refresh floor correction

Definition	A claimed lower bound on how often a certificate must be renewed. The proportional-to-coherence-time version was refuted and replaced by a sealed horizon. Chapter 13. Also refresh law.
Example	At 10 hertz Doppler the sealed refresh floor was 4 slots of one millisecond.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `refresh-floor`, kind correction.
Status	refutes or corrects [refuted]; refutes or corrects [void]. Corrections: 3 item(s), see below.
Defining equation	Book equation 13.2.
Assumptions and scope	The proportional law, a floor of about 0.177 times the coherence time, was fit at a relaxed threshold against a fresh baseline that never met the budget. It is refuted, the record is kept, and it is not cited. The sealed replacement calibrated the baseline to the budget first and found floors of a few transmission intervals at 10 hertz and one at 50 hertz and above, with the optimal linear predictor unable to beat the one-coherence-time wall. Volume 14’s book outline still cites the refuted law, an open item.
Prior art	none recorded
Evidence	`geometric-observation/claims/LEDGER.md:36`, `geometric-observation/claims/LEDGER.md:48`, `observation-theory-campaigns/analysis/mongo/PREREG-XPROTO-MG.md:42`, `observation-theory-campaigns/experiments/ROUTING-TELEMETRY-TRACK.md:130-150`, `geometric-observation/BOOK-OUTLINE.md:75`, `observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:20-35`, `observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:41-47`, `observation-theory-campaigns/analysis/csi/PREREG-XPROTO-CSI-SWEEP2.md:1-60`, `observation-theory-campaigns/analysis/csi/XPROTO-CSI-SWEEP2-graded.json`, `observation-theory-campaigns/experiments/SEALS.md:90`, `geometric-observation/BOOK-OUTLINE.md:70-90`, `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.

The shortest renewal that keeps a certificate within its error.

Equation

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

The proportional law, a floor of about 0.177 times the coherence time, was fit at a relaxed threshold against a fresh baseline that never met the budget. It is refuted, the record is kept, and it is not cited.
The sealed replacement calibrated the baseline to the budget first and found floors of a few transmission intervals at 10 hertz and one at 50 hertz and above, with the optimal linear predictor unable to beat the one-coherence-time wall.
Volume 14’s book outline still cites the refuted law, an open item.

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

Ledger

refutes or corrects. OT-4 [refuted]. Operator drift predicts a real long-generation degradation and a derived refresh intervention moves it. geometric-observation/claims/LEDGER.md:36.
refutes or corrects. OT-11 [void]. Feedback-free staleness: streaming-retrieval damage tracks measured drift; derived-cadence re-allocation removes it. geometric-observation/claims/LEDGER.md:48.

First stated

An unsealed exploration in the radio freshness track, observation-theory-campaigns/analysis/csi/CSI-refreshfloor.json, refuted and replaced by the sealed sweep observation-theory-campaigns/analysis/csi/PREREG-XPROTO-CSI-SWEEP2.md.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 13 section 13.3	BGP 0.351, IS-IS 0.184, OSPF 0.083, second collector	`observation-theory-campaigns/analysis/mongo/PREREG-XPROTO-MG.md:42`; `observation-theory-campaigns/experiments/ROUTING-TELEMETRY-TRACK.md:130-150`; `geometric-observation/BOOK-OUTLINE.md:75`
chapter 13 section 13.3	radio 0.27 to 0.42 naive to 0.055 to 0.13, neural reconstruction 0.28 to 0.13	`observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:20-35`
chapter 13 section 13.4	refuted fit 0.177 T_coh R² 0.915, 0.15 threshold vs 0.10 claim, fresh baseline 0.113, do not cite	`observation-theory-campaigns\analysis\csi\CSI-refreshfloor.json:2,111-114`; `observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:41-47`
chapter 13 section 13.4	sealed correction, 0.5 dB calibration, floors 4/6/4, 2/2/3, 1, slopes 0.1008, 0.1398, 0.1086, R² 0.7376, 0.9218, 0.6174, bars B1 to B4 and MC1 to MC4 all true, seeds 20260827 to 20260829, sealed 1d3de4a	`observation-theory-campaigns/analysis/csi/PREREG-XPROTO-CSI-SWEEP2.md:1-60`; `observation-theory-campaigns/analysis/csi/XPROTO-CSI-SWEEP2-graded.json`; `observation-theory-campaigns/experiments/SEALS.md:90`
chapter 13 section 13.4	freshness sweep classes, sensing refuted at about 1.6 times	`geometric-observation/BOOK-OUTLINE.md:70-90`

Failures and corrections

OT-4, [refuted]. Operator drift predicts a real long-generation degradation and a derived refresh intervention moves it. geometric-observation/claims/LEDGER.md:36.
OT-11, [void]. Feedback-free staleness: streaming-retrieval damage tracks measured drift; derived-cadence re-allocation removes it. geometric-observation/claims/LEDGER.md:48.
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.

coherence time; certificate; false-clear rate.

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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