Polyphonic Stationarity Paper

**Author:** Henry Carstens **Date:** April 10, 2026 **Pages:** 8 **Project:** Stationarity Project **Full paper:**.

polyphonic-stationarity regime-detection heuristic-algebra lucid-judgment stationarity financial-markets
source Updated 2026-04-10

Polyphonic Stationarity: Detecting Regime Shifts in Financial Time Series via Frequency Decomposition, Synthetic Drift Generation, and Lucid Judgment

Author: Henry Carstens Date: April 10, 2026 Pages: 8 Project: Stationarity Project Full paper: PDF

Abstract

Introduces the Polyphonic Stationarity Metric. Decomposes time series via FFT into four voices at target frequencies (252, 126, 63, 31 trading days — a harmonic series). Computes a Polyphonic Drift Score (PDS, 0–1) based on amplitude stability, phase coherence, inter-voice coupling, and consonance ratios interpreted as musical intervals.

Central conclusion: stationarity breaks are not forecastable from market data — either internal dynamics or external cross-market “spiderweb” signals — but are reliably detectable after the fact.

Three falsifications

Test Hypothesis Result Key finding
Orbital Internal topology predicts drops Falsified Bounded noise
Tuning Autocorrelation predicts drops Falsified Independent but non-predictive
Spiderweb Cross-market web predicts target drops Falsified (0% lift) Consonance is local

SFF heuristics confirmed

  • SFF1 (Frequency-Specific Stationarity): Stationarity is per-voice, not aggregate. Global tests (ADF) mask this.
  • SFF2 (The Keynote): Longest-horizon pair maintains 100% consonance (unison/octave).
  • SFF3 (Mid-Range Fragility): Breaks originate in middle frequencies (63–126), where tritones and beating occur.

Spiderweb test results

5-asset FIIJ panel (copper, natgas, TNX, EURUSD, QQQ) vs. USD target:

Metric Value Status
Best lead correlation 0.062 FAIL (1st percentile vs null 95th at 0.171)
Zero-lag correlation 0.015 Near zero
Predictive lift -0.005 FAIL
Per-asset correlations -0.029 to +0.044 Noise

Consonance is a strictly local property of each market’s internal frequency spectrum. No structural propagation across assets at measurable lags.

Real series baselines

Dataset PDS Amp Stability Phase Coherence Coupling
USD Daily 0.42 0.64 0.60 0.03
SPY Hourly 0.33 0.38 0.60 0.00
CPI Monthly 0.55 0.61 0.93 0.10

All below 0.75 threshold, consistent with regime shifts.

Lucid Judgment application

LJ1–LJ7 governed the entire research program. LJ1 raised evidence bar to require beating FIIJ cascade (41.2% hit rate). LJ2 revised confidence from 35–45% (pre-test) to 5–10% for prediction, >80% for post-facto detection. LJ3 overweighted disconfirming evidence. LJ4 crossed threshold after spiderweb test — retired prediction-seeking. LJ6 confirmed no epistemic collapse. LJ7 activated return trigger on prediction orthodoxy.

Operational tools

  • Polyphonic Drift Score (PDS): composite metric, ≥0.75 = stationary, sharp drop = drift
  • Lag Sum Estimator: total lag = statistical + fidelity + cognitive tax
  • Conservation Triple Audit: theory/measurement/bias layers per LJ6
  • Atomic Fragility Flip: triggers on independence collapse
  • Drift-Decay Parallel Plot: lockstep confirmation of regime change

Connections to other work

  • Grounded in heuristic-algebra — uses ⊕ha, ⊕inn, ¬, π operators
  • lucid-judgment as meta-governance for the research program
  • Synthetic data generation follows SDG1–SDG5 axioms
  • Musical analogy from Heuristics of Harmony (Ha1–Ha7)

See Also