hv-chemical-memory

A NumPy-only toolkit for retention across four chemical substrates. One API. Four physics models. No training, no model artifact.

Size: ~15 KB source, no weights. Runtime: ~0.03 s for the full benchmark. Dependencies: NumPy only.

The four substrates

substrate	protection mechanism	protected quantity
Amber dielectric	τ ladder of relaxations	polarization fraction
Genome sequence	Eigen error threshold	master sequence identity
Topological invariant	mod-2 writhe	discrete knot class
Self-modifying genome	adaptive μ	tracks environmental drift

Each answers the same question — how long does a pattern survive? — with different physics.

Headline numbers

Amber dielectric (τ ladder: 3 yr → 300 kyr, 8 log-uniform modes):

time	retention
1 year	0.955
100 years	0.628
1 kyr	0.452
10 kyr	0.278
100 kyr	0.112
1 Myr	0.005
10 Myr	≈ 0

50% retention after 536 years; 10% after 119 kyr; 1% after 758 kyr.

Eigen error threshold (L·μ_crit = 1/(1-1/σ), confirmed):

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

The L·μ_crit column is the invariant — it depends only on σ.

Topological protection — writhe under Reidemeister moves:

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

Mod-2 writhe is invariant under R2 and R3. This is the protected quantity.

Self-modifying genome — μ evolves with environment:

scenario	μ_init	μ_final	predicted
static (drift=0)	0.010	0.000	0
constant drift=0.05	0.010	0.250	α·d/β = 0.25
linear drift	0.010	2.450	grows
sinusoidal drift	0.010	0.000	oscillates

Steady-state formula μ* = α·d/β confirmed exactly under constant drift.

21/21 consistency checks pass.

The retention ladder

From the source archive. This toolkit implements four of the seven rungs:

rung	memory type	mechanism	implemented
1	agent trajectory	fitness gradient	no
2	population pattern	mean-broadcast	no
3	classical phase	parameter region	partial (amber)
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

The ladder's claim: each rung replaces a decaying quantity with a more protected one. Amber sits between rungs 2 and 3 (rate-limited decay). Genome is rung 4 (sharp boundary). Topological is rung 6 (discrete protection). Self-modifying is rung 7 (tracks drift).

How to use

from hv_chemical_memory import (
    AmberMemory, ErrorThreshold, TopologicalMemory,
    SelfModifyingGenome, SubstrateOS,
)

os_ = SubstrateOS()

# Amber
r = os_.simulate_amber()
# r['retention_time_years'] = 536.1
# r['t_50pct_years'] = 536.1
# r['t_01pct_years'] = 757700

# Genome
r = os_.simulate_genome(L=100, sigma=2.0, mu=0.005)
# r['is_informational'] = True
# r['retention_estimate'] = fraction of master sequence preserved

# Topological
r = os_.simulate_topological(initial_writhe=0,
                              moves=('R3', 'R2_+', 'R1_+', 'R3'))
# r['protected_quantity'] = final mod-2 writhe

# Self-modifying
r = os_.simulate_selfmod(mu_init=0.01,
                          drift_schedule=lambda i: 0.05,
                          n_steps=500)
# r['mu_final'] = 0.25

# Or use the classes directly
amber = AmberMemory()
print(f"50% retention after {amber.retention_time(0.5):.0f} years")

et = ErrorThreshold(L=1000, sigma=5.0)
print(f"μ_crit = {et.critical_mutation_rate():.5f}")
print(f"informational at μ=0.001? {et.is_informational(0.001)}")

tm = TopologicalMemory(0)
tm.apply('R2_+')
print(f"writhe = {tm.writhe}, mod-2 = {tm.mod2_invariant()}")