false-clear rate concept

Definition	The fraction of the decisions a certificate cleared in which the witness said otherwise, conditional on clearing and reported beside the certificate's coverage. Equation 0.26.
Example	Of 1000 clearances the witness refuted 206, a false-clear rate of 0.206 at whatever coverage the certificate had.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `false-clear-rate`, kind concept.
Status	no ledger row names this entry. Corrections: 3 item(s), see below.
Defining equation	Book equation 0.26.
Assumptions and scope	A witness must exist. Where none exists the rate is not measurable and the certificate is unassessed, not safe. The rate is per consumer, given per read operator, slice, group, or footprint, never as one aggregate. Coverage is reported with it. A witnessed certificate clears fewer decisions than a naive one, and the two numbers are read together.
Prior art	none recorded
Evidence	`observation-theory-campaigns/experiments/LLM-EVAL-TRACK.md:1-50`, `observation-theory-campaigns/analysis/llm/XPROTO-LLM-graded.json`, `observation-theory-campaigns/experiments/SEALS.md:85`, `observation-theory-campaigns/experiments/DATABASE-FRESHNESS-TRACK.md:1-45`, `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`, `observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:33-39`, `observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:41-50`, `geometric-observation/chapters/ch19_the_certificate_that_ages.md:69-76`, `lean/DataMiningAsObservation/Certificate.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

How often a clearance was wrong, conditional on clearing.

Equation

Book equation 0.26.

\[\mathrm{FC}=\Pr\big[W\ \text{refutes}\ \big|\ \mathcal C_t\ \text{clears}\big],\qquad \text{coverage}=\Pr\big[\mathcal C_t\ \text{clears}\big].\]

Book equation 13.1.

\[\mathrm{FC}=\Pr\big[W\ \text{refutes}\ \big|\ \mathcal C_t\ \text{clears}\big],\qquad d_O(\Delta)=\operatorname{tr}\big(P_C\,M_{\mathrm{drift}}(\Delta)\big),\qquad M_{\mathrm{drift}}(\Delta)=\mathbb E\big[\delta_\Delta\delta_\Delta^{\top}\big].\]

Book equation 12.4.

\[\begin{gathered} \mathrm{FC}_{\text{naive}}=\Pr\big[\mathrm{acc}_s<\text{target}\ \big|\ \text{benchmark}\ge\text{target}\big]=\frac1S\sum_{s=1}^{S}\mathbf 1\big[\mathrm{acc}_s<\text{target}\big] \\ \text{when the benchmark clears, so that the naive certificate's coverage is 1.} \end{gathered}\]

Conditions

A witness must exist. Where none exists the rate is not measurable and the certificate is unassessed, not safe.
The rate is per consumer, given per read operator, slice, group, or footprint, never as one aggregate.
Coverage is reported with it. A witnessed certificate clears fewer decisions than a naive one, and the two numbers are read together.

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

Ledger

none

First stated

Volume 14 chapter 19, geometric-observation/chapters/ch19_the_certificate_that_ages.md:61-76, and the freshness program’s umbrella document observation-theory-campaigns/experiments/FRESHNESS-PROGRAM.md, re-homed into the campaigns repository on 2026-08-24.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 12 section 12.6	XPROTO-LLM, benchmark 0.909, 0.920, 0.909, thirty slices, target 0.8, naive 0.333, aware 0.033, spread 0.380, deployment mean 0.736, six bars on three seeds, sealed 2026-08-25 at b61f7f1	`observation-theory-campaigns/experiments/LLM-EVAL-TRACK.md:1-50`; `observation-theory-campaigns/analysis/llm/XPROTO-LLM-graded.json`; `observation-theory-campaigns/experiments/SEALS.md:85`
chapter 13 section 13.3	ZooKeeper hot 0.99 cold 0.01 witnessed 0.0, Postgres 0.50 to 0.06, MongoDB 0.47 to 0.03, production Postgres 0.47 to 0.02, real substrates, disjoint seeds	`observation-theory-campaigns/experiments/DATABASE-FRESHNESS-TRACK.md:1-45`
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`

From observation-theory-campaigns/experiments/DATABASE-FRESHNESS-TRACK.md at f7b7c77.

line 23. XPROTO-PG (analysis/pgrep); Postgres, recovery_min_apply_delay; WAL LSN; ~0.50 → ~0.06
line 24. XPROTO-MG (analysis/mongo); MongoDB delayed secondary; oplog ts; ~0.47 → ~0.03
line 25. XPROTO-PGX (analysis/pgx); production PG, netem lag; WAL LSN, pg_stat_statements footprint; ~0.47 → ~0.02
line 27. XPROTO-ZK (analysis/zk); ZooKeeper 3.9 ensemble; zxid, sync(); hot 0.99 / cold 0.01, witnessed 0.0

From observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md at f7b7c77.

line 25. XPROTO-CSI (analysis/csi); CQI → MCS; HARQ; 0.34–0.37 → 0.10 (OLLA); ✅ 08-23
line 26. XPROTO-BEAM (analysis/beam); mmWave beam index; HARQ; 0.31 → 0.02 (BFR); ✅ 08-23
line 27. XPROTO-AICSI (analysis/aicsi); neural-CSI recon (turboquant bridge); precoder/HARQ; recon wins yet 0.28 → 0.13; ✅ 08-23, scope-corrected 08-25 ⚠️
line 28. XPROTO-HO (analysis/ho); RSRP → serving cell; RLF; 0.31–0.44 → 0.09–0.12; ✅ 08-23
line 30. XPROTO-PHY (analysis/phy); PMI / RI / TA; HARQ; 0.27–0.42 → 0.055–0.13; ✅ 08-24

Failures and corrections

observation-theory-campaigns/experiments/RADIO-FRESHNESS-TRACK.md:33-39 at f7b7c77. ⚠️ XPROTO-AICSI scope correction (2026-08-25). The v1 seal stands for what it tested, but the reconstruction-vs-consumer dissociation does not survive the community-standard substrate. On real 3GPP CDL-C with a CsiNet-class codec the NMSE-optimal codec reconstructs near-perfectly (NMSE ≈ 0.03) and false-clears 0.0 on all seeds; the pre-registered kill fired. See analysis/aicsi/PREREG-XPROTO-AICSI-V2.md (REFUTED AT SHAKEDOWN, NOT SEALED, kept negative). This is a scope correction, not a retraction. Do not headline the AICSI row; WCNC §III-C is dropped.
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).
geometric-observation/chapters/ch19_the_certificate_that_ages.md:69-76 at b2626a6. — the rate at which a clearance is wrong, conditional on the certificate having cleared, reported beside the certificate’s coverage. (An earlier draft wrote the joint probability \(\Pr[\text{clears} \wedge \text{refutes}]\); the joint rate is the product of the two and is what a naive certificate that clears everything reports, since its coverage is one. Corrected 2026-09-03.) A certificate whose false-clear rate exceeds the target it purports to guarantee is vacuous for that consumer, however confident it looks. FC is measurable wherever a witness exists, which — per the table — is nearly everywhere it matters.

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Certificate.lean, theorems falseClear_mul_coverage, coverage_empty, falseClear_mem_unit, minOverStrata_passes_iff, minOverStrata_le_weighted_mean, 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, 12, 13, 14.

certificate; witness; coverage; coherence time; refresh floor; min-over-strata.

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.

← F1false positive rate →