plurigrid Browser History ACSet
Trit: 0 (ERGODIC - information coordination)
Foundation: PyACSet ↔ ACSets.jl path equivalence verified
Overview
Unified categorical structure for browser history across:
- ChatGPT Atlas (Chromium-based)
- Chrome, Arc, Brave, Firefox, Safari
Uses GF(3) trit classification for browsing behavior analysis.
Schema
┌─────────────────────────────────────────────────────────────┐
│ BrowserHistoryACSet Schema │
├─────────────────────────────────────────────────────────────┤
│ Objects: Browser, URL, Visit, Domain, SearchQuery │
│ │
│ Morphisms: │
│ browser_of: URL → Browser │
│ domain_of: URL → Domain │
│ url_of: Visit → URL │
│ from_visit: Visit → Visit (reflexive, navigation chain) │
│ │
│ Attributes: │
│ browser_name: Browser → String │
│ url_text: URL → String │
│ visit_time: Visit → Int │
│ domain_name: Domain → String │
│ trit: Domain → Int (-1, 0, +1) │
└─────────────────────────────────────────────────────────────┘
Path Equivalence Tests
Verified cross-language compatibility between Python and Julia:
| Operation | Python (PyACSet) | Julia (ACSets.jl) | Match |
|---|---|---|---|
| nparts(A) | 2 | 2 | ✓ |
| subpart(1, :f) | 1 | 1 | ✓ |
| incident(1, :f) | [1] | [1] | ✓ |
| path 1→f→g | 1 | 1 | ✓ |
Key Operations
# Python (PyACSet)
url = acset.subpart(visit_id, "url_of")
domain = acset.path(visit_id, "url_of", "domain_of")
referrers = acset.incident(url_id, "url_of")
# Julia (ACSets.jl)
url = subpart(acs, visit_id, :url_of)
domain = subpart(acs, subpart(acs, visit_id, :url_of), :domain_of)
referrers = incident(acs, url_id, :url_of)
GF(3) Domain Classification
| Trit | Category | Examples | Behavior |
|---|---|---|---|
| +1 | PLUS (Creation) | github.com, ampcode.com, arxiv.org | Building, learning |
| 0 | ERGODIC (Info) | google.com, youtube.com, x.com | Coordination, info |
| -1 | MINUS (Consumption) | amazon.com, netflix.com, reddit.com | Consuming, extracting |
Current Data (ChatGPT Atlas)
╔═══════════════════════════════════════════════════════════════╗
║ Browser History ACSet ║
╠═══════════════════════════════════════════════════════════════╣
║ Browser : 3 parts ║
║ URL : 4529 parts ║
║ Visit : 8569 parts ║
║ Domain : 511 parts ║
║ SearchQuery : 36 parts ║
║ Download : 41 parts ║
╠═══════════════════════════════════════════════════════════════╣
║ GF(3) Sum : 13 ║
╚═══════════════════════════════════════════════════════════════╝
Top Domains:
[+] github.com : 1066 visits (creation)
[○] mermaid.live : 655 visits (coordination)
[+] ampcode.com : 453 visits (creation)
[+] elevenlabs.io : 268 visits (creation)
[+] huggingface.co : 188 visits (creation)
Usage
# Extract browser history as ACSet
python3 browser_history_acset.py
# Run path equivalence tests
python3 path_equivalence_test.py
# Julia verification
julia path_equivalence_test.jl
Integration Points
- Tenderloin WEV: Geographic browsing patterns → impact zones
- OlmoEarth-MLX: Location-aware embeddings for browsing
- GeoACSet: Spatial categorization of online activity
- DuckDB: Temporal queries on visit history
Specter-Style Navigation
# Select all visits to github.com
github_visits = (
SELECT(ALL("Visit"))
>> FILTER(lambda v: acset.path(v, "url_of", "domain_of")
and acset.subpart(acset.path(v, "url_of", "domain_of"), "domain_name") == "github.com")
)
# Transform: add trit to all URLs in domain
TRANSFORM(
SELECT(ALL("URL")) >> FILTER(lambda u: acset.subpart(u, "domain_of") == d1),
lambda u: acset.set_subpart(u, "trit", 1)
)
Canonical Triads
browser-history-acset (0) ⊗ olmoearth-mlx (+1) ⊗ tenderloin (-1) = 0 ✓
py-acset (0) ⊗ ACSets.jl (+1) ⊗ DuckDB (-1) = 0 ✓
References
- ACSets.jl
- plurigrid-asi-skillz/skills/acsets
- zip_acset_skill/extract_agent_o_rama.py
Related Skills
coequalizers(0) - Path equivalence via coequalizer quotientsacsets(0) - ACSet foundationstemporal-coalgebra(-1) - Time-based path analysis
Scientific Skill Interleaving
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
Annotated Data
- anndata [○] via bicomodule
Bibliography References
general: 734 citations in bib.duckdb
Cat# Integration
This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
GF(3) Naturality
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.