HOME-DASP Border Atlas: A Parameter-Free Cyclotomic Framework for Structural Mathematical Physics (v0.391)

HOME-DASP is a mathematical physics research program investigating whatalgebraic and physical structure follows, without free continuousparameters, from a single deterministic generator on finite cyclicalgebraic structures. Every claim is classified under a strict trichotomy-- Theorem (machine-verified), Axiom (a declared structural move), or Wall(an honest negative result, recorded rather than omitted) -- and checkedagainst a companion computational verifier before being written into theaccompanying working document (the "Border Atlas"). This deposit (v0.391) contains the current state of the Border Atlas(249 pages, organised into a numbered main sequence plus supportingappendices), its reproducibility companion (a Python verification suiteof over 800 machine-checked claims, all currently passing), and adevelopment log recording the full history of the work, includingcorrections made explicit rather than silently patched. The program draws on and contributes to several areas of mathematicaland theoretical physics, discrete dynamical systems, number theory, andquantum information, under a discipline that treats negative results andhonest limitations as permanently recorded outcomes rather thanomissions. This is a restricted deposit intended to establish timestamped priorityand provenance for an active, single-author research program, while thework is prepared for peer-reviewed publication in separate, focusedpapers. The deposit record (title, abstract, metadata) is public; accessto the underlying files may be requested and is granted at thedepositor's discretion.