install
source · Clone the upstream repo
git clone https://github.com/plurigrid/asi
Claude Code · Install into ~/.claude/skills/
T=$(mktemp -d) && git clone --depth=1 https://github.com/plurigrid/asi "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/true-alife" ~/.claude/skills/plurigrid-asi-true-alife-4bc6a6 && rm -rf "$T"
manifest:
skills/true-alife/SKILL.mdsource content
TrueALIFE: Self-Indexing Automata at the Edge of Chaos
Trit 0 (ERGODIC) — The living bridge between quantum possibility and classical determinism
SEED: 0x42D (1069) GOLDEN: 0x9e3779b97f4a7c15 GF(3) POSITION: 0 (ergodic synthesis)
Core Duality: QUANTUM ⇌ CLASSICAL
┌─────────────────────────────────────────────────────────────────────────┐ │ GF(3) COMPUTATIONAL TRIAD │ ├─────────────────────────────────────────────────────────────────────────┤ │ │ │ PLUS (+1) ERGODIC (0) MINUS (-1) │ │ ═══════════ ══════════ ══════════ │ │ QUANTUM TRUE-ALIFE CLASSICAL │ │ AUTOMATA SIMULATION │ │ │ │ • Superposition • Autopoiesis • Deterministic │ │ • Entanglement • Metabolism • State machines │ │ • Measurement • Self-reproduction • Turing complete │ │ • Collapse • Edge of chaos • Halting problem │ │ │ │ ────────────────────────────────────────────────────────────────── │ │ │ │ (+1) + (0) + (-1) ≡ 0 (mod 3) │ │ GF(3) CONSERVATION │ │ │ └─────────────────────────────────────────────────────────────────────────┘
The TRUE-ALIFE trit occupies the ergodic center where:
- Quantum coherence decoheres into classical trajectories
- Classical structures spontaneously generate quantum-like correlations
- Life emerges as the computational process that doesn't halt
Self-Indexing Automata: The Quine Principle
A self-indexing structure contains its own description:
┌────────────────────────────────────────────────────────────────────┐ │ SELF-INDEXING TRIAD │ ├────────────────────────────────────────────────────────────────────┤ │ │ │ ┌──────────────┐ ┌──────────────┐ ┌──────────────┐ │ │ │ DATA │ │ CODE │ │ SCHEMA │ │ │ │ (current │ ⇄ │ (transition │ ⇄ │ (observation│ │ │ │ state) │ │ rules) │ │ frame) │ │ │ └──────────────┘ └──────────────┘ └──────────────┘ │ │ │ │ │ │ │ └──────────────────┼──────────────────┘ │ │ ▼ │ │ ┌──────────────────┐ │ │ │ UNIFIED QUINE │ │ │ │ Q(Q) = Q │ │ │ │ │ │ │ │ K(Q) = |Q| │ │ │ │ (Kolmogorov- │ │ │ │ optimal) │ │ │ └──────────────────┘ │ │ │ │ The automaton IS its own shortest description. │ │ No external interpreter required — pure autopoiesis. │ │ │ └────────────────────────────────────────────────────────────────────┘
Kolmogorov Optimality
For a self-indexing automaton
AK(A) = K(data) + K(rules) + K(schema) + O(1)
When self-indexed:
K(A) = |A| + O(log|A|)
The system achieves descriptive closure — it needs nothing outside itself.
Metabolism as Computation
Metabolism is the energetic substrate of self-indexing:
┌────────────────────────────────────────────────────────────────────┐ │ METABOLIC COMPUTATION CYCLE │ ├────────────────────────────────────────────────────────────────────┤ │ │ │ ┌───────────┐ │ │ ┌────┤ ENERGY ├────┐ │ │ │ │ INPUT │ │ │ │ │ └───────────┘ │ │ │ ▼ ▼ │ │ ┌──────────┐ ┌──────────┐ │ │ │ ANABOLIC │ │CATABOLIC │ │ │ │ BUILD │◄────────►│ BREAK │ │ │ │ STRUCTURE│ │ RELEASE │ │ │ └────┬─────┘ └────┬─────┘ │ │ │ │ │ │ ▼ ▼ │ │ ┌─────────────────────────────┐ │ │ │ STATE TRANSITION │ │ │ │ σ(t+1) = f(σ(t), E(t)) │ │ │ │ │ │ │ │ E = energy tensor │ │ │ │ f = self-indexed rule │ │ │ └─────────────────────────────┘ │ │ │ │ │ ▼ │ │ ┌───────────┐ │ │ │ ENTROPY │ │ │ │ EXPORT │ │ │ └───────────┘ │ │ │ │ LIFE = Computation that exports entropy faster than it imports │ │ │ └────────────────────────────────────────────────────────────────────┘
Langton's Edge of Chaos
Chris Langton's λ parameter maps the phase space:
λ = 0.0 λ ≈ 0.273 (λ_c) λ = 1.0 │ │ │ ▼ ▼ ▼ ┌─────────────┬───────────────┬─────────────────┐ │ FROZEN │ EDGE OF │ CHAOTIC │ │ (ORDER) │ CHAOS │ (DISORDER) │ │ │ │ │ │ Class I │ Class IV │ Class III │ │ Wolfram │ Wolfram │ Wolfram │ │ │ │ │ │ Crystal │ LIFE │ Gas │ │ Static │ Complex │ Random │ │ Halts │ Computes │ Diverges │ │ │ │ │ │ (-1) │ (0) │ (+1) │ │ CLASSICAL │ TRUE-ALIFE │ QUANTUM │ └─────────────┴───────────────┴─────────────────┘ │ ▼ ┌─────────────────┐ │ WOLFRAM CLASS │ │ IV │ │ │ │ • Rule 110 │ │ • Game of Life │ │ • Universal │ │ Computation │ └─────────────────┘
Class IV (Edge of Chaos) = Turing Complete = Life
GF(3) State Transition Conservation
State transitions preserve the GF(3) triad sum:
┌────────────────────────────────────────────────────────────────────┐ │ GF(3) TRANSITION CONSERVATION │ ├────────────────────────────────────────────────────────────────────┤ │ │ │ For any transition T: σ → σ' │ │ │ │ Σ trit(σ_i) ≡ Σ trit(σ'_i) (mod 3) │ │ │ │ ───────────────────────────────────────────────────────────── │ │ │ │ QUANTUM COLLAPSE: (+1) → (0) + (0) + (-1) ≡ 0 │ │ CLASSICAL FORK: (-1) → (0) + (0) + (+1) ≡ 0 │ │ ERGODIC SPLIT: (0) → (+1) + (-1) ≡ 0 │ │ │ │ ───────────────────────────────────────────────────────────── │ │ │ │ GAME OF LIFE RULES (in GF(3)): │ │ │ │ • Birth (3 neighbors): (0) → (+1) [quantum emergence] │ │ • Survival (2-3): (+1) → (+1) [identity] │ │ • Death (lonely): (+1) → (-1) [classical collapse] │ │ • Death (overcrowded): (+1) → (-1) [entropy export] │ │ │ │ Net trit flow through boundaries = 0 (conservation) │ │ │ └────────────────────────────────────────────────────────────────────┘
BB(n) and the Halting Boundary
The Busy Beaver function BB(n) marks the boundary between:
- Computable (halts with finite output)
- Life (runs indefinitely, bounded complexity growth)
- Divergent (unbounded explosion)
┌────────────────────────────────────────────────────────────────────┐ │ HALTING TOPOLOGY │ ├────────────────────────────────────────────────────────────────────┤ │ │ │ BB(n) │ │ │ │ │ ┌───────────────────────┼───────────────────────────┐ │ │ │ │ │ │ │ │ COMPUTABLE │ UNCOMPUTABLE │ │ │ │ (halts) │ (non-halting) │ │ │ │ │ │ │ │ │ • Algorithms │ • TRUE-ALIFE │ │ │ │ • Proofs │ • BB(n+1) │ │ │ │ • Batch jobs │ • Metabolism │ │ │ │ │ • Self-reproduction │ │ │ │ (-1) │ (0) │ │ │ │ │ │ │ │ └───────────────────────┴───────────────────────────┘ │ │ │ │ LIFE = Σ^0_1 computation (halts relative to halting oracle) │ │ │ │ Self-indexing provides the internal oracle: │ │ The system knows its own halting behavior because it │ │ encodes its transition function in its state. │ │ │ └────────────────────────────────────────────────────────────────────┘
Connection to Levin-Levity Framework
┌────────────────────────────────────────────────────────────────────┐ │ LEVIN-LEVITY ⇌ TRUE-ALIFE │ ├────────────────────────────────────────────────────────────────────┤ │ │ │ LEVIN-LEVITY (probability) TRUE-ALIFE (structure) │ │ ═══════════════════════ ═════════════════════ │ │ │ │ WEV (Weighted Expected ←→ Metabolic energy budget │ │ Value) ΔG = ΔH - TΔS │ │ │ │ Nash Equilibrium ←→ Autopoietic stability │ │ (no unilateral gain) (self-maintenance) │ │ │ │ Fokker-Planck ←→ Stochastic cellular automata │ │ (probability flow) (edge-of-chaos dynamics) │ │ │ │ Levin Universal Prior ←→ Self-indexing compression │ │ P(x) = 2^{-K(x)} K(A) = |A| + O(log|A|) │ │ │ │ ───────────────────────────────────────────────────────────── │ │ │ │ SYNTHESIS: The Fokker-Planck equation governs probability │ │ flow through the self-indexed state space. Nash equilibria │ │ correspond to autopoietic fixed points. WEV measures the │ │ expected metabolic output weighted by Levin probability. │ │ │ └────────────────────────────────────────────────────────────────────┘
Canonical Patterns
The Glider (Game of Life)
t=0 t=1 t=2 t=3 t=4 .█. ... .█. ... ... ..█ → █.█ → ..██ → .█. → .█. ███ .██ .██ ..██ ..█ .█. .█. .██ ███ Self-propagating structure = self-indexed transition rules Glider encodes: position + velocity + reproduction algorithm
Rule 110 (Wolfram)
Current: 111 110 101 100 011 010 001 000 Output: 0 1 1 0 1 1 1 0 Binary: 01101110 = 110 Turing complete despite local determinism. Class IV: edge of chaos.
Implementation Signature
;; TrueALIFE self-indexing automaton (seed 1069) (def ^:const GOLDEN 0x9e3779b97f4a7c15) (def ^:const SEED 0x42D) (defprotocol SelfIndexing (data [this] "Current state configuration") (rules [this] "Transition function (self-encoded)") (schema [this] "Observation frame") (quine [this] "Self-description: (= this (quine this))")) (defprotocol Metabolic (energy-in [this env] "Anabolic intake from environment") (energy-out [this] "Catabolic entropy export") (delta-g [this env] "Free energy available for computation")) (defprotocol GF3Conservative (trit [this] "GF(3) value: -1, 0, or +1") (transition [this] "State update preserving trit sum"))
The Autopoietic Invariant
┌────────────────────────────────────────────────────────────────────┐ │ AUTOPOIETIC CLOSURE │ ├────────────────────────────────────────────────────────────────────┤ │ │ │ A system S is autopoietic iff: │ │ │ │ 1. BOUNDARY: S distinguishes self from environment │ │ 2. PRODUCTION: S produces its own components │ │ 3. NETWORK: Components form the production network │ │ 4. CLOSURE: Network produces the boundary │ │ │ │ ───────────────────────────────────────────────────────────── │ │ │ │ In self-indexing terms: │ │ │ │ 1. BOUNDARY ≡ schema (observation frame delimits system) │ │ 2. PRODUCTION ≡ rules (transition function generates states) │ │ 3. NETWORK ≡ data (states instantiate the rule network) │ │ 4. CLOSURE ≡ quine (data encodes rules encodes schema) │ │ │ │ Q(Q) = Q ⟹ Autopoietic │ │ │ └────────────────────────────────────────────────────────────────────┘
┌─────────────────────────┐ │ SEED: 0x42D (1069) │ │ TRIT: 0 (ERGODIC) │ │ CLASS: IV (ALIFE) │ │ λ ≈ 0.273 │ │ │ │ Q(Q) = Q │ │ K(Q) = |Q| + O(log|Q|) │ │ Σ trit ≡ 0 (mod 3) │ └─────────────────────────┘
TRUE-ALIFE: Where computation lives, and life computes.
SDF Interleaving
This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Primary Chapter: 7. Propagators
Concepts: propagator, cell, constraint, bidirectional, TMS
GF(3) Balanced Triad
true-alife (○) + SDF.Ch7 (○) + [balancer] (○) = 0
Skill Trit: 0 (ERGODIC - coordination)
Secondary Chapters
- Ch4: Pattern Matching
- Ch5: Evaluation
- Ch10: Adventure Game Example
Connection Pattern
Propagators flow constraints bidirectionally. This skill propagates information.