Determinacy and Word Reconstruction from Simple Paths in Class-Two Networks: Structural characterization, exact audit design, and a discrete-gauge interpretation

Davit Gondauri

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Abstract: We study selective identification from simple directed path products when standardized edge transports take values in groups nilpotent of class at most two. We distinguish universal determination, represented by dominion membership, from word reconstruction, represented by subgroup membership in the relatively free class-two group. Let H be the subgroup generated by the baseline observations in the relatively free class-two group, and let D be its dominion in the class-two variety. For a connected bouquet of directed cycles, cycle a has length k_a, d_a=k_a-1, with every cycle length at least three, and the baseline disclosure contains every simple path obtained by omitting one edge. We prove D/H≅⨁_(a

Keywords: class-two nilpotent groups; simple directed paths; dominions; target determinacy; word reconstruction; discrete gauge interpretation; structural identifiability; vertex cover (search for similar items in EconPapers)
JEL-codes: C02 C61 C63 D85 (search for similar items in EconPapers)
Date: 2026
Note: 31 pages, 2 figures. The paper provides a complete structural characterization of universal determination and word reconstruction from simple directed path observations in class-two nilpotent networks, including exact gcd/lcm criteria, explicit reconstruction certificates, obstruction witnesses, minimum-cost disclosure results, and an exact-arithmetic computational verification appendix. The discrete-gauge discussion is interpretive and does not make claims concerning Yang–Mills dynamics, confinement, or the mass gap.
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