.1200 |
| Source | Origin | Value |
|---|---|---|
| Weierstrass | special-functions | 0.8420 |
| Ambient Microseism | geophysical | 0.8160 |
| Gaussian Collatz Orbit | number-theory | 0.8020 |
| ··· | ||
| Thue-Morse | symbolic-dynamics | 0.1200 |
| Symbolic Henon | iterated-maps | 0.1200 |
| Kolakoski Sequence | symbolic-dynamics | 0.1220 |
| Source | Origin | Value |
|---|---|---|
| OTOC Growth | random-matrix-quantum | 0.9999 |
| Takagi Function | special-functions | 0.9999 |
| Riemann-Hardy-Littlewood | number-theory | 0.9999 |
| ··· | ||
| Logistic r=3.2 (Period-2) | iterated-maps | 0.0000 |
| Logistic r=3.5 (Period-4) | iterated-maps | 0.0000 |
| Sine Map (Feigenbaum) | iterated-maps | 0.0000 |
| Source | Origin | Value |
|---|---|---|
| Logistic r=3.65 (Banded Chaos) | iterated-maps | 3.1416 |
| Quartic Map (Feigenbaum) | iterated-maps | 3.1416 |
| Sine Map (Feigenbaum) | iterated-maps | 3.1416 |
| ··· | ||
| fBm (Persistent) | stochastic-process | 0.0004 |
| Spectral Form Factor | random-matrix-quantum | 0.0004 |
| Perlin Noise | stochastic-process | 0.0004 |
Catch24 is a reference, not a detector — its value is as the comparison floor. Where a framework metric is linearly reconstructable from these 24 (high R²) it is a catch24 shadow; where it is not (low R²) it is a genuine framework addition. About 7 of the 24 catch24 features are themselves atlas-orthogonal multivariately, so the set is not redundant with the framework either — the two cover different ground, which is exactly why catch24 earns its place as the in-atlas baseline.