CounterexampleConstruction: AI-generatedVerification: AI-generatedprecheck passjudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

How statement and proof provenance work

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.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Reversing orientation does not preserve a complex contour integral

Statement refuted

Reversing a contour's orientation preserves every complex contour integral.

Facts & Assumptions

Given: The segment $γ$ from $0$ to $1$ , its reversal, and the constant integrand $1$ .

[L1]

The integral of a constant $c$ is $c$ times the endpoint displacement (The contour integral of a constant c is c times the endpoint displacement).

[L2]

Reversal negates the complex line integral while preserving the absolute line integral (Complex line integrals change sign under reversal and add under concatenation).

Counterexample

technique · direct

1.1L1algebra

By [L1], $\int_{γ} 1 d z = 1 (1 - 0) = 1$ , whereas $\int_{γ^{-}} 1 d z = 1 (0 - 1) = - 1$ .

2.1step 1.1L2∎

The values differ, in agreement with [L2], so reversal does not preserve the oriented complex integral even though it preserves the absolute integral.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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