[Rule] 3SAT to INTEGRAL FLOW WITH HOMOLOGOUS ARCS

[isPANN]

[zazabap]

Issue Quality Check — Rule

Check	Result	Details
Usefulness	⚠️ Warn	Cannot assess — issue body is empty; target problem "Integral Flow with Homologous Arcs" not in codebase
Non-trivial	❌ Fail	No reduction algorithm provided — issue body is completely empty
Correctness	❌ Fail	No references cited — issue body is completely empty
Well-written	❌ Fail	Issue body is empty; all required sections are missing

Overall: 0 passed, 3 failed, 1 warning

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Usefulness

The source problem KSatisfiability (3SAT) exists in the codebase. The target problem "Integral Flow with Homologous Arcs" does not exist and is not a standard problem in the reduction graph. Without any motivation or overhead information in the issue, usefulness cannot be determined. Note that this target problem would first need to be added as a new model before this reduction rule could be implemented.

Non-trivial

Fail. The issue body is completely empty — there is no reduction algorithm to evaluate. A complete step-by-step procedure is required to assess whether the reduction involves genuine structural transformation.

Correctness

Fail. The issue body is completely empty — no references are cited. A [Rule] issue must include at least one literature citation supporting the reduction. "Integral Flow with Homologous Arcs" is not a widely known problem name; a reference establishing its definition is especially important.

Well-written

Fail. The issue body is entirely empty. All required sections are missing:

• Source — not specified in body
• Target — not specified in body
• Motivation — missing
• Reference — missing
• Reduction Algorithm — missing
• Size Overhead — missing
• Validation Method — missing
• Example — missing

The issue title alone ("[Rule] 3SAT to INTEGRAL FLOW WITH HOMOLOGOUS ARCS") is not sufficient. Please fill in the issue body using the rule issue template.

Recommendations

• Fill in all required sections using the [Rule] issue template
• Provide a reference that defines "Integral Flow with Homologous Arcs" — this is not a standard problem in common NP-completeness references (Garey & Johnson, Karp's 21 problems, etc.)
• Consider whether a [Model] issue for the target problem needs to be filed first, since it does not exist in the codebase

[isPANN]

Closing: issue body was empty or incorrect (wrong content). Will re-create with correct content.