Catch24

Standard time-series features: autocorrelation timescale, distribution shape, automutual information, fluctuation/DFA scaling, Welch spectral summaries, symbolic motifs
referencedim 24 features24 metrics

What It Measures

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.

Metrics

DN_HistogramMode_5

Mode of the value distribution (5-bin histogram).

DN_HistogramMode_10

Mode of the value distribution (10-bin histogram).

DN_Mean

Mean of the normalized signal (the first catch24 location feature).

DN_Spread_Std

Standard deviation of the normalized signal (the second catch24 scale feature).

DN_OutlierInclude_p_001_mdrmd

How the median shifts as positive outliers are progressively included (upper-tail timing).

DN_OutlierInclude_n_001_mdrmd

Same, for negative outliers (lower-tail timing).

MD_hrv_classic_pnn40

Fraction of successive differences exceeding 40 — a heart-rate-variability measure of step-to-step jumpiness. Autocorrelation & predictability

CO_f1ecac

First lag where the autocorrelation decays below 1/e (correlation length).

CO_FirstMin_ac

First lag at which the autocorrelation reaches a local minimum.

CO_HistogramAMI_even_2_5

Automutual information at lag 2 (5 bins) — nonlinear lag-2 dependence.

CO_trev_1_num

Time-reversal-asymmetry statistic (mean cubed lag-1 difference).

CO_Embed2_Dist_tau_d_expfit_meandiff

Exponential-fit residual of the distance distribution in a 2-D delay embedding.

IN_AutoMutualInfoStats_40_gaussian_fmmi

First minimum of the Gaussian automutual information (decorrelation lag).

FC_LocalSimple_mean1_tauresrat

Change in correlation timescale after one-step mean forecasting.

FC_LocalSimple_mean3_stderr

Error of a 3-step local-mean forecast (short-range predictability). Scaling & fluctuation

SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1

Detrended-fluctuation-analysis scaling proportion (long-range correlation).

SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1

Rescaled-range (Hurst) scaling proportion. Spectral & periodicity

SP_Summaries_welch_rect_centroid

Centroid (center of mass) of the Welch power spectrum.

SP_Summaries_welch_rect_area_5_1

Power in the lowest fifth of the spectrum.

PD_PeriodicityWang_th0_01

Wang periodicity measure (strongest period at threshold 0.01). Symbolic & motif

SB_BinaryStats_mean_longstretch1

Longest run of consecutive values above the mean.

SB_BinaryStats_diff_longstretch0

Longest run of consecutive decreasing steps.

SB_TransitionMatrix_3ac_sumdiagcov

Covariance of the 3-symbol transition-matrix diagonal (coarse-grained predictability).

SB_MotifThree_quantile_hh

Entropy of length-3 motifs over three quantile bins.

Atlas Rankings

CO_Embed2_Dist_tau_d_expfit_meandiff
SourceOriginValue
Takagi Functionspecial-functions98.7170
Magnetic Pendulum (3-Magnet)continuous-flows56.9308
fBm (Persistent)stochastic-process37.4338
···
Sine Wavesignal-synthesis0.0000
Logistic r=3.2 (Period-2)iterated-maps0.0000
Rudin-Shapirosymbolic-dynamics0.0000
CO_FirstMin_ac
SourceOriginValue
OTOC Growthrandom-matrix-quantum13359.0000
Levy Flightstochastic-process6815.5000
Rudin-Shapirosymbolic-dynamics6455.5333
···
Henon Mapiterated-maps1.0000
Fibonacci Wordsymbolic-dynamics1.0000
Collatz Cycle Wordnumber-theory1.0000
CO_HistogramAMI_even_2_5
SourceOriginValue
Riemann-Hardy-Littlewoodnumber-theory1.5593
Sawtooth Wavesignal-synthesis1.5092
Chua's Circuitcontinuous-flows1.4760
···
Penrose Substitutionsymbolic-dynamics0.0000
Fibonacci Wordsymbolic-dynamics0.0000
Rule 30symbolic-dynamics0.0000
CO_f1ecac
SourceOriginValue
Levy Flightstochastic-process2722.4283
ETH/BTC Ratiofinancial2380.4553
Spectral Form Factorrandom-matrix-quantum2362.3976
···
Logistic r=3.2 (Period-2)iterated-maps0.3161
Logistic r=3.5 (Period-4)iterated-maps0.3236
Sine Map (Feigenbaum)iterated-maps0.3307
CO_trev_1_num
SourceOriginValue
Rainfall (ORD Hourly)atmospheric2.4267
Critical Circle Mapiterated-maps2.3464
Circle Map Quasiperiodiciterated-maps2.3164
···
Logistic r=3.83 (Period-3 Window)iterated-maps-3.5814
Critical Circle Map (Bronze Mean)iterated-maps-3.1434
Henon Mapiterated-maps-2.9043
DN_HistogramMode_10
SourceOriginValue
Aubry-André Criticalrandom-matrix-quantum3.6296
Fibonacci Tight-Bindingrandom-matrix-quantum2.5806
Rainfall (ORD Hourly)atmospheric2.5671
···
Shuffled Blocksstochastic-process-1.4390
Network Packet Sizesalgorithmic-bytes-1.2776
Copeland-Erdősnumber-theory-1.1043
DN_HistogramMode_5
SourceOriginValue
Aubry-André Criticalrandom-matrix-quantum7.3919
Fibonacci Tight-Bindingrandom-matrix-quantum5.3090
Rainfall (ORD Hourly)atmospheric5.2444
···
MFPT Inner Unloadedmachine-vibration-1.9998
Nikkei Returnsfinancial-1.2091
Network Packet Sizesalgorithmic-bytes-1.1063
DN_Mean
SourceOriginValue
Forest Fireself-organized-criticality0.9799
ECG Beat Conformityphysiological0.9361
Henon Near-Crisis (a=1.43)iterated-maps0.8984
···
Aubry-André Criticalrandom-matrix-quantum0.0018
Rainfall (ORD Hourly)atmospheric0.0021
Fibonacci Tight-Bindingrandom-matrix-quantum0.0027
DN_OutlierInclude_n_001_mdrmd
SourceOriginValue
Nikkei Returnsfinancial0.3841
GOES X-Ray Fluxastrophysical0.3833
Potomac River Flowgeophysical0.3344
···
SIR Epidemiccontinuous-flows-0.8051
Critical Transition (Fold)iterated-maps-0.5100
BTC Close Pricefinancial-0.4519
DN_OutlierInclude_p_001_mdrmd
SourceOriginValue
Critical Transition (Fold)iterated-maps0.9291
Goldbach r(2n)number-theory0.5231
Ambient Microseismgeophysical0.3714
···
SIR Epidemiccontinuous-flows-0.9744
OTOC Growthrandom-matrix-quantum-0.8563
Spectral Form Factorrandom-matrix-quantum-0.7830
DN_Spread_Std
SourceOriginValue
Logistic r=3.2 (Period-2)iterated-maps0.5000
Thue-Morsesymbolic-dynamics0.5000
L-System (Dragon Curve)symbolic-dynamics0.5000
···
Aubry-André Criticalrandom-matrix-quantum0.0133
Stable Noisestochastic-process0.0174
Fibonacci Tight-Bindingrandom-matrix-quantum0.0183
FC_LocalSimple_mean1_tauresrat
SourceOriginValue
Van der Pol Oscillatorcontinuous-flows1.0084
Sine Wavesignal-synthesis1.0003
Blue Noisestochastic-process1.0000
···
Critical Transition (Fold)iterated-maps0.0002
Spectral Form Factorrandom-matrix-quantum0.0003
fBm (Antipersistent)stochastic-process0.0003
FC_LocalSimple_mean3_stderr
SourceOriginValue
Logistic r=3.5 (Period-4)iterated-maps1.3333
Logistic r=3.2 (Period-2)iterated-maps1.3333
Sine Map (Feigenbaum)iterated-maps1.3316
···
Takagi Functionspecial-functions0.0047
OTOC Growthrandom-matrix-quantum0.0075
Riemann-Hardy-Littlewoodnumber-theory0.0089
IN_AutoMutualInfoStats_40_gaussian_fmmi
SourceOriginValue
Brownian Walkstochastic-process40.0000
Takagi Functionspecial-functions40.0000
fBm (Antipersistent)stochastic-process40.0000
···
Henon Mapiterated-maps1.0000
Collatz Cycle Wordnumber-theory1.0000
DNA SARS-CoV-2genomic1.0000
MD_hrv_classic_pnn40
SourceOriginValue
Stern-Brocot Walknumber-theory1.0000
Logistic r=3.74 (Period-5 Window)iterated-maps1.0000
Phyllotaxisnumber-theory1.0000
···
fBm (Persistent)stochastic-process0.0000
Sine Wavesignal-synthesis0.0000
Period-Doubled Wavesignal-synthesis0.0000
PD_PeriodicityWang_th0_01
SourceOriginValue
Potomac River Flowgeophysical3990.0000
Rudin-Shapirosymbolic-dynamics3529.8000
PID Controllercontrol-systems3512.5333
···
OTOC Growthrandom-matrix-quantum0.0000
Critical Transition (Fold)iterated-maps0.0000
Critical Circle Map (Bronze Mean)iterated-maps2.0000
SB_BinaryStats_diff_longstretch0
SourceOriginValue
Spectral Form Factorrandom-matrix-quantum4014.5000
OTOC Growthrandom-matrix-quantum3549.0000
Exponential Chirpsignal-synthesis1993.0000
···
Logistic Chaositerated-maps2.0000
Kolakoski Sequencesymbolic-dynamics2.0000
Logistic r=3.83 (Period-3 Window)iterated-maps2.0000
SB_BinaryStats_mean_longstretch1
SourceOriginValue
Levy Flightstochastic-process6449.7000
fBm (Persistent)stochastic-process6235.3000
Hilbert Walksymbolic-dynamics5470.9000
···
Logistic r=3.2 (Period-2)iterated-maps2.0000
Golden-Mean β-Shiftsymbolic-dynamics2.0000
Periodic Wordsymbolic-dynamics2.0000
SB_MotifThree_quantile_hh
SourceOriginValue
Ramanujan Taunumber-theory2.1972
BSL Residuesnumber-theory2.1972
Benford's Lawstochastic-process2.1971
···
Forest Fireself-organized-criticality0.0000
Mian-Chowlanumber-theory0.0600
Devil's Staircasespecial-functions0.2422
SB_TransitionMatrix_3ac_sumdiagcov
SourceOriginValue
Forest Fireself-organized-criticality0.3333
Mian-Chowlanumber-theory0.3240
Devil's Staircasespecial-functions0.2749
···
Ramanujan Taunumber-theory0.0000
White Noisestochastic-process0.0000
ChaCha20algorithmic-bytes0.0000
SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1
SourceOriginValue
Riemann-Hardy-Littlewoodnumber-theory0.8720
Pulse-Width Modulationsignal-synthesis0.8340
Takagi Functionspecial-functions0.8200
···
Tribonacci Wordsymbolic-dynamics0.1200
Periodic Wordsymbolic-dynamics0.1200
Ocean Swellgeophysical0.1200
SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1
SourceOriginValue
Weierstrassspecial-functions0.8420
Ambient Microseismgeophysical0.8160
Gaussian Collatz Orbitnumber-theory0.8020
···
Thue-Morsesymbolic-dynamics0.1200
Symbolic Henoniterated-maps0.1200
Kolakoski Sequencesymbolic-dynamics0.1220
SP_Summaries_welch_rect_area_5_1
SourceOriginValue
OTOC Growthrandom-matrix-quantum0.9999
Takagi Functionspecial-functions0.9999
Riemann-Hardy-Littlewoodnumber-theory0.9999
···
Logistic r=3.2 (Period-2)iterated-maps0.0000
Logistic r=3.5 (Period-4)iterated-maps0.0000
Sine Map (Feigenbaum)iterated-maps0.0000
SP_Summaries_welch_rect_centroid
SourceOriginValue
Logistic r=3.65 (Banded Chaos)iterated-maps3.1416
Quartic Map (Feigenbaum)iterated-maps3.1416
Sine Map (Feigenbaum)iterated-maps3.1416
···
fBm (Persistent)stochastic-process0.0004
Spectral Form Factorrandom-matrix-quantum0.0004
Perlin Noisestochastic-process0.0004

When It Lights Up

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.

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