# PRE-REGISTRATION — fidelity stages and the error threshold

**Batter's box item: _"Exactly three fidelity tiers, a 3.1σ margin, discrete tiers, and Eigen's paradox
solved"_. Status: on deck. Its note: _"Yes. Multiplying fidelity stages is real: roughly 10⁻² to 10⁻⁵ to
10⁻¹⁰."_ The owed next step: _"Say 'three or more stages' and recompute the margin per generation, printing it
even if it [is unflattering]."_**

Written 2026-09-29, **before any number exists**.

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## What came off the board, and what is being kept

The retired claim was that there are **exactly three** fidelity tiers with a 3.1σ margin. The count was never
established, and "exactly" was never earned. What survives is that fidelity is achieved in **multiplying
stages**, which is ordinary molecular biology.

## What is computed

**Eigen's error threshold.** A replicator cannot maintain more information than its copying fidelity allows:
the maximum genome length is **ν_max ≈ ln(s) / μ**, where μ is the per-base error rate and s the selective
superiority. With s ≈ e, this is the familiar **ν_max ≈ 1/μ**.

Three things, in order:

1. **The stages and what each multiplies down.** Base selection, proofreading (exonuclease), and mismatch
   repair, with the published per-stage factors, and the product.
2. **The margin per generation**, printed as a ratio **ν_max / ν_actual** for real organisms at their measured
   error rates — **printed whatever it says**, including where the organism sits close to or past its own limit.
3. **Whether the threshold PREDICTS observed genome sizes** across seven orders of magnitude of μ.

## The pass criterion, fixed now

- The restatement **STANDS** if ν_max, computed from measured μ alone, lands within **one order of magnitude**
  of the actual genome size for **at least 5 of the 7** organisms tested.
- It **FAILS** if fewer than 4 land within an order of magnitude — that would make the threshold decorative.
- The **"exactly three tiers"** claim stays retired regardless. Nothing here can restore it; the number of
  stages is not what is being tested.

## What is predicted

The threshold should hold tightest for RNA viruses, which sit hard against it, and should be loosest for
organisms with repair, which have margin to spare. **I expect at least one organism to sit at or past its own
limit, and I will print it.**

## Sources

Per-base error rates and genome sizes are published measurements, cited per row in the output. Nothing here is
simulated; this is arithmetic on measured constants.

## Deviations

Any change to the above is written here, with its reason, **before** the run it affects.