hatchery-papers

# 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 ```