alignment concept

Definition	The normalized overlap between a consumer's average read operator and the covariance of the data on the read subspace, written kappa, between zero and one. Near one the read subspace and the high-variance subspace coincide and no flip is possible. Chapter 4, equation 4.6. Also coupling null.
Example	A read operator that lies wholly in one direction and a covariance with half its variance in that direction have alignment one half.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `alignment`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 4.6.
Assumptions and scope	Defined as the normalized overlap between the averaged read operator and the source covariance on the read subspace, between zero and one, and so a statement about one workload. The alignment law that relates it to the size of the flip is a retrospective fit with a single prospective point and is carried as exploratory, not as a theorem.
Prior art	none recorded
Evidence	`geometric-observation/chapters/ch12_failure_taxonomy_and_kappa.md:56-82`, `lean/DataMiningAsObservation/Alignment.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

The overlap between the consumer's read direction and the data's covariance.

Equation

Book equation 4.6.

\[\kappa=\operatorname{tr}\big(\bar P_C\,\bar\Sigma_x\big)\in[0,1],\qquad \kappa\to1\ \text{is the coupling null (no flip)}.\]

Conditions

Defined as the normalized overlap between the averaged read operator and the source covariance on the read subspace, between zero and one, and so a statement about one workload.
The alignment law that relates it to the size of the flip is a retrospective fit with a single prospective point and is carried as exploratory, not as a theorem.

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

Ledger

none

First stated

Volume 14, chapter 12, geometric-observation/chapters/ch12_failure_taxonomy_and_kappa.md:56-82, DOI 10.5281/zenodo.21776291, where the alignment law is a retrospective fit carried as exploratory with one prospective point.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 4 section 4.4	alignment law, retrospective fit exploratory, one prospective point	`geometric-observation/chapters/ch12_failure_taxonomy_and_kappa.md:56-82`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Alignment.lean, theorems overlap_sq_le, alignment_le_one, alignment_nonneg, alignment_eq_one_of_proportional, coupling_null, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 2, 4, 7, 11, 14.

the flip; read distortion; coupling null; water-filling.

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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