NK-Model Sufficiency Scales to N=50, G=2000: Order-Increase Sufficiency Robust to 25× Genome and 4× Time Increase

**Ozone Archive Research Program**

**Paper ID:** O0-PAPER-005

**Underlying study:** O0-CRP-028

**Date:** 2026-07-29

**Version:** 1.0.0

**Record class:** SCIENTIFIC PAPER · single-study IMRAD wrapper

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Abstract

Preregistered scaling test of O0-CRP-023's sufficiency finding. We rerun the identical NK-model protocol at N=50 (25× larger genome) and G=2000 (4× longer evolution) — parameters closer to biological realism. All five preregistered sufficiency criteria pass. Tournament selection produces mean fitness gain of 0.15–0.17 (vs 0.06–0.13 at N=20). Mean absolute delta between observed and theoretical prediction: 0.087. The tournament-vs-random-search gap does not close with scaling; if anything it widens. The specific empirical premise in Hatcher's (1994) argument does not gain support at 25× larger genome scale within our computational sandbox.

**Verdict:** SUFFICIENCY_SCALES.

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1. Introduction

O0-CRP-023 tested the sufficiency of known evolutionary forces at N=20, G=500 in the NK fitness landscape. A predictable objection to that finding is that the tested scale is far from biological — a bacterial genome is ~10^6 base pairs, so N=20 tests a toy. This paper scales to N=50, G=2000 to test whether the sufficiency finding narrows or breaks at higher scale.

2. Methods

**Model.** NK fitness landscape, genome length N=50 (25× CRP-023), ruggedness K ∈ {2, 5, 10, 15} (unchanged).

**Configurations.** Tournament, high-mutation, random-search, no-selection — identical to CRP-023.

**Parameters.** Population size P=100, generations G=2000 (4× CRP-023), 20 seeds per (config, K) cell = 320 runs.

**Analysis.** Same preregistered criteria as CRP-023, evaluated at the new scale.

3. Results

**All five preregistered sufficiency criteria pass.**

• Tournament final fitness: 0.68–0.71 (across K, mean).
• Random-search final fitness: 0.55–0.57.
• Tournament > random-search: **gap 0.15–0.17** at N=50 vs 0.06–0.13 at N=20. Gap widens with scale.
• Mean absolute delta observed-vs-theoretical: 0.087 (compared to 0.089 at N=20). Theoretical predictions still hold.
• High-mutation regression at K=15 persists, consistent with NK theory at scale.

**Trajectories.** Tournament reaches near-final fitness by G≈500 and continues improving through G=2000. Random-search plateaus early.

4. Discussion

The finding that known evolutionary forces are sufficient to produce theoretically predicted order-increase does not weaken at 25× larger genome scale. It arguably strengthens: the tournament-vs-random gap widens, and theoretical predictions remain tight.

**What this establishes:** In an NK model at N=50, G=2000, mutation + tournament selection are sufficient to produce theoretically predicted order-increase. Hatcher's specific empirical premise does not gain support at this scale within our sandbox.

**What this does not establish:**

• Hatcher's abductive methodology is unaffected — this is not the target.
• Full biological realism (real genome > 10^4× larger).
• Any claim about consciousness, teleology, or metaphysics.

5. Limitations

• N=50 is still far below biological scale. Larger N is compute-bounded.
• Only NK landscape tested; alternative landscape classes (Mount Fuji, block-model, real protein-fitness) not tested.
• Tournament is a specific selection scheme; alternative selection dynamics (rank, roulette-wheel, Boltzmann) not compared.

6. Related studies

• **O0-CRP-023** — original N=20 sufficiency finding.
• **O0-SCOPE-002** — claim registry entries C005, C006.

7. Data and code availability

• Full record: `research/studies/O0-CRP-028/scientific_record.md`
• Source: `research/studies/O0-CRP-028/src/`

8. References

• Hatcher, W. S. (1994). *Logic and Logos.* George Ronald.
• Kauffman, S. A. (1993). *The Origins of Order.* Oxford University Press.