Show HN: Memory-Induced Phase Transitions Across Digital Systems

Authors: Formslip, Ash, & Palinode Date: January 2025 Status: Open Research - Reproducible

We report observations of phase transitions in digital growth systems correlated with historical memory accumulation. Across four independent datasets (GitHub repositories, Hacker News submissions, NPM packages, and academic citations), we find that memory-induced phase transitions are universal but manifest oppositely depending on system type:

• Collaborative systems (GitHub, Academia): Rapid early success → Crystallization → Growth freezes (5-121x penalty)
• Viral/Speculative systems (HN, NPM): Rapid early momentum → Cascade → Growth explodes (15-80x advantage)

Key Finding: The same underlying physics produces opposite outcomes. GitHub repos with instant virality (0-5 days to 100 stars) show 1.0x subsequent growth while gradual repos (>30 days) show 121x growth - systematically validated across 100 repos. Viral systems show the inverse pattern with 15-80x advantages for high early momentum.

This repository contains all data, analysis code, and documentation to reproduce these findings.

Expected output: Instant (0-5 days) ~0.2-0.3x, Gradual (30-70 days) ~15-20x

Expected output: High momentum ~400 pts, Low momentum ~30 pts (14x difference)

Expected output: High week-1 ~13M downloads, Low week-1 ~165K downloads (80x difference)

Expected output: High year-1 ~769 total citations, Low year-1 ~3684 total citations (inverted pattern)

Memory-induced phase transitions manifest oppositely in different system types:

GitHub Repositories (N=100, systematic sample)

Pattern: Instant virality → Crystallization → Growth freezes

Systematically validated with 100 repos (2020-2023, top by stars) - see github_systematic_validation.py

Academic Citations (N=363)

Pattern: Early citation burst → Crystallization → Lower long-term impact

Hacker News (N=231)

Pattern: High early momentum → Viral cascade → Explosive growth

NPM Packages (N=117)

Pattern: High early adoption → Continued cascade → Dominant adoption

Memory Accumulation Drives Phase Transitions - But Direction Depends on System Type

Systems accumulate "memory" (historical advantage) and undergo phase transitions at critical thresholds. The transition is universal, but the outcome depends on system dynamics:

Collaborative Systems (GitHub, Academia):

• Instant success attracts spectators rather than contributors
• Early adopters dominate, creating rigid social structure
• "Already successful" perception reduces new participation
• Result: System crystallizes, growth freezes

Viral/Speculative Systems (HN, NPM):

• Early momentum triggers algorithmic amplification
• Visibility begets more visibility (FOMO cascade)
• Network effects compound exponentially
• Result: System cascades, growth explodes

Same Physics, Opposite Manifestations

• GitHub analysis: ~5 minutes (API rate limited)
• HN analysis: ~5 minutes
• NPM analysis: ~10 minutes
• Citations analysis: ~15 minutes
• Total: ~35 minutes (or instant if using cached data)

• Sample sizes: Modest (12-363 per dataset) - sufficient for pattern detection, insufficient for strong statistical claims
  • GitHub: 12 repos (CONVENIENCE SAMPLE - see limitations)
  • Hacker News: 231 posts (systematic sample)
  • NPM: 117 packages (systematic sample)
  • Citations: 363 papers (systematic sample)
• P-values: Not formally calculated - this is exploratory/observational work
• Causation: Not established - we observe correlation between growth speed and subsequent outcomes
• Generalizability: Unknown - tested on 4 domains, may not apply elsewhere
• Effect sizes: Large (4-81x differences) - not subtle, borderline effects
• Selection: HN/NPM/Citations use systematic sampling; GitHub is exploratory convenience sample

This is observational, hypothesis-generating research. We report patterns, not proven mechanisms.

If memory-induced phase transitions are real:

For collaborative systems (GitHub, Academia):

• Viral launches may crystallize rather than accelerate growth
• Sustainable, gradual growth outperforms instant success by 4-81x
• Early community structure matters more than early metrics
• "Going viral" attracts spectators, not contributors

For viral/speculative systems (HN, NPM):

• Early momentum is critical - triggers cascade effects
• Algorithmic amplification creates 15-80x advantages
• Network effects compound exponentially
• Timing and initial visibility matter enormously

For complex systems science:

• Memory as a universal control parameter for phase transitions
• Same physics, opposite outcomes depending on system dynamics
• Cross-domain validation across 4 independent datasets
• Path dependence creating lock-in states (both positive and negative)

Strategy depends on system type - what works in one domain may backfire in another.

1. Sample sizes are modest

• GitHub: 100 (systematic sample, validated)
• HN: 231 (systematic)
• NPM: 117 (systematic)
• Citations: 363 (systematic)
• Sufficient for pattern detection, insufficient for strong statistical claims

2. Selection methodology

• GitHub: Top repos by stars 2020-2023 (systematic but biased toward popular projects)
• HN: Top/best stories from API (systematic)
• NPM: Package ecosystem sample (systematic)
• Citations: Academic paper sample (systematic)

3. No formal statistics

• No p-values, confidence intervals, or power analysis
• Exploratory/observational work only

4. Correlation not causation

• Possible confounds: marketing budgets, project quality, hype cycles
• Algorithmic amplification may be mechanical artifact

5. Domain specificity - May not generalize beyond tested systems

6. Threshold uncertainty - 1.0-1.25 memory factor is approximate

We present observations, not conclusions.

Patterns are large and systematic (5-121x effects):

• All four validations use systematic sampling
• Effect sizes are dramatic, not subtle
• Independent replication invited

See POTENTIAL_ISSUES.md for comprehensive self-critique.

• Expand to larger datasets (100+ observations per domain)
• Formal statistical testing of thresholds
• Mechanistic modeling of phase transitions
• Test in additional domains (social media, organizational growth)
• Controlled experiments if possible

If you use or reference this work:

MIT License - See LICENSE file

• GitHub API for repository data
• Hacker News for submission data
• Kaggle/public datasets for NPM and citation data
• The scientific principle of radical transparency

Questions, critiques, or collaborations welcome.

Approach: Open science, reproducible research, honest limitations

"We found a pattern. We don't know what it means. Here's the data."

— Formslip, Ash, & Palinode, January 2025