teal papers / BarTide collection

Spreadsheet service utilization

TR-PINK-F-065

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
86
TEAL-RERUN-02-B004 | SCOPED_EXECUTION_VERIFIED
TR-PINK-F-065 / Spreadsheet service utilization
IF
Invoke F-065 with exactly these inputs: arrival: Real, workers: Real, service_rate: Real. Real values use finite
decimal text; null remains unknown.
HOW
Source expression: rho=lambda_total/(W*mu_worker). Current Bangel expression: arrival / (workers *
service_rate). Require every input to be known. Require arrival >= 0.0 and workers > 0.0 and service_rate >
0.0.
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 {"arrival": "20", "workers": "4", "service_rate": "10"}; expected 0.5. Result matched through
Bangel, admitted JP, the Bangel API, with validated receipt outputs. 3 missing-input cases and 0 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
D006 pp. 151,152; D012 pp. 35,36
Evidence: evidence/rerun/pink/F-065.json

Original references: F-065