r-irbe Time Series Analysis & Temporal Mathematics
Comprehensive methodology for temporal mathematics — the computational backbone of phase trajectory computation, early warning signal detection, and multi-timescale architectures.
Routing
- USE FOR: Time series analysis, signal processing, temporal pattern detection, and multi-scale temporal dynamics. Use for mathematical reasoning about time-varying data, smoothing, derivative estimation, spectral analysis, changepoint detection, and temporal trajectory computation. Covers both theory and computational methodology.
- DO NOT USE FOR: measure-theoretic / probabilistic basis (use @math-measure-probability); Lean proofs (use @lean-math-stochastic); nonlinear dynamics (use @math-nonlinear-dynamics).
- TRIGGERS: time series, signal processing, temporal pattern, multi-scale temporal, spectral analysis.
Workflow
- Classify the signal: stationary / non-stationary, univariate / multivariate, discrete / continuous time.
- Pick the matching section (autocorrelation, spectral, wavelet, change-point, multi-scale).
- Produce the analytical answer; identify the Mathlib (or external) tool needed for implementation.
- Hand off: to
@lean-math-stochasticif a probabilistic guarantee is needed, to@math-measure-probabilityfor measure-theoretic basis, to@lean-zettelkasten.
Recovery & STOP
- STOP if the question is purely measure-theoretic — delegate to
@math-measure-probability. - STOP if nonlinear-dynamics methods are what's needed — delegate to
@math-nonlinear-dynamics. - STOP if a Mathlib pin-verified lemma is required — escalate to
@lean-research.
Handoffs
- Predecessors:
agent:gateway,skill:lean-research. - Successors:
skill:lean-math-stochastic,skill:math-measure-probability,skill:lean-zettelkasten.
Detailed reference
Full content for math-time-series lives in
references/math-time-series-handbook.md.
Load that file when the skill is convened; the SKILL.md only carries
the dispatch contract and the parts index.
| Section | Topic |
|---|---|
| Part 1 | Project Temporal Context |
| Part 2 | Smoothing and Derivative Estimation |
| Part 3 | Spectral Analysis |
| Part 4 | Changepoint Detection |
| Part 5 | Stochastic Time Series Models |
| Part 6 | Multi-Scale Temporal Methods |
| Part 7 | Connections to Formalization |
See also
../../references/math-time-series-handbook.md— Full handbook (extracted from this skill)../lean-math-stochastic/SKILL.md— Successor../math-measure-probability/SKILL.md— Successor../lean-zettelkasten/SKILL.md— Successor