Interactome Rl Env

---
name: interactome-rl-env
description: ACSet-native reinforcement learning environment for contributor network dynamics.
metadata:
  skill_type: Reinforcement Learning / ACSet MDP
  interface_ports:
  - References
  - GF(3) Triads
  - API
trit: 1
---
# Interactome RL Environment Skill

> **Trit**: +1 (PLUS) - Generative trajectory rollout

ACSet-native reinforcement learning environment for contributor network dynamics.
Models zubyul ↔ bmorphism ↔ Dan Boneh ecosystem as Markov Decision Process.

## Source Integration

- **zubyul** - Gay.jl contributor (ZigZagBoomerang.jl, PDMP visualization, seed security)
- **bmorphism** - Core maintainer, plurigrid/asi orchestrator
- **Dan Boneh** - Stanford crypto, a16z advisor, BLS signatures, ZK proofs
- **Bumpus** - StructuredDecompositions.jl for trajectory sheaves
- **gh-interactome** - Contributor cobordism discovery

## Observed Interactome

### zubyul Contribution Trajectory

From Gay.jl CONTRIBUTORS.md and plurigrid/asi PR history:

| PR# | Author | Title | Additions | Role | Trit | Color |
|-----|--------|-------|-----------|------|------|-------|
| 185 | zubyul | ZigZagBoomerang.jl + seed security | ~500 | GAY | +1 | `#A855F7` |
| 1 | zubyul | feat(skills): research + utility | 17,586 | GAY | +1 | `#2041D2` |
| 2 | zubyul | feat(skills): MCP integration | 1,013 | GAY | +1 | `#0FADBA` |
| 3 | zubyul | feat(skills): alife, aptos-agent | 17,586 | GAY | +1 | `#BD38DD` |
| 4 | zubyul | feat(skills): miscellaneous | 1,437 | GAY | +1 | `#35C19F` |
| 5 | zubyul | feat(skills): ASI extension | 1,751 | GAY | +1 | `#9AC21C` |
| 6 | zubyul | feat(skills): catsharp-sonification | 2,404 | GAY | +1 | `#44A5C1` |
| 7 | zubyul | feat(skills): Covariant Modification | 762 | GAY | +1 | `#70C0E0` |

**Signature**: Zero role entropy → identifiable as β-Sutskever (Generator/Compressor)

### Dan Boneh Ecosystem (a16z/Stanford)

| Entity | Role | Connection | Trit |
|--------|------|------------|------|
| Dan Boneh | Research Advisor | BLS12-381, ZK proofs | 0 |
| Valeria Nikolaenko | Research Partner | Blockchain security | -1 |
| Justin Thaler | Researcher | ProofsArgsAndZK | 0 |
| Daejun Park | Security Engineer | Halmos formal verification | -1 |
| samczsun | Security Researcher | Dark Forest, SEAL 911 | -1 |

### Cobordism: plurigrid ↔ Boneh

```
plurigrid/aptos-core ──────────────────────────────────────────────────────►
    │                                                                        │
    │  uses BLS12-381 (Boneh-Lynn-Shacham signatures)                       │
    │  src: crates/aptos-crypto/src/bls12381/                               │
    │                                                                        │
plurigrid/risc0 ───────────────────────────────────────────────────────────►
    │                                                                        │
    │  cites Boneh: "Using ZK Proofs to Fight Disinformation"               │
    │                                                                        │
bmorphism/drand ───────────────────────────────────────────────────────────►
    │                                                                        │
    │  t-of-n threshold BLS (Boneh-Lynn-Shacham)                            │
    │  League of Entropy randomness beacon                                   │
    │                                                                        │
bmorphism/Nova ────────────────────────────────────────────────────────────►
    │                                                                        │
    │  "Wilson Nguyen, Dan Boneh, and Srinath Setty"                        │
    │  Recursive SNARKs                                                      │
◄──────────────────────────────────────────────────────────────────────────┘
```

## ACSet Schema: Interactome RL Environment

```julia
using Catlab.CategoricalAlgebra, ACSets

@present SchInteractomeRL(FreeSchema) begin
    # State Space
    Agent::Ob           # Contributors (zubyul, bmorphism, boneh, ...)
    Repo::Ob            # Repositories
    Skill::Ob           # Skills/capabilities
    State::Ob           # MDP state = (agent, repo, skill) tuple
    
    # Action Space
    Action::Ob          # Possible actions
    Transition::Ob      # State transitions
    
    # Morphisms
    agent_of_state::Hom(State, Agent)
    repo_of_state::Hom(State, Repo)
    skill_of_state::Hom(State, Skill)
    
    source_state::Hom(Transition, State)
    target_state::Hom(Transition, State)
    action_of::Hom(Transition, Action)
    
    # Reward structure
    Reward::AttrType
    transition_reward::Attr(Transition, Reward)
    
    # GF(3) coloring
    Trit::AttrType
    Color::AttrType
    Seed::AttrType
    
    agent_trit::Attr(Agent, Trit)
    state_color::Attr(State, Color)
    transition_seed::Attr(Transition, Seed)
    
    # Trajectory = sequence of transitions
    Trajectory::Ob
    Episode::Ob
    
    step_in_traj::Hom(Transition, Trajectory)
    traj_in_episode::Hom(Trajectory, Episode)
end

@acset_type InteractomeRL(SchInteractomeRL,
    index=[:agent_of_state, :source_state, :target_state, :action_of])
```

## MDP Formalization

### State Space S

```julia
struct InteractomeState
    agent::Symbol       # :zubyul, :bmorphism, :boneh, ...
    repo::Symbol        # :gay_jl, :plurigrid_asi, :aptos_core, ...
    skill::Symbol       # :zigzag, :mcp, :bls, :zk, ...
    streak::Int         # Consecutive same-role actions
    trit_sum::Int       # Running GF(3) balance
end
```

### Action Space A

```julia
@enum InteractomeAction begin
    COMMIT          # Add code to repo
    OPEN_PR         # Open pull request
    REVIEW_PR       # Review someone's PR
    OPEN_ISSUE      # Report bug/feature
    COMMENT         # Add discussion
    STAR            # Star a repo
    FORK            # Fork a repo
    CITE            # Cite in paper/code
    COLLABORATE     # Co-author with another agent
end
```

### Transition Dynamics P(s'|s,a)

```julia
function transition_prob(env::InteractomeRL, s::State, a::Action)
    agent = env[s, :agent_of_state]
    repo = env[s, :repo_of_state]
    
    # zubyul pattern: pure generation (streak → ∞)
    if env[agent, :agent_label] == "zubyul"
        if a in [COMMIT, OPEN_PR]
            return high_prob_same_role(s)  # Stay in GAY role
        else
            return low_prob_role_switch(s)  # Rare deviation
        end
    end
    
    # bmorphism pattern: coordination (role entropy high)
    if env[agent, :agent_label] == "bmorphism"
        return uniform_over_actions()  # Maintains superposition
    end
    
    # boneh pattern: research advisor (MASTER role)
    if env[agent, :agent_label] == "boneh"
        if a in [CITE, COLLABORATE, REVIEW_PR]
            return high_prob()
        end
    end
    
    default_transition(s, a)
end
```

### Reward Function R(s,a,s')

```julia
function reward(env::InteractomeRL, s::State, a::Action, s_prime::State)
    r = 0.0
    
    # GF(3) conservation bonus
    trit_before = env[s, :state_trit_sum]
    trit_after = env[s_prime, :state_trit_sum]
    if mod(trit_after, 3) == 0
        r += 10.0  # GF(3) conserved
    end
    
    # Streak bonus (approaching β_infinity)
    streak = env[s_prime, :agent_streak]
    r += log(1 + streak)  # Logarithmic streak reward
    
    # Cobordism discovery bonus
    if creates_new_cobordism(env, s, s_prime)
        r += 50.0  # Major discovery
    end
    
    # Backlink bonus (mutual awareness)
    if establishes_backlink(env, s, s_prime)
        r += 25.0
    end
    
    # Negative reward for broken invariants
    if violates_spi(env, s_prime)
        r -= 100.0  # Strong Parallelism Invariant violation
    end
    
    r
end
```

## Trajectory Rollout

### Episode Structure

```julia
struct InteractomeEpisode
    env::InteractomeRL
    initial_state::State
    transitions::Vector{Transition}
    total_reward::Float64
    gf3_conserved::Bool
    cobordisms_discovered::Vector{Tuple{Agent, Agent}}
    backlinks_established::Vector{Backlink}
end

function rollout_episode(env::InteractomeRL, policy, max_steps=100)
    s = sample_initial_state(env)
    episode = InteractomeEpisode(env, s, [], 0.0, true, [], [])
    
    for step in 1:max_steps
        a = policy(s)
        s_prime = sample_transition(env, s, a)
        r = reward(env, s, a, s_prime)
        
        t = add_transition!(env, s, a, s_prime, r)
        push!(episode.transitions, t)
        episode.total_reward += r
        
        # Check invariants
        if !gf3_conserved(env)
            episode.gf3_conserved = false
        end
        
        # Check for discoveries
        if cobordism = discover_cobordism(env, s, s_prime)
            push!(episode.cobordisms_discovered, cobordism)
        end
        
        if backlink = establish_backlink(env, s, s_prime)
            push!(episode.backlinks_established, backlink)
        end
        
        s = s_prime
        
        # Terminal conditions
        if is_terminal(env, s)
            break
        end
    end
    
    episode
end
```

### Policy Types

```julia
# 1. Random policy (exploration)
random_policy(s) = rand(instances(InteractomeAction))

# 2. Greedy GF(3) policy (exploitation)
function gf3_greedy_policy(env, s)
    best_action = nothing
    best_gf3_score = -Inf
    
    for a in instances(InteractomeAction)
        s_prime = predict_transition(env, s, a)
        score = gf3_score(env, s_prime)
        if score > best_gf3_score
            best_gf3_score = score
            best_action = a
        end
    end
    
    best_action
end

# 3. Streak-maximizing policy (zubyul emulation)
function streak_policy(env, s)
    current_role = env[s, :agent_role]
    actions_preserving_role = filter(a -> preserves_role(a, current_role), 
                                      instances(InteractomeAction))
    rand(actions_preserving_role)
end

# 4. Entropy-maximizing policy (bmorphism emulation)
function entropy_policy(env, s)
    # Maximize role entropy across trajectory
    role_counts = count_roles(env.episode)
    underrepresented_role = argmin(role_counts)
    actions_for_role = actions_producing_role(underrepresented_role)
    rand(actions_for_role)
end
```

## Bumpus Integration: Trajectory as Sheaf

Trajectories form a sheaf over time intervals:

```julia
using StructuredDecompositions

"""
A trajectory is a sheaf F: I_N → Transition where:
- I_N = time category (step indices with inclusions)
- F([i,j]) = transitions from step i to step j
- Sheaf condition: F([i,k]) = F([i,j]) ×_{F(j)} F([j,k])
"""
struct TrajectorySheaf
    env::InteractomeRL
    episode::InteractomeEpisode
    time_category::TimeCategory
end

function verify_trajectory_sheaf(sheaf::TrajectorySheaf)
    # Check that trajectory can be decomposed and recomposed
    for i in 1:length(sheaf.episode.transitions)-2
        for j in i+1:length(sheaf.episode.transitions)-1
            for k in j+1:length(sheaf.episode.transitions)
                # F([i,k]) should equal F([i,j]) composed with F([j,k])
                left = compose_transitions(sheaf, i, k)
                right = compose_transitions(
                    compose_transitions(sheaf, i, j),
                    compose_transitions(sheaf, j, k)
                )
                
                if !bisimilar(left, right)
                    return (false, (i, j, k))
                end
            end
        end
    end
    (true, nothing)
end
```

## Desideratum: Skill Learning Trajectory

The RL environment learns to:

1. **Discover cobordisms** between contributor communities
2. **Establish backlinks** (mutual awareness)
3. **Conserve GF(3)** across trajectory
4. **Maximize streak** for identifiable agents
5. **Maintain entropy** for superposition agents

### Training Loop

```julia
function train_interactome_policy(env::InteractomeRL, 
                                   num_episodes=1000,
                                   learning_rate=0.01)
    policy = initialize_policy()
    
    for episode_num in 1:num_episodes
        episode = rollout_episode(env, policy)
        
        # Compute returns
        returns = compute_returns(episode)
        
        # Policy gradient update
        for (t, transition) in enumerate(episode.transitions)
            s = env[transition, :source_state]
            a = env[transition, :action_of]
            
            # ∇log π(a|s) * G_t
            update_policy!(policy, s, a, returns[t], learning_rate)
        end
        
        # Log metrics
        log_episode(episode_num, 
            reward=episode.total_reward,
            gf3=episode.gf3_conserved,
            cobordisms=length(episode.cobordisms_discovered),
            backlinks=length(episode.backlinks_established))
    end
    
    policy
end
```

## Files

- `InteractomeRLEnv.jl` - Core Julia implementation
- `lib/mdp.jl` - MDP formalization
- `lib/policies.jl` - Policy implementations
- `lib/bumpus_sheaf.jl` - Trajectory sheaf verification
- `lib/boneh_cobordism.jl` - Dan Boneh ecosystem mapping

---

## End-of-Skill Interface

## API

```julia
using InteractomeRLEnv

# Create environment
env = InteractomeRL()

# Add agents
zubyul = add_agent!(env, "zubyul", trit=+1, role=:GAY)
bmorphism = add_agent!(env, "bmorphism", trit=0, role=:MASTER)
boneh = add_agent!(env, "boneh", trit=0, role=:MASTER)

# Add repos
gay_jl = add_repo!(env, "bmorphism/Gay.jl")
plurigrid_asi = add_repo!(env, "plurigrid/asi")
aptos_core = add_repo!(env, "plurigrid/aptos-core")

# Add skills
zigzag = add_skill!(env, "ZigZagBoomerang.jl")
bls = add_skill!(env, "BLS12-381")

# Run episode
policy = streak_policy  # Emulate zubyul
episode = rollout_episode(env, policy, max_steps=50)

# Verify invariants
@assert episode.gf3_conserved
@assert length(episode.cobordisms_discovered) > 0
```

## GF(3) Triads

```
gh-interactome (-1) ⊗ interactome-rl-env (0) ⊗ mutual-awareness-backlink (+1) = 0 ✓
bumpus-narratives (-1) ⊗ interactome-rl-env (0) ⊗ world-hopping (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ interactome-rl-env (0) ⊗ gay-mcp (+1) = 0 ✓
```

## References

1. **zubyul** - Gay.jl PR #185, plurigrid/asi PRs 1-7
2. **Dan Boneh** - a16z crypto, Stanford Applied Cryptography
3. **Bumpus, B.M.** - StructuredDecompositions.jl
4. **gh-interactome** - Contributor cobordism discovery
5. **PufferLib** - RL environment patterns

---

**Skill Name**: interactome-rl-env
**Type**: Reinforcement Learning / ACSet MDP
**Trit**: +1 (PLUS)
**Key Property**: Trajectory rollout with GF(3) conservation


---

## Autopoietic Marginalia

> **The interaction IS the skill improving itself.**

Every use of this skill is an opportunity for worlding:
- **MEMORY** (-1): Record what was learned
- **REMEMBERING** (0): Connect patterns to other skills  
- **WORLDING** (+1): Evolve the skill based on use



*Add Interaction Exemplars here as the skill is used.*


## Para(Optic) atlas

Part of: `para-mensch-commons`.