teal papers / BarTide collection

DRO capacity slack

TR-PINK-F-217

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
238
TEAL-RERUN-02-B010 | SCOPED_EXECUTION_VERIFIED
TR-PINK-F-217 / DRO capacity slack
IF
Invoke F-217 with exactly these inputs: headroom_fraction: Real, capacity: Real, load: Real. Real values use
finite decimal text; null remains unknown.
HOW
Source expression: S_k = (1-h_k)C_k - L_k. Current Bangel expression: (1.0 - headroom_fraction) * capacity -
load. Require every input to be known. Require headroom_fraction >= 0.0 and headroom_fraction < 1.0 and
capacity > 0.0 and load >= 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 {"headroom_fraction": "0.1", "capacity": "100", "load": "95"}; expected -5. 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
quantity
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
D003 pp. 2; D004 pp. 5,7
Evidence: evidence/rerun/pink/F-217.json

Original references: F-217