coherence time concept

Definition	The interval over which a changing quantity stays correlated with itself. A value measured longer ago than the coherence time is a guess. Equation 0.25.
Example	A channel whose fading repeats every 20 milliseconds has a coherence time of 20 milliseconds.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `coherence-time`, kind concept.
Status	no ledger row names this entry. Corrections: 1 item(s), see below.
Defining equation	Book equation 0.25.
Assumptions and scope	Clarke’s formula gives the coherence time from the Doppler frequency alone and assumes the fading model behind it. A value measured longer ago than the coherence time is a guess, and a certificate issued that long ago has decorrelated from the state it certified. The proportional refresh-floor law that was fit to it was refuted and is not cited. Its sealed replacement calibrated the baseline first and found floors at a few transmission intervals.
Prior art	none recorded
Evidence	`observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:41-50`, `lean/DataMiningAsObservation/CoherenceTime.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

How long a quantity stays what it was.

Equation

Book equation 0.25.

\[T_{\mathrm{coh}}=\frac{0.423}{f_D}.\]

Book equation 13.2.

\[\begin{gathered} T_{\mathrm{coh}}=\frac{0.423}{f_D}, \\ \text{refuted fit:}\ \ \phi\approx0.177\,T_{\mathrm{coh}}\ (R^{2}=0.915), \qquad \text{sealed:}\ \ \phi\le 6\ \text{TTI at }10\ \text{Hz},\ \ 1\ \text{TTI at}\ \ge50\ \text{Hz}. \end{gathered}\]

Conditions

Clarke’s formula gives the coherence time from the Doppler frequency alone and assumes the fading model behind it.
A value measured longer ago than the coherence time is a guess, and a certificate issued that long ago has decorrelated from the state it certified.
The proportional refresh-floor law that was fit to it was refuted and is not cited. Its sealed replacement calibrated the baseline first and found floors at a few transmission intervals.

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Clarke’s model of mobile-radio reception for the formula, and Volume 14 chapter 19 for its role as the interval past which a certificate has decorrelated.

Measurements

none

Failures and corrections

observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:41-50 at f7b7c77. The age horizon (analysis/csi/, XPROTO-CSI-SWEEP2 sealed 2026-08-27, graded PASS): at the calibrated 0.10 budget the largest compliant report period is a few TTI at 10 Hz and 1 TTI at 50 Hz and above, so there is no proportionality law to fit. The earlier CSI-refreshfloor.* claim of a floor ≈ 0.177·T_coh (R²=0.915) was an unsealed exploration measured at a relaxed 0.15 threshold against the 0.10 target, with a fresh baseline that never met the budget. It is refuted; the record is kept, not cited. Separately, the optimal linear predictor cannot beat the one-coherence-time wall (Gaussian fading → Wiener optimal), and that wall sits well outside the budget horizon. The RAN governor (analysis/ran) is the reference O-RAN rApp core: observe→measure false-clear→refresh at the floor→escalate (diversity / re-route).

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/CoherenceTime.lean, theorems clarke_to_three_decimals, examples, refuted_law_exceeds_sealed, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 0, 13.

certificate; false-clear rate; refresh floor; witness.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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