teal papers / BarTide collection

Data-performance correlation

TR-PINK-F-166

MJ Physics Engineering | Bangel Language | MJos Operating System
Owned and operated by Michael Bangel | Clearwater, Florida

Updated collection edition: BarTide branding and navigation added September 26, 2026. The original paper text below retains its historical scope. Inclusion does not claim its research is implemented in BarTide.

Terminology revised · September 12 evidence

TEAL LIBRARY RERUN  |  12 SEPTEMBER 2026  |  Michael Patrick Bangel
187
TEAL-RERUN-02-B008 | SCOPED_EXECUTION_VERIFIED
TR-PINK-F-166 / Data-performance correlation
IF
Invoke F-166 with exactly these inputs: covariance: Real, sigma_data: Real, sigma_performance: Real. Real
values use finite decimal text; null remains unknown.
HOW
Source expression: rho_DP = cov(D,P)/(sigma_D*sigma_P). Current Bangel expression: covariance /
(sigma_data * sigma_performance). Require every input to be known. Require sigma_data > 0.0 and
sigma_performance > 0.0 and math.abs(covariance) <= sigma_data * sigma_performance.
THEN
Emit the scoped calculation result. Missing inputs produce their specific PINK_MISSING_* HOLD; failed profile
checks produce PINK_DOMAIN. A false numeric predicate can occur in a PASS calculation receipt; it is not
permission.
CURRENT EVIDENCE
Fixture inputs {"covariance": "6", "sigma_data": "2", "sigma_performance": "3"}; expected 1. Result matched
through Bangel, admitted JP, the Bangel API, with validated receipt outputs. 3 missing-input cases and 1
supplied domain cases passed.
SOURCE DIMENSION
ratio
REMAINING REQUIREMENT
Complete the source-defined measurement/evidence contract, units and calibration bindings. Native C# and Hagar formula-ID
bindings remain unverified in this rerun.
SOURCE REFERENCES
D020 pp. 5,11
Evidence: evidence/rerun/pink/F-166.json

Original references: F-166