The $(2,1)$-Gapped Consecutive-Ones Property Problem is NP-complete

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This event attributed to Maciej Nowicki

This event attributed to GPT-5.6 Sol High

The $(2,1)$-Gapped Consecutive-Ones Property Problem is NP-complete evidence for this event

Original 2009 hardness paper leaving $(2,1)$-C1P open evidence for this event

2011 follow-up explicitly stating that $(2,1)$-C1P remains open evidence for this event

The manuscript claims a polynomial-time reduction from 3-SAT proving $(2,1)$-C1P NP-hard; together with membership in NP, this establishes NP-completeness and closes the sole unresolved $(k,\delta)$ case from the earlier classification. It also implies NP-completeness of the equivalent completion problem. The proof package further shows that, within its specific nested-prefix/internal-local gadget architecture, no 3-OR gadget exists with at most six internal columns; at seven columns at least three local rows are required, and all optimal three-row gadgets form one symmetry class. These optimality claims are architecture-specific and are not needed for the NP-completeness result. Independent verification remains pending. parent of this event

The $(2,1)$-Gapped Consecutive-Ones Property Problem is NP-complete parent of this event

Initial Zenodo record announcing the NP-completeness proof evidence for this event

VibeMathed record: The $(2,1)$-Gapped Consecutive-Ones Property Problem is NP-complete evidence for this event