---
slug: predictability_horizon
name: Predictability Horizon
one_liner: "The temporal consequence of chaos: because small uncertainties in a sensitively-dependent system grow exponentially at a rate set by the largest Lyapunov exponent, useful prediction is possible only up to a finite time — beyond that horizon, forecasts decay to no better than climatology."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, mathematical, physical]
origin_domain: dynamical_systems
alternate_origin_domains: [meteorology, celestial_mechanics, fluid_dynamics, epidemiology]
aliases: [lyapunov_time, forecast_horizon, finite_prediction_limit, limit_of_forecastability, error_doubling_time]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-03 temporalization, flavor 3b/3c) — the TEMPORAL/anticipatory structure obtained by temporalizing `chaos`: the static property of sensitive dependence on initial conditions, run forward in time, yields a hard finite limit on forecastability (the Lyapunov time). Discovered in the op-03 temporalization sweep 2026-07-03. MODERATE hold (verified absent from corpus; established scientific name — Lyapunov time, predictability horizon; the ~2-week limit on weather forecasting). STATUS: HOLD pending owner keep/cut."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Phase-C action: re-similarity-check vs `chaos` (the input / parent — HIGH SIMILARITY ~0.55–0.65, the primary keep/cut risk) and `sensitive_dependence` (if present), `nonlinearity`, any butterfly-effect prime, and any general forecasting/uncertainty prime; confirm it is the genuine temporal lift (a quantifiable forecast-time limit) and not merely a restatement of chaos or of generic uncertainty; draw a subsumption/relation edge chaos→predictability_horizon at incorporation; write a v1 draft and sync the one_liner across v1/v2 per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 5
  structural_abstraction: 4
  transfer_evidence: 4
  reasoning: 'The bare structure — exponential growth of initial uncertainty at a rate set by the largest Lyapunov exponent, so that prediction stays useful only up to a finite horizon fixed by that rate and the measurement precision — is a genuinely substrate-neutral temporal form. It recurs wherever a nonlinear dynamical system exhibits sensitive dependence: the ~2-week horizon in numerical weather prediction, the ~5-million-year predictability limit of the solar system in celestial mechanics, the loss of forecastability in turbulent fluid flow, and the divergence of long-run epidemic trajectories. These are structurally-unlike siblings sharing only the abstract error-growth-to-finite-horizon anatomy, so domain_breadth scores 5. Structural abstraction is 4 because the core is a pure statement relating an exponential divergence rate and an initial precision to a time bound, requiring no physical substance to hold; it stays just short of 5 because the "useful prediction" threshold carries a mild evaluative/pragmatic residue (how good is good enough sets where the horizon lands). Transfer evidence is strong (Lyapunov time is an independently named, quantitatively deployed construct across meteorology, celestial mechanics, and dynamical-systems theory).'
similarity_to_nearest_existing_prime:
  slug: chaos
  similarity: 0.60
structural_framed:
  label: structural
  aggregate: 0.40
  criteria: {vocab_travels: 0.7, evaluative_weight: 0.4, institutional_origin: 0.1, human_practice_bound: 0.3, import_vs_recognize: 0.4}
  rationale: 'Reads structural-to-mixed. The core claim — exponentially growing uncertainty imposes a finite, quantifiable prediction horizon — is recognized rather than imported, and travels cleanly from weather to celestial mechanics to any nonlinear dynamical system without carrying meteorological vocabulary. The frame residue is light but nonzero: "useful prediction" and "forecast" import a mild human-practice / evaluative cast (keeping human_practice_bound and evaluative_weight off the floor), because where exactly the horizon falls depends on a pragmatic threshold for acceptable forecast skill. The underlying temporal structure — exponential error growth against a fixed measurement precision yielding a time bound — is substrate-neutral. Comparable framing to its parent `chaos`, with a slightly larger epistemic/forecasting tint.'
phase_b_passes_completed: []
---
# Predictability Horizon

## Core Idea

Predictability horizon is the *temporal* consequence of `chaos`: run a sensitively-dependent nonlinear system forward in time, and the finite structure that emerges is a hard, quantifiable limit on how far ahead its future can be usefully predicted. The static prime `chaos` names the *property* — sensitive dependence on initial conditions, in which arbitrarily small differences in the starting state grow into large differences in the trajectory. Temporalize that property, and it acquires a clock: the initial uncertainty does not merely grow, it grows *exponentially*, at a rate set by the largest Lyapunov exponent, so that after a characteristic time (the Lyapunov time, one over that exponent) the error has swelled to the size of the system's own variability. Beyond that point the forecast carries no information — it is no better than climatology, no better than guessing from the long-run distribution. The load-bearing anatomy is the passage *exponential error growth → finite horizon*: a divergence rate and a measurement precision jointly fix a time, and past that time prediction fails not gradually but decisively.

The feature present at the temporal level but absent at the static one is precisely this *finite forecast-time bound*. `chaos` as a static property tells you that trajectories diverge; it does not, on its own, name *when* prediction gives out, or that the failure has a definite time scale computable from the divergence rate and the initial precision. Temporalization supplies exactly that missing structure — the horizon is a temporal object, a limit measured in units of time (two weeks for weather, roughly five million years for the inner solar system), not a property of the phase-space geometry as such. Two systems can both be chaotic yet have wildly different horizons; the horizon, not the mere fact of chaos, is what governs whether forecasting is worth attempting and for how long. This is the temporal/epistemic signature of chaos, distinct from the dynamical property that generates it.

Read structurally, the same shape recurs wherever a nonlinear system exhibits sensitive dependence, and the siblings are genuinely unlike. In *meteorology* it is the forecast horizon — the reason numerical weather prediction saturates at around two weeks regardless of model or data quality. In *celestial mechanics* it is the predictability limit of the solar system — chaotic planetary orbits whose detailed future is computable only some millions of years out. In *fluid dynamics* it is the loss of forecastability in turbulent flow; in *epidemiology* it is the divergence of long-run outbreak trajectories from any early projection. And as a general *epistemic* point it is a substrate-neutral statement about the limits of forecasting: whenever errors compound exponentially, more data and better models buy only logarithmically more lead time, so there is a wall no forecasting effort can push past. Across these, the shared abstract structure is exponential uncertainty growth against a fixed precision yielding a finite prediction horizon; the weather case is one species of the genus.

## Notes

**Provenance.** Produced by operator 03 (temporalization), flavor 3b/3c, as the temporal/anticipatory structure obtained by temporalizing `chaos` — running the static property of sensitive dependence on initial conditions forward in time to expose the finite forecast-time limit it implies. Surfaced in the op-03 temporalization sweep on 2026-07-03. Established scientific construct: the *Lyapunov time* (the reciprocal of the largest Lyapunov exponent) and the *predictability horizon* — canonically, the ~2-week limit on weather forecasting and the ~5-million-year predictability limit of the solar system. Claimed siblings: forecast horizons in meteorology, predictability limits in celestial mechanics, loss of forecastability in turbulent fluid flow and long-run epidemic projection, and the general epistemic point about exponential error growth capping forecast lead time. Verified absent from the corpus. Manifest: MODERATE hold.

**For owner evaluation (keep/cut).** The case FOR: predictability horizon is a *canonical, named scientific construct* (Lyapunov time; the "weather is unpredictable beyond two weeks" limit), verified absent, with a clean and quantifiable anatomy — exponential error growth against a fixed precision yields a finite time bound — and broad, structurally-unlike reach across meteorology, celestial mechanics, fluid dynamics, and epidemiology. It captures something the corpus does not: a *quantifiable limit on forecastability*, an idea of real importance that is not the same object as the dynamical property of chaos. The RISKS Kurt should weigh: (1) **fairly high similarity (~0.55–0.65) to its parent `chaos`** — this is the primary keep/cut risk; the discriminating claim is that predictability_horizon is the *temporal / epistemic consequence* (a forecast-time limit set by the Lyapunov time), not the dynamical property itself. `chaos` names sensitive dependence as a static feature of the system; predictability_horizon names *when prediction fails and by how long*, a temporal object computable from the divergence rate and the initial precision. The owner should decide whether that temporal lift earns a distinct prime or is best treated as a facet of `chaos`. (2) **Overlap with general uncertainty/forecasting primes** — screen against any prime covering forecast error, epistemic limits, or uncertainty growth, since the "useful prediction gives out" framing borders on generic forecasting. Sharp keep/cut question: *is "the finite Lyapunov-time limit on forecasting" a distinct prime, or is it just `chaos` seen from the forecaster's chair?* — the proposer's answer is that the finite forecast-time bound, quantified by the divergence rate and precision, is a temporal feature the static property does not carry.

**At incorporation.** Re-run similarity against `chaos` (input / parent — the high-similarity risk to resolve first), `sensitive_dependence` (if present in the corpus), `nonlinearity`, any butterfly-effect prime, and any general forecasting / uncertainty / epistemic-limit prime to confirm no collapse. If kept: draw a subsumption or relation edge `chaos` → `predictability_horizon` (the temporal consequence of the dynamical property), and add a missing-edge note flagging the `chaos`-as-static vs `predictability_horizon`-as-temporal contrast explicitly so the two are not later confused or merged. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
