DisCoPy categorical color streams via Hy with 3 parallel TAP streams and 7 operad variants
/plugin marketplace add plurigrid/asi/plugin install plurigrid-asi-skills@plurigrid/asiThis skill inherits all available tools. When active, it can use any tool Claude has access to.
Provides personalized color streams using DisCoPy categorical diagrams via Hy (discohy). Each human gets a self-learning color embedding with 3 parallel streams, now extended with 7 operad variants for compositional structure.
Trit: 0 (ERGODIC - Coordinator)
GF(3) Triad: three-match (-1) ⊗ discohy-streams (0) ⊗ gay-mcp (+1) = 0 ✓
color://human-id/LIVE → +1 (forward, real-time)
color://human-id/VERIFY → 0 (verification, BEAVER)
color://human-id/BACKFILL → -1 (historical, archived)
| Operad | File | Trit | Structure |
|---|---|---|---|
| Little Disks (E₂) | discohy_operad_1_little_disks.py | ⊕ +1 | Configuration of non-overlapping disks |
| Cubes (E_∞) | discohy_operad_2_cubes.py | ⊖ -1 | Hypercube parallel structures |
| Cactus | discohy_operad_3_cactus.py | ⊖ -1 | Trees with cycles (self-modification) |
| Thread | discohy_operad_4_thread.py | ⊙ 0 | Thread continuations + DuckDB |
| Gravity | discohy_operad_5_gravity.lisp | ⊖ -1 | Moduli M_{0,n} with involutions |
| Modular | discohy_operad_6_modular.bb | ⊕ +1 | Genus-labeled runtime polymorphism |
| Swiss-Cheese | discohy_operad_7_swiss_cheese.py | ⊕ +1 | Open/closed for forward-only learning |
GF(3) Total: (+1) + (-1) + (-1) + (0) + (-1) + (+1) + (+1) = 0 ✓
From Sophie Libkind's thesis and AlgebraicJulia:
| Operad | Trit | Description |
|---|---|---|
| Directed (⊳) | +1 | Output→Input wiring diagrams |
| Undirected (○) | -1 | Interface matching via pullback |
| Machines | 0 | State machines with dynamics |
| Dynamical | +1 | Open ODEs: dx/dt = f(x,u) |
| Model | Description |
|---|---|
| Dendroidal | Trees as colored operads (Cisinski-Moerdijk) |
| Lurie | coCartesian fibrations over Fin_* |
| Segal | Quillen equivalent to simplicial operads |
from discopy.monoidal import Ty, Box, Id
from discopy.drawing import draw
# Types for operad network
LittleDisks = Ty('E₂')
Cubes = Ty('E_∞')
Thread = Ty('Thread')
# Morphisms (operad maps)
stabilize = Box('stabilization', LittleDisks, Cubes)
linearize = Box('linearization', LittleDisks, Thread)
# Compose diagram
diagram = stabilize >> linearize.dom @ linearize
#!/usr/bin/env hy
(import [discohy_thread_operad [RootedColorOperad build-operad-from-threads]])
;; Build operad from thread tree
(setv threads [
{:id "T-001" :title "Root" :parent nil}
{:id "T-002" :title "Child1" :parent "T-001"}
{:id "T-003" :title "Child2" :parent "T-001"}])
(setv operad (build-operad-from-threads threads 0x42D))
;; Get operad variant
(.set-variant operad "dendroidal")
;; Compose operations
(setv composed (.compose operad "T-001" ["T-002" "T-003"]))
@present SchOperadNetwork(FreeSchema) begin
Operad::Ob
Morphism::Ob
src::Hom(Morphism, Operad)
tgt::Hom(Morphism, Operad)
Name::AttrType
Trit::AttrType
name::Attr(Operad, Name)
trit::Attr(Operad, Trit)
morph_type::Attr(Morphism, Name)
end
@acset_type OperadNetwork(SchOperadNetwork)
The 7 operads form a relational network (ACSet):
┌─────────────┐
│ Modular │⊕
└──────┬──────┘
┌──────┴──────┐
┌────┴────┐ ┌────┴────┐
│ Cactus │⊖ │ Swiss │⊕
└────┬────┘ │ Cheese │
│ └────┬────┘
▼ │
┌─────────┐ │
│ Thread │⊙◄─────┘
└────┬────┘
┌────────┼────────┐
▼ ▼ ▼
┌────────┐ ┌──────┐ ┌─────────┐
│ Cubes │⊖│Gravity│⊖│ Little │⊕
│ E_∞ │ │ M_0,n │ │ Disks │
└────────┘ └──────┘ └─────────┘
Build balanced schedules with GF(3) = 0 per triplet:
from operads.relational_operad_interleave import build_triad_from_operads
triad = build_triad_from_operads()
schedule = triad.build_round_robin(7)
# Output:
# 0: cubes ⊗ thread ⊗ little_disks
# 1: cactus ⊗ thread ⊗ modular
# 2: gravity ⊗ thread ⊗ swiss_cheese
# ...
-- Query operad compositions
SELECT
src.name as source,
tgt.name as target,
m.morph_type,
(src.trit + tgt.trit) % 3 as combined_trit
FROM operad_morphisms m
JOIN operads src ON m.src_id = src.id
JOIN operads tgt ON m.tgt_id = tgt.id;
-- Find GF(3)-conserving triads
SELECT o1.name, o2.name, o3.name
FROM operads o1, operads o2, operads o3
WHERE (o1.trit + o2.trit + o3.trit) % 3 = 0
AND o1.id < o2.id AND o2.id < o3.id;
src/operads/
├── __init__.py # Registry
├── relational_operad_interleave.py # ACSet + Triad
├── libkind_spivak_dynamics.py # Directed/Undirected/Machines
└── infinity_operads.py # Dendroidal + Lurie
scripts/
├── discohy_operad_1_little_disks.py
├── discohy_operad_2_cubes.py
├── discohy_operad_3_cactus.py
├── discohy_operad_4_thread.py
├── discohy_operad_5_gravity.lisp
├── discohy_operad_6_modular.bb
└── discohy_operad_7_swiss_cheese.py
# Run relational interleaving demo
python3 src/operads/relational_operad_interleave.py
# Run Libkind-Spivak operads
python3 src/operads/libkind_spivak_dynamics.py
# Test individual operad
python3 scripts/discohy_operad_4_thread.py
acsets - Algebraic databases (schema category)triad-interleave - GF(3) balanced schedulinggay-mcp - Deterministic color generationthree-match - 3-SAT via colored subgraph isomorphismworld-hopping - Badiou triangle navigation