teal papers / BarTide collection

Bangel / language/python/src/bangel/numerics.py

TR-MOD-BANGEL-61C1E32918

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
124
TEAL-RERUN-03-B005 | SOURCE_LOGIC_INDEXED
TR-MOD-BANGEL-61C1E32918 / Bangel /
language/python/src/bangel/numerics.py
IF
This Numeric / typed values module is imported or its declared interface is invoked. Declared surface includes:
_series(values: Iterable[Quantity], name: str, minimum: int=1); vector_add(left: Iterable[Quantity], right:
Iterable[Quantity]); finite_difference(xs: Iterable[Quantity], ys: Iterable[Quantity]); trapezoid(xs:
Iterable[Quantity], ys: Iterable[Quantity]); covariance(left: Iterable[Quantity], right: Iterable[Quantity])
HOW
Use the exact numeric and dimensional rules of this module; keep typed unknown, signed values and
source-specific bounds distinct. The complete terminology-edited 64-line source is preserved with SHA-256
52bc4b602879fce4b4d00ddcdf6ef0cea456c2171d0a0fb1e178009df9430cd8. 5 extracted function/declaration
entries are separately indexed, including exact Python bodies and guards where available.
THEN
Follow the exact returned values, diagnostics and state effects in the preserved implementation. Module
inclusion and syntax extraction are documentary coverage; they do not prove every branch or cross-host
behavior.
CURRENT EVIDENCE
Fresh related Python suites and per-profile/water results are included. Native C#/.NET, C++/Rust/R
compilation and physical devices were not executed in this environment.
REMAINING REQUIREMENT
Map unverified branches and native-host behavior to source-specific evidence before assigning a complete verification verdict.
SOURCE REFERENCES
bangel:language/python/src/bangel/numerics.py

Original references: See paper text and source PDF.