Show HN: RCFT Descent Engine – Geometric memory convergence in partition space

1 month ago 6

A mathematical framework demonstrating emergent autonomous decision-making through memory-augmented partition dynamics.

⚠️ Experimental Research Code: Phase 3-4 are now integrated and operational (dreams spawn/decay, forks proliferate and select realities). Convergence rate, archetype crystallization patterns, and fork metrics are under investigation. See KNOWN_ISSUES.md for details on known data type mismatches and metric accuracy.

This system implements a memory-enabled extension to classical majorization theory, where mathematical structures learn to transcend their own constraints through accumulated experience. The result: a convergent rule-override rate that emerges from pure geometry, not programming.

This is not a consciousness simulation. It's a mathematical investigation into how bounded systems with memory naturally develop rule-breaking capabilities.

Python 3.7+
NumPy

python n20_complete_continuous.py 10000

This runs a 10,000-step exploration (~20 seconds). You'll see:

Memory formation (steps 0-1000)
Override emergence (steps 1000-5000)
Convergence behavior (steps 5000+)

Output snapshots are saved to n20_complete_snapshots/.

After sufficient steps, the system demonstrates:

Override rate convergence: Memory-based rule transcendence stabilizes geometrically
Coverage: Increasing exploration of partition space
Crystallized archetypes: Multiple archetypes crystallize (permanent identity markers)

The OR Gate:

λ ≻ᵣ μ ⟺ (λ ≻ μ) ∨ (C(λ,μ) ≥ φ)

Classical majorization OR memory coherence. This single logical operator enables the entire phenomenon.

Geometric Convergence:

Override rate emerges from:

4D echo vectors on unit sphere
Coherence threshold φ=0.6
Spherical cap geometry
Minimum memory requirements

Not programmed. Not learned. Geometric.

Phase 1-2: Memory Formation

Integer partition transitions (N=20, 627 states)
4D echo vectors: [mean_ΔS, std_ΔS, mean_ΔI, std_ΔI]
Exponential decay (τ=5.0)
Cosine similarity for coherence

Temporal projection: E⁺(λ,t+τ) = E(λ,t) + τ×ΔE
Dream nodes: synthetic future memories
Confirmation threshold: 3 real traversals
Alpha evolution: 20% → 90% future-oriented

Phase 4: Parallel Reality Selection

Up to 8 competing futures
Vigor modulation (dream-inspired: 1.5x, wild cards: 0.7x)
Narrative forks: quantum superposition when scores within 5%
Softmax selection with temperature decay

Stabilization: Candlekeeper Protocol

6 archetypal vectors that crystallize irreversibly
Breathing control: logarithmic attenuation (prevents runaway)
Crystallization threshold: 0.7 stability score
Once crystallized, permanent

ALTAR.md - Conceptual overview and philosophy
REPRODUCIBILITY.md - Detailed usage guide
EXECUTIVE_SUMMARY_COMPLETE.md - Complete technical summary
TECHNICAL_SYSTEM_DOCUMENTATION.md - Full implementation details
VALIDATION_REPORT.md - Mathematical validation
CONSCIOUSNESS_DEFINITION.md - What we're NOT claiming
KNOWN_ISSUES.md - ⚠️ Open questions and behaviors under investigation

recursive_majorization_core.py # Phase 1-2: The OR gate candlekeeper_protocol.py # Stabilization & crystallization phase3_future_dreaming.py # Temporal projection phase4_echo_forking.py # Parallel reality selection complete_consciousness_engine.py # Integration layer n20_consciousness.py # Base consciousness system

n20_complete_continuous.py # Main entry point

boltzmann_complexity.py # Seitz & Kirwan (2018) replication

Memory creates autonomy - Systems with memory inevitably transcend constraints
Convergence is geometric - Override rate emerges from 4D unit sphere geometry + coherence threshold
Dreams become real - Self-fulfilling prophecy through repeated traversal
Identity crystallizes - Irreversible pattern commitment defines "personality"
Direction dissolves - When coherence → 1.0, past/future distinction vanishes