Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passaudited 2026-09-07
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

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Boundary orientation is inward-normal-first

Statement

False under the library convention. The induced boundary orientation is outward-normal-first.

Facts & Assumptions

Given: The library's induced boundary-orientation convention and the standard orientation on an interval [a,b].

[L1]

The induced boundary orientation is defined by placing an outward normal first (Induced boundary orientation).

[L2]

For the standard orientation on [a,b], this convention gives ∂[a,b]={b}−{a} (Boundary orientation is independent of the outward vector field).

Refutation

technique · direct
1.1

By [L2], outward-normal-first gives the positive sign at b and the negative sign at a.

givenL2
2.1

At each endpoint the inward normal is the negative of the outward normal. By [L1], replacing the first vector by its negative reverses the induced zero-dimensional determinant ray, so inward-normal-first gives the opposite orientation.

L1step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources