sim05 Coexistence Analysis — What Distinguishes the 2/6

Status: Analysis complete (2026-07-27). Pure analysis of committed results.json — no new code. Addresses queued-topics #52. Tests H10 directly.

The question

Corrected sim05 gives 2/6 L2 coexistence. What distinguishes the two pairs that coexisted from the four that did not?

The data

Findings

1. Size symmetry is necessary but not sufficient

Both coexisting pairs have both organizations with >=10 species, and size ratios of 2.0 and 1.05. But pair [0,3] is 10v10 (ratio 1.0) and fails — run 3 dominates run 0 at the same size. Size alone does not predict coexistence.

What does distinguish the coexisting pairs is that neither organization is run 3. Run 3 appears in 3 of 6 pairs and destroys or is destroyed in all three. Removing run 3, the remaining 3 pairs give 2 coexistence and 1 dominance — coexistence is the majority outcome when run 3 is absent.

2. Run 3 is lethally self-referential

Run 3's top species are structurally distinct from the others. Its dominant expression is λv102.(λv103.(v102 (λv104.(λv105.v102)))) — a self-applicative form where v102 is applied to a function that returns v102. The next two are λv218.(λv216.(λv218.v216)) and its nested variant — a function that applies its argument to itself. These are fixed-point-like forms: when they collide with other expressions, they tend to reproduce themselves while consuming the partner.

Run 0 and run 1, by contrast, are built around identity-like forms (λv248.(λv249.v249) — the K-combinator returning the second argument) and nested applications of a small set of variables. These are less destructive in collision.

3. Run 1 is the resilient organization

Run 1 (20 species) coexists with both run 0 and run 2. It only fails with run 3, and even there the outcome is mutual destruction, not dominance — run 3 cannot dominate run 1. Run 1's species are diverse (20 unique types) and include a mix of identity-like forms and nested combinators. The diversity may provide buffer: losing some species to collision still leaves enough survivors above the 0.5 threshold.

4. Shared species: one coexisting pair has substantial overlap

Pair [0,1] — one of the two coexisting pairs — shares 8 of Run 0's 10 species with Run 1's 20. The other 5 pairs are disjoint. This contradicts the blanket "zero shared species" claim made in an earlier version of this analysis, which was based on a truncated top-species list in results.json rather than the full populations.

This means the "not glue" conclusion needs qualification. Shared species are not necessary for coexistence (pair [1,2] coexists with zero shared species), but they are not incompatible with it either (pair [0,1] coexists with 80% overlap). The presence of shared species in one coexisting pair and their absence in the other suggests that coexistence is not determined by structural overlap in either direction — it is compatible with both overlap and disjointness.

5. The mechanism: collision dynamics, with structural overlap neutral

The L2 test combines two populations and runs 20,000 random collisions. Each collision applies one expression to another via beta-reduction. If the result is a new expression (not identity, not equal to either parent, and size <= 30), it replaces a random member of the population.

Destructive dynamics: if org A's species tend to reduce org B's species to themselves (or to expressions outside B's set), B's survival fraction drops. Run 3's self-applicative forms do this — they consume other expressions and produce more of themselves or their close variants.

Coexistence happens when neither organization's species systematically eliminates the other. This is a property of the collision dynamics between the two specific sets, not of their structure in isolation. Structural overlap is neither necessary nor sufficient: pair [0,1] coexists with 80% shared species, pair [1,2] coexists with zero shared species.

What this means for H10

H10 (the Unbounded Space Insufficiency Hypothesis) claimed that unbounded molecule space alone is insufficient for composition — that 0/6 coexistence shows composition fails even with infinite species space. The corrected 2/6 weakens this: composition is not impossible, it is the minority outcome (33%).

This analysis sharpens the picture. The failure is not uniform — it is driven by specific organizations with destructive collision dynamics (run 3). When neither organization is destructive, coexistence is the majority outcome (2/3 of pairs without run 3).

The implication for H10: the bottleneck may not be space (bounded vs unbounded) but collision dynamics — whether the organizations that arise are dynamically compatible. This is closer to Fontana & Buss's original framing: the question is not whether composition can happen, but what properties of the component organizations determine whether it does. Structural overlap is neutral — one coexisting pair shares 80% of species, the other shares none — so "glue" is neither the explanation nor the obstacle.

Limitations

• n=6 pairs from 4 L1 runs. The pattern (run 3 is lethal, size matters secondarily) is clear but the sample is small.
• "L1 organizations" are surviving species sets, not verified closure + self-maintenance (see queued-topics #56). The L1/L2 framing assumes these are organizations in the COT sense, which is unvalidated.
• The analysis is post-hoc: we are explaining a pattern in 6 data points, not predicting out of sample. A stronger test would generate more L1 runs and predict which pairs coexist based on structural properties.