teal papers / BarTide collection

Cone partial volume

TR-PINK-F-088

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
109
TEAL-RERUN-02-B005 | SCOPED_EXECUTION_VERIFIED
TR-PINK-F-088 / Cone partial volume
IF
Invoke F-088 with exactly these inputs: base_area: Real, width_ratio: Real, height: Real, cone_height: Real.
Real values use finite decimal text; null remains unknown.
HOW
Source expression: V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2)). Current Bangel expression:
base_area * (height + (width_ratio - 1.0) * height * height / cone_height + (width_ratio - 1.0) * (width_ratio -
1.0) * height * height * height / (3.0 * cone_height * cone_height)). Require every input to be known. Require
base_area > 0.0 and width_ratio > 0.0 and cone_height > 0.0 and height >= 0.0 and height <= cone_height.
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 {"base_area": "3", "width_ratio": "2", "height": "3", "cone_height": "3"}; expected 21. Result
matched through Bangel, admitted JP, the Bangel API, with validated receipt outputs. 4 missing-input cases
and 1 supplied domain cases passed.
SOURCE DIMENSION
volume
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. 197,198; D012 pp. 81,82
Evidence: evidence/rerun/pink/F-088.json

Original references: F-088