contraction instrument
| Definition | A formula that reduces several axes to one verdict. The instrument's contraction from ten axes is fairness minus the general valence component. Chapter 14 section 14.5. |
|---|---|
| Example | Ten axis scores contracted to fairness minus the general component is one number a person can read. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id contraction, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | gtc-prototype/docs/SPECTRUM_FINDINGS.md:66-99, gtc-prototype/docs/SPECTRUM_FINDINGS.md:90-99, lean/DataMiningAsObservation/ReadOperator.lean, lean/DataMiningAsObservation/Attribution.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A formula that reduces several axes to one verdict, here ten axes to a toxicity verdict. An affine contraction has a rank-one read operator, the outer product of its weights, and its attributions sum exactly to the change in verdict.
- The contraction found by chapter 6’s tool is fairness minus the general valence component, moved accuracy from 0.779 to 0.863 on 1600 items, and is a consumer a person can read.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 14 section 14.5 of Data Mining as Observation, with
the formula in
gtc-prototype/docs/SPECTRUM_FINDINGS.md:90-99.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 14 section 14.3 | contraction 0.779 to 0.863, 77 of 1600, 4.8 percent, 0.872 to 0.863, weight 2.69 | gtc-prototype/docs/SPECTRUM_FINDINGS.md:66-99 |
| chapter 14 section 14.5 | the contraction formula fairness minus the general component | gtc-prototype/docs/SPECTRUM_FINDINGS.md:90-99 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/ReadOperator.lean,
theorems rank_one_reads_one_direction,
readOp_mulVec, quad_readOp,
quad_readOp_nonneg, readOp_mulVec_eq_zero_iff,
readOp_diag, readOp_offdiag,
readOp_symm, readOp_neg,
affine_const_along_nuisance, readOp_affine,
readOp_sqLength_basis, at observation-data-mining f3914f0;
what the check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/Attribution.lean,
theorems attr_sum_affine, attr_unread,
sq_sensitivity_eq_readOp_diag, at observation-data-mining
f3914f0; what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 14.
Related
attribution; read operator; residualization; importance.
See also
Book equations stated beside the entry’s terms, not defining it: 14.5, 0.9.
Ledger rows that cite the entry’s records without naming it: GO-EC-3.
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.