Hatchery & Papers: Research Resources Skill

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)

;; 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

(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

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

"Higher Observational Type Theory" (Altenkirch, Kaposi, Shulman)
- nLab: https://ncatlab.org/nlab/show/higher+observational+type+theory
- Internal parametricity
- Displayed type theory
"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
"2-dimensional TFTs via modular ∞-operads" (Steinebrunner, 2025)
- arXiv:2506.22104
- Modular ∞-operads
- Cobordism categories
- Spectral sequences for moduli spaces

Spectral Gap & Mixing

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

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

Integration Guide

Using Narya with gay.el

;; 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

;;; 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

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

Commands

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.

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