The Six-Trap Conjecture

The Six-Trap Conjecture is an integer-dynamics problem created and directed by Adrien Washington. For each integer n ≥ 2, let D(n) denote the largest positive proper divisor of n and define T(n) = n + D(n) − D(n+1). The conjecture is that every starting integer n ≥ 2 eventually enters one of six recorded periodic cycles with minima 2, 3286, 4210, 5182, 54214, and 127330. Version 1.0 reports a complete finite census of 999,999,999 consecutive starting values from 2 through 1,000,000,000. Every tested start reached one of the six observed cycles, and no seventh trap was found in that census. This is finite computational evidence, not a general proof; the universal conjecture remains unresolved. The release also contains the complete six-cycle register, a computer-assisted 50-move forward-descent lower natural density bound Q50 ≈ 0.8695739413707237 with its stated scope, selected source code, machine-readable census outputs, certificate material, internal verification tools, SHA-256 checksums, reproduction instructions, originality limitations, and challenge mechanics. Six-Trap was created and directed by Adrien Washington. AI tools assisted with mathematical exploration, computation, code development, derivations, and adversarial testing. The project is released openly so its claims can be independently examined, reproduced, challenged, extended, proved, or disproved.