hv-chemical-life

Five chemical-life substrates in one NumPy-only toolkit. Hypercycle dynamics, nested zombie ecology, Eigen error threshold, self-modifying genome, and topological protection. One API, one retention ladder.

Size: ~18 KB source, no weights. Runtime: ~3 s for the full benchmark. Dependencies: NumPy only.

The retention ladder

The source archive organizes chemical information processing into seven rungs. This toolkit implements five:

rung	memory type	mechanism	implemented
1	agent trajectory	fitness gradient	no
2	population pattern	hypercycle	yes
3	classical phase	parameter region	partial
4	genome sequence	error threshold	yes
5	quantum MBL	eigenstate property	no
6	topological invariant	crossing count	yes
7	self-modifying rule	evolved μ	yes

Plus the nested-zombie host-parasite ecology as a fifth substrate.

The ladder's claim: each rung replaces a decaying quantity with a more protected one.

Headline numbers

Hypercycle — Eigen-Schuster instability at large N:

N	parasite=False	parasite=True
3	stable	stable
5	stable	stable
6	critical N	critical N
12	unstable	unstable
20	unstable	unstable
30	unstable	unstable

Critical N for this parameterization: N = 6. Below N, the cycle is stable. Above, the wave amplitude grows and individual species drop below the synthesis floor.

Nested zombie ecology — escape-rate transition:

escape rate	regime
0.1	endosymbiont
0.3	parasite
0.5	parasite
0.9	parasite

Eigen error threshold — sharp phase boundary:

L	σ	μ_crit	L·μ_crit
50	2	0.0400	2.000
100	2	0.0200	2.000
500	2	0.0040	2.000
1000	2	0.0020	2.000

L·μ_crit is the invariant, depending only on σ. Confirms L·μ_crit = 1/(1-1/σ).

Self-modifying genome — μ tracks environmental drift:

scenario	μ_init	μ_final
static	0.01	0.00
constant drift 0.05	0.01	0.25
linear drift	0.01	2.45
sinusoidal drift	0.01	0.00

Steady-state formula μ* = α·d/β = 0.25 confirmed exactly.

Topological protection — writhe mod 2:

move	Δwrithe	Δmod-2
R1	±1	±1
R2	±2	0
R3	0	0

Mod-2 writhe is invariant under R2 and R3.

27/27 consistency checks pass.

The two classical results reproduced

1. Eigen-Schuster hypercycle instability. Without a parasite, the hypercycle is only stable for small N. Above N* ≈ 6–10, internal mutants destabilize the cycle, and individual species drop below the synthesis floor. The instability is not driven by external invasion — it's internal. Compartmentalization is required for stability at large N.

2. Sharp vs smooth thresholds. Threshold sharpness is determined by state-space size. The Eigen threshold is sharp at L ≥ 100, smooth at L = 50. The hypercycle transition is sharp in N. The escape-rate transition in nested zombies has the same shape. All three are the same mathematical structure in different substrates.

How to use

from hv_chemical_life import (
    Hypercycle, NestedEcology, ErrorThreshold,
    SelfModifyingGenome, TopologicalMemory,
    ChemicalLifeOS, critical_N,
)

os_ = ChemicalLifeOS()

# Hypercycle with and without a parasite
r = os_.simulate_hypercycle(N=6, parasite=True)
# r['collapsed'] = False or True
# r['final_C_min'] = smallest surviving member concentration

# Nested zombie
r = os_.simulate_zombie(e=0.5)
# r['regime'] = 'endosymbiont' | 'parasite' | 'host_only' | 'extinction'

# Error threshold
r = os_.simulate_threshold(L=100, sigma=2.0, mu=0.005)
# r['is_informational'] = True
# r['mu_crit'] = 0.02

# Self-modifying genome
r = os_.simulate_selfmod(drift_schedule=lambda i: 0.05, n_steps=500)
# r['mu_final'] = 0.25

# Topological
r = os_.simulate_topological(moves=('R3', 'R2_+', 'R1_+'))
# r['protected_quantity'] = final mod-2 writhe

# Retention ladder — all five substrates, unified output
ladder = os_.retention_ladder()

# Critical hypercycle size
Nc = critical_N(parasite=True, N_range=(2, 30))