Information Dna Storage Density Rs Dnastorage Cert

What the certificate proves

DNA storage density is a measure of how much digital information can be packed into a gram of DNA. A 2012 experiment by Church, Gao, and Kosuri stored about 215 million gigabytes per gram, a figure that remains a common reference point. The Recognition Science framework's ledger, a discrete record of recognition events, models costs that scale with information content. The declaration DNAStorageCert is a machine-checked certificate, a formal object that packages three proved facts about one such cost function.

The cost function in question is Jcost, which measures the price of a recognition event relative to a baseline. The certificate proves three things. First, when the measured amount equals the expected amount, the cost is zero. Second, for any two positive amounts, the cost is never negative. Third, a particular threshold value, phi minus 1.5, is positive, meaning phi is greater than 1.5. These are general properties of the cost function, not facts about DNA.

The module also contains a research note, a paragraph that records an intended direction: that DNA storage density might follow a phi-power law, with phi^52 bytes per gram. That note is explicitly labeled as not a result. The machine-checked theorems prove nothing about DNA storage density, because the cost function is defined as Jcost of a ratio of two real numbers, without any definition of what those numbers mean for DNA. The certificate is a template, not a measurement.

In Recognition Science, this pattern is deliberate. The framework proves structural facts about cost functions in general; applying them to a specific subject requires a definition of the subject's own terms. DNAStorageCert establishes that the cost function has the three listed properties. It does not establish that DNA storage density follows any particular law, nor that the research note's phi-power speculation is correct. The certificate is a foundation stone, not a claim about biology.

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

What this page does not claim

DNAStorageCert does not prove any specific density value or scaling law for DNA storage. The research note's phi^52 estimate is a speculation, not a derived result. The certificate says nothing about the physical implementation of DNA storage.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Information/DNA_Storage_Density_RS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: