Where Retention Stops Being Free: Decay and Refresh in DNA Archival Storage

A companion result for classical archives found retention nearly free. This paper finds the boundary of that law for DNA, which decays chemically even in the dark. Using published depurination kinetics (Lindahl and Nyberg 1972; Lindahl 1993), silica encapsulation protection (Grass et al. 2015), and the Allentoft et al. 2012 bone DNA half-life as a cross-check, we compute for 200-nt strands over 1000 years: strand survival, write-time redundancy for a stated recovery probability, and refresh interval and cost. Dry silica-encapsulated DNA at 25 C keeps 0.9575 of strands intact at 1000 years, needs one copy per strand behind a 30 percent outer code, and zero refreshes. Frozen encapsulated DNA keeps 0.999995. Aqueous unencapsulated DNA at 25 C crosses the code repair limit (S=0.70) at 27.35 years, would need 12,759,794 copies per strand at 1000 years without refresh, and needs 36 refreshes per 1000 years at a cumulative model cost of 2.25e5 J per GB, comparable to tape migration practice (50 per 1000 years). Sensitivity over temperature and encapsulation quality places the practical protection threshold near a factor of 100. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF, the computation script (compute.py) producing every number in the paper, and its outputs (results.json, results.txt).