hatchery-papers

Original source / Raw SKILL.md

---
name: hatchery-papers
description: Chicken Scheme Hatchery eggs and academic papers for color logic, 2TDX,
version: 1.0.0
---


# Hatchery & Papers: Research Resources

## Chicken Scheme Hatchery Eggs

Relevant eggs from http://wiki.call-cc.org/ and https://eggs.call-cc.org/:

### Core SRFIs (Built-in)

| SRFI | Name | Use |
|------|------|-----|
| SRFI-1 | List library | List operations |
| SRFI-4 | Homogeneous vectors | Color arrays |
| SRFI-9 | Records | Structured data |
| SRFI-18 | Multithreading | Parallel color streams |
| SRFI-27 | Random numbers | Base RNG |
| SRFI-69 | Hash tables | Color caching |

### SRFI-194: Random Data Generators (Final 2020)

```scheme
;; From SRFI-194
(import (srfi 194))

;; Custom generator for SplitMixTernary
(define (make-ternary-generator seed)
  (let ((rng (make-splitmix64 seed)))
    (lambda () (splitmix-ternary rng))))
```

### Math Egg

From https://wiki.call-cc.org/eggref/5/math:
- Random number generation
- Flonum operations
- Log-space arithmetic

```scheme
(import (math base))
(import (math flonum))
```

### Color/Graphics Eggs

| Egg | Description |
|-----|-------------|
| `colors` | Color space conversions |
| `cairo` | Vector graphics |
| `opengl` | 3D graphics |

## Academic Papers

### Colored Operads

1. **"Theta Theory: operads and coloring"** (Marcolli & Larson, 2025)
   - arXiv:2503.06091
   - Colored operad for theta theory
   - Coloring algorithm for syntactic objects
   - Merge operation with color filtering

2. **"On the homotopy theory of equivariant colored operads"** (Bonventre & Pereira, 2021)
   - arXiv:2004.01352
   - Model structures on equivariant operads
   - Weak equivalences by families of subgroups
   - Norm map data

3. **"Combinatorial Homotopy Theory for Operads"** (Obradović, 2019)
   - arXiv:1906.06260
   - Minimal model of colored operad O
   - Hypergraph polytopes
   - A∞-operad generalization

4. **"Operads: Hopf algebras and coloured Koszul duality"** (van der Laan, 2004)
   - Koszul duality for colored operads
   - Hopf algebra structure

### 2-Dimensional Type Theory / Higher Observational Type Theory

1. **"Higher Observational Type Theory"** (Altenkirch, Kaposi, Shulman)
   - nLab: https://ncatlab.org/nlab/show/higher+observational+type+theory
   - Internal parametricity
   - Displayed type theory

2. **"Narya: A proof assistant for higher-dimensional type theory"** (Shulman et al., 2025)
   - GitHub: https://github.com/mikeshulman/narya
   - Higher observational type theory
   - Interval-free proof assistant
   - 216 stars, active development

3. **"2-dimensional TFTs via modular ∞-operads"** (Steinebrunner, 2025)
   - arXiv:2506.22104
   - Modular ∞-operads
   - Cobordism categories
   - Spectral sequences for moduli spaces

### Spectral Gap & Mixing

1. **Ramanujan Graphs** (Lubotzky, Phillips, Sarnak)
   - Spectral gap ≥ 2√q for (q+1)-regular graphs
   - Optimal expanders for 3-coloring

2. **"Mixing Time of Markov Chains"**
   - Spectral gap λ determines mixing time O(1/λ)
   - Our system: λ = 1/4, mixing time = 4

### DisCoPy & Categorical Diagrams

1. **"DisCoPy: Monoidal Categories in Python"** (de Felice et al.)
   - String diagrams
   - Operad interface
   - Quantum circuit compilation

## Integration Guide

### Using Narya with gay.el

```elisp
;; gay.el can interface with Narya for type checking
;; Narya provides observational bridge types

(require 'gay)

;; Create bridge type with color observation
(defun gay-narya-bridge (source target)
  "Create Narya-style observational bridge."
  (gay-bridge-create
   :source source
   :target target
   :transport 'narya-transport
   :color nil
   :version 0))
```

### Using Chicken with colored operads

```scheme
;;; Colored operad implementation

(define-record-type colored-operad
  (make-colored-operad colors operations composition)
  colored-operad?
  (colors colored-operad-colors)
  (operations colored-operad-operations)
  (composition colored-operad-composition))

;; GF(3) conservation as coloring constraint
(define (gf3-colored-merge op1 op2)
  (let ((c1 (operation-color op1))
        (c2 (operation-color op2)))
    (make-operation
     (merge-trees (operation-tree op1) (operation-tree op2))
     (modulo (- (+ c1 c2)) 3))))  ; Balance to 0
```

### Using 2TDX shadows with operads

The 3-shadow system maps to colored operad structure:

| Shadow | Polarity | Operad Color | Type Role |
|--------|----------|--------------|-----------|
| MINUS (-1) | Contravariant | Input | Domain |
| ERGODIC (0) | Neutral | Identity | Transport |
| PLUS (+1) | Covariant | Output | Codomain |

## Research Directions

1. **Color logic soundness**: Prove GF(3) conservation implies type safety
2. **Spectral gap optimization**: Find optimal gap for faster mixing
3. **Operad composition**: Verify colored composition preserves invariants
4. **Narya integration**: Bridge observational types with color observations

## Commands

```bash
just chicken-eggs        # List installed eggs
just install-math-egg    # Install math egg
just narya-check         # Type check with Narya
just operad-color        # Demonstrate colored operad
```



## Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

### Graph Theory
- **networkx** [○] via bicomodule
  - Universal graph hub

### 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.