template match instrument

Definition	Comparing a measured list of numbers, such as eigenvalue ratios, to a stored list for each candidate shape and picking the smallest distance between the logarithms. Equation 0.32. Also template.
Example	The lowest eight eigenvalue ratios matched the sphere template within tolerance, and the torus template did not.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `template-match`, kind instrument.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 0.32.
Assumptions and scope	Comparing a measured list of numbers, the eigenvalue ratios, to a stored list for each candidate shape and picking the smallest root-mean-square distance between the logarithms. The distance is zero between a list and itself, symmetric, and unchanged when both lists are scaled by the same factor, so the match reads shape and not size. The templates are frozen before the battery is run, with their code hash recorded, and the match can only name shapes in its template set, which is why the recognizer also certifies that none is present.
Prior art	none recorded
Evidence	`lean/DataMiningAsObservation/Recognizer.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

The spectrum's ratios against a stored template.

Equation

Book equation 0.32.

\[\operatorname{dist}(m,t)=\sqrt{\frac18\sum_{k=1}^{8}\big(\ln m_k-\ln t_k\big)^{2}}.\]

Conditions

Comparing a measured list of numbers, the eigenvalue ratios, to a stored list for each candidate shape and picking the smallest root-mean-square distance between the logarithms. The distance is zero between a list and itself, symmetric, and unchanged when both lists are scaled by the same factor, so the match reads shape and not size.
The templates are frozen before the battery is run, with their code hash recorded, and the match can only name shapes in its template set, which is why the recognizer also certifies that none is present.

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

Ledger

none

First stated

Volume 14, chapter 11, geometric-observation/chapters/ch11_the_recognizer.md:1-95, DOI 10.5281/zenodo.21776291, and the recognizer battery in the-angular-observer.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 9 section 9.2	the battery, three new templates, frozen ratios, code hash, bars at least 10 of 12 and the dimension ordering, eccentricity scope	`the-angular-observer/PREREG_RECOGNIZER_BATTERY.md:1-80`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Recognizer.lean, theorems templateDist_self, templateDist_comm, templateDist_scale, templateDist_nonneg, 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, 2, 8, 9, 14.

recognizer; vacuity threshold; intrinsic dimension; Laplacian.

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.

← teacher forcingtest statistic →