Ortho

A small mathematical toy for handling orthants directly: render them, turn them in your hand, and see how the experience changes with dimension and sign choice.

The first slice is deliberately not a proof interface. It is a draggable three-dimensional positive orthant: three translucent coordinate-face patches meeting at a visible corner. One-finger drag rotates the object.

The mathematical geometry lives in Idriç under src/. src/Generate.idric emits app/src/main/cpp/orthant_model.h; the Android shell is the same small native pattern used by the other math viewers: NativeActivity + android_native_app_glue + EGL + GLES3.

Android build

Requirements: JDK 17, Android SDK 36, NDK 29.0.14206865, CMake 3.22.1, and Gradle 8.13.

gradle :app:assembleDebug

The APK is written under app/build/outputs/apk/debug/.

Idriç model

src/Orthant.idric is the source of the face and edge vertices. The generated C header is checked in so an Android build does not need to bootstrap the compiler.

If an Idriç checkout is available at ../Idric:

scripts/regenerate-model.sh

Set IDRIC=/path/to/Idric/build/exec/idris2 to use a different checkout.

Touch

• one finger: rotate the orthant
• lift: leave it where it is

Pinch, dimension changes, and sign changes are intentionally not in this first slice.

Reference

Kenneth O. May, “The Impossibility of a Division Algebra of Vectors in Three Dimensional Space,” American Mathematical Monthly 73(3), 1966, 289–291. See references/may-1966.md.

The maintained C arithmetic uses ÷ and is compiled directly by pinned ICK. The Android and unsigned-release workflows qualify the compiler for each maintained ABI, restore the stages under build/ick/<abi>, and check out the pinned shared source producer under .ai-ci-ick. Local Gradle builds require these same stages and checkout; no source rewrite or stock-C fallback is used. NDK r29 still assembles ICK output, compiles unchanged NativeActivity glue, and links the application. Existing Fortify2, stack protection and API26 are retained. Native-library proofs do not replace the existing APK, emulator or device checks.