teal papers / BarTide collection

Required buffer volume

TR-PINK-F-107

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
128
TEAL-RERUN-02-B006 | SCOPED_EXECUTION_VERIFIED
TR-PINK-F-107 / Required buffer volume
IF
Invoke F-107 with exactly these inputs: hold_time: Real, outflow_high: Real, return_low: Real, residual_high:
Real. Real values use finite decimal text; null remains unknown.
HOW
Source expression: V_L,req=T_hold*max(0,Q_out,H-Q_return,L)+V_residual,H. Current Bangel expression:
hold_time * math.max(0.0, outflow_high - return_low) + residual_high. Require every input to be known.
Require hold_time >= 0.0 and outflow_high >= 0.0 and return_low >= 0.0 and residual_high >= 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 {"hold_time": "3", "outflow_high": "8", "return_low": "5", "residual_high": "2"}; expected 11.
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. 224,241,242; D013 pp. 2,19,20
Evidence: evidence/rerun/pink/F-107.json

Original references: F-107