surrogate instrument

Definition	A quadratic stand-in for the consumer's output metric, the read distortion, used to allocate bits when the output itself cannot be. Chapter 4 section 4.2.
Example	The read distortion 0.3 stands in for the consumer’s own loss when bits are allocated.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `surrogate`, kind instrument.
Status	measures [demonstrated]. Corrections: none recorded.
Defining equation	none
Assumptions and scope	A quadratic stand-in for the consumer’s output metric, the read distortion, used to allocate bits when the output itself cannot be. The read distortion is a quadratic form in the read operator, and two readers at different angles rank the same two errors differently. At every rate the output coder is at or below the surrogate, which is at or below reconstruction, and the surrogate-to-output gap shrinks from 0.41 to 0.005 as the rate grows, while the read distortion is a control and not a complete rank statistic.
Prior art	none recorded
Evidence	`geometric-observation/claims/LEDGER.md:68`, `readscope/readscope/allocate.py:1-100`, `geometric-observation/claims/LEDGER.md`, `geometric-observation/chapters/ch07_cost.md`, `lean/DataMiningAsObservation/ReadDistortion.lean`, `lean/DataMiningAsObservation/Isotropy.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

A quadratic stand-in for the consumer's output metric.

Equation

none

Conditions

A quadratic stand-in for the consumer’s output metric, the read distortion, used to allocate bits when the output itself cannot be. The read distortion is a quadratic form in the read operator, and two readers at different angles rank the same two errors differently.
At every rate the output coder is at or below the surrogate, which is at or below reconstruction, and the surrogate-to-output gap shrinks from 0.41 to 0.005 as the rate grows, while the read distortion is a control and not a complete rank statistic.

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

Ledger

measures. GO-6 [demonstrated]. At matched rate, output coding ≤ surrogate ≤ reconstruction on the consumer metric; the output–reconstruction gap is governed by the \(\ker P_C\) entropy share, and the surrogate–output gap vanishes as rate grows. geometric-observation/claims/LEDGER.md:68.

First stated

Chapter 4 section 4.2 of Data Mining as Observation, with the surrogate ordering in geometric-observation/claims/LEDGER.md row GO-6.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 4 section 4.2	water-filling formula, directions below the water get no bits, the surrogate caveat	`readscope/readscope/allocate.py:1-100`
chapter 4 section 4.2	GO-6, d 8 and r 4, output at or below surrogate at or below reconstruction at every rate, about 500 times, gap 0.41 to 0.005, isotropic control collapses	`geometric-observation/claims/LEDGER.md` row GO-6; `geometric-observation/chapters/ch07_cost.md`

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.

lean/DataMiningAsObservation/Isotropy.lean, theorems isotropic_reads_same, isotropic_no_flip, anisotropic_readers_differ, flip_iff_anisotropic, 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, 4, 8.

read distortion; distortion; output metric; identity reader.

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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