identity reader concept
| Definition | The consumer whose read operator is the identity, for which read distortion is mean squared error. Every consumer-blind metric assumes it. Chapter 0 section 0.5. Also identity quotient. |
|---|---|
| Example | The identity reader charges 0.3 + 1.7 = 2.0 for either of the two codes and cannot tell them apart. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id identity-reader, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.10. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/ReadDistortion.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.10.
\[d_O=\operatorname{tr}(P_C\,M_\delta)=\mathbb E\!\left[\delta^{\top}P_C\,\delta\right],\qquad M_\delta=\mathbb E\!\left[\delta\delta^{\top}\right],\qquad P_C=I\ \Rightarrow\ d_O=\operatorname{tr}M_\delta.\]
Book equation 1.2.
\[d_O=\operatorname{tr}(P_C\,M_\delta),\qquad \big(d_O=\operatorname{tr}M_\delta\ \text{ for every admissible } M_\delta\big)\ \Longleftrightarrow\ P_C=I.\]
Conditions
- Read distortion equals the trace of the error’s second moment for every admissible error exactly when the read operator is the identity. A particular error can make the two agree by accident.
- Explained variance and the rule of picking rank at 95 percent are the identity reader’s criteria, and the book records them as the benchmark’s rules rather than its own.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Volume 14, chapter 2,
geometric-observation/chapters/ch02_failure_of_observer_free_measurement.md,
DOI 10.5281/zenodo.21776291, where reconstruction error is the
distortion of the reader that reads every direction equally.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/ReadDistortion.lean,
theorems read_distortion, identity_reader,
quad_one, at observation-data-mining f3914f0; what the
check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation primer L, chapters 0, 1, 2, 3, 4, 8, 9, 10, 12, 13.
Related
read operator; read distortion; the flip; quotient.
See also
Book equations stated beside the entry’s terms, not defining it: 4.1.
Ledger rows that cite the entry’s records without naming it: GO-2 (neg. half: not reconstruction).
Sources-table rows that share a record with the entry without naming it: chapter 1 section 1.4, chapter 4 section 4.3, chapter 4 section 4.5.
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.